Research ArticleJoint Virtual Energy Storage Modeling with Electric VehicleParticipation in Energy Local Area Smart Grid

Rui-Cheng Dai1 Bi Zhao1 Xiao-Di Zhang 1 Jun-Wei Yu2 Bo Fan3 and Biao Liu2

1State Grid Beijing Electric Maintenance Company Beijing 100080 China2State Grid Xinjiang Urumchi Electric Power Supply Company Urumchi 830011 China3Office of Scientific Research and Development Wuhan University Wuhan 430072 China

Correspondence should be addressed to Xiao-Di Zhang 534053362qqcom

Received 4 July 2020 Revised 17 August 2020 Accepted 12 October 2020 Published 28 October 2020

Academic Editor Jingang Lai

Copyright copy 2020 Rui-ChengDai et al-is is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this research the joint virtual energy storage modeling with electric vehicle participation in energy local area Smart Grid isconsidered-is article first constructs a virtual energy storage model and a joint virtual energy storage model for air conditioningand electric vehicles -erefore for the optimization problem of virtual energy storage power a continuous rolling optimizationalgorithm to determine the feasible solution of the high-dimensional complex constraint optimization problem is proposed tosolve the optimization problem Finally the analysis for example illustrates the economics of joint virtual energy storage in theSmart Grid -e results prove that air conditioning and electric vehicles have the ability to jointly participate in virtual energystorage and the comparison proves that joint virtual energy storage can effectively improve the economics ofelectricity consumption

1 Introduction

Due to the access of large-scale distributed power equip-ment especially the strong randomness of wind power andsolar energy energy storage capacity is of vital importance inthe Smart Grid [1ndash5] However batteries are expensive andeasily cause pollution [6] In recent years a large number ofscholars have put forward the concept of virtual energystorage and thus have studied the virtual energy storage withair conditioning participation -e study in [7] analyzes theway of virtual energy storage in the Smart Grid from twoaspects electricity price control and direct control-e studyin [8] used the buildingrsquos heat storage capacity to establish abuilding-based virtual energy storage system model bymanaging the charging (or discharging) power of the virtualenergy storage system according to the userrsquos indoor tem-perature limit and applying it to the microgrid this literaturesuccessfully improved running economy -e study in [9]established a thermodynamic model of air conditioning loadwith the air conditioning set value as the dependent variableand used it to absorb the strong random distributed new

energy power generation equipment output which im-proved the energy utilization as well as the stability of thesystem operation -e study in [10] conducted an in-depthanalysis of the direct controllability of some demand-sideloads and thus dug into the potential of air conditioning loadvirtual energy storage Based on the premise of satisfying theuserrsquos comfort requirements relying on its virtual energystorage to suppress the output of distributed wind turbineswith strong randomness in order to reduce the configu-ration capacity of energy storage equipment and reduce thecost of energy Internet management regulation for thecontrollable load equipment air conditioning with con-sideration of its load-adjustable space the study in [11]established an air conditioning load double-layer optimalscheduling and control model and maximized the interestsfor both parties through the coordination and optimizationbetween the macrolevel power company and the microleveldirect load control agents-e study in [12ndash14] improves theeconomy of energy consumption through the demand re-sponse of air conditioning and refrigerator respectively onthe premise that user comfort can be guaranteed Although

HindawiComplexityVolume 2020 Article ID 3102729 15 pageshttpsdoiorg10115520203102729

the virtual energy storage is not explicitly proposed de-scribing control objects with controllable load and demandresponse instead the control method is consistent with thatin the research of virtual energy storage

Furthermore there are many optimization algorithmsapplied to multienergy optimization [15 16] in Smart GridIn literature [17] a hybrid constraint handling strategy(HCHS) based on nondominated sorting genetic algorithmII (NSGAII) is proposed to deal with the typical constraintsby which the constraint violations can be removed in severalsteps during the evolutionary process -e study in [1]proposed an artificial shark optimization (ASO) method toremove the limitation of existing algorithms for solving theeconomical operation problem of microgrid -e study in[18] presents a new metaheuristic optimization algorithmthe firefly algorithm and an enhanced version of it calledchaos mutation firefly algorithm (CMFA) for solving powereconomic dispatch problems while considering variouspower constraints such as valve-point effects ramp ratelimits prohibited operating zones and multiple generatorfuel options In literature [19] an improved genetic algo-rithm is proposed to overcome the obstacle of infeasibilityand exhibit better economic dispatch -e study in [20]proposes a new distributed method namely the neural-network-based Lagrange multiplier selection (NN-LMS) toprominently reduce the iterations and avoid an oscillation Acalibrated building simulation model was developed in lit-erature [21] and used to assess the effectiveness of demandresponse strategies under different time-of-use electricitytariffs in conjunction with zone thermal control

-is article first constructs a virtual energy storagemodeland a joint virtual energy storage model for air conditioningand electric vehicles -erefore for the optimizationproblem of virtual energy storage power a continuousrolling optimization algorithm to determine the feasiblesolution of the high-dimensional complex constraint opti-mization problem is proposed to solve the optimizationproblem Finally the analysis for example illustrates theeconomics of joint virtual energy storage in the Smart Grid

2 Virtual Energy Storage Modeling with AirConditioning and ElectricVehicles Participation

21 e Overall Structure of Virtual Energy Storage Systemwith Air Conditioning Participation

211 Physical Model of Virtual Energy Storage with AirConditioning Participation For the air conditioning andbuilding virtual energy storage system that relies on tem-perature for adjustment the overall structure diagram isshown in Figure 1

-e virtual energy storage of air conditioning andbuilding can be abstracted as a closed-loop system withfeedback as shown in Figure 2

212 ermodynamic Model of ermoelectric Conversion ofAir Conditioning -e commonly used thermodynamicequivalent equations [22 23] are expressed as follows

dTin(t)

dt

Qac(t)

SC+

Tout(t) minus Tin(t)( 1113857

RSC (1)

In equation (1) Tin(t) and Tout(t) are the indoor andoutdoor temperatures respectively in units of degC Qac(t) isthe air conditioning cooling capacity in units of kW R is theequivalent thermal resistance in units of degCkW C is thebuilding equivalent heat capacity in units of kJdegC S is thebuilding area -e above environmental parameters all havean impact on the virtual energy storage capacity of the airconditioning

-e relationship between the electric power of the airconditioning equipment and the cooling capacity is asfollows

Pac(t) Qac(t)

η (2)

Pac(t) is the air conditioning power in kW η is the airconditioning thermoelectric conversion coefficient

Cooling capacityA

ir co

nditi

onin

g

Temperature upper bound

Current temperature

Temperature lower bound

Rated power

Current power

Virtual energy storage with air conditioning

participation

Air conditioning andbuilding system

Indoor

Figure 1 Schematic diagram for virtual energy storage with airconditioning participation

Tin

Tout

Tset

Pac Qac

Air conditioning Room Computing

center

Figure 2 Schematic diagram of a closed-loop system in virtualenergy storage with air conditioning participation

2 Complexity

22 Important Parameters of Virtual Energy Storage with AirConditioning Participation

221 Air Conditioning Virtual Energy Storage RemainingPower and Rated Capacity When the indoor temperaturereaches the comfort zone boundary if the virtual energystorage remaining power is set to 0 it can be determinedthat at time t the air conditioning virtual energy storagepower Sacminus virtual(t) is

Sacminus virtual(t)

SC Tmax minus Tin(t)( 1113857

η summer

SC Tin(t) minus Tmin( 1113857

η winter

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(3)

Besides the expression of air conditioner virtual energystorage rated capacity Sacminus virtualminus N is

Sacminus virtualminus N SC Tmax minus Tmin

11138681113868111386811138681113868111386811138681113868

η (4)

From the above derivation the relationship among theremaining power of virtual energy storage the rated ca-pacity and the equivalent heat capacity of the building aswell as the comfortable temperature range of the humanbody can be clearly shown

222 Natural Power Consumption in Virtual Energy Storagewith Air Conditioning Participation For the virtual energystorage with air conditioner participation when the indoorand outdoor temperatures are different there is always heatexchange in the air conditioning and building virtual energystorage system At this time the air conditioning needs acertain amount of power to maintain the indoor tempera-ture equal to the set temperature that is natural powerconsumption for virtual energy storage of air conditioning

Pacminus o(t) Qs(t)

η minus

Tout(t) minus Tin(t)

ηR (5)

Pacminus o(t) will change according to the change of indoorand outdoor temperatures When the air conditioner poweris Pacminus o(t) the balance of indoor and outdoor temperaturecan be maintained

223 Virtual Charge and Discharge Power of Virtual EnergyStorage with Air Conditioning Participation When the airconditioning is running in the time period which containstime t it can be known from equation (2) that its averageoperating power is Pac(t) Considering the natural loss ofelectric energy of the air conditioner virtual energy storagePacminus o(t) the virtual power of the air conditioning virtualenergy storage is shown in the following equation

Pacminus virtual(t) Pac(t) minus Pacminus o(t) (6)

In equation (6) Pacminus virtual(t) is the virtual power of thevirtual energy storage that the air conditioning participatesin For equation (1) within a period of time the temperature

in the room where the air conditioner works will change tothe set temperature where τ is the length of the time period-en equation (1) has

ΔTin(t) Tset(t) minus Tin(t) (7)

Δt τ (8)

After organization

Tset(t) minus Tin(t) τ timesQac(t)

SC+

Tout(t) minus Tin(t)( 1113857

RSC1113888 1113889 (9)

After calculation with respect to equation (2) the re-lationship between the air conditioning power and the in-door and outdoor temperature as well as the set temperatureand the length of the time period in the tth time period isobtained as follows

Pac(t) RSCTset(t) minus (RSC minus τ)Tin(t) minus τTout(t)

τηR (10)

Equations (2) (5)ndash(7) and (10) are combined to obtainthe relationship between the virtual charging power andtemperature of the virtual energy storage as follows

Pacminus virtual(t) SC Tset(t) minus Tin(t)( 1113857

τη (11)

23 e Overall Structure of the Virtual Energy StorageSystem with the Participation of Electric Vehicles -eschematic diagram of virtual energy storage with electricvehicle participation is shown in Figure 3

-e total capacity of the electric vehicle battery is fixed-e battery capacity of each electric vehicle can be used forenergy storage in addition to the daily required power-erefore the amount of electricity that can be used forvirtual energy storage of a single electric vehicle can bedetermined and then the total virtual energy storage powerof the electric vehicle cluster can be determined

24 Important Parameters of Virtual Energy Storage forElectric Vehicle Participation

241 Rated Capacity of Virtual Energy Storage for ElectricVehicle Clusters Let the number of electric vehicles in the ithregion at time t be NEi(t) the electric vehicles arriving beNEarrivei(t) the electric vehicles leaving be NEleavei(t) andthe number of distributed charging piles be Pi -en in theperiod of time t the maximum controllable number ofelectric vehicles in the entire area is shown in

maxNEi(t) maxNEi(t minus 1) + maxNEarrivei(t)

minus minNEleavei(t)(12)

-en in the area i the number of electric vehiclesparticipating in the virtual energy storage in the time periodt is shown in

Complexity 3

NEi(t) min Pi maxNEi(t)( 1113857 (13)

-en for the remaining energy in the virtual energystorage at different times in the area i equation (14) is asfollows

SEVminus virtuali(t) 1113944

NEi(t)

j1Wji(t) minus W

0ji1113872 1113873 (14)

In equation (14) SEVminus virtuali(t) is the virtual energystorage capacity of electric vehicles in the period of t in the ithregion Wji(t) is the remaining power of the jth electricvehicle in the ith region in the time period t W0

ji is theminimum electric power required for the jth electric car inthe ith area which does not change with time

-en the rated energy storage of electric vehicles in theith area is

SEVminus virtualiN(t) 1113944

NEi(t)

j1WjiN(t) minus W

0ji1113872 1113873 (15)

where SEVminus virtualiN(t) is the rated energy storage capacity ofthe virtual energy storage in the time period t andWjiN(t) isthe rated battery capacity of the jth electric vehicle in the areai in the time period t

242 Virtual Charging and Discharging Power for VirtualEnergy Storage of Electric Vehicles -e charge and dischargepower of the virtual energy storage of electric vehicles can beexpressed by the following equation

PEVminus virtuali(t) PEV times NEi(t) (16)

In equation (16) PEV is the charging and dischargingpower of the electric vehicle charging and discharging pilesPEVminus virtuali(t) is the virtual charging power of the virtualenergy storage of the electric vehicle in the area i with timeperiod which includes time t and NEi(t) is the number ofelectric vehicles participating in the virtual energy storage inthe area i with time period which includes time t

From the perspective of the electric vehiclersquos virtualenergy storage capacity its charging power meets

PEVminus virtualiin(t) SEVminus virtualiN(t) minus SEVminus virtuali(t)

τ (17)

From the perspective of the virtual energy storage ca-pacity of electric vehicles the discharge power meets

PEVminus virtualiout(t)SEVvi

τ (18)

In equations (17) and (18) τ is the length of the dischargetime period

3 Construction of the Mathematical Model ofJoint Virtual Energy Storage OptimizationBased on the Rolling Optimization Method

Aiming at the problem of determination of high-dimen-sional complex constraint decision variables in global op-timization of electric vehicle virtual energy storage modelthis paper proposes a feasible solution continuous rollingcorrection algorithm

Aiming at the global optimization problem of electricvehicle virtual energy storage output power during theinitialization process due to the complexity of mutualcoupling of local constraints and global constraints theprobability of obtaining a feasible solution is low and ini-tialization cannot be completed In order to solve the aboveproblems this paper proposes constructing a standardfunction to measure the global constraint error that satisfiesthe local constraint decision variables during initializationand thus continuously revising the decision variablesthrough continuous rolling optimization Experiments showthat this method can effectively improve the initializationefficiency of complex constrained optimization problemswith high-dimensional decision variables and then obtainthe global optimized output power of electric vehicle virtualenergy storage which verifies the economics of electricvehicle with the combination of virtual energy storage

31 RollingOptimization Process For the value of the virtualenergy storage power in different time periods the opti-mization result of the previous period will affect the virtualenergy storage power range in the next period Drawing onthe idea of rolling optimization the value of virtual energystorage power can be adjusted continuously with the ad-vancement of the sampling time to determine the power ofvirtual energy storage in each period -e process is shownin Figure 4

-e state in the time period t mainly includes the out-door temperature and the number of arriving and leaving

Electric vehicle battery

Virtual energy storage

Electric vehicles

Rated capacity of virtual energy storage for electric vehicles

The minimum daily battery endurance requirements for electric vehicles

bull bull bull

Figure 3 Schematic diagram of the virtual energy storage processof electric vehicles

4 Complexity

electric vehicles as well as the remaining power of the powerbattery-e state at time t refers to the indoor temperature attime t and the total remaining capacity of the electric ve-hiclersquos virtual energy storage at time t

For the virtual energy storage in which air conditioningparticipate

Tin(t + 1) Tset(t) SCTin(t) + τηPacv(t)

SC (19)

For electric vehicles for the virtual energy storage state attime t + 1 during the rolling optimization process in theregion i when the virtual energy storage state SEVminus virtuali(t)the input power PEVminus virtualminus in(t) and the output powerPEVminus virtualminus out(t) at the previous time are known the status ofthe virtual energy storage capacity of electric vehicles at thebeginning of the next time period can be determined

SEVminus virtuali(t + 1) SEVminus virtuali(t) minus PEVminus virtualminus out(t)

times τ + PEVminus virtualminus in(t) times τ(20)

32 Objective Function In the case where other conditionsare certain and uncontrollable for the virtual energy storageoptimization scheduling in which air conditioning andelectric vehicles jointly participate the optimization

objective function has the lowest total cost of electricityconsumption throughout the day

minC min1113944T

t11113944

M

i1CWTi(t) + CPVi(t) + Cgridi(t)1113872 1113873

+ 1113944M

i1CEVi + CACi1113872 1113873

(21)

In equation (21)M is the total number of residential areaand units in the area in the area i at the time t CWTi(t) andCPVi(t) are the total cost of wind power and photovoltaicpower respectively Cgridi(t) is the cost of purchasingelectricity from the power grid CEVi is the cost of virtualenergy storage with electric vehicles participation in the areai throughout the day CACi is the cost of air conditioningvirtual energy storage throughout the day in the area i

In addition

CWTi(t) pWTirepare times EWTi(t)

CPVi(t) pPVirepare times EPVi(t)(22)

In equation (22) pWTirepare and pPVirepare are the powergeneration maintenance costs of wind turbines and pho-tovoltaic power generation respectively And their units areCNYkWh EWTi(t) and EPVi(t) are the power generationcapacity of wind turbines and photovoltaic power generationduring the time period which contains time t

Cgridi(t) pgrid(t) times Egridi(t) (23)

In equation (23) pgrid(t) is the price of electric energy inthe time period which contains time t which can be stepprice peak-valley price time-sharing price or real-timeprice and Egridi(t) represents time t

CEVi pEV times EEVi (24)

In equation (24) pEV is the cost of virtual energy storagewith electric vehicles participation the unit is CNYkWhEEVi is the total amount of virtual energy storage withelectric vehicles participation in the ith area in the whole day

CACi pAC times EACi (25)

In equation (25) pAC is the cost of in virtual energystorage with air conditioning participation the unit is CNYkWh EACi is the total amount of virtual energy storage withair conditioning participation in the ith area throughout theday

33 Restrictions

331 Energy Balance Constraint -e output power of allpower sources and energy storage devices at time t should be

No

Yes

Output the state at time t and the state in time period t

Generate the independent variable X that meets the requirements

Determine the power of virtual energy storage for air conditioning and electric vehicles

Determine the final state of the virtual energy storage device at the end of time period t

t = 96

t = t+1

Determine the independent variable range according to the given state

Output X

t = 1

Figure 4 Flowchart of virtual energy storage capacity and outputpower rolling optimization

Complexity 5

equal to the electricity consumption at that time as shown inequation (26)

Pacminus o + PEVminus o + demand PWT + PPV + Pacminus virtual

+ Pgrid + PEVminus virtual(26)

Pacminus o is the natural power consumption load curve of thevirtual energy storage of the air conditioning PEVminus o is thecharging power load curve of the electric vehicle demand isthe daily load demand PWT is the wind power PPV is thephotovoltaic power Pacminus virtual is the input (or output) powerof the virtual energy storage with air conditioning partici-pation Pgrid is the power of the power grid and PEVminus virtual isthe input (or output) power of the virtual energy storageinvolved in electric vehicles

332 Output Power Constraints Any distributed powersupply and virtual energy storage device have a limitation forpower rating as shown in equation (27)

Pimin(t)ltPi(t)ltPimax(t) (27)

In this equation Pimin(t) and Pimax(t) are the mini-mum and maximum values of the average output power ofthe ith device in the period of time t respectively

333 Restrictions on the Basic Driving Power Demand of theNext Day after the Electric Vehicle Participates in the VirtualEnergy Storage -e remaining power of any electric vehiclecan at least meet the needs of traveling the next day asshown in equation (28)

Wji minus W0ji gt 0 (28)

Wji is the remaining power of the jth electric car in the itharea and W0

ji is the minimum power required for the jthelectric vehicle in the ith area

-e remaining power constraint for electric vehicles isparticipating in virtual energy storage

-e remaining power of virtual energy storage cannot benegative

SEVminus virtuali gt 0 (29)

SEVminus virtuali is the remaining power of the ith electricvehicle

4 Continuous Rolling Optimization of FeasibleSolution Initialization for High-DimensionalComplex Constrained Optimization Problem

By analyzing the rolling optimization model proposedabove we can find that themodel built in this chapter has thefollowing characteristics

(1) -e dimension of decision variables is high(2) -ere are local constraints described by the rolling

optimization model among decision variables(3) -ere are global constraints on decision variables

-is section proposes a continuous rolling optimizationalgorithm for initializing feasible solutions for high-di-mensional complex constrained optimization problems forrolling optimization models and complex constraints so asto obtain decision variables that simultaneously satisfymultiple types of constraints

41 Treatment Strategy forMulticonstraint Problems A largenumber of inequality constraints will result in multiplefeasible regions with irregular shapes in the feasible solutionspace and the decision variables must satisfy all the con-straints which requires the determination of the range offeasible regions Take the feasible region of a two-dimen-sional optimization problem as an example as shown inFigure 5

In the figure shown above A1 and A2 are respectivelyfeasible regions of decision variables for two differentconstraints Since the area of A2 is small processing theconstraints in parallel will greatly reduce the probability ofthe decision variable falling in A2 -is will make it difficultfor a large number of decision variables to meet the A2constraint conditions resulting in inefficient decision var-iable selection However when the problem to be solved is ahigh-dimensional optimization problem the shape of thefeasible region corresponding to the constraint conditions ismore difficult to determine and the intersection between thefeasible regions is also more difficult to obtain For theoptimization problems shown in this chapter the dimensionof its solution space is shown in equation (30) as follows

D D1 + D2 N1 times T1 + N2 times T2 (30)

In equation (30) N1 and N2 are the number of timeperiods divided per hour which are both 4 in the questionsin this chapter Besides T1 and T2 are the total time of theoptimization cycle which are both 24 in this paper so for theoptimization problem given in this chapter its dimension is192 In practical problems as the influence factors con-sidered increase its dimensions may become larger

42 Solution Feasible Probability For the determination ofthe feasible solution with multiple constraints this sectionuses the solution feasible probability to evaluate its effi-ciency as shown in equation (31)

P A1capA2( ) A1( ) PA1 capA2

PA1

(31)

-e following is an analysis of its value first of all for theone-dimensional optimization problem -e feasible solu-tion selection process is shown in Figure 6

In the two one-dimensional constraints given in theabove figure if N feasible solutions are determined inparallel the process is to first generate N feasible solutionsfor A1 constraint in the [x1 x2] interval and then judgewhether it meets A2 According to the range covered by A1and A2 we can know the solution feasible probability whenthe feasible solutions are evenly distributed

6 Complexity

P A1 capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1 (32)

Claim after choosing a feasible solution with A1 con-straint the probability of satisfying A2 constraint isP(A1 capA2)(A1)

-e following dimension of the optimization problem isincreased In the two-dimensional optimization problemthe solution feasible probability is discussed -e simplerinequality constraint is selected thus the selection processof a feasible solution is shown in Figure 7

-e feasible probability is shown in

P A1capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1times

y2 minus y3

y2 minus y1 (33)

According to the solution feasible probability of the low-dimensional complex constrained optimization problem ifits P(A1capA2)(A1) in each dimension is P then the solutionfeasible probability of the N-dimensional multiconstrainedoptimization problem should be PN When N is too largethe probability of its feasible solution selection probabilitywill be very small and it is easy to make the optimizationprocess fall into an infinite loop -e following experimentdetermines the feasible probability of the solution of theoptimization problem in different dimensions and sets P to05 -e results are shown in Table 1

In view of the dimensional disaster in this paper theundeterminable problem of feasible solutions in this chaptercould be analyzed and solved -erefore this section pro-poses a continuous rolling optimization algorithm to solvethe inefficiency problem of multiconstrained feasiblesolutions

43 Algorithm Flow For the high-dimensional complexconstrained optimization problem the analysis is first basedon the two-dimensional optimization problem When theoptimization problem is faced with global constraints andlocal constraints the optimization process is shown inFigure 8 where A1 represents the constraint condition 1 andA2 represents the constraint condition 2

In the figure shown above the red and blue paths are theoptimization paths of the results with two consecutive

0x

y A1 A2

Figure 5 Schematic diagram of the feasible domain for the so-lution of a two-dimensional optimization problem

A1

x1 x2x3 x4

A2

Figure 6 Schematic diagram of feasible solutions for one-di-mensional optimization problems

0

A1

A2

y1

x1 x2x3

y2

y3

Figure 7 Schematic diagram of the feasible solution of the two-dimensional optimization problem

Table 1 Probability comparison of random initialization solutionsfor optimization problems in different dimensions

-e dimension ofoptimizationproblem

Solution feasibleprobability with

theoreticalcalculation ()

-e solution feasibleprobability errorwith experimental

results ()1 50 502 25 253 125 1255 3125 312510 009765625 009765625

0

A1

A2

x1

x2

Figure 8 Continuous rolling revision selection process of feasiblesolutions for two-dimensional optimization problems

Complexity 7

optimizations Since A1 represents local constraints and x1has a mutual influence with x2 combined with the rollingoptimization model proposed in the previous section theevolutionary process of the continuous rolling optimizationalgorithm determined by the local constraint and the globalconstraint common feasible region of the optimizationproblem can be determined as shown in Figure 9

-e specific steps are as follows

(1) Determine the value of the N-dimensional decisionvariable x1 xi

(2) Determine whether the global optimization re-quirements are met thus directly output the Nfeasible domain decision variable x1 xi if the re-quirements are all met Based on the feasibleprobability of the solution the N-dimensional de-cision variable x1 xi at this time is difficult tomeet the requirements if not go to step (3)

(3) Introduce the global constraint condition discrimi-nant function G(x) which is related to the constraintcondition of the optimization problem but not di-rectly a constraint condition It needs to be formulatedaccording to different global constraints -e condi-tional discriminant function G(x) selected in thischapter is the remaining power of virtual energystorage with electric vehicle participation Under

actual operating conditions when all electric vehiclesleave the residential area the remaining power ofvirtual energy storage with electric vehicle partici-pation should be 0 so its standard function g(x) 0

(4) Determine the average error according to the con-ditional discriminant function G(x) and its standardfunction value g(x)

(5) Obtain a new N-dimensional decision variablex1prime xi

prime based on xiprime xi + e judge whether it

meets the global optimization requirements anddirectly output the N-dimensional feasible regiondecision variable x1prime xi

prime if it meets all require-ments if not go to step (6)

(6) Determine the new average error eprime based on the N-dimensional feasible region decision variable x1prime xi

primeand the global constraint discriminant function G(x)as well as its standard function value g(x)

(7) Compare e with eprime if the error becomes larger afterthe correlation for average error e (ie eprime gt e) thenlet e eprime and go back to step (5) Recalculate the N-dimensional feasible domain decision variablex1prime xi

prime if the error is significantly reduced (ieeprime lt e) then update the N-dimensional feasible re-gion decision variable x1 xi obtain the new N-dimensional decision variable x1prime xi

prime for the new

Optimization problem dimension N

Determine the value of Xi

The Xi+1 value based on rolling optimization is determined

i + 1 = I

i + 1 = I i + 1 = I

Discrimination of global constraints

Discrimination of global constraints

Discrimination of global constraints

Output (Xi XI)

Introduce discriminant function G (x) and criteria g (x) for global

constraints

(G (Xi XI) ndash g (x))N = e

(G (Xi XI)prime ndash g (x))N = eprime

Xiprime = Xi + e Xiprime = Xi + eprime

Determination of Xprimei+1 value based on rolling optimization

Determination of Xprimei+1 value based on rolling optimization

i = i + 1i = i + 1

e gt eprime

Yes

Yes

No

No

No

Yes

No

Yes

Yes

No

Yes Yes

No

No

Utilize (Xiprime XIprime) calculateG (Xi XI)prime

Xi = Xiprimee = eprime

eprime = e

I = I i = 1

i = i + 1

Figure 9 Flowchart of continuous rolling optimization algorithm

8 Complexity

average error eprime and then determine whether theglobal optimization requirements are met thusdirectly output the N-dimensional feasible domaindecision variable x1prime xi

prime if it meets all require-ments if not go to step (8)

(8) Update the newly generated eprime so that e eprimetherefore determine the new average error eprime basedon the updated N-dimensional feasible domain de-cision variable x1prime xi

prime and then go to step (7)

44 Optimization Effect Analysis In the problem solved inthis chapter one of the decision variables is the input andoutput power of the virtual energy storage with electricvehicle participation in each time period and the remainingpower of the electric vehicle virtual energy storage is used asthe standard to detect whether the global optimization iscompleted -e distribution diagram of the arrival anddeparture time of electric vehicles in this simulation isshown in Figure 10 -e results of the comparison betweenthe unoptimized and optimized global constraint detectionstandard function values are shown in Figure 11

As can be seen from Figure 10 the last two vehicles in thearea left within the time period of 1000ndash1015 and the totalpower 4778 kWh can be determined by calculation

As can be seen from Figure 11 at 1000 before rollingoptimization when the last two electric vehicles have notleft the remaining power of virtual energy storage is1544 kWh According to simulation calculations theremaining power of the two electric vehicles is 4778 kWh-at is after the last two vehicles have left the remainingenergy of the virtual energy storage is still not 0 whichobviously does not meet the global constraints indicatingthat the decision variables fall outside the feasible domain ofthe global constraints and the initialization fails If thecontinuous rolling optimization algorithm is not adoptedthe decision variables need to be initialized again

After the continuous rolling optimization determinedfor the high-dimensional complex constraint optimizationfeasible solution the results are consistent with the electricvehicle arrival and departure states indicating that thecontinuous rolling optimization algorithm [5 24] for thehigh-dimensional optimization of global constraints andlocal constraints that jointly govern the feasible domain caneffectively limit the decision variables within the globalconstraints and local constraints that jointly govern thefeasible domain for the problems in this chapter which helpsimprove the optimization efficiency

5 Analysis

-is section first simulates the virtual energy storage ca-pacity of air conditioning and electric vehicles and illustratesthe feasibility of virtual energy storage -en virtual energystorage is optimized for scheduling In the example calcu-lation process the virtual energy storage power range of airconditioning and electric vehicles is first determined andthen the day is divided into 96 time periods to optimize thevirtual energy storage power within the power range

51 Analysis of Air Conditioning and Electric Vehicle VirtualEnergy Storage Capacity

511 Output Power of the Virtual Energy Storage Model withEV Participation In the virtual energy storage in whichelectric vehicles participate the input and output power ofthe virtual energy storage and the arrival and departure ofthe electric vehicle will affect the remaining power of thevirtual energy storage Under rolling optimization the re-lationship can be obtained by Figure 12

As can be seen from Figure 12 the continuous energyoptimization of the electric vehiclersquos virtual energy storageoutput meets the local constraints the virtual energy storageremaining power becomes 0 after all the electric vehiclesleave indicating that the virtual energy storage output powermeets the global constraint conditions

512 Output Power of Virtual Energy Storage Model with AirConditioning Participation In the virtual energy storagewith air conditioning participation the input and outputpower of the virtual energy storage and the natural powerloss of the virtual energy storage based on the indoor andoutdoor temperature difference will affect the remainingpower of the virtual energy storage and the change of roomtemperature Under rolling optimization the changes of theabove four parameters are shown in Figures 13 and 14

It can be seen from the comparison that within thetemperature constraint range the virtual energy storage ofthe air conditioner can realize the virtual power change ofthe virtual energy storage through the change of the airconditioner power

52 Determination of the Range of Virtual Energy StoragePower for Air Conditioning and Electric Vehicles

521 Virtual Energy Storage Charge and Discharge PowerRange with EV Participation For the virtual energy storageof electric vehicles according to the spatial and temporaldistribution of electric vehicles given in Figure 12 and thepower demand for driving on the day according to equations(17) and (18) the input and output power range of virtualenergy storage with electric vehicles participation can bedetermined -e results are shown in Figure 15

522 Determination of the Range of Charge and DischargePower at the Starting Time in the Virtual Energy Storage withAir Conditioning Participation -e daily temperaturechange curve in this area is shown in the red line in Fig-ure 13 Considering the natural consumption rate of thevirtual energy storage of the air conditioning the outputpower of the virtual energy storage reaches the maximumwhen the air conditioner is not running which is Pacminus O(t)when the air conditioner is running its input and outputpower are shown in equation (11) -e maximum value ofthe virtual energy storage discharge power changesaccording to the change of the set temperature -e tem-peratures are set to 195degC 205degC and 215degC respectively

Complexity 9

in the following figure the upper limit of the virtual energystorage output power changes as shown in Figure 16

It can be seen from the above figure that the outputpower of the virtual energy storage decreases as temperatureincreases

523 Economic Analysis of Optimization for Joint VirtualEnergy Storage Based on air conditioning electric vehicleshave the ability to adjust the operating power within acertain range to convert electrical energy into thermal en-ergy storage or perform bidirectional energy exchange withthe power grid to achieve the virtual energy storage capacityof energy transfer -e following is the simulation of theeffect of virtual energy storage of air conditioning andelectric vehicles in this example Regarding the load of the

resident users in the constant temperature communityconsider a total of about 650 small high-rise (five-story)households with a total construction area of 65000 squaremeters a total air conditioning power of 1000 kW and anaverage of about 15 kW per household on the top floorthere is about 6500 square meters of photovoltaic panelsinstalled and 10 wind turbines equipped the power of itsdistributed power generation equipment is shown inFigure 17

Considering that virtual energy storage with electricvehicles participation only charges 04883CNYkWh sowhen actually using electric vehicles for virtual energystorage the discharge cost of electric vehicles is 06883CNYkWh and the discharge efficiency is 80 In addition themaintenance cost for wind turbines and photovoltaic powergeneration is shown in Table 2 [8]

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash40ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Number of EV arrivedNumber of EV left

Figure 10 -e distribution of vehicle arrival and departure times in this optimization

1200 1500 1800 2100 2400 300 600 900 1200Time

0

500

1000

1500

2000

2500

3000

3500

Elec

tric

ity q

uant

ity (k

Wh)

Remaining power value before rolling optimizationRemaining power value after rolling optimization

X 136Y 4778

X 136Y 1544

X 75Y 7894

X 75Y 7905

900Time

0

100

200

300

X 136Y 4778

X 136Y 1544

Figure 11 Comparison result of standard function value of global constraint detection

10 Complexity

000 300 600 900 1200 1500 1800 2100 2400Time

1516171819202122232425262728293031323334353637

Tem

pera

ture

(degC)

Outdoor temperatureIndoor temperature after virtual energy storage with air conditioning participation

Figure 13 Comparison of indoor and outdoor temperature change curves

300 600 900 1200 1500 1800 2100 2400Time

050

100150200250

Pow

er (k

W) Natural loss power of virtual energy storage with air conditioning participation

ndash2000

200400600800

Pow

er (k

W) Virtual energy storage power with air conditioning participation

Air conditioning output power

300600900

1200

Pow

er (k

W)

Figure 14 Comparison chart of the natural power consumption of the virtual energy storage with air conditioning participation airconditioning power and virtual power of virtual energy storage

ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Distribution of arrival and departure times of electric vehicles

Number of EV arrived

Number of EV le

Virtual energy storage power

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400

Pow

er (k

W)

Virtual energy storage remaining power S

10002000300040005000

Elec

tric

ity q

uant

ity(k

Wh)

Figure 12 Comparison chart of electric vehiclersquos space-time distribution remaining power and power

Complexity 11

-e total load demand curve of the residents is shown inFigure 18

-is environment corresponds to four scenesrespectively

Scenario 1 Electric vehicle and air conditioner jointlyparticipate in virtual energy storage

000 300 600 900 1200 1500 1800 2100 2400Time

ndash350ndash330ndash310ndash290ndash270ndash250ndash230ndash210ndash190ndash170ndash150ndash130ndash110

ndash90ndash70ndash50

Pow

er (k

W)

The upper limit of virtual energy storage output power at 195 degCThe upper limit of virtual energy storage output power at 205 degCThe upper limit of virtual energy storage output power at 215 degC

Figure 16 Comparison of the maximum output power of virtual energy storage at different set temperatures

000 300 600 900 1200 1500 1800 2100 2400Time

0

150

300

450

600

750

900

Pow

er (k

W)

Total power of photovoltaic power generationTotal power of wind generation

Figure 17 -e total power of the wind turbine and photovoltaic power generation of the constant temperature small high-rise building innumber 1 residential area

Table 2 Maintenance cost table for wind turbine and photovoltaicpower generation

Parameter (CNYkWh) ValueWind turbine maintenance cost 011PV maintenance cost 008

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400500600

Pow

er (k

W)

Figure 15 Chart of power range of virtual energy storage with electric vehicle participation

12 Complexity

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

22 Important Parameters of Virtual Energy Storage with AirConditioning Participation

221 Air Conditioning Virtual Energy Storage RemainingPower and Rated Capacity When the indoor temperaturereaches the comfort zone boundary if the virtual energystorage remaining power is set to 0 it can be determinedthat at time t the air conditioning virtual energy storagepower Sacminus virtual(t) is

Sacminus virtual(t)

SC Tmax minus Tin(t)( 1113857

η summer

SC Tin(t) minus Tmin( 1113857

η winter

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(3)

Besides the expression of air conditioner virtual energystorage rated capacity Sacminus virtualminus N is

Sacminus virtualminus N SC Tmax minus Tmin

11138681113868111386811138681113868111386811138681113868

η (4)

From the above derivation the relationship among theremaining power of virtual energy storage the rated ca-pacity and the equivalent heat capacity of the building aswell as the comfortable temperature range of the humanbody can be clearly shown

222 Natural Power Consumption in Virtual Energy Storagewith Air Conditioning Participation For the virtual energystorage with air conditioner participation when the indoorand outdoor temperatures are different there is always heatexchange in the air conditioning and building virtual energystorage system At this time the air conditioning needs acertain amount of power to maintain the indoor tempera-ture equal to the set temperature that is natural powerconsumption for virtual energy storage of air conditioning

Pacminus o(t) Qs(t)

η minus

Tout(t) minus Tin(t)

ηR (5)

Pacminus o(t) will change according to the change of indoorand outdoor temperatures When the air conditioner poweris Pacminus o(t) the balance of indoor and outdoor temperaturecan be maintained

223 Virtual Charge and Discharge Power of Virtual EnergyStorage with Air Conditioning Participation When the airconditioning is running in the time period which containstime t it can be known from equation (2) that its averageoperating power is Pac(t) Considering the natural loss ofelectric energy of the air conditioner virtual energy storagePacminus o(t) the virtual power of the air conditioning virtualenergy storage is shown in the following equation

Pacminus virtual(t) Pac(t) minus Pacminus o(t) (6)

In equation (6) Pacminus virtual(t) is the virtual power of thevirtual energy storage that the air conditioning participatesin For equation (1) within a period of time the temperature

in the room where the air conditioner works will change tothe set temperature where τ is the length of the time period-en equation (1) has

ΔTin(t) Tset(t) minus Tin(t) (7)

Δt τ (8)

After organization

Tset(t) minus Tin(t) τ timesQac(t)

SC+

Tout(t) minus Tin(t)( 1113857

RSC1113888 1113889 (9)

After calculation with respect to equation (2) the re-lationship between the air conditioning power and the in-door and outdoor temperature as well as the set temperatureand the length of the time period in the tth time period isobtained as follows

Pac(t) RSCTset(t) minus (RSC minus τ)Tin(t) minus τTout(t)

τηR (10)

Equations (2) (5)ndash(7) and (10) are combined to obtainthe relationship between the virtual charging power andtemperature of the virtual energy storage as follows

Pacminus virtual(t) SC Tset(t) minus Tin(t)( 1113857

τη (11)

23 e Overall Structure of the Virtual Energy StorageSystem with the Participation of Electric Vehicles -eschematic diagram of virtual energy storage with electricvehicle participation is shown in Figure 3

-e total capacity of the electric vehicle battery is fixed-e battery capacity of each electric vehicle can be used forenergy storage in addition to the daily required power-erefore the amount of electricity that can be used forvirtual energy storage of a single electric vehicle can bedetermined and then the total virtual energy storage powerof the electric vehicle cluster can be determined

24 Important Parameters of Virtual Energy Storage forElectric Vehicle Participation

241 Rated Capacity of Virtual Energy Storage for ElectricVehicle Clusters Let the number of electric vehicles in the ithregion at time t be NEi(t) the electric vehicles arriving beNEarrivei(t) the electric vehicles leaving be NEleavei(t) andthe number of distributed charging piles be Pi -en in theperiod of time t the maximum controllable number ofelectric vehicles in the entire area is shown in

maxNEi(t) maxNEi(t minus 1) + maxNEarrivei(t)

minus minNEleavei(t)(12)

-en in the area i the number of electric vehiclesparticipating in the virtual energy storage in the time periodt is shown in

Complexity 3

NEi(t) min Pi maxNEi(t)( 1113857 (13)

-en for the remaining energy in the virtual energystorage at different times in the area i equation (14) is asfollows

SEVminus virtuali(t) 1113944

NEi(t)

j1Wji(t) minus W

0ji1113872 1113873 (14)

In equation (14) SEVminus virtuali(t) is the virtual energystorage capacity of electric vehicles in the period of t in the ithregion Wji(t) is the remaining power of the jth electricvehicle in the ith region in the time period t W0

ji is theminimum electric power required for the jth electric car inthe ith area which does not change with time

-en the rated energy storage of electric vehicles in theith area is

SEVminus virtualiN(t) 1113944

NEi(t)

j1WjiN(t) minus W

0ji1113872 1113873 (15)

where SEVminus virtualiN(t) is the rated energy storage capacity ofthe virtual energy storage in the time period t andWjiN(t) isthe rated battery capacity of the jth electric vehicle in the areai in the time period t

242 Virtual Charging and Discharging Power for VirtualEnergy Storage of Electric Vehicles -e charge and dischargepower of the virtual energy storage of electric vehicles can beexpressed by the following equation

PEVminus virtuali(t) PEV times NEi(t) (16)

In equation (16) PEV is the charging and dischargingpower of the electric vehicle charging and discharging pilesPEVminus virtuali(t) is the virtual charging power of the virtualenergy storage of the electric vehicle in the area i with timeperiod which includes time t and NEi(t) is the number ofelectric vehicles participating in the virtual energy storage inthe area i with time period which includes time t

From the perspective of the electric vehiclersquos virtualenergy storage capacity its charging power meets

PEVminus virtualiin(t) SEVminus virtualiN(t) minus SEVminus virtuali(t)

τ (17)

From the perspective of the virtual energy storage ca-pacity of electric vehicles the discharge power meets

PEVminus virtualiout(t)SEVvi

τ (18)

In equations (17) and (18) τ is the length of the dischargetime period

3 Construction of the Mathematical Model ofJoint Virtual Energy Storage OptimizationBased on the Rolling Optimization Method

Aiming at the problem of determination of high-dimen-sional complex constraint decision variables in global op-timization of electric vehicle virtual energy storage modelthis paper proposes a feasible solution continuous rollingcorrection algorithm

Aiming at the global optimization problem of electricvehicle virtual energy storage output power during theinitialization process due to the complexity of mutualcoupling of local constraints and global constraints theprobability of obtaining a feasible solution is low and ini-tialization cannot be completed In order to solve the aboveproblems this paper proposes constructing a standardfunction to measure the global constraint error that satisfiesthe local constraint decision variables during initializationand thus continuously revising the decision variablesthrough continuous rolling optimization Experiments showthat this method can effectively improve the initializationefficiency of complex constrained optimization problemswith high-dimensional decision variables and then obtainthe global optimized output power of electric vehicle virtualenergy storage which verifies the economics of electricvehicle with the combination of virtual energy storage

31 RollingOptimization Process For the value of the virtualenergy storage power in different time periods the opti-mization result of the previous period will affect the virtualenergy storage power range in the next period Drawing onthe idea of rolling optimization the value of virtual energystorage power can be adjusted continuously with the ad-vancement of the sampling time to determine the power ofvirtual energy storage in each period -e process is shownin Figure 4

-e state in the time period t mainly includes the out-door temperature and the number of arriving and leaving

Electric vehicle battery

Virtual energy storage

Electric vehicles

Rated capacity of virtual energy storage for electric vehicles

The minimum daily battery endurance requirements for electric vehicles

bull bull bull

Figure 3 Schematic diagram of the virtual energy storage processof electric vehicles

4 Complexity

electric vehicles as well as the remaining power of the powerbattery-e state at time t refers to the indoor temperature attime t and the total remaining capacity of the electric ve-hiclersquos virtual energy storage at time t

For the virtual energy storage in which air conditioningparticipate

Tin(t + 1) Tset(t) SCTin(t) + τηPacv(t)

SC (19)

For electric vehicles for the virtual energy storage state attime t + 1 during the rolling optimization process in theregion i when the virtual energy storage state SEVminus virtuali(t)the input power PEVminus virtualminus in(t) and the output powerPEVminus virtualminus out(t) at the previous time are known the status ofthe virtual energy storage capacity of electric vehicles at thebeginning of the next time period can be determined

SEVminus virtuali(t + 1) SEVminus virtuali(t) minus PEVminus virtualminus out(t)

times τ + PEVminus virtualminus in(t) times τ(20)

32 Objective Function In the case where other conditionsare certain and uncontrollable for the virtual energy storageoptimization scheduling in which air conditioning andelectric vehicles jointly participate the optimization

objective function has the lowest total cost of electricityconsumption throughout the day

minC min1113944T

t11113944

M

i1CWTi(t) + CPVi(t) + Cgridi(t)1113872 1113873

+ 1113944M

i1CEVi + CACi1113872 1113873

(21)

In equation (21)M is the total number of residential areaand units in the area in the area i at the time t CWTi(t) andCPVi(t) are the total cost of wind power and photovoltaicpower respectively Cgridi(t) is the cost of purchasingelectricity from the power grid CEVi is the cost of virtualenergy storage with electric vehicles participation in the areai throughout the day CACi is the cost of air conditioningvirtual energy storage throughout the day in the area i

In addition

CWTi(t) pWTirepare times EWTi(t)

CPVi(t) pPVirepare times EPVi(t)(22)

In equation (22) pWTirepare and pPVirepare are the powergeneration maintenance costs of wind turbines and pho-tovoltaic power generation respectively And their units areCNYkWh EWTi(t) and EPVi(t) are the power generationcapacity of wind turbines and photovoltaic power generationduring the time period which contains time t

Cgridi(t) pgrid(t) times Egridi(t) (23)

In equation (23) pgrid(t) is the price of electric energy inthe time period which contains time t which can be stepprice peak-valley price time-sharing price or real-timeprice and Egridi(t) represents time t

CEVi pEV times EEVi (24)

In equation (24) pEV is the cost of virtual energy storagewith electric vehicles participation the unit is CNYkWhEEVi is the total amount of virtual energy storage withelectric vehicles participation in the ith area in the whole day

CACi pAC times EACi (25)

In equation (25) pAC is the cost of in virtual energystorage with air conditioning participation the unit is CNYkWh EACi is the total amount of virtual energy storage withair conditioning participation in the ith area throughout theday

33 Restrictions

331 Energy Balance Constraint -e output power of allpower sources and energy storage devices at time t should be

No

Yes

Output the state at time t and the state in time period t

Generate the independent variable X that meets the requirements

Determine the power of virtual energy storage for air conditioning and electric vehicles

Determine the final state of the virtual energy storage device at the end of time period t

t = 96

t = t+1

Determine the independent variable range according to the given state

Output X

t = 1

Figure 4 Flowchart of virtual energy storage capacity and outputpower rolling optimization

Complexity 5

equal to the electricity consumption at that time as shown inequation (26)

Pacminus o + PEVminus o + demand PWT + PPV + Pacminus virtual

+ Pgrid + PEVminus virtual(26)

Pacminus o is the natural power consumption load curve of thevirtual energy storage of the air conditioning PEVminus o is thecharging power load curve of the electric vehicle demand isthe daily load demand PWT is the wind power PPV is thephotovoltaic power Pacminus virtual is the input (or output) powerof the virtual energy storage with air conditioning partici-pation Pgrid is the power of the power grid and PEVminus virtual isthe input (or output) power of the virtual energy storageinvolved in electric vehicles

332 Output Power Constraints Any distributed powersupply and virtual energy storage device have a limitation forpower rating as shown in equation (27)

Pimin(t)ltPi(t)ltPimax(t) (27)

In this equation Pimin(t) and Pimax(t) are the mini-mum and maximum values of the average output power ofthe ith device in the period of time t respectively

333 Restrictions on the Basic Driving Power Demand of theNext Day after the Electric Vehicle Participates in the VirtualEnergy Storage -e remaining power of any electric vehiclecan at least meet the needs of traveling the next day asshown in equation (28)

Wji minus W0ji gt 0 (28)

Wji is the remaining power of the jth electric car in the itharea and W0

ji is the minimum power required for the jthelectric vehicle in the ith area

-e remaining power constraint for electric vehicles isparticipating in virtual energy storage

-e remaining power of virtual energy storage cannot benegative

SEVminus virtuali gt 0 (29)

SEVminus virtuali is the remaining power of the ith electricvehicle

4 Continuous Rolling Optimization of FeasibleSolution Initialization for High-DimensionalComplex Constrained Optimization Problem

By analyzing the rolling optimization model proposedabove we can find that themodel built in this chapter has thefollowing characteristics

(1) -e dimension of decision variables is high(2) -ere are local constraints described by the rolling

optimization model among decision variables(3) -ere are global constraints on decision variables

-is section proposes a continuous rolling optimizationalgorithm for initializing feasible solutions for high-di-mensional complex constrained optimization problems forrolling optimization models and complex constraints so asto obtain decision variables that simultaneously satisfymultiple types of constraints

41 Treatment Strategy forMulticonstraint Problems A largenumber of inequality constraints will result in multiplefeasible regions with irregular shapes in the feasible solutionspace and the decision variables must satisfy all the con-straints which requires the determination of the range offeasible regions Take the feasible region of a two-dimen-sional optimization problem as an example as shown inFigure 5

In the figure shown above A1 and A2 are respectivelyfeasible regions of decision variables for two differentconstraints Since the area of A2 is small processing theconstraints in parallel will greatly reduce the probability ofthe decision variable falling in A2 -is will make it difficultfor a large number of decision variables to meet the A2constraint conditions resulting in inefficient decision var-iable selection However when the problem to be solved is ahigh-dimensional optimization problem the shape of thefeasible region corresponding to the constraint conditions ismore difficult to determine and the intersection between thefeasible regions is also more difficult to obtain For theoptimization problems shown in this chapter the dimensionof its solution space is shown in equation (30) as follows

D D1 + D2 N1 times T1 + N2 times T2 (30)

In equation (30) N1 and N2 are the number of timeperiods divided per hour which are both 4 in the questionsin this chapter Besides T1 and T2 are the total time of theoptimization cycle which are both 24 in this paper so for theoptimization problem given in this chapter its dimension is192 In practical problems as the influence factors con-sidered increase its dimensions may become larger

42 Solution Feasible Probability For the determination ofthe feasible solution with multiple constraints this sectionuses the solution feasible probability to evaluate its effi-ciency as shown in equation (31)

P A1capA2( ) A1( ) PA1 capA2

PA1

(31)

-e following is an analysis of its value first of all for theone-dimensional optimization problem -e feasible solu-tion selection process is shown in Figure 6

In the two one-dimensional constraints given in theabove figure if N feasible solutions are determined inparallel the process is to first generate N feasible solutionsfor A1 constraint in the [x1 x2] interval and then judgewhether it meets A2 According to the range covered by A1and A2 we can know the solution feasible probability whenthe feasible solutions are evenly distributed

6 Complexity

P A1 capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1 (32)

Claim after choosing a feasible solution with A1 con-straint the probability of satisfying A2 constraint isP(A1 capA2)(A1)

-e following dimension of the optimization problem isincreased In the two-dimensional optimization problemthe solution feasible probability is discussed -e simplerinequality constraint is selected thus the selection processof a feasible solution is shown in Figure 7

-e feasible probability is shown in

P A1capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1times

y2 minus y3

y2 minus y1 (33)

According to the solution feasible probability of the low-dimensional complex constrained optimization problem ifits P(A1capA2)(A1) in each dimension is P then the solutionfeasible probability of the N-dimensional multiconstrainedoptimization problem should be PN When N is too largethe probability of its feasible solution selection probabilitywill be very small and it is easy to make the optimizationprocess fall into an infinite loop -e following experimentdetermines the feasible probability of the solution of theoptimization problem in different dimensions and sets P to05 -e results are shown in Table 1

In view of the dimensional disaster in this paper theundeterminable problem of feasible solutions in this chaptercould be analyzed and solved -erefore this section pro-poses a continuous rolling optimization algorithm to solvethe inefficiency problem of multiconstrained feasiblesolutions

43 Algorithm Flow For the high-dimensional complexconstrained optimization problem the analysis is first basedon the two-dimensional optimization problem When theoptimization problem is faced with global constraints andlocal constraints the optimization process is shown inFigure 8 where A1 represents the constraint condition 1 andA2 represents the constraint condition 2

In the figure shown above the red and blue paths are theoptimization paths of the results with two consecutive

0x

y A1 A2

Figure 5 Schematic diagram of the feasible domain for the so-lution of a two-dimensional optimization problem

A1

x1 x2x3 x4

A2

Figure 6 Schematic diagram of feasible solutions for one-di-mensional optimization problems

0

A1

A2

y1

x1 x2x3

y2

y3

Figure 7 Schematic diagram of the feasible solution of the two-dimensional optimization problem

Table 1 Probability comparison of random initialization solutionsfor optimization problems in different dimensions

-e dimension ofoptimizationproblem

Solution feasibleprobability with

theoreticalcalculation ()

-e solution feasibleprobability errorwith experimental

results ()1 50 502 25 253 125 1255 3125 312510 009765625 009765625

0

A1

A2

x1

x2

Figure 8 Continuous rolling revision selection process of feasiblesolutions for two-dimensional optimization problems

Complexity 7

optimizations Since A1 represents local constraints and x1has a mutual influence with x2 combined with the rollingoptimization model proposed in the previous section theevolutionary process of the continuous rolling optimizationalgorithm determined by the local constraint and the globalconstraint common feasible region of the optimizationproblem can be determined as shown in Figure 9

-e specific steps are as follows

(1) Determine the value of the N-dimensional decisionvariable x1 xi

(2) Determine whether the global optimization re-quirements are met thus directly output the Nfeasible domain decision variable x1 xi if the re-quirements are all met Based on the feasibleprobability of the solution the N-dimensional de-cision variable x1 xi at this time is difficult tomeet the requirements if not go to step (3)

(3) Introduce the global constraint condition discrimi-nant function G(x) which is related to the constraintcondition of the optimization problem but not di-rectly a constraint condition It needs to be formulatedaccording to different global constraints -e condi-tional discriminant function G(x) selected in thischapter is the remaining power of virtual energystorage with electric vehicle participation Under

actual operating conditions when all electric vehiclesleave the residential area the remaining power ofvirtual energy storage with electric vehicle partici-pation should be 0 so its standard function g(x) 0

(4) Determine the average error according to the con-ditional discriminant function G(x) and its standardfunction value g(x)

(5) Obtain a new N-dimensional decision variablex1prime xi

prime based on xiprime xi + e judge whether it

meets the global optimization requirements anddirectly output the N-dimensional feasible regiondecision variable x1prime xi

prime if it meets all require-ments if not go to step (6)

(6) Determine the new average error eprime based on the N-dimensional feasible region decision variable x1prime xi

primeand the global constraint discriminant function G(x)as well as its standard function value g(x)

(7) Compare e with eprime if the error becomes larger afterthe correlation for average error e (ie eprime gt e) thenlet e eprime and go back to step (5) Recalculate the N-dimensional feasible domain decision variablex1prime xi

prime if the error is significantly reduced (ieeprime lt e) then update the N-dimensional feasible re-gion decision variable x1 xi obtain the new N-dimensional decision variable x1prime xi

prime for the new

Optimization problem dimension N

Determine the value of Xi

The Xi+1 value based on rolling optimization is determined

i + 1 = I

i + 1 = I i + 1 = I

Discrimination of global constraints

Discrimination of global constraints

Discrimination of global constraints

Output (Xi XI)

Introduce discriminant function G (x) and criteria g (x) for global

constraints

(G (Xi XI) ndash g (x))N = e

(G (Xi XI)prime ndash g (x))N = eprime

Xiprime = Xi + e Xiprime = Xi + eprime

Determination of Xprimei+1 value based on rolling optimization

Determination of Xprimei+1 value based on rolling optimization

i = i + 1i = i + 1

e gt eprime

Yes

Yes

No

No

No

Yes

No

Yes

Yes

No

Yes Yes

No

No

Utilize (Xiprime XIprime) calculateG (Xi XI)prime

Xi = Xiprimee = eprime

eprime = e

I = I i = 1

i = i + 1

Figure 9 Flowchart of continuous rolling optimization algorithm

8 Complexity

average error eprime and then determine whether theglobal optimization requirements are met thusdirectly output the N-dimensional feasible domaindecision variable x1prime xi

prime if it meets all require-ments if not go to step (8)

(8) Update the newly generated eprime so that e eprimetherefore determine the new average error eprime basedon the updated N-dimensional feasible domain de-cision variable x1prime xi

prime and then go to step (7)

44 Optimization Effect Analysis In the problem solved inthis chapter one of the decision variables is the input andoutput power of the virtual energy storage with electricvehicle participation in each time period and the remainingpower of the electric vehicle virtual energy storage is used asthe standard to detect whether the global optimization iscompleted -e distribution diagram of the arrival anddeparture time of electric vehicles in this simulation isshown in Figure 10 -e results of the comparison betweenthe unoptimized and optimized global constraint detectionstandard function values are shown in Figure 11

As can be seen from Figure 10 the last two vehicles in thearea left within the time period of 1000ndash1015 and the totalpower 4778 kWh can be determined by calculation

As can be seen from Figure 11 at 1000 before rollingoptimization when the last two electric vehicles have notleft the remaining power of virtual energy storage is1544 kWh According to simulation calculations theremaining power of the two electric vehicles is 4778 kWh-at is after the last two vehicles have left the remainingenergy of the virtual energy storage is still not 0 whichobviously does not meet the global constraints indicatingthat the decision variables fall outside the feasible domain ofthe global constraints and the initialization fails If thecontinuous rolling optimization algorithm is not adoptedthe decision variables need to be initialized again

After the continuous rolling optimization determinedfor the high-dimensional complex constraint optimizationfeasible solution the results are consistent with the electricvehicle arrival and departure states indicating that thecontinuous rolling optimization algorithm [5 24] for thehigh-dimensional optimization of global constraints andlocal constraints that jointly govern the feasible domain caneffectively limit the decision variables within the globalconstraints and local constraints that jointly govern thefeasible domain for the problems in this chapter which helpsimprove the optimization efficiency

5 Analysis

-is section first simulates the virtual energy storage ca-pacity of air conditioning and electric vehicles and illustratesthe feasibility of virtual energy storage -en virtual energystorage is optimized for scheduling In the example calcu-lation process the virtual energy storage power range of airconditioning and electric vehicles is first determined andthen the day is divided into 96 time periods to optimize thevirtual energy storage power within the power range

51 Analysis of Air Conditioning and Electric Vehicle VirtualEnergy Storage Capacity

511 Output Power of the Virtual Energy Storage Model withEV Participation In the virtual energy storage in whichelectric vehicles participate the input and output power ofthe virtual energy storage and the arrival and departure ofthe electric vehicle will affect the remaining power of thevirtual energy storage Under rolling optimization the re-lationship can be obtained by Figure 12

As can be seen from Figure 12 the continuous energyoptimization of the electric vehiclersquos virtual energy storageoutput meets the local constraints the virtual energy storageremaining power becomes 0 after all the electric vehiclesleave indicating that the virtual energy storage output powermeets the global constraint conditions

512 Output Power of Virtual Energy Storage Model with AirConditioning Participation In the virtual energy storagewith air conditioning participation the input and outputpower of the virtual energy storage and the natural powerloss of the virtual energy storage based on the indoor andoutdoor temperature difference will affect the remainingpower of the virtual energy storage and the change of roomtemperature Under rolling optimization the changes of theabove four parameters are shown in Figures 13 and 14

It can be seen from the comparison that within thetemperature constraint range the virtual energy storage ofthe air conditioner can realize the virtual power change ofthe virtual energy storage through the change of the airconditioner power

52 Determination of the Range of Virtual Energy StoragePower for Air Conditioning and Electric Vehicles

521 Virtual Energy Storage Charge and Discharge PowerRange with EV Participation For the virtual energy storageof electric vehicles according to the spatial and temporaldistribution of electric vehicles given in Figure 12 and thepower demand for driving on the day according to equations(17) and (18) the input and output power range of virtualenergy storage with electric vehicles participation can bedetermined -e results are shown in Figure 15

522 Determination of the Range of Charge and DischargePower at the Starting Time in the Virtual Energy Storage withAir Conditioning Participation -e daily temperaturechange curve in this area is shown in the red line in Fig-ure 13 Considering the natural consumption rate of thevirtual energy storage of the air conditioning the outputpower of the virtual energy storage reaches the maximumwhen the air conditioner is not running which is Pacminus O(t)when the air conditioner is running its input and outputpower are shown in equation (11) -e maximum value ofthe virtual energy storage discharge power changesaccording to the change of the set temperature -e tem-peratures are set to 195degC 205degC and 215degC respectively

Complexity 9

in the following figure the upper limit of the virtual energystorage output power changes as shown in Figure 16

It can be seen from the above figure that the outputpower of the virtual energy storage decreases as temperatureincreases

523 Economic Analysis of Optimization for Joint VirtualEnergy Storage Based on air conditioning electric vehicleshave the ability to adjust the operating power within acertain range to convert electrical energy into thermal en-ergy storage or perform bidirectional energy exchange withthe power grid to achieve the virtual energy storage capacityof energy transfer -e following is the simulation of theeffect of virtual energy storage of air conditioning andelectric vehicles in this example Regarding the load of the

resident users in the constant temperature communityconsider a total of about 650 small high-rise (five-story)households with a total construction area of 65000 squaremeters a total air conditioning power of 1000 kW and anaverage of about 15 kW per household on the top floorthere is about 6500 square meters of photovoltaic panelsinstalled and 10 wind turbines equipped the power of itsdistributed power generation equipment is shown inFigure 17

Considering that virtual energy storage with electricvehicles participation only charges 04883CNYkWh sowhen actually using electric vehicles for virtual energystorage the discharge cost of electric vehicles is 06883CNYkWh and the discharge efficiency is 80 In addition themaintenance cost for wind turbines and photovoltaic powergeneration is shown in Table 2 [8]

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash40ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Number of EV arrivedNumber of EV left

Figure 10 -e distribution of vehicle arrival and departure times in this optimization

1200 1500 1800 2100 2400 300 600 900 1200Time

0

500

1000

1500

2000

2500

3000

3500

Elec

tric

ity q

uant

ity (k

Wh)

Remaining power value before rolling optimizationRemaining power value after rolling optimization

X 136Y 4778

X 136Y 1544

X 75Y 7894

X 75Y 7905

900Time

0

100

200

300

X 136Y 4778

X 136Y 1544

Figure 11 Comparison result of standard function value of global constraint detection

10 Complexity

000 300 600 900 1200 1500 1800 2100 2400Time

1516171819202122232425262728293031323334353637

Tem

pera

ture

(degC)

Outdoor temperatureIndoor temperature after virtual energy storage with air conditioning participation

Figure 13 Comparison of indoor and outdoor temperature change curves

300 600 900 1200 1500 1800 2100 2400Time

050

100150200250

Pow

er (k

W) Natural loss power of virtual energy storage with air conditioning participation

ndash2000

200400600800

Pow

er (k

W) Virtual energy storage power with air conditioning participation

Air conditioning output power

300600900

1200

Pow

er (k

W)

Figure 14 Comparison chart of the natural power consumption of the virtual energy storage with air conditioning participation airconditioning power and virtual power of virtual energy storage

ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Distribution of arrival and departure times of electric vehicles

Number of EV arrived

Number of EV le

Virtual energy storage power

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400

Pow

er (k

W)

Virtual energy storage remaining power S

10002000300040005000

Elec

tric

ity q

uant

ity(k

Wh)

Figure 12 Comparison chart of electric vehiclersquos space-time distribution remaining power and power

Complexity 11

-e total load demand curve of the residents is shown inFigure 18

-is environment corresponds to four scenesrespectively

Scenario 1 Electric vehicle and air conditioner jointlyparticipate in virtual energy storage

000 300 600 900 1200 1500 1800 2100 2400Time

ndash350ndash330ndash310ndash290ndash270ndash250ndash230ndash210ndash190ndash170ndash150ndash130ndash110

ndash90ndash70ndash50

Pow

er (k

W)

The upper limit of virtual energy storage output power at 195 degCThe upper limit of virtual energy storage output power at 205 degCThe upper limit of virtual energy storage output power at 215 degC

Figure 16 Comparison of the maximum output power of virtual energy storage at different set temperatures

000 300 600 900 1200 1500 1800 2100 2400Time

0

150

300

450

600

750

900

Pow

er (k

W)

Total power of photovoltaic power generationTotal power of wind generation

Figure 17 -e total power of the wind turbine and photovoltaic power generation of the constant temperature small high-rise building innumber 1 residential area

Table 2 Maintenance cost table for wind turbine and photovoltaicpower generation

Parameter (CNYkWh) ValueWind turbine maintenance cost 011PV maintenance cost 008

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400500600

Pow

er (k

W)

Figure 15 Chart of power range of virtual energy storage with electric vehicle participation

12 Complexity

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

NEi(t) min Pi maxNEi(t)( 1113857 (13)

-en for the remaining energy in the virtual energystorage at different times in the area i equation (14) is asfollows

SEVminus virtuali(t) 1113944

NEi(t)

j1Wji(t) minus W

0ji1113872 1113873 (14)

In equation (14) SEVminus virtuali(t) is the virtual energystorage capacity of electric vehicles in the period of t in the ithregion Wji(t) is the remaining power of the jth electricvehicle in the ith region in the time period t W0

ji is theminimum electric power required for the jth electric car inthe ith area which does not change with time

-en the rated energy storage of electric vehicles in theith area is

SEVminus virtualiN(t) 1113944

NEi(t)

j1WjiN(t) minus W

0ji1113872 1113873 (15)

where SEVminus virtualiN(t) is the rated energy storage capacity ofthe virtual energy storage in the time period t andWjiN(t) isthe rated battery capacity of the jth electric vehicle in the areai in the time period t

242 Virtual Charging and Discharging Power for VirtualEnergy Storage of Electric Vehicles -e charge and dischargepower of the virtual energy storage of electric vehicles can beexpressed by the following equation

PEVminus virtuali(t) PEV times NEi(t) (16)

In equation (16) PEV is the charging and dischargingpower of the electric vehicle charging and discharging pilesPEVminus virtuali(t) is the virtual charging power of the virtualenergy storage of the electric vehicle in the area i with timeperiod which includes time t and NEi(t) is the number ofelectric vehicles participating in the virtual energy storage inthe area i with time period which includes time t

From the perspective of the electric vehiclersquos virtualenergy storage capacity its charging power meets

PEVminus virtualiin(t) SEVminus virtualiN(t) minus SEVminus virtuali(t)

τ (17)

From the perspective of the virtual energy storage ca-pacity of electric vehicles the discharge power meets

PEVminus virtualiout(t)SEVvi

τ (18)

In equations (17) and (18) τ is the length of the dischargetime period

3 Construction of the Mathematical Model ofJoint Virtual Energy Storage OptimizationBased on the Rolling Optimization Method

Aiming at the problem of determination of high-dimen-sional complex constraint decision variables in global op-timization of electric vehicle virtual energy storage modelthis paper proposes a feasible solution continuous rollingcorrection algorithm

Aiming at the global optimization problem of electricvehicle virtual energy storage output power during theinitialization process due to the complexity of mutualcoupling of local constraints and global constraints theprobability of obtaining a feasible solution is low and ini-tialization cannot be completed In order to solve the aboveproblems this paper proposes constructing a standardfunction to measure the global constraint error that satisfiesthe local constraint decision variables during initializationand thus continuously revising the decision variablesthrough continuous rolling optimization Experiments showthat this method can effectively improve the initializationefficiency of complex constrained optimization problemswith high-dimensional decision variables and then obtainthe global optimized output power of electric vehicle virtualenergy storage which verifies the economics of electricvehicle with the combination of virtual energy storage

31 RollingOptimization Process For the value of the virtualenergy storage power in different time periods the opti-mization result of the previous period will affect the virtualenergy storage power range in the next period Drawing onthe idea of rolling optimization the value of virtual energystorage power can be adjusted continuously with the ad-vancement of the sampling time to determine the power ofvirtual energy storage in each period -e process is shownin Figure 4

-e state in the time period t mainly includes the out-door temperature and the number of arriving and leaving

Electric vehicle battery

Virtual energy storage

Electric vehicles

Rated capacity of virtual energy storage for electric vehicles

The minimum daily battery endurance requirements for electric vehicles

bull bull bull

Figure 3 Schematic diagram of the virtual energy storage processof electric vehicles

4 Complexity

electric vehicles as well as the remaining power of the powerbattery-e state at time t refers to the indoor temperature attime t and the total remaining capacity of the electric ve-hiclersquos virtual energy storage at time t

For the virtual energy storage in which air conditioningparticipate

Tin(t + 1) Tset(t) SCTin(t) + τηPacv(t)

SC (19)

For electric vehicles for the virtual energy storage state attime t + 1 during the rolling optimization process in theregion i when the virtual energy storage state SEVminus virtuali(t)the input power PEVminus virtualminus in(t) and the output powerPEVminus virtualminus out(t) at the previous time are known the status ofthe virtual energy storage capacity of electric vehicles at thebeginning of the next time period can be determined

SEVminus virtuali(t + 1) SEVminus virtuali(t) minus PEVminus virtualminus out(t)

times τ + PEVminus virtualminus in(t) times τ(20)

32 Objective Function In the case where other conditionsare certain and uncontrollable for the virtual energy storageoptimization scheduling in which air conditioning andelectric vehicles jointly participate the optimization

objective function has the lowest total cost of electricityconsumption throughout the day

minC min1113944T

t11113944

M

i1CWTi(t) + CPVi(t) + Cgridi(t)1113872 1113873

+ 1113944M

i1CEVi + CACi1113872 1113873

(21)

In equation (21)M is the total number of residential areaand units in the area in the area i at the time t CWTi(t) andCPVi(t) are the total cost of wind power and photovoltaicpower respectively Cgridi(t) is the cost of purchasingelectricity from the power grid CEVi is the cost of virtualenergy storage with electric vehicles participation in the areai throughout the day CACi is the cost of air conditioningvirtual energy storage throughout the day in the area i

In addition

CWTi(t) pWTirepare times EWTi(t)

CPVi(t) pPVirepare times EPVi(t)(22)

In equation (22) pWTirepare and pPVirepare are the powergeneration maintenance costs of wind turbines and pho-tovoltaic power generation respectively And their units areCNYkWh EWTi(t) and EPVi(t) are the power generationcapacity of wind turbines and photovoltaic power generationduring the time period which contains time t

Cgridi(t) pgrid(t) times Egridi(t) (23)

In equation (23) pgrid(t) is the price of electric energy inthe time period which contains time t which can be stepprice peak-valley price time-sharing price or real-timeprice and Egridi(t) represents time t

CEVi pEV times EEVi (24)

In equation (24) pEV is the cost of virtual energy storagewith electric vehicles participation the unit is CNYkWhEEVi is the total amount of virtual energy storage withelectric vehicles participation in the ith area in the whole day

CACi pAC times EACi (25)

In equation (25) pAC is the cost of in virtual energystorage with air conditioning participation the unit is CNYkWh EACi is the total amount of virtual energy storage withair conditioning participation in the ith area throughout theday

33 Restrictions

331 Energy Balance Constraint -e output power of allpower sources and energy storage devices at time t should be

No

Yes

Output the state at time t and the state in time period t

Generate the independent variable X that meets the requirements

Determine the power of virtual energy storage for air conditioning and electric vehicles

Determine the final state of the virtual energy storage device at the end of time period t

t = 96

t = t+1

Determine the independent variable range according to the given state

Output X

t = 1

Figure 4 Flowchart of virtual energy storage capacity and outputpower rolling optimization

Complexity 5

equal to the electricity consumption at that time as shown inequation (26)

Pacminus o + PEVminus o + demand PWT + PPV + Pacminus virtual

+ Pgrid + PEVminus virtual(26)

Pacminus o is the natural power consumption load curve of thevirtual energy storage of the air conditioning PEVminus o is thecharging power load curve of the electric vehicle demand isthe daily load demand PWT is the wind power PPV is thephotovoltaic power Pacminus virtual is the input (or output) powerof the virtual energy storage with air conditioning partici-pation Pgrid is the power of the power grid and PEVminus virtual isthe input (or output) power of the virtual energy storageinvolved in electric vehicles

332 Output Power Constraints Any distributed powersupply and virtual energy storage device have a limitation forpower rating as shown in equation (27)

Pimin(t)ltPi(t)ltPimax(t) (27)

In this equation Pimin(t) and Pimax(t) are the mini-mum and maximum values of the average output power ofthe ith device in the period of time t respectively

333 Restrictions on the Basic Driving Power Demand of theNext Day after the Electric Vehicle Participates in the VirtualEnergy Storage -e remaining power of any electric vehiclecan at least meet the needs of traveling the next day asshown in equation (28)

Wji minus W0ji gt 0 (28)

Wji is the remaining power of the jth electric car in the itharea and W0

ji is the minimum power required for the jthelectric vehicle in the ith area

-e remaining power constraint for electric vehicles isparticipating in virtual energy storage

-e remaining power of virtual energy storage cannot benegative

SEVminus virtuali gt 0 (29)

SEVminus virtuali is the remaining power of the ith electricvehicle

4 Continuous Rolling Optimization of FeasibleSolution Initialization for High-DimensionalComplex Constrained Optimization Problem

By analyzing the rolling optimization model proposedabove we can find that themodel built in this chapter has thefollowing characteristics

(1) -e dimension of decision variables is high(2) -ere are local constraints described by the rolling

optimization model among decision variables(3) -ere are global constraints on decision variables

-is section proposes a continuous rolling optimizationalgorithm for initializing feasible solutions for high-di-mensional complex constrained optimization problems forrolling optimization models and complex constraints so asto obtain decision variables that simultaneously satisfymultiple types of constraints

41 Treatment Strategy forMulticonstraint Problems A largenumber of inequality constraints will result in multiplefeasible regions with irregular shapes in the feasible solutionspace and the decision variables must satisfy all the con-straints which requires the determination of the range offeasible regions Take the feasible region of a two-dimen-sional optimization problem as an example as shown inFigure 5

In the figure shown above A1 and A2 are respectivelyfeasible regions of decision variables for two differentconstraints Since the area of A2 is small processing theconstraints in parallel will greatly reduce the probability ofthe decision variable falling in A2 -is will make it difficultfor a large number of decision variables to meet the A2constraint conditions resulting in inefficient decision var-iable selection However when the problem to be solved is ahigh-dimensional optimization problem the shape of thefeasible region corresponding to the constraint conditions ismore difficult to determine and the intersection between thefeasible regions is also more difficult to obtain For theoptimization problems shown in this chapter the dimensionof its solution space is shown in equation (30) as follows

D D1 + D2 N1 times T1 + N2 times T2 (30)

In equation (30) N1 and N2 are the number of timeperiods divided per hour which are both 4 in the questionsin this chapter Besides T1 and T2 are the total time of theoptimization cycle which are both 24 in this paper so for theoptimization problem given in this chapter its dimension is192 In practical problems as the influence factors con-sidered increase its dimensions may become larger

42 Solution Feasible Probability For the determination ofthe feasible solution with multiple constraints this sectionuses the solution feasible probability to evaluate its effi-ciency as shown in equation (31)

P A1capA2( ) A1( ) PA1 capA2

PA1

(31)

-e following is an analysis of its value first of all for theone-dimensional optimization problem -e feasible solu-tion selection process is shown in Figure 6

In the two one-dimensional constraints given in theabove figure if N feasible solutions are determined inparallel the process is to first generate N feasible solutionsfor A1 constraint in the [x1 x2] interval and then judgewhether it meets A2 According to the range covered by A1and A2 we can know the solution feasible probability whenthe feasible solutions are evenly distributed

6 Complexity

P A1 capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1 (32)

Claim after choosing a feasible solution with A1 con-straint the probability of satisfying A2 constraint isP(A1 capA2)(A1)

-e following dimension of the optimization problem isincreased In the two-dimensional optimization problemthe solution feasible probability is discussed -e simplerinequality constraint is selected thus the selection processof a feasible solution is shown in Figure 7

-e feasible probability is shown in

P A1capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1times

y2 minus y3

y2 minus y1 (33)

According to the solution feasible probability of the low-dimensional complex constrained optimization problem ifits P(A1capA2)(A1) in each dimension is P then the solutionfeasible probability of the N-dimensional multiconstrainedoptimization problem should be PN When N is too largethe probability of its feasible solution selection probabilitywill be very small and it is easy to make the optimizationprocess fall into an infinite loop -e following experimentdetermines the feasible probability of the solution of theoptimization problem in different dimensions and sets P to05 -e results are shown in Table 1

In view of the dimensional disaster in this paper theundeterminable problem of feasible solutions in this chaptercould be analyzed and solved -erefore this section pro-poses a continuous rolling optimization algorithm to solvethe inefficiency problem of multiconstrained feasiblesolutions

43 Algorithm Flow For the high-dimensional complexconstrained optimization problem the analysis is first basedon the two-dimensional optimization problem When theoptimization problem is faced with global constraints andlocal constraints the optimization process is shown inFigure 8 where A1 represents the constraint condition 1 andA2 represents the constraint condition 2

In the figure shown above the red and blue paths are theoptimization paths of the results with two consecutive

0x

y A1 A2

Figure 5 Schematic diagram of the feasible domain for the so-lution of a two-dimensional optimization problem

A1

x1 x2x3 x4

A2

Figure 6 Schematic diagram of feasible solutions for one-di-mensional optimization problems

0

A1

A2

y1

x1 x2x3

y2

y3

Figure 7 Schematic diagram of the feasible solution of the two-dimensional optimization problem

Table 1 Probability comparison of random initialization solutionsfor optimization problems in different dimensions

-e dimension ofoptimizationproblem

Solution feasibleprobability with

theoreticalcalculation ()

-e solution feasibleprobability errorwith experimental

results ()1 50 502 25 253 125 1255 3125 312510 009765625 009765625

0

A1

A2

x1

x2

Figure 8 Continuous rolling revision selection process of feasiblesolutions for two-dimensional optimization problems

Complexity 7

optimizations Since A1 represents local constraints and x1has a mutual influence with x2 combined with the rollingoptimization model proposed in the previous section theevolutionary process of the continuous rolling optimizationalgorithm determined by the local constraint and the globalconstraint common feasible region of the optimizationproblem can be determined as shown in Figure 9

-e specific steps are as follows

(1) Determine the value of the N-dimensional decisionvariable x1 xi

(2) Determine whether the global optimization re-quirements are met thus directly output the Nfeasible domain decision variable x1 xi if the re-quirements are all met Based on the feasibleprobability of the solution the N-dimensional de-cision variable x1 xi at this time is difficult tomeet the requirements if not go to step (3)

(3) Introduce the global constraint condition discrimi-nant function G(x) which is related to the constraintcondition of the optimization problem but not di-rectly a constraint condition It needs to be formulatedaccording to different global constraints -e condi-tional discriminant function G(x) selected in thischapter is the remaining power of virtual energystorage with electric vehicle participation Under

actual operating conditions when all electric vehiclesleave the residential area the remaining power ofvirtual energy storage with electric vehicle partici-pation should be 0 so its standard function g(x) 0

(4) Determine the average error according to the con-ditional discriminant function G(x) and its standardfunction value g(x)

(5) Obtain a new N-dimensional decision variablex1prime xi

prime based on xiprime xi + e judge whether it

meets the global optimization requirements anddirectly output the N-dimensional feasible regiondecision variable x1prime xi

prime if it meets all require-ments if not go to step (6)

(6) Determine the new average error eprime based on the N-dimensional feasible region decision variable x1prime xi

primeand the global constraint discriminant function G(x)as well as its standard function value g(x)

(7) Compare e with eprime if the error becomes larger afterthe correlation for average error e (ie eprime gt e) thenlet e eprime and go back to step (5) Recalculate the N-dimensional feasible domain decision variablex1prime xi

prime if the error is significantly reduced (ieeprime lt e) then update the N-dimensional feasible re-gion decision variable x1 xi obtain the new N-dimensional decision variable x1prime xi

prime for the new

Optimization problem dimension N

Determine the value of Xi

The Xi+1 value based on rolling optimization is determined

i + 1 = I

i + 1 = I i + 1 = I

Discrimination of global constraints

Discrimination of global constraints

Discrimination of global constraints

Output (Xi XI)

Introduce discriminant function G (x) and criteria g (x) for global

constraints

(G (Xi XI) ndash g (x))N = e

(G (Xi XI)prime ndash g (x))N = eprime

Xiprime = Xi + e Xiprime = Xi + eprime

Determination of Xprimei+1 value based on rolling optimization

Determination of Xprimei+1 value based on rolling optimization

i = i + 1i = i + 1

e gt eprime

Yes

Yes

No

No

No

Yes

No

Yes

Yes

No

Yes Yes

No

No

Utilize (Xiprime XIprime) calculateG (Xi XI)prime

Xi = Xiprimee = eprime

eprime = e

I = I i = 1

i = i + 1

Figure 9 Flowchart of continuous rolling optimization algorithm

8 Complexity

average error eprime and then determine whether theglobal optimization requirements are met thusdirectly output the N-dimensional feasible domaindecision variable x1prime xi

prime if it meets all require-ments if not go to step (8)

(8) Update the newly generated eprime so that e eprimetherefore determine the new average error eprime basedon the updated N-dimensional feasible domain de-cision variable x1prime xi

prime and then go to step (7)

44 Optimization Effect Analysis In the problem solved inthis chapter one of the decision variables is the input andoutput power of the virtual energy storage with electricvehicle participation in each time period and the remainingpower of the electric vehicle virtual energy storage is used asthe standard to detect whether the global optimization iscompleted -e distribution diagram of the arrival anddeparture time of electric vehicles in this simulation isshown in Figure 10 -e results of the comparison betweenthe unoptimized and optimized global constraint detectionstandard function values are shown in Figure 11

As can be seen from Figure 10 the last two vehicles in thearea left within the time period of 1000ndash1015 and the totalpower 4778 kWh can be determined by calculation

As can be seen from Figure 11 at 1000 before rollingoptimization when the last two electric vehicles have notleft the remaining power of virtual energy storage is1544 kWh According to simulation calculations theremaining power of the two electric vehicles is 4778 kWh-at is after the last two vehicles have left the remainingenergy of the virtual energy storage is still not 0 whichobviously does not meet the global constraints indicatingthat the decision variables fall outside the feasible domain ofthe global constraints and the initialization fails If thecontinuous rolling optimization algorithm is not adoptedthe decision variables need to be initialized again

After the continuous rolling optimization determinedfor the high-dimensional complex constraint optimizationfeasible solution the results are consistent with the electricvehicle arrival and departure states indicating that thecontinuous rolling optimization algorithm [5 24] for thehigh-dimensional optimization of global constraints andlocal constraints that jointly govern the feasible domain caneffectively limit the decision variables within the globalconstraints and local constraints that jointly govern thefeasible domain for the problems in this chapter which helpsimprove the optimization efficiency

5 Analysis

-is section first simulates the virtual energy storage ca-pacity of air conditioning and electric vehicles and illustratesthe feasibility of virtual energy storage -en virtual energystorage is optimized for scheduling In the example calcu-lation process the virtual energy storage power range of airconditioning and electric vehicles is first determined andthen the day is divided into 96 time periods to optimize thevirtual energy storage power within the power range

51 Analysis of Air Conditioning and Electric Vehicle VirtualEnergy Storage Capacity

511 Output Power of the Virtual Energy Storage Model withEV Participation In the virtual energy storage in whichelectric vehicles participate the input and output power ofthe virtual energy storage and the arrival and departure ofthe electric vehicle will affect the remaining power of thevirtual energy storage Under rolling optimization the re-lationship can be obtained by Figure 12

As can be seen from Figure 12 the continuous energyoptimization of the electric vehiclersquos virtual energy storageoutput meets the local constraints the virtual energy storageremaining power becomes 0 after all the electric vehiclesleave indicating that the virtual energy storage output powermeets the global constraint conditions

512 Output Power of Virtual Energy Storage Model with AirConditioning Participation In the virtual energy storagewith air conditioning participation the input and outputpower of the virtual energy storage and the natural powerloss of the virtual energy storage based on the indoor andoutdoor temperature difference will affect the remainingpower of the virtual energy storage and the change of roomtemperature Under rolling optimization the changes of theabove four parameters are shown in Figures 13 and 14

It can be seen from the comparison that within thetemperature constraint range the virtual energy storage ofthe air conditioner can realize the virtual power change ofthe virtual energy storage through the change of the airconditioner power

52 Determination of the Range of Virtual Energy StoragePower for Air Conditioning and Electric Vehicles

521 Virtual Energy Storage Charge and Discharge PowerRange with EV Participation For the virtual energy storageof electric vehicles according to the spatial and temporaldistribution of electric vehicles given in Figure 12 and thepower demand for driving on the day according to equations(17) and (18) the input and output power range of virtualenergy storage with electric vehicles participation can bedetermined -e results are shown in Figure 15

522 Determination of the Range of Charge and DischargePower at the Starting Time in the Virtual Energy Storage withAir Conditioning Participation -e daily temperaturechange curve in this area is shown in the red line in Fig-ure 13 Considering the natural consumption rate of thevirtual energy storage of the air conditioning the outputpower of the virtual energy storage reaches the maximumwhen the air conditioner is not running which is Pacminus O(t)when the air conditioner is running its input and outputpower are shown in equation (11) -e maximum value ofthe virtual energy storage discharge power changesaccording to the change of the set temperature -e tem-peratures are set to 195degC 205degC and 215degC respectively

Complexity 9

in the following figure the upper limit of the virtual energystorage output power changes as shown in Figure 16

It can be seen from the above figure that the outputpower of the virtual energy storage decreases as temperatureincreases

523 Economic Analysis of Optimization for Joint VirtualEnergy Storage Based on air conditioning electric vehicleshave the ability to adjust the operating power within acertain range to convert electrical energy into thermal en-ergy storage or perform bidirectional energy exchange withthe power grid to achieve the virtual energy storage capacityof energy transfer -e following is the simulation of theeffect of virtual energy storage of air conditioning andelectric vehicles in this example Regarding the load of the

resident users in the constant temperature communityconsider a total of about 650 small high-rise (five-story)households with a total construction area of 65000 squaremeters a total air conditioning power of 1000 kW and anaverage of about 15 kW per household on the top floorthere is about 6500 square meters of photovoltaic panelsinstalled and 10 wind turbines equipped the power of itsdistributed power generation equipment is shown inFigure 17

Considering that virtual energy storage with electricvehicles participation only charges 04883CNYkWh sowhen actually using electric vehicles for virtual energystorage the discharge cost of electric vehicles is 06883CNYkWh and the discharge efficiency is 80 In addition themaintenance cost for wind turbines and photovoltaic powergeneration is shown in Table 2 [8]

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash40ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Number of EV arrivedNumber of EV left

Figure 10 -e distribution of vehicle arrival and departure times in this optimization

1200 1500 1800 2100 2400 300 600 900 1200Time

0

500

1000

1500

2000

2500

3000

3500

Elec

tric

ity q

uant

ity (k

Wh)

Remaining power value before rolling optimizationRemaining power value after rolling optimization

X 136Y 4778

X 136Y 1544

X 75Y 7894

X 75Y 7905

900Time

0

100

200

300

X 136Y 4778

X 136Y 1544

Figure 11 Comparison result of standard function value of global constraint detection

10 Complexity

000 300 600 900 1200 1500 1800 2100 2400Time

1516171819202122232425262728293031323334353637

Tem

pera

ture

(degC)

Outdoor temperatureIndoor temperature after virtual energy storage with air conditioning participation

Figure 13 Comparison of indoor and outdoor temperature change curves

300 600 900 1200 1500 1800 2100 2400Time

050

100150200250

Pow

er (k

W) Natural loss power of virtual energy storage with air conditioning participation

ndash2000

200400600800

Pow

er (k

W) Virtual energy storage power with air conditioning participation

Air conditioning output power

300600900

1200

Pow

er (k

W)

Figure 14 Comparison chart of the natural power consumption of the virtual energy storage with air conditioning participation airconditioning power and virtual power of virtual energy storage

ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Distribution of arrival and departure times of electric vehicles

Number of EV arrived

Number of EV le

Virtual energy storage power

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400

Pow

er (k

W)

Virtual energy storage remaining power S

10002000300040005000

Elec

tric

ity q

uant

ity(k

Wh)

Figure 12 Comparison chart of electric vehiclersquos space-time distribution remaining power and power

Complexity 11

-e total load demand curve of the residents is shown inFigure 18

-is environment corresponds to four scenesrespectively

Scenario 1 Electric vehicle and air conditioner jointlyparticipate in virtual energy storage

000 300 600 900 1200 1500 1800 2100 2400Time

ndash350ndash330ndash310ndash290ndash270ndash250ndash230ndash210ndash190ndash170ndash150ndash130ndash110

ndash90ndash70ndash50

Pow

er (k

W)

The upper limit of virtual energy storage output power at 195 degCThe upper limit of virtual energy storage output power at 205 degCThe upper limit of virtual energy storage output power at 215 degC

Figure 16 Comparison of the maximum output power of virtual energy storage at different set temperatures

000 300 600 900 1200 1500 1800 2100 2400Time

0

150

300

450

600

750

900

Pow

er (k

W)

Total power of photovoltaic power generationTotal power of wind generation

Figure 17 -e total power of the wind turbine and photovoltaic power generation of the constant temperature small high-rise building innumber 1 residential area

Table 2 Maintenance cost table for wind turbine and photovoltaicpower generation

Parameter (CNYkWh) ValueWind turbine maintenance cost 011PV maintenance cost 008

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400500600

Pow

er (k

W)

Figure 15 Chart of power range of virtual energy storage with electric vehicle participation

12 Complexity

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

electric vehicles as well as the remaining power of the powerbattery-e state at time t refers to the indoor temperature attime t and the total remaining capacity of the electric ve-hiclersquos virtual energy storage at time t

For the virtual energy storage in which air conditioningparticipate

Tin(t + 1) Tset(t) SCTin(t) + τηPacv(t)

SC (19)

For electric vehicles for the virtual energy storage state attime t + 1 during the rolling optimization process in theregion i when the virtual energy storage state SEVminus virtuali(t)the input power PEVminus virtualminus in(t) and the output powerPEVminus virtualminus out(t) at the previous time are known the status ofthe virtual energy storage capacity of electric vehicles at thebeginning of the next time period can be determined

SEVminus virtuali(t + 1) SEVminus virtuali(t) minus PEVminus virtualminus out(t)

times τ + PEVminus virtualminus in(t) times τ(20)

32 Objective Function In the case where other conditionsare certain and uncontrollable for the virtual energy storageoptimization scheduling in which air conditioning andelectric vehicles jointly participate the optimization

objective function has the lowest total cost of electricityconsumption throughout the day

minC min1113944T

t11113944

M

i1CWTi(t) + CPVi(t) + Cgridi(t)1113872 1113873

+ 1113944M

i1CEVi + CACi1113872 1113873

(21)

In equation (21)M is the total number of residential areaand units in the area in the area i at the time t CWTi(t) andCPVi(t) are the total cost of wind power and photovoltaicpower respectively Cgridi(t) is the cost of purchasingelectricity from the power grid CEVi is the cost of virtualenergy storage with electric vehicles participation in the areai throughout the day CACi is the cost of air conditioningvirtual energy storage throughout the day in the area i

In addition

CWTi(t) pWTirepare times EWTi(t)

CPVi(t) pPVirepare times EPVi(t)(22)

In equation (22) pWTirepare and pPVirepare are the powergeneration maintenance costs of wind turbines and pho-tovoltaic power generation respectively And their units areCNYkWh EWTi(t) and EPVi(t) are the power generationcapacity of wind turbines and photovoltaic power generationduring the time period which contains time t

Cgridi(t) pgrid(t) times Egridi(t) (23)

In equation (23) pgrid(t) is the price of electric energy inthe time period which contains time t which can be stepprice peak-valley price time-sharing price or real-timeprice and Egridi(t) represents time t

CEVi pEV times EEVi (24)

In equation (24) pEV is the cost of virtual energy storagewith electric vehicles participation the unit is CNYkWhEEVi is the total amount of virtual energy storage withelectric vehicles participation in the ith area in the whole day

CACi pAC times EACi (25)

In equation (25) pAC is the cost of in virtual energystorage with air conditioning participation the unit is CNYkWh EACi is the total amount of virtual energy storage withair conditioning participation in the ith area throughout theday

33 Restrictions

331 Energy Balance Constraint -e output power of allpower sources and energy storage devices at time t should be

No

Yes

Output the state at time t and the state in time period t

Generate the independent variable X that meets the requirements

Determine the power of virtual energy storage for air conditioning and electric vehicles

Determine the final state of the virtual energy storage device at the end of time period t

t = 96

t = t+1

Determine the independent variable range according to the given state

Output X

t = 1

Figure 4 Flowchart of virtual energy storage capacity and outputpower rolling optimization

Complexity 5

equal to the electricity consumption at that time as shown inequation (26)

Pacminus o + PEVminus o + demand PWT + PPV + Pacminus virtual

+ Pgrid + PEVminus virtual(26)

Pacminus o is the natural power consumption load curve of thevirtual energy storage of the air conditioning PEVminus o is thecharging power load curve of the electric vehicle demand isthe daily load demand PWT is the wind power PPV is thephotovoltaic power Pacminus virtual is the input (or output) powerof the virtual energy storage with air conditioning partici-pation Pgrid is the power of the power grid and PEVminus virtual isthe input (or output) power of the virtual energy storageinvolved in electric vehicles

332 Output Power Constraints Any distributed powersupply and virtual energy storage device have a limitation forpower rating as shown in equation (27)

Pimin(t)ltPi(t)ltPimax(t) (27)

In this equation Pimin(t) and Pimax(t) are the mini-mum and maximum values of the average output power ofthe ith device in the period of time t respectively

333 Restrictions on the Basic Driving Power Demand of theNext Day after the Electric Vehicle Participates in the VirtualEnergy Storage -e remaining power of any electric vehiclecan at least meet the needs of traveling the next day asshown in equation (28)

Wji minus W0ji gt 0 (28)

Wji is the remaining power of the jth electric car in the itharea and W0

ji is the minimum power required for the jthelectric vehicle in the ith area

-e remaining power constraint for electric vehicles isparticipating in virtual energy storage

-e remaining power of virtual energy storage cannot benegative

SEVminus virtuali gt 0 (29)

SEVminus virtuali is the remaining power of the ith electricvehicle

4 Continuous Rolling Optimization of FeasibleSolution Initialization for High-DimensionalComplex Constrained Optimization Problem

By analyzing the rolling optimization model proposedabove we can find that themodel built in this chapter has thefollowing characteristics

(1) -e dimension of decision variables is high(2) -ere are local constraints described by the rolling

optimization model among decision variables(3) -ere are global constraints on decision variables

-is section proposes a continuous rolling optimizationalgorithm for initializing feasible solutions for high-di-mensional complex constrained optimization problems forrolling optimization models and complex constraints so asto obtain decision variables that simultaneously satisfymultiple types of constraints

41 Treatment Strategy forMulticonstraint Problems A largenumber of inequality constraints will result in multiplefeasible regions with irregular shapes in the feasible solutionspace and the decision variables must satisfy all the con-straints which requires the determination of the range offeasible regions Take the feasible region of a two-dimen-sional optimization problem as an example as shown inFigure 5

In the figure shown above A1 and A2 are respectivelyfeasible regions of decision variables for two differentconstraints Since the area of A2 is small processing theconstraints in parallel will greatly reduce the probability ofthe decision variable falling in A2 -is will make it difficultfor a large number of decision variables to meet the A2constraint conditions resulting in inefficient decision var-iable selection However when the problem to be solved is ahigh-dimensional optimization problem the shape of thefeasible region corresponding to the constraint conditions ismore difficult to determine and the intersection between thefeasible regions is also more difficult to obtain For theoptimization problems shown in this chapter the dimensionof its solution space is shown in equation (30) as follows

D D1 + D2 N1 times T1 + N2 times T2 (30)

In equation (30) N1 and N2 are the number of timeperiods divided per hour which are both 4 in the questionsin this chapter Besides T1 and T2 are the total time of theoptimization cycle which are both 24 in this paper so for theoptimization problem given in this chapter its dimension is192 In practical problems as the influence factors con-sidered increase its dimensions may become larger

42 Solution Feasible Probability For the determination ofthe feasible solution with multiple constraints this sectionuses the solution feasible probability to evaluate its effi-ciency as shown in equation (31)

P A1capA2( ) A1( ) PA1 capA2

PA1

(31)

-e following is an analysis of its value first of all for theone-dimensional optimization problem -e feasible solu-tion selection process is shown in Figure 6

In the two one-dimensional constraints given in theabove figure if N feasible solutions are determined inparallel the process is to first generate N feasible solutionsfor A1 constraint in the [x1 x2] interval and then judgewhether it meets A2 According to the range covered by A1and A2 we can know the solution feasible probability whenthe feasible solutions are evenly distributed

6 Complexity

P A1 capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1 (32)

Claim after choosing a feasible solution with A1 con-straint the probability of satisfying A2 constraint isP(A1 capA2)(A1)

-e following dimension of the optimization problem isincreased In the two-dimensional optimization problemthe solution feasible probability is discussed -e simplerinequality constraint is selected thus the selection processof a feasible solution is shown in Figure 7

-e feasible probability is shown in

P A1capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1times

y2 minus y3

y2 minus y1 (33)

According to the solution feasible probability of the low-dimensional complex constrained optimization problem ifits P(A1capA2)(A1) in each dimension is P then the solutionfeasible probability of the N-dimensional multiconstrainedoptimization problem should be PN When N is too largethe probability of its feasible solution selection probabilitywill be very small and it is easy to make the optimizationprocess fall into an infinite loop -e following experimentdetermines the feasible probability of the solution of theoptimization problem in different dimensions and sets P to05 -e results are shown in Table 1

In view of the dimensional disaster in this paper theundeterminable problem of feasible solutions in this chaptercould be analyzed and solved -erefore this section pro-poses a continuous rolling optimization algorithm to solvethe inefficiency problem of multiconstrained feasiblesolutions

43 Algorithm Flow For the high-dimensional complexconstrained optimization problem the analysis is first basedon the two-dimensional optimization problem When theoptimization problem is faced with global constraints andlocal constraints the optimization process is shown inFigure 8 where A1 represents the constraint condition 1 andA2 represents the constraint condition 2

In the figure shown above the red and blue paths are theoptimization paths of the results with two consecutive

0x

y A1 A2

Figure 5 Schematic diagram of the feasible domain for the so-lution of a two-dimensional optimization problem

A1

x1 x2x3 x4

A2

Figure 6 Schematic diagram of feasible solutions for one-di-mensional optimization problems

0

A1

A2

y1

x1 x2x3

y2

y3

Figure 7 Schematic diagram of the feasible solution of the two-dimensional optimization problem

Table 1 Probability comparison of random initialization solutionsfor optimization problems in different dimensions

-e dimension ofoptimizationproblem

Solution feasibleprobability with

theoreticalcalculation ()

-e solution feasibleprobability errorwith experimental

results ()1 50 502 25 253 125 1255 3125 312510 009765625 009765625

0

A1

A2

x1

x2

Figure 8 Continuous rolling revision selection process of feasiblesolutions for two-dimensional optimization problems

Complexity 7

optimizations Since A1 represents local constraints and x1has a mutual influence with x2 combined with the rollingoptimization model proposed in the previous section theevolutionary process of the continuous rolling optimizationalgorithm determined by the local constraint and the globalconstraint common feasible region of the optimizationproblem can be determined as shown in Figure 9

-e specific steps are as follows

(1) Determine the value of the N-dimensional decisionvariable x1 xi

(2) Determine whether the global optimization re-quirements are met thus directly output the Nfeasible domain decision variable x1 xi if the re-quirements are all met Based on the feasibleprobability of the solution the N-dimensional de-cision variable x1 xi at this time is difficult tomeet the requirements if not go to step (3)

(3) Introduce the global constraint condition discrimi-nant function G(x) which is related to the constraintcondition of the optimization problem but not di-rectly a constraint condition It needs to be formulatedaccording to different global constraints -e condi-tional discriminant function G(x) selected in thischapter is the remaining power of virtual energystorage with electric vehicle participation Under

actual operating conditions when all electric vehiclesleave the residential area the remaining power ofvirtual energy storage with electric vehicle partici-pation should be 0 so its standard function g(x) 0

(4) Determine the average error according to the con-ditional discriminant function G(x) and its standardfunction value g(x)

(5) Obtain a new N-dimensional decision variablex1prime xi

prime based on xiprime xi + e judge whether it

meets the global optimization requirements anddirectly output the N-dimensional feasible regiondecision variable x1prime xi

prime if it meets all require-ments if not go to step (6)

(6) Determine the new average error eprime based on the N-dimensional feasible region decision variable x1prime xi

primeand the global constraint discriminant function G(x)as well as its standard function value g(x)

(7) Compare e with eprime if the error becomes larger afterthe correlation for average error e (ie eprime gt e) thenlet e eprime and go back to step (5) Recalculate the N-dimensional feasible domain decision variablex1prime xi

prime if the error is significantly reduced (ieeprime lt e) then update the N-dimensional feasible re-gion decision variable x1 xi obtain the new N-dimensional decision variable x1prime xi

prime for the new

Optimization problem dimension N

Determine the value of Xi

The Xi+1 value based on rolling optimization is determined

i + 1 = I

i + 1 = I i + 1 = I

Discrimination of global constraints

Discrimination of global constraints

Discrimination of global constraints

Output (Xi XI)

Introduce discriminant function G (x) and criteria g (x) for global

constraints

(G (Xi XI) ndash g (x))N = e

(G (Xi XI)prime ndash g (x))N = eprime

Xiprime = Xi + e Xiprime = Xi + eprime

Determination of Xprimei+1 value based on rolling optimization

Determination of Xprimei+1 value based on rolling optimization

i = i + 1i = i + 1

e gt eprime

Yes

Yes

No

No

No

Yes

No

Yes

Yes

No

Yes Yes

No

No

Utilize (Xiprime XIprime) calculateG (Xi XI)prime

Xi = Xiprimee = eprime

eprime = e

I = I i = 1

i = i + 1

Figure 9 Flowchart of continuous rolling optimization algorithm

8 Complexity

average error eprime and then determine whether theglobal optimization requirements are met thusdirectly output the N-dimensional feasible domaindecision variable x1prime xi

prime if it meets all require-ments if not go to step (8)

(8) Update the newly generated eprime so that e eprimetherefore determine the new average error eprime basedon the updated N-dimensional feasible domain de-cision variable x1prime xi

prime and then go to step (7)

44 Optimization Effect Analysis In the problem solved inthis chapter one of the decision variables is the input andoutput power of the virtual energy storage with electricvehicle participation in each time period and the remainingpower of the electric vehicle virtual energy storage is used asthe standard to detect whether the global optimization iscompleted -e distribution diagram of the arrival anddeparture time of electric vehicles in this simulation isshown in Figure 10 -e results of the comparison betweenthe unoptimized and optimized global constraint detectionstandard function values are shown in Figure 11

As can be seen from Figure 10 the last two vehicles in thearea left within the time period of 1000ndash1015 and the totalpower 4778 kWh can be determined by calculation

As can be seen from Figure 11 at 1000 before rollingoptimization when the last two electric vehicles have notleft the remaining power of virtual energy storage is1544 kWh According to simulation calculations theremaining power of the two electric vehicles is 4778 kWh-at is after the last two vehicles have left the remainingenergy of the virtual energy storage is still not 0 whichobviously does not meet the global constraints indicatingthat the decision variables fall outside the feasible domain ofthe global constraints and the initialization fails If thecontinuous rolling optimization algorithm is not adoptedthe decision variables need to be initialized again

After the continuous rolling optimization determinedfor the high-dimensional complex constraint optimizationfeasible solution the results are consistent with the electricvehicle arrival and departure states indicating that thecontinuous rolling optimization algorithm [5 24] for thehigh-dimensional optimization of global constraints andlocal constraints that jointly govern the feasible domain caneffectively limit the decision variables within the globalconstraints and local constraints that jointly govern thefeasible domain for the problems in this chapter which helpsimprove the optimization efficiency

5 Analysis

-is section first simulates the virtual energy storage ca-pacity of air conditioning and electric vehicles and illustratesthe feasibility of virtual energy storage -en virtual energystorage is optimized for scheduling In the example calcu-lation process the virtual energy storage power range of airconditioning and electric vehicles is first determined andthen the day is divided into 96 time periods to optimize thevirtual energy storage power within the power range

51 Analysis of Air Conditioning and Electric Vehicle VirtualEnergy Storage Capacity

511 Output Power of the Virtual Energy Storage Model withEV Participation In the virtual energy storage in whichelectric vehicles participate the input and output power ofthe virtual energy storage and the arrival and departure ofthe electric vehicle will affect the remaining power of thevirtual energy storage Under rolling optimization the re-lationship can be obtained by Figure 12

As can be seen from Figure 12 the continuous energyoptimization of the electric vehiclersquos virtual energy storageoutput meets the local constraints the virtual energy storageremaining power becomes 0 after all the electric vehiclesleave indicating that the virtual energy storage output powermeets the global constraint conditions

512 Output Power of Virtual Energy Storage Model with AirConditioning Participation In the virtual energy storagewith air conditioning participation the input and outputpower of the virtual energy storage and the natural powerloss of the virtual energy storage based on the indoor andoutdoor temperature difference will affect the remainingpower of the virtual energy storage and the change of roomtemperature Under rolling optimization the changes of theabove four parameters are shown in Figures 13 and 14

It can be seen from the comparison that within thetemperature constraint range the virtual energy storage ofthe air conditioner can realize the virtual power change ofthe virtual energy storage through the change of the airconditioner power

52 Determination of the Range of Virtual Energy StoragePower for Air Conditioning and Electric Vehicles

521 Virtual Energy Storage Charge and Discharge PowerRange with EV Participation For the virtual energy storageof electric vehicles according to the spatial and temporaldistribution of electric vehicles given in Figure 12 and thepower demand for driving on the day according to equations(17) and (18) the input and output power range of virtualenergy storage with electric vehicles participation can bedetermined -e results are shown in Figure 15

522 Determination of the Range of Charge and DischargePower at the Starting Time in the Virtual Energy Storage withAir Conditioning Participation -e daily temperaturechange curve in this area is shown in the red line in Fig-ure 13 Considering the natural consumption rate of thevirtual energy storage of the air conditioning the outputpower of the virtual energy storage reaches the maximumwhen the air conditioner is not running which is Pacminus O(t)when the air conditioner is running its input and outputpower are shown in equation (11) -e maximum value ofthe virtual energy storage discharge power changesaccording to the change of the set temperature -e tem-peratures are set to 195degC 205degC and 215degC respectively

Complexity 9

in the following figure the upper limit of the virtual energystorage output power changes as shown in Figure 16

It can be seen from the above figure that the outputpower of the virtual energy storage decreases as temperatureincreases

523 Economic Analysis of Optimization for Joint VirtualEnergy Storage Based on air conditioning electric vehicleshave the ability to adjust the operating power within acertain range to convert electrical energy into thermal en-ergy storage or perform bidirectional energy exchange withthe power grid to achieve the virtual energy storage capacityof energy transfer -e following is the simulation of theeffect of virtual energy storage of air conditioning andelectric vehicles in this example Regarding the load of the

resident users in the constant temperature communityconsider a total of about 650 small high-rise (five-story)households with a total construction area of 65000 squaremeters a total air conditioning power of 1000 kW and anaverage of about 15 kW per household on the top floorthere is about 6500 square meters of photovoltaic panelsinstalled and 10 wind turbines equipped the power of itsdistributed power generation equipment is shown inFigure 17

Considering that virtual energy storage with electricvehicles participation only charges 04883CNYkWh sowhen actually using electric vehicles for virtual energystorage the discharge cost of electric vehicles is 06883CNYkWh and the discharge efficiency is 80 In addition themaintenance cost for wind turbines and photovoltaic powergeneration is shown in Table 2 [8]

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash40ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Number of EV arrivedNumber of EV left

Figure 10 -e distribution of vehicle arrival and departure times in this optimization

1200 1500 1800 2100 2400 300 600 900 1200Time

0

500

1000

1500

2000

2500

3000

3500

Elec

tric

ity q

uant

ity (k

Wh)

Remaining power value before rolling optimizationRemaining power value after rolling optimization

X 136Y 4778

X 136Y 1544

X 75Y 7894

X 75Y 7905

900Time

0

100

200

300

X 136Y 4778

X 136Y 1544

Figure 11 Comparison result of standard function value of global constraint detection

10 Complexity

000 300 600 900 1200 1500 1800 2100 2400Time

1516171819202122232425262728293031323334353637

Tem

pera

ture

(degC)

Outdoor temperatureIndoor temperature after virtual energy storage with air conditioning participation

Figure 13 Comparison of indoor and outdoor temperature change curves

300 600 900 1200 1500 1800 2100 2400Time

050

100150200250

Pow

er (k

W) Natural loss power of virtual energy storage with air conditioning participation

ndash2000

200400600800

Pow

er (k

W) Virtual energy storage power with air conditioning participation

Air conditioning output power

300600900

1200

Pow

er (k

W)

Figure 14 Comparison chart of the natural power consumption of the virtual energy storage with air conditioning participation airconditioning power and virtual power of virtual energy storage

ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Distribution of arrival and departure times of electric vehicles

Number of EV arrived

Number of EV le

Virtual energy storage power

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400

Pow

er (k

W)

Virtual energy storage remaining power S

10002000300040005000

Elec

tric

ity q

uant

ity(k

Wh)

Figure 12 Comparison chart of electric vehiclersquos space-time distribution remaining power and power

Complexity 11

-e total load demand curve of the residents is shown inFigure 18

-is environment corresponds to four scenesrespectively

Scenario 1 Electric vehicle and air conditioner jointlyparticipate in virtual energy storage

000 300 600 900 1200 1500 1800 2100 2400Time

ndash350ndash330ndash310ndash290ndash270ndash250ndash230ndash210ndash190ndash170ndash150ndash130ndash110

ndash90ndash70ndash50

Pow

er (k

W)

The upper limit of virtual energy storage output power at 195 degCThe upper limit of virtual energy storage output power at 205 degCThe upper limit of virtual energy storage output power at 215 degC

Figure 16 Comparison of the maximum output power of virtual energy storage at different set temperatures

000 300 600 900 1200 1500 1800 2100 2400Time

0

150

300

450

600

750

900

Pow

er (k

W)

Total power of photovoltaic power generationTotal power of wind generation

Figure 17 -e total power of the wind turbine and photovoltaic power generation of the constant temperature small high-rise building innumber 1 residential area

Table 2 Maintenance cost table for wind turbine and photovoltaicpower generation

Parameter (CNYkWh) ValueWind turbine maintenance cost 011PV maintenance cost 008

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400500600

Pow

er (k

W)

Figure 15 Chart of power range of virtual energy storage with electric vehicle participation

12 Complexity

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

equal to the electricity consumption at that time as shown inequation (26)

Pacminus o + PEVminus o + demand PWT + PPV + Pacminus virtual

+ Pgrid + PEVminus virtual(26)

Pacminus o is the natural power consumption load curve of thevirtual energy storage of the air conditioning PEVminus o is thecharging power load curve of the electric vehicle demand isthe daily load demand PWT is the wind power PPV is thephotovoltaic power Pacminus virtual is the input (or output) powerof the virtual energy storage with air conditioning partici-pation Pgrid is the power of the power grid and PEVminus virtual isthe input (or output) power of the virtual energy storageinvolved in electric vehicles

332 Output Power Constraints Any distributed powersupply and virtual energy storage device have a limitation forpower rating as shown in equation (27)

Pimin(t)ltPi(t)ltPimax(t) (27)

In this equation Pimin(t) and Pimax(t) are the mini-mum and maximum values of the average output power ofthe ith device in the period of time t respectively

333 Restrictions on the Basic Driving Power Demand of theNext Day after the Electric Vehicle Participates in the VirtualEnergy Storage -e remaining power of any electric vehiclecan at least meet the needs of traveling the next day asshown in equation (28)

Wji minus W0ji gt 0 (28)

Wji is the remaining power of the jth electric car in the itharea and W0

ji is the minimum power required for the jthelectric vehicle in the ith area

-e remaining power constraint for electric vehicles isparticipating in virtual energy storage

-e remaining power of virtual energy storage cannot benegative

SEVminus virtuali gt 0 (29)

SEVminus virtuali is the remaining power of the ith electricvehicle

4 Continuous Rolling Optimization of FeasibleSolution Initialization for High-DimensionalComplex Constrained Optimization Problem

By analyzing the rolling optimization model proposedabove we can find that themodel built in this chapter has thefollowing characteristics

(1) -e dimension of decision variables is high(2) -ere are local constraints described by the rolling

optimization model among decision variables(3) -ere are global constraints on decision variables

-is section proposes a continuous rolling optimizationalgorithm for initializing feasible solutions for high-di-mensional complex constrained optimization problems forrolling optimization models and complex constraints so asto obtain decision variables that simultaneously satisfymultiple types of constraints

41 Treatment Strategy forMulticonstraint Problems A largenumber of inequality constraints will result in multiplefeasible regions with irregular shapes in the feasible solutionspace and the decision variables must satisfy all the con-straints which requires the determination of the range offeasible regions Take the feasible region of a two-dimen-sional optimization problem as an example as shown inFigure 5

In the figure shown above A1 and A2 are respectivelyfeasible regions of decision variables for two differentconstraints Since the area of A2 is small processing theconstraints in parallel will greatly reduce the probability ofthe decision variable falling in A2 -is will make it difficultfor a large number of decision variables to meet the A2constraint conditions resulting in inefficient decision var-iable selection However when the problem to be solved is ahigh-dimensional optimization problem the shape of thefeasible region corresponding to the constraint conditions ismore difficult to determine and the intersection between thefeasible regions is also more difficult to obtain For theoptimization problems shown in this chapter the dimensionof its solution space is shown in equation (30) as follows

D D1 + D2 N1 times T1 + N2 times T2 (30)

In equation (30) N1 and N2 are the number of timeperiods divided per hour which are both 4 in the questionsin this chapter Besides T1 and T2 are the total time of theoptimization cycle which are both 24 in this paper so for theoptimization problem given in this chapter its dimension is192 In practical problems as the influence factors con-sidered increase its dimensions may become larger

42 Solution Feasible Probability For the determination ofthe feasible solution with multiple constraints this sectionuses the solution feasible probability to evaluate its effi-ciency as shown in equation (31)

P A1capA2( ) A1( ) PA1 capA2

PA1

(31)

-e following is an analysis of its value first of all for theone-dimensional optimization problem -e feasible solu-tion selection process is shown in Figure 6

In the two one-dimensional constraints given in theabove figure if N feasible solutions are determined inparallel the process is to first generate N feasible solutionsfor A1 constraint in the [x1 x2] interval and then judgewhether it meets A2 According to the range covered by A1and A2 we can know the solution feasible probability whenthe feasible solutions are evenly distributed

6 Complexity

P A1 capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1 (32)

Claim after choosing a feasible solution with A1 con-straint the probability of satisfying A2 constraint isP(A1 capA2)(A1)

-e following dimension of the optimization problem isincreased In the two-dimensional optimization problemthe solution feasible probability is discussed -e simplerinequality constraint is selected thus the selection processof a feasible solution is shown in Figure 7

-e feasible probability is shown in

P A1capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1times

y2 minus y3

y2 minus y1 (33)

According to the solution feasible probability of the low-dimensional complex constrained optimization problem ifits P(A1capA2)(A1) in each dimension is P then the solutionfeasible probability of the N-dimensional multiconstrainedoptimization problem should be PN When N is too largethe probability of its feasible solution selection probabilitywill be very small and it is easy to make the optimizationprocess fall into an infinite loop -e following experimentdetermines the feasible probability of the solution of theoptimization problem in different dimensions and sets P to05 -e results are shown in Table 1

In view of the dimensional disaster in this paper theundeterminable problem of feasible solutions in this chaptercould be analyzed and solved -erefore this section pro-poses a continuous rolling optimization algorithm to solvethe inefficiency problem of multiconstrained feasiblesolutions

43 Algorithm Flow For the high-dimensional complexconstrained optimization problem the analysis is first basedon the two-dimensional optimization problem When theoptimization problem is faced with global constraints andlocal constraints the optimization process is shown inFigure 8 where A1 represents the constraint condition 1 andA2 represents the constraint condition 2

In the figure shown above the red and blue paths are theoptimization paths of the results with two consecutive

0x

y A1 A2

Figure 5 Schematic diagram of the feasible domain for the so-lution of a two-dimensional optimization problem

A1

x1 x2x3 x4

A2

Figure 6 Schematic diagram of feasible solutions for one-di-mensional optimization problems

0

A1

A2

y1

x1 x2x3

y2

y3

Figure 7 Schematic diagram of the feasible solution of the two-dimensional optimization problem

Table 1 Probability comparison of random initialization solutionsfor optimization problems in different dimensions

-e dimension ofoptimizationproblem

Solution feasibleprobability with

theoreticalcalculation ()

-e solution feasibleprobability errorwith experimental

results ()1 50 502 25 253 125 1255 3125 312510 009765625 009765625

0

A1

A2

x1

x2

Figure 8 Continuous rolling revision selection process of feasiblesolutions for two-dimensional optimization problems

Complexity 7

optimizations Since A1 represents local constraints and x1has a mutual influence with x2 combined with the rollingoptimization model proposed in the previous section theevolutionary process of the continuous rolling optimizationalgorithm determined by the local constraint and the globalconstraint common feasible region of the optimizationproblem can be determined as shown in Figure 9

-e specific steps are as follows

(1) Determine the value of the N-dimensional decisionvariable x1 xi

(2) Determine whether the global optimization re-quirements are met thus directly output the Nfeasible domain decision variable x1 xi if the re-quirements are all met Based on the feasibleprobability of the solution the N-dimensional de-cision variable x1 xi at this time is difficult tomeet the requirements if not go to step (3)

(3) Introduce the global constraint condition discrimi-nant function G(x) which is related to the constraintcondition of the optimization problem but not di-rectly a constraint condition It needs to be formulatedaccording to different global constraints -e condi-tional discriminant function G(x) selected in thischapter is the remaining power of virtual energystorage with electric vehicle participation Under

actual operating conditions when all electric vehiclesleave the residential area the remaining power ofvirtual energy storage with electric vehicle partici-pation should be 0 so its standard function g(x) 0

(4) Determine the average error according to the con-ditional discriminant function G(x) and its standardfunction value g(x)

(5) Obtain a new N-dimensional decision variablex1prime xi

prime based on xiprime xi + e judge whether it

meets the global optimization requirements anddirectly output the N-dimensional feasible regiondecision variable x1prime xi

prime if it meets all require-ments if not go to step (6)

(6) Determine the new average error eprime based on the N-dimensional feasible region decision variable x1prime xi

primeand the global constraint discriminant function G(x)as well as its standard function value g(x)

(7) Compare e with eprime if the error becomes larger afterthe correlation for average error e (ie eprime gt e) thenlet e eprime and go back to step (5) Recalculate the N-dimensional feasible domain decision variablex1prime xi

prime if the error is significantly reduced (ieeprime lt e) then update the N-dimensional feasible re-gion decision variable x1 xi obtain the new N-dimensional decision variable x1prime xi

prime for the new

Optimization problem dimension N

Determine the value of Xi

The Xi+1 value based on rolling optimization is determined

i + 1 = I

i + 1 = I i + 1 = I

Discrimination of global constraints

Discrimination of global constraints

Discrimination of global constraints

Output (Xi XI)

Introduce discriminant function G (x) and criteria g (x) for global

constraints

(G (Xi XI) ndash g (x))N = e

(G (Xi XI)prime ndash g (x))N = eprime

Xiprime = Xi + e Xiprime = Xi + eprime

Determination of Xprimei+1 value based on rolling optimization

Determination of Xprimei+1 value based on rolling optimization

i = i + 1i = i + 1

e gt eprime

Yes

Yes

No

No

No

Yes

No

Yes

Yes

No

Yes Yes

No

No

Utilize (Xiprime XIprime) calculateG (Xi XI)prime

Xi = Xiprimee = eprime

eprime = e

I = I i = 1

i = i + 1

Figure 9 Flowchart of continuous rolling optimization algorithm

8 Complexity

average error eprime and then determine whether theglobal optimization requirements are met thusdirectly output the N-dimensional feasible domaindecision variable x1prime xi

prime if it meets all require-ments if not go to step (8)

(8) Update the newly generated eprime so that e eprimetherefore determine the new average error eprime basedon the updated N-dimensional feasible domain de-cision variable x1prime xi

prime and then go to step (7)

44 Optimization Effect Analysis In the problem solved inthis chapter one of the decision variables is the input andoutput power of the virtual energy storage with electricvehicle participation in each time period and the remainingpower of the electric vehicle virtual energy storage is used asthe standard to detect whether the global optimization iscompleted -e distribution diagram of the arrival anddeparture time of electric vehicles in this simulation isshown in Figure 10 -e results of the comparison betweenthe unoptimized and optimized global constraint detectionstandard function values are shown in Figure 11

As can be seen from Figure 10 the last two vehicles in thearea left within the time period of 1000ndash1015 and the totalpower 4778 kWh can be determined by calculation

As can be seen from Figure 11 at 1000 before rollingoptimization when the last two electric vehicles have notleft the remaining power of virtual energy storage is1544 kWh According to simulation calculations theremaining power of the two electric vehicles is 4778 kWh-at is after the last two vehicles have left the remainingenergy of the virtual energy storage is still not 0 whichobviously does not meet the global constraints indicatingthat the decision variables fall outside the feasible domain ofthe global constraints and the initialization fails If thecontinuous rolling optimization algorithm is not adoptedthe decision variables need to be initialized again

After the continuous rolling optimization determinedfor the high-dimensional complex constraint optimizationfeasible solution the results are consistent with the electricvehicle arrival and departure states indicating that thecontinuous rolling optimization algorithm [5 24] for thehigh-dimensional optimization of global constraints andlocal constraints that jointly govern the feasible domain caneffectively limit the decision variables within the globalconstraints and local constraints that jointly govern thefeasible domain for the problems in this chapter which helpsimprove the optimization efficiency

5 Analysis

-is section first simulates the virtual energy storage ca-pacity of air conditioning and electric vehicles and illustratesthe feasibility of virtual energy storage -en virtual energystorage is optimized for scheduling In the example calcu-lation process the virtual energy storage power range of airconditioning and electric vehicles is first determined andthen the day is divided into 96 time periods to optimize thevirtual energy storage power within the power range

51 Analysis of Air Conditioning and Electric Vehicle VirtualEnergy Storage Capacity

511 Output Power of the Virtual Energy Storage Model withEV Participation In the virtual energy storage in whichelectric vehicles participate the input and output power ofthe virtual energy storage and the arrival and departure ofthe electric vehicle will affect the remaining power of thevirtual energy storage Under rolling optimization the re-lationship can be obtained by Figure 12

As can be seen from Figure 12 the continuous energyoptimization of the electric vehiclersquos virtual energy storageoutput meets the local constraints the virtual energy storageremaining power becomes 0 after all the electric vehiclesleave indicating that the virtual energy storage output powermeets the global constraint conditions

512 Output Power of Virtual Energy Storage Model with AirConditioning Participation In the virtual energy storagewith air conditioning participation the input and outputpower of the virtual energy storage and the natural powerloss of the virtual energy storage based on the indoor andoutdoor temperature difference will affect the remainingpower of the virtual energy storage and the change of roomtemperature Under rolling optimization the changes of theabove four parameters are shown in Figures 13 and 14

It can be seen from the comparison that within thetemperature constraint range the virtual energy storage ofthe air conditioner can realize the virtual power change ofthe virtual energy storage through the change of the airconditioner power

52 Determination of the Range of Virtual Energy StoragePower for Air Conditioning and Electric Vehicles

521 Virtual Energy Storage Charge and Discharge PowerRange with EV Participation For the virtual energy storageof electric vehicles according to the spatial and temporaldistribution of electric vehicles given in Figure 12 and thepower demand for driving on the day according to equations(17) and (18) the input and output power range of virtualenergy storage with electric vehicles participation can bedetermined -e results are shown in Figure 15

522 Determination of the Range of Charge and DischargePower at the Starting Time in the Virtual Energy Storage withAir Conditioning Participation -e daily temperaturechange curve in this area is shown in the red line in Fig-ure 13 Considering the natural consumption rate of thevirtual energy storage of the air conditioning the outputpower of the virtual energy storage reaches the maximumwhen the air conditioner is not running which is Pacminus O(t)when the air conditioner is running its input and outputpower are shown in equation (11) -e maximum value ofthe virtual energy storage discharge power changesaccording to the change of the set temperature -e tem-peratures are set to 195degC 205degC and 215degC respectively

Complexity 9

in the following figure the upper limit of the virtual energystorage output power changes as shown in Figure 16

It can be seen from the above figure that the outputpower of the virtual energy storage decreases as temperatureincreases

523 Economic Analysis of Optimization for Joint VirtualEnergy Storage Based on air conditioning electric vehicleshave the ability to adjust the operating power within acertain range to convert electrical energy into thermal en-ergy storage or perform bidirectional energy exchange withthe power grid to achieve the virtual energy storage capacityof energy transfer -e following is the simulation of theeffect of virtual energy storage of air conditioning andelectric vehicles in this example Regarding the load of the

resident users in the constant temperature communityconsider a total of about 650 small high-rise (five-story)households with a total construction area of 65000 squaremeters a total air conditioning power of 1000 kW and anaverage of about 15 kW per household on the top floorthere is about 6500 square meters of photovoltaic panelsinstalled and 10 wind turbines equipped the power of itsdistributed power generation equipment is shown inFigure 17

Considering that virtual energy storage with electricvehicles participation only charges 04883CNYkWh sowhen actually using electric vehicles for virtual energystorage the discharge cost of electric vehicles is 06883CNYkWh and the discharge efficiency is 80 In addition themaintenance cost for wind turbines and photovoltaic powergeneration is shown in Table 2 [8]

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash40ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Number of EV arrivedNumber of EV left

Figure 10 -e distribution of vehicle arrival and departure times in this optimization

1200 1500 1800 2100 2400 300 600 900 1200Time

0

500

1000

1500

2000

2500

3000

3500

Elec

tric

ity q

uant

ity (k

Wh)

Remaining power value before rolling optimizationRemaining power value after rolling optimization

X 136Y 4778

X 136Y 1544

X 75Y 7894

X 75Y 7905

900Time

0

100

200

300

X 136Y 4778

X 136Y 1544

Figure 11 Comparison result of standard function value of global constraint detection

10 Complexity

000 300 600 900 1200 1500 1800 2100 2400Time

1516171819202122232425262728293031323334353637

Tem

pera

ture

(degC)

Outdoor temperatureIndoor temperature after virtual energy storage with air conditioning participation

Figure 13 Comparison of indoor and outdoor temperature change curves

300 600 900 1200 1500 1800 2100 2400Time

050

100150200250

Pow

er (k

W) Natural loss power of virtual energy storage with air conditioning participation

ndash2000

200400600800

Pow

er (k

W) Virtual energy storage power with air conditioning participation

Air conditioning output power

300600900

1200

Pow

er (k

W)

Figure 14 Comparison chart of the natural power consumption of the virtual energy storage with air conditioning participation airconditioning power and virtual power of virtual energy storage

ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Distribution of arrival and departure times of electric vehicles

Number of EV arrived

Number of EV le

Virtual energy storage power

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400

Pow

er (k

W)

Virtual energy storage remaining power S

10002000300040005000

Elec

tric

ity q

uant

ity(k

Wh)

Figure 12 Comparison chart of electric vehiclersquos space-time distribution remaining power and power

Complexity 11

-e total load demand curve of the residents is shown inFigure 18

-is environment corresponds to four scenesrespectively

Scenario 1 Electric vehicle and air conditioner jointlyparticipate in virtual energy storage

000 300 600 900 1200 1500 1800 2100 2400Time

ndash350ndash330ndash310ndash290ndash270ndash250ndash230ndash210ndash190ndash170ndash150ndash130ndash110

ndash90ndash70ndash50

Pow

er (k

W)

The upper limit of virtual energy storage output power at 195 degCThe upper limit of virtual energy storage output power at 205 degCThe upper limit of virtual energy storage output power at 215 degC

Figure 16 Comparison of the maximum output power of virtual energy storage at different set temperatures

000 300 600 900 1200 1500 1800 2100 2400Time

0

150

300

450

600

750

900

Pow

er (k

W)

Total power of photovoltaic power generationTotal power of wind generation

Figure 17 -e total power of the wind turbine and photovoltaic power generation of the constant temperature small high-rise building innumber 1 residential area

Table 2 Maintenance cost table for wind turbine and photovoltaicpower generation

Parameter (CNYkWh) ValueWind turbine maintenance cost 011PV maintenance cost 008

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400500600

Pow

er (k

W)

Figure 15 Chart of power range of virtual energy storage with electric vehicle participation

12 Complexity

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

P A1 capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1 (32)

Claim after choosing a feasible solution with A1 con-straint the probability of satisfying A2 constraint isP(A1 capA2)(A1)

-e following dimension of the optimization problem isincreased In the two-dimensional optimization problemthe solution feasible probability is discussed -e simplerinequality constraint is selected thus the selection processof a feasible solution is shown in Figure 7

-e feasible probability is shown in

P A1capA2( ) A1( ) PA1capA2

PA1

x2 minus x3

x2 minus x1times

y2 minus y3

y2 minus y1 (33)

According to the solution feasible probability of the low-dimensional complex constrained optimization problem ifits P(A1capA2)(A1) in each dimension is P then the solutionfeasible probability of the N-dimensional multiconstrainedoptimization problem should be PN When N is too largethe probability of its feasible solution selection probabilitywill be very small and it is easy to make the optimizationprocess fall into an infinite loop -e following experimentdetermines the feasible probability of the solution of theoptimization problem in different dimensions and sets P to05 -e results are shown in Table 1

In view of the dimensional disaster in this paper theundeterminable problem of feasible solutions in this chaptercould be analyzed and solved -erefore this section pro-poses a continuous rolling optimization algorithm to solvethe inefficiency problem of multiconstrained feasiblesolutions

43 Algorithm Flow For the high-dimensional complexconstrained optimization problem the analysis is first basedon the two-dimensional optimization problem When theoptimization problem is faced with global constraints andlocal constraints the optimization process is shown inFigure 8 where A1 represents the constraint condition 1 andA2 represents the constraint condition 2

In the figure shown above the red and blue paths are theoptimization paths of the results with two consecutive

0x

y A1 A2

Figure 5 Schematic diagram of the feasible domain for the so-lution of a two-dimensional optimization problem

A1

x1 x2x3 x4

A2

Figure 6 Schematic diagram of feasible solutions for one-di-mensional optimization problems

0

A1

A2

y1

x1 x2x3

y2

y3

Figure 7 Schematic diagram of the feasible solution of the two-dimensional optimization problem

Table 1 Probability comparison of random initialization solutionsfor optimization problems in different dimensions

-e dimension ofoptimizationproblem

Solution feasibleprobability with

theoreticalcalculation ()

-e solution feasibleprobability errorwith experimental

results ()1 50 502 25 253 125 1255 3125 312510 009765625 009765625

0

A1

A2

x1

x2

Figure 8 Continuous rolling revision selection process of feasiblesolutions for two-dimensional optimization problems

Complexity 7

optimizations Since A1 represents local constraints and x1has a mutual influence with x2 combined with the rollingoptimization model proposed in the previous section theevolutionary process of the continuous rolling optimizationalgorithm determined by the local constraint and the globalconstraint common feasible region of the optimizationproblem can be determined as shown in Figure 9

-e specific steps are as follows

(1) Determine the value of the N-dimensional decisionvariable x1 xi

(2) Determine whether the global optimization re-quirements are met thus directly output the Nfeasible domain decision variable x1 xi if the re-quirements are all met Based on the feasibleprobability of the solution the N-dimensional de-cision variable x1 xi at this time is difficult tomeet the requirements if not go to step (3)

(3) Introduce the global constraint condition discrimi-nant function G(x) which is related to the constraintcondition of the optimization problem but not di-rectly a constraint condition It needs to be formulatedaccording to different global constraints -e condi-tional discriminant function G(x) selected in thischapter is the remaining power of virtual energystorage with electric vehicle participation Under

actual operating conditions when all electric vehiclesleave the residential area the remaining power ofvirtual energy storage with electric vehicle partici-pation should be 0 so its standard function g(x) 0

(4) Determine the average error according to the con-ditional discriminant function G(x) and its standardfunction value g(x)

(5) Obtain a new N-dimensional decision variablex1prime xi

prime based on xiprime xi + e judge whether it

meets the global optimization requirements anddirectly output the N-dimensional feasible regiondecision variable x1prime xi

prime if it meets all require-ments if not go to step (6)

(6) Determine the new average error eprime based on the N-dimensional feasible region decision variable x1prime xi

primeand the global constraint discriminant function G(x)as well as its standard function value g(x)

(7) Compare e with eprime if the error becomes larger afterthe correlation for average error e (ie eprime gt e) thenlet e eprime and go back to step (5) Recalculate the N-dimensional feasible domain decision variablex1prime xi

prime if the error is significantly reduced (ieeprime lt e) then update the N-dimensional feasible re-gion decision variable x1 xi obtain the new N-dimensional decision variable x1prime xi

prime for the new

Optimization problem dimension N

Determine the value of Xi

The Xi+1 value based on rolling optimization is determined

i + 1 = I

i + 1 = I i + 1 = I

Discrimination of global constraints

Discrimination of global constraints

Discrimination of global constraints

Output (Xi XI)

Introduce discriminant function G (x) and criteria g (x) for global

constraints

(G (Xi XI) ndash g (x))N = e

(G (Xi XI)prime ndash g (x))N = eprime

Xiprime = Xi + e Xiprime = Xi + eprime

Determination of Xprimei+1 value based on rolling optimization

Determination of Xprimei+1 value based on rolling optimization

i = i + 1i = i + 1

e gt eprime

Yes

Yes

No

No

No

Yes

No

Yes

Yes

No

Yes Yes

No

No

Utilize (Xiprime XIprime) calculateG (Xi XI)prime

Xi = Xiprimee = eprime

eprime = e

I = I i = 1

i = i + 1

Figure 9 Flowchart of continuous rolling optimization algorithm

8 Complexity

average error eprime and then determine whether theglobal optimization requirements are met thusdirectly output the N-dimensional feasible domaindecision variable x1prime xi

prime if it meets all require-ments if not go to step (8)

(8) Update the newly generated eprime so that e eprimetherefore determine the new average error eprime basedon the updated N-dimensional feasible domain de-cision variable x1prime xi

prime and then go to step (7)

44 Optimization Effect Analysis In the problem solved inthis chapter one of the decision variables is the input andoutput power of the virtual energy storage with electricvehicle participation in each time period and the remainingpower of the electric vehicle virtual energy storage is used asthe standard to detect whether the global optimization iscompleted -e distribution diagram of the arrival anddeparture time of electric vehicles in this simulation isshown in Figure 10 -e results of the comparison betweenthe unoptimized and optimized global constraint detectionstandard function values are shown in Figure 11

As can be seen from Figure 10 the last two vehicles in thearea left within the time period of 1000ndash1015 and the totalpower 4778 kWh can be determined by calculation

As can be seen from Figure 11 at 1000 before rollingoptimization when the last two electric vehicles have notleft the remaining power of virtual energy storage is1544 kWh According to simulation calculations theremaining power of the two electric vehicles is 4778 kWh-at is after the last two vehicles have left the remainingenergy of the virtual energy storage is still not 0 whichobviously does not meet the global constraints indicatingthat the decision variables fall outside the feasible domain ofthe global constraints and the initialization fails If thecontinuous rolling optimization algorithm is not adoptedthe decision variables need to be initialized again

After the continuous rolling optimization determinedfor the high-dimensional complex constraint optimizationfeasible solution the results are consistent with the electricvehicle arrival and departure states indicating that thecontinuous rolling optimization algorithm [5 24] for thehigh-dimensional optimization of global constraints andlocal constraints that jointly govern the feasible domain caneffectively limit the decision variables within the globalconstraints and local constraints that jointly govern thefeasible domain for the problems in this chapter which helpsimprove the optimization efficiency

5 Analysis

-is section first simulates the virtual energy storage ca-pacity of air conditioning and electric vehicles and illustratesthe feasibility of virtual energy storage -en virtual energystorage is optimized for scheduling In the example calcu-lation process the virtual energy storage power range of airconditioning and electric vehicles is first determined andthen the day is divided into 96 time periods to optimize thevirtual energy storage power within the power range

51 Analysis of Air Conditioning and Electric Vehicle VirtualEnergy Storage Capacity

511 Output Power of the Virtual Energy Storage Model withEV Participation In the virtual energy storage in whichelectric vehicles participate the input and output power ofthe virtual energy storage and the arrival and departure ofthe electric vehicle will affect the remaining power of thevirtual energy storage Under rolling optimization the re-lationship can be obtained by Figure 12

As can be seen from Figure 12 the continuous energyoptimization of the electric vehiclersquos virtual energy storageoutput meets the local constraints the virtual energy storageremaining power becomes 0 after all the electric vehiclesleave indicating that the virtual energy storage output powermeets the global constraint conditions

512 Output Power of Virtual Energy Storage Model with AirConditioning Participation In the virtual energy storagewith air conditioning participation the input and outputpower of the virtual energy storage and the natural powerloss of the virtual energy storage based on the indoor andoutdoor temperature difference will affect the remainingpower of the virtual energy storage and the change of roomtemperature Under rolling optimization the changes of theabove four parameters are shown in Figures 13 and 14

It can be seen from the comparison that within thetemperature constraint range the virtual energy storage ofthe air conditioner can realize the virtual power change ofthe virtual energy storage through the change of the airconditioner power

52 Determination of the Range of Virtual Energy StoragePower for Air Conditioning and Electric Vehicles

521 Virtual Energy Storage Charge and Discharge PowerRange with EV Participation For the virtual energy storageof electric vehicles according to the spatial and temporaldistribution of electric vehicles given in Figure 12 and thepower demand for driving on the day according to equations(17) and (18) the input and output power range of virtualenergy storage with electric vehicles participation can bedetermined -e results are shown in Figure 15

522 Determination of the Range of Charge and DischargePower at the Starting Time in the Virtual Energy Storage withAir Conditioning Participation -e daily temperaturechange curve in this area is shown in the red line in Fig-ure 13 Considering the natural consumption rate of thevirtual energy storage of the air conditioning the outputpower of the virtual energy storage reaches the maximumwhen the air conditioner is not running which is Pacminus O(t)when the air conditioner is running its input and outputpower are shown in equation (11) -e maximum value ofthe virtual energy storage discharge power changesaccording to the change of the set temperature -e tem-peratures are set to 195degC 205degC and 215degC respectively

Complexity 9

in the following figure the upper limit of the virtual energystorage output power changes as shown in Figure 16

It can be seen from the above figure that the outputpower of the virtual energy storage decreases as temperatureincreases

523 Economic Analysis of Optimization for Joint VirtualEnergy Storage Based on air conditioning electric vehicleshave the ability to adjust the operating power within acertain range to convert electrical energy into thermal en-ergy storage or perform bidirectional energy exchange withthe power grid to achieve the virtual energy storage capacityof energy transfer -e following is the simulation of theeffect of virtual energy storage of air conditioning andelectric vehicles in this example Regarding the load of the

resident users in the constant temperature communityconsider a total of about 650 small high-rise (five-story)households with a total construction area of 65000 squaremeters a total air conditioning power of 1000 kW and anaverage of about 15 kW per household on the top floorthere is about 6500 square meters of photovoltaic panelsinstalled and 10 wind turbines equipped the power of itsdistributed power generation equipment is shown inFigure 17

Considering that virtual energy storage with electricvehicles participation only charges 04883CNYkWh sowhen actually using electric vehicles for virtual energystorage the discharge cost of electric vehicles is 06883CNYkWh and the discharge efficiency is 80 In addition themaintenance cost for wind turbines and photovoltaic powergeneration is shown in Table 2 [8]

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash40ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Number of EV arrivedNumber of EV left

Figure 10 -e distribution of vehicle arrival and departure times in this optimization

1200 1500 1800 2100 2400 300 600 900 1200Time

0

500

1000

1500

2000

2500

3000

3500

Elec

tric

ity q

uant

ity (k

Wh)

Remaining power value before rolling optimizationRemaining power value after rolling optimization

X 136Y 4778

X 136Y 1544

X 75Y 7894

X 75Y 7905

900Time

0

100

200

300

X 136Y 4778

X 136Y 1544

Figure 11 Comparison result of standard function value of global constraint detection

10 Complexity

000 300 600 900 1200 1500 1800 2100 2400Time

1516171819202122232425262728293031323334353637

Tem

pera

ture

(degC)

Outdoor temperatureIndoor temperature after virtual energy storage with air conditioning participation

Figure 13 Comparison of indoor and outdoor temperature change curves

300 600 900 1200 1500 1800 2100 2400Time

050

100150200250

Pow

er (k

W) Natural loss power of virtual energy storage with air conditioning participation

ndash2000

200400600800

Pow

er (k

W) Virtual energy storage power with air conditioning participation

Air conditioning output power

300600900

1200

Pow

er (k

W)

Figure 14 Comparison chart of the natural power consumption of the virtual energy storage with air conditioning participation airconditioning power and virtual power of virtual energy storage

ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Distribution of arrival and departure times of electric vehicles

Number of EV arrived

Number of EV le

Virtual energy storage power

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400

Pow

er (k

W)

Virtual energy storage remaining power S

10002000300040005000

Elec

tric

ity q

uant

ity(k

Wh)

Figure 12 Comparison chart of electric vehiclersquos space-time distribution remaining power and power

Complexity 11

-e total load demand curve of the residents is shown inFigure 18

-is environment corresponds to four scenesrespectively

Scenario 1 Electric vehicle and air conditioner jointlyparticipate in virtual energy storage

000 300 600 900 1200 1500 1800 2100 2400Time

ndash350ndash330ndash310ndash290ndash270ndash250ndash230ndash210ndash190ndash170ndash150ndash130ndash110

ndash90ndash70ndash50

Pow

er (k

W)

The upper limit of virtual energy storage output power at 195 degCThe upper limit of virtual energy storage output power at 205 degCThe upper limit of virtual energy storage output power at 215 degC

Figure 16 Comparison of the maximum output power of virtual energy storage at different set temperatures

000 300 600 900 1200 1500 1800 2100 2400Time

0

150

300

450

600

750

900

Pow

er (k

W)

Total power of photovoltaic power generationTotal power of wind generation

Figure 17 -e total power of the wind turbine and photovoltaic power generation of the constant temperature small high-rise building innumber 1 residential area

Table 2 Maintenance cost table for wind turbine and photovoltaicpower generation

Parameter (CNYkWh) ValueWind turbine maintenance cost 011PV maintenance cost 008

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400500600

Pow

er (k

W)

Figure 15 Chart of power range of virtual energy storage with electric vehicle participation

12 Complexity

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

optimizations Since A1 represents local constraints and x1has a mutual influence with x2 combined with the rollingoptimization model proposed in the previous section theevolutionary process of the continuous rolling optimizationalgorithm determined by the local constraint and the globalconstraint common feasible region of the optimizationproblem can be determined as shown in Figure 9

-e specific steps are as follows

(1) Determine the value of the N-dimensional decisionvariable x1 xi

(2) Determine whether the global optimization re-quirements are met thus directly output the Nfeasible domain decision variable x1 xi if the re-quirements are all met Based on the feasibleprobability of the solution the N-dimensional de-cision variable x1 xi at this time is difficult tomeet the requirements if not go to step (3)

(3) Introduce the global constraint condition discrimi-nant function G(x) which is related to the constraintcondition of the optimization problem but not di-rectly a constraint condition It needs to be formulatedaccording to different global constraints -e condi-tional discriminant function G(x) selected in thischapter is the remaining power of virtual energystorage with electric vehicle participation Under

actual operating conditions when all electric vehiclesleave the residential area the remaining power ofvirtual energy storage with electric vehicle partici-pation should be 0 so its standard function g(x) 0

(4) Determine the average error according to the con-ditional discriminant function G(x) and its standardfunction value g(x)

(5) Obtain a new N-dimensional decision variablex1prime xi

prime based on xiprime xi + e judge whether it

meets the global optimization requirements anddirectly output the N-dimensional feasible regiondecision variable x1prime xi

prime if it meets all require-ments if not go to step (6)

(6) Determine the new average error eprime based on the N-dimensional feasible region decision variable x1prime xi

primeand the global constraint discriminant function G(x)as well as its standard function value g(x)

(7) Compare e with eprime if the error becomes larger afterthe correlation for average error e (ie eprime gt e) thenlet e eprime and go back to step (5) Recalculate the N-dimensional feasible domain decision variablex1prime xi

prime if the error is significantly reduced (ieeprime lt e) then update the N-dimensional feasible re-gion decision variable x1 xi obtain the new N-dimensional decision variable x1prime xi

prime for the new

Optimization problem dimension N

Determine the value of Xi

The Xi+1 value based on rolling optimization is determined

i + 1 = I

i + 1 = I i + 1 = I

Discrimination of global constraints

Discrimination of global constraints

Discrimination of global constraints

Output (Xi XI)

Introduce discriminant function G (x) and criteria g (x) for global

constraints

(G (Xi XI) ndash g (x))N = e

(G (Xi XI)prime ndash g (x))N = eprime

Xiprime = Xi + e Xiprime = Xi + eprime

Determination of Xprimei+1 value based on rolling optimization

Determination of Xprimei+1 value based on rolling optimization

i = i + 1i = i + 1

e gt eprime

Yes

Yes

No

No

No

Yes

No

Yes

Yes

No

Yes Yes

No

No

Utilize (Xiprime XIprime) calculateG (Xi XI)prime

Xi = Xiprimee = eprime

eprime = e

I = I i = 1

i = i + 1

Figure 9 Flowchart of continuous rolling optimization algorithm

8 Complexity

average error eprime and then determine whether theglobal optimization requirements are met thusdirectly output the N-dimensional feasible domaindecision variable x1prime xi

prime if it meets all require-ments if not go to step (8)

(8) Update the newly generated eprime so that e eprimetherefore determine the new average error eprime basedon the updated N-dimensional feasible domain de-cision variable x1prime xi

prime and then go to step (7)

44 Optimization Effect Analysis In the problem solved inthis chapter one of the decision variables is the input andoutput power of the virtual energy storage with electricvehicle participation in each time period and the remainingpower of the electric vehicle virtual energy storage is used asthe standard to detect whether the global optimization iscompleted -e distribution diagram of the arrival anddeparture time of electric vehicles in this simulation isshown in Figure 10 -e results of the comparison betweenthe unoptimized and optimized global constraint detectionstandard function values are shown in Figure 11

As can be seen from Figure 10 the last two vehicles in thearea left within the time period of 1000ndash1015 and the totalpower 4778 kWh can be determined by calculation

As can be seen from Figure 11 at 1000 before rollingoptimization when the last two electric vehicles have notleft the remaining power of virtual energy storage is1544 kWh According to simulation calculations theremaining power of the two electric vehicles is 4778 kWh-at is after the last two vehicles have left the remainingenergy of the virtual energy storage is still not 0 whichobviously does not meet the global constraints indicatingthat the decision variables fall outside the feasible domain ofthe global constraints and the initialization fails If thecontinuous rolling optimization algorithm is not adoptedthe decision variables need to be initialized again

After the continuous rolling optimization determinedfor the high-dimensional complex constraint optimizationfeasible solution the results are consistent with the electricvehicle arrival and departure states indicating that thecontinuous rolling optimization algorithm [5 24] for thehigh-dimensional optimization of global constraints andlocal constraints that jointly govern the feasible domain caneffectively limit the decision variables within the globalconstraints and local constraints that jointly govern thefeasible domain for the problems in this chapter which helpsimprove the optimization efficiency

5 Analysis

-is section first simulates the virtual energy storage ca-pacity of air conditioning and electric vehicles and illustratesthe feasibility of virtual energy storage -en virtual energystorage is optimized for scheduling In the example calcu-lation process the virtual energy storage power range of airconditioning and electric vehicles is first determined andthen the day is divided into 96 time periods to optimize thevirtual energy storage power within the power range

51 Analysis of Air Conditioning and Electric Vehicle VirtualEnergy Storage Capacity

511 Output Power of the Virtual Energy Storage Model withEV Participation In the virtual energy storage in whichelectric vehicles participate the input and output power ofthe virtual energy storage and the arrival and departure ofthe electric vehicle will affect the remaining power of thevirtual energy storage Under rolling optimization the re-lationship can be obtained by Figure 12

As can be seen from Figure 12 the continuous energyoptimization of the electric vehiclersquos virtual energy storageoutput meets the local constraints the virtual energy storageremaining power becomes 0 after all the electric vehiclesleave indicating that the virtual energy storage output powermeets the global constraint conditions

512 Output Power of Virtual Energy Storage Model with AirConditioning Participation In the virtual energy storagewith air conditioning participation the input and outputpower of the virtual energy storage and the natural powerloss of the virtual energy storage based on the indoor andoutdoor temperature difference will affect the remainingpower of the virtual energy storage and the change of roomtemperature Under rolling optimization the changes of theabove four parameters are shown in Figures 13 and 14

It can be seen from the comparison that within thetemperature constraint range the virtual energy storage ofthe air conditioner can realize the virtual power change ofthe virtual energy storage through the change of the airconditioner power

52 Determination of the Range of Virtual Energy StoragePower for Air Conditioning and Electric Vehicles

521 Virtual Energy Storage Charge and Discharge PowerRange with EV Participation For the virtual energy storageof electric vehicles according to the spatial and temporaldistribution of electric vehicles given in Figure 12 and thepower demand for driving on the day according to equations(17) and (18) the input and output power range of virtualenergy storage with electric vehicles participation can bedetermined -e results are shown in Figure 15

522 Determination of the Range of Charge and DischargePower at the Starting Time in the Virtual Energy Storage withAir Conditioning Participation -e daily temperaturechange curve in this area is shown in the red line in Fig-ure 13 Considering the natural consumption rate of thevirtual energy storage of the air conditioning the outputpower of the virtual energy storage reaches the maximumwhen the air conditioner is not running which is Pacminus O(t)when the air conditioner is running its input and outputpower are shown in equation (11) -e maximum value ofthe virtual energy storage discharge power changesaccording to the change of the set temperature -e tem-peratures are set to 195degC 205degC and 215degC respectively

Complexity 9

in the following figure the upper limit of the virtual energystorage output power changes as shown in Figure 16

It can be seen from the above figure that the outputpower of the virtual energy storage decreases as temperatureincreases

523 Economic Analysis of Optimization for Joint VirtualEnergy Storage Based on air conditioning electric vehicleshave the ability to adjust the operating power within acertain range to convert electrical energy into thermal en-ergy storage or perform bidirectional energy exchange withthe power grid to achieve the virtual energy storage capacityof energy transfer -e following is the simulation of theeffect of virtual energy storage of air conditioning andelectric vehicles in this example Regarding the load of the

resident users in the constant temperature communityconsider a total of about 650 small high-rise (five-story)households with a total construction area of 65000 squaremeters a total air conditioning power of 1000 kW and anaverage of about 15 kW per household on the top floorthere is about 6500 square meters of photovoltaic panelsinstalled and 10 wind turbines equipped the power of itsdistributed power generation equipment is shown inFigure 17

Considering that virtual energy storage with electricvehicles participation only charges 04883CNYkWh sowhen actually using electric vehicles for virtual energystorage the discharge cost of electric vehicles is 06883CNYkWh and the discharge efficiency is 80 In addition themaintenance cost for wind turbines and photovoltaic powergeneration is shown in Table 2 [8]

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash40ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Number of EV arrivedNumber of EV left

Figure 10 -e distribution of vehicle arrival and departure times in this optimization

1200 1500 1800 2100 2400 300 600 900 1200Time

0

500

1000

1500

2000

2500

3000

3500

Elec

tric

ity q

uant

ity (k

Wh)

Remaining power value before rolling optimizationRemaining power value after rolling optimization

X 136Y 4778

X 136Y 1544

X 75Y 7894

X 75Y 7905

900Time

0

100

200

300

X 136Y 4778

X 136Y 1544

Figure 11 Comparison result of standard function value of global constraint detection

10 Complexity

000 300 600 900 1200 1500 1800 2100 2400Time

1516171819202122232425262728293031323334353637

Tem

pera

ture

(degC)

Outdoor temperatureIndoor temperature after virtual energy storage with air conditioning participation

Figure 13 Comparison of indoor and outdoor temperature change curves

300 600 900 1200 1500 1800 2100 2400Time

050

100150200250

Pow

er (k

W) Natural loss power of virtual energy storage with air conditioning participation

ndash2000

200400600800

Pow

er (k

W) Virtual energy storage power with air conditioning participation

Air conditioning output power

300600900

1200

Pow

er (k

W)

Figure 14 Comparison chart of the natural power consumption of the virtual energy storage with air conditioning participation airconditioning power and virtual power of virtual energy storage

ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Distribution of arrival and departure times of electric vehicles

Number of EV arrived

Number of EV le

Virtual energy storage power

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400

Pow

er (k

W)

Virtual energy storage remaining power S

10002000300040005000

Elec

tric

ity q

uant

ity(k

Wh)

Figure 12 Comparison chart of electric vehiclersquos space-time distribution remaining power and power

Complexity 11

-e total load demand curve of the residents is shown inFigure 18

-is environment corresponds to four scenesrespectively

Scenario 1 Electric vehicle and air conditioner jointlyparticipate in virtual energy storage

000 300 600 900 1200 1500 1800 2100 2400Time

ndash350ndash330ndash310ndash290ndash270ndash250ndash230ndash210ndash190ndash170ndash150ndash130ndash110

ndash90ndash70ndash50

Pow

er (k

W)

The upper limit of virtual energy storage output power at 195 degCThe upper limit of virtual energy storage output power at 205 degCThe upper limit of virtual energy storage output power at 215 degC

Figure 16 Comparison of the maximum output power of virtual energy storage at different set temperatures

000 300 600 900 1200 1500 1800 2100 2400Time

0

150

300

450

600

750

900

Pow

er (k

W)

Total power of photovoltaic power generationTotal power of wind generation

Figure 17 -e total power of the wind turbine and photovoltaic power generation of the constant temperature small high-rise building innumber 1 residential area

Table 2 Maintenance cost table for wind turbine and photovoltaicpower generation

Parameter (CNYkWh) ValueWind turbine maintenance cost 011PV maintenance cost 008

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400500600

Pow

er (k

W)

Figure 15 Chart of power range of virtual energy storage with electric vehicle participation

12 Complexity

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

average error eprime and then determine whether theglobal optimization requirements are met thusdirectly output the N-dimensional feasible domaindecision variable x1prime xi

prime if it meets all require-ments if not go to step (8)

(8) Update the newly generated eprime so that e eprimetherefore determine the new average error eprime basedon the updated N-dimensional feasible domain de-cision variable x1prime xi

prime and then go to step (7)

44 Optimization Effect Analysis In the problem solved inthis chapter one of the decision variables is the input andoutput power of the virtual energy storage with electricvehicle participation in each time period and the remainingpower of the electric vehicle virtual energy storage is used asthe standard to detect whether the global optimization iscompleted -e distribution diagram of the arrival anddeparture time of electric vehicles in this simulation isshown in Figure 10 -e results of the comparison betweenthe unoptimized and optimized global constraint detectionstandard function values are shown in Figure 11

As can be seen from Figure 10 the last two vehicles in thearea left within the time period of 1000ndash1015 and the totalpower 4778 kWh can be determined by calculation

As can be seen from Figure 11 at 1000 before rollingoptimization when the last two electric vehicles have notleft the remaining power of virtual energy storage is1544 kWh According to simulation calculations theremaining power of the two electric vehicles is 4778 kWh-at is after the last two vehicles have left the remainingenergy of the virtual energy storage is still not 0 whichobviously does not meet the global constraints indicatingthat the decision variables fall outside the feasible domain ofthe global constraints and the initialization fails If thecontinuous rolling optimization algorithm is not adoptedthe decision variables need to be initialized again

After the continuous rolling optimization determinedfor the high-dimensional complex constraint optimizationfeasible solution the results are consistent with the electricvehicle arrival and departure states indicating that thecontinuous rolling optimization algorithm [5 24] for thehigh-dimensional optimization of global constraints andlocal constraints that jointly govern the feasible domain caneffectively limit the decision variables within the globalconstraints and local constraints that jointly govern thefeasible domain for the problems in this chapter which helpsimprove the optimization efficiency

5 Analysis

-is section first simulates the virtual energy storage ca-pacity of air conditioning and electric vehicles and illustratesthe feasibility of virtual energy storage -en virtual energystorage is optimized for scheduling In the example calcu-lation process the virtual energy storage power range of airconditioning and electric vehicles is first determined andthen the day is divided into 96 time periods to optimize thevirtual energy storage power within the power range

51 Analysis of Air Conditioning and Electric Vehicle VirtualEnergy Storage Capacity

511 Output Power of the Virtual Energy Storage Model withEV Participation In the virtual energy storage in whichelectric vehicles participate the input and output power ofthe virtual energy storage and the arrival and departure ofthe electric vehicle will affect the remaining power of thevirtual energy storage Under rolling optimization the re-lationship can be obtained by Figure 12

As can be seen from Figure 12 the continuous energyoptimization of the electric vehiclersquos virtual energy storageoutput meets the local constraints the virtual energy storageremaining power becomes 0 after all the electric vehiclesleave indicating that the virtual energy storage output powermeets the global constraint conditions

512 Output Power of Virtual Energy Storage Model with AirConditioning Participation In the virtual energy storagewith air conditioning participation the input and outputpower of the virtual energy storage and the natural powerloss of the virtual energy storage based on the indoor andoutdoor temperature difference will affect the remainingpower of the virtual energy storage and the change of roomtemperature Under rolling optimization the changes of theabove four parameters are shown in Figures 13 and 14

It can be seen from the comparison that within thetemperature constraint range the virtual energy storage ofthe air conditioner can realize the virtual power change ofthe virtual energy storage through the change of the airconditioner power

52 Determination of the Range of Virtual Energy StoragePower for Air Conditioning and Electric Vehicles

521 Virtual Energy Storage Charge and Discharge PowerRange with EV Participation For the virtual energy storageof electric vehicles according to the spatial and temporaldistribution of electric vehicles given in Figure 12 and thepower demand for driving on the day according to equations(17) and (18) the input and output power range of virtualenergy storage with electric vehicles participation can bedetermined -e results are shown in Figure 15

522 Determination of the Range of Charge and DischargePower at the Starting Time in the Virtual Energy Storage withAir Conditioning Participation -e daily temperaturechange curve in this area is shown in the red line in Fig-ure 13 Considering the natural consumption rate of thevirtual energy storage of the air conditioning the outputpower of the virtual energy storage reaches the maximumwhen the air conditioner is not running which is Pacminus O(t)when the air conditioner is running its input and outputpower are shown in equation (11) -e maximum value ofthe virtual energy storage discharge power changesaccording to the change of the set temperature -e tem-peratures are set to 195degC 205degC and 215degC respectively

Complexity 9

in the following figure the upper limit of the virtual energystorage output power changes as shown in Figure 16

It can be seen from the above figure that the outputpower of the virtual energy storage decreases as temperatureincreases

523 Economic Analysis of Optimization for Joint VirtualEnergy Storage Based on air conditioning electric vehicleshave the ability to adjust the operating power within acertain range to convert electrical energy into thermal en-ergy storage or perform bidirectional energy exchange withthe power grid to achieve the virtual energy storage capacityof energy transfer -e following is the simulation of theeffect of virtual energy storage of air conditioning andelectric vehicles in this example Regarding the load of the

resident users in the constant temperature communityconsider a total of about 650 small high-rise (five-story)households with a total construction area of 65000 squaremeters a total air conditioning power of 1000 kW and anaverage of about 15 kW per household on the top floorthere is about 6500 square meters of photovoltaic panelsinstalled and 10 wind turbines equipped the power of itsdistributed power generation equipment is shown inFigure 17

Considering that virtual energy storage with electricvehicles participation only charges 04883CNYkWh sowhen actually using electric vehicles for virtual energystorage the discharge cost of electric vehicles is 06883CNYkWh and the discharge efficiency is 80 In addition themaintenance cost for wind turbines and photovoltaic powergeneration is shown in Table 2 [8]

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash40ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Number of EV arrivedNumber of EV left

Figure 10 -e distribution of vehicle arrival and departure times in this optimization

1200 1500 1800 2100 2400 300 600 900 1200Time

0

500

1000

1500

2000

2500

3000

3500

Elec

tric

ity q

uant

ity (k

Wh)

Remaining power value before rolling optimizationRemaining power value after rolling optimization

X 136Y 4778

X 136Y 1544

X 75Y 7894

X 75Y 7905

900Time

0

100

200

300

X 136Y 4778

X 136Y 1544

Figure 11 Comparison result of standard function value of global constraint detection

10 Complexity

000 300 600 900 1200 1500 1800 2100 2400Time

1516171819202122232425262728293031323334353637

Tem

pera

ture

(degC)

Outdoor temperatureIndoor temperature after virtual energy storage with air conditioning participation

Figure 13 Comparison of indoor and outdoor temperature change curves

300 600 900 1200 1500 1800 2100 2400Time

050

100150200250

Pow

er (k

W) Natural loss power of virtual energy storage with air conditioning participation

ndash2000

200400600800

Pow

er (k

W) Virtual energy storage power with air conditioning participation

Air conditioning output power

300600900

1200

Pow

er (k

W)

Figure 14 Comparison chart of the natural power consumption of the virtual energy storage with air conditioning participation airconditioning power and virtual power of virtual energy storage

ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Distribution of arrival and departure times of electric vehicles

Number of EV arrived

Number of EV le

Virtual energy storage power

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400

Pow

er (k

W)

Virtual energy storage remaining power S

10002000300040005000

Elec

tric

ity q

uant

ity(k

Wh)

Figure 12 Comparison chart of electric vehiclersquos space-time distribution remaining power and power

Complexity 11

-e total load demand curve of the residents is shown inFigure 18

-is environment corresponds to four scenesrespectively

Scenario 1 Electric vehicle and air conditioner jointlyparticipate in virtual energy storage

000 300 600 900 1200 1500 1800 2100 2400Time

ndash350ndash330ndash310ndash290ndash270ndash250ndash230ndash210ndash190ndash170ndash150ndash130ndash110

ndash90ndash70ndash50

Pow

er (k

W)

The upper limit of virtual energy storage output power at 195 degCThe upper limit of virtual energy storage output power at 205 degCThe upper limit of virtual energy storage output power at 215 degC

Figure 16 Comparison of the maximum output power of virtual energy storage at different set temperatures

000 300 600 900 1200 1500 1800 2100 2400Time

0

150

300

450

600

750

900

Pow

er (k

W)

Total power of photovoltaic power generationTotal power of wind generation

Figure 17 -e total power of the wind turbine and photovoltaic power generation of the constant temperature small high-rise building innumber 1 residential area

Table 2 Maintenance cost table for wind turbine and photovoltaicpower generation

Parameter (CNYkWh) ValueWind turbine maintenance cost 011PV maintenance cost 008

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400500600

Pow

er (k

W)

Figure 15 Chart of power range of virtual energy storage with electric vehicle participation

12 Complexity

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

in the following figure the upper limit of the virtual energystorage output power changes as shown in Figure 16

It can be seen from the above figure that the outputpower of the virtual energy storage decreases as temperatureincreases

523 Economic Analysis of Optimization for Joint VirtualEnergy Storage Based on air conditioning electric vehicleshave the ability to adjust the operating power within acertain range to convert electrical energy into thermal en-ergy storage or perform bidirectional energy exchange withthe power grid to achieve the virtual energy storage capacityof energy transfer -e following is the simulation of theeffect of virtual energy storage of air conditioning andelectric vehicles in this example Regarding the load of the

resident users in the constant temperature communityconsider a total of about 650 small high-rise (five-story)households with a total construction area of 65000 squaremeters a total air conditioning power of 1000 kW and anaverage of about 15 kW per household on the top floorthere is about 6500 square meters of photovoltaic panelsinstalled and 10 wind turbines equipped the power of itsdistributed power generation equipment is shown inFigure 17

Considering that virtual energy storage with electricvehicles participation only charges 04883CNYkWh sowhen actually using electric vehicles for virtual energystorage the discharge cost of electric vehicles is 06883CNYkWh and the discharge efficiency is 80 In addition themaintenance cost for wind turbines and photovoltaic powergeneration is shown in Table 2 [8]

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash40ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Number of EV arrivedNumber of EV left

Figure 10 -e distribution of vehicle arrival and departure times in this optimization

1200 1500 1800 2100 2400 300 600 900 1200Time

0

500

1000

1500

2000

2500

3000

3500

Elec

tric

ity q

uant

ity (k

Wh)

Remaining power value before rolling optimizationRemaining power value after rolling optimization

X 136Y 4778

X 136Y 1544

X 75Y 7894

X 75Y 7905

900Time

0

100

200

300

X 136Y 4778

X 136Y 1544

Figure 11 Comparison result of standard function value of global constraint detection

10 Complexity

000 300 600 900 1200 1500 1800 2100 2400Time

1516171819202122232425262728293031323334353637

Tem

pera

ture

(degC)

Outdoor temperatureIndoor temperature after virtual energy storage with air conditioning participation

Figure 13 Comparison of indoor and outdoor temperature change curves

300 600 900 1200 1500 1800 2100 2400Time

050

100150200250

Pow

er (k

W) Natural loss power of virtual energy storage with air conditioning participation

ndash2000

200400600800

Pow

er (k

W) Virtual energy storage power with air conditioning participation

Air conditioning output power

300600900

1200

Pow

er (k

W)

Figure 14 Comparison chart of the natural power consumption of the virtual energy storage with air conditioning participation airconditioning power and virtual power of virtual energy storage

ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Distribution of arrival and departure times of electric vehicles

Number of EV arrived

Number of EV le

Virtual energy storage power

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400

Pow

er (k

W)

Virtual energy storage remaining power S

10002000300040005000

Elec

tric

ity q

uant

ity(k

Wh)

Figure 12 Comparison chart of electric vehiclersquos space-time distribution remaining power and power

Complexity 11

-e total load demand curve of the residents is shown inFigure 18

-is environment corresponds to four scenesrespectively

Scenario 1 Electric vehicle and air conditioner jointlyparticipate in virtual energy storage

000 300 600 900 1200 1500 1800 2100 2400Time

ndash350ndash330ndash310ndash290ndash270ndash250ndash230ndash210ndash190ndash170ndash150ndash130ndash110

ndash90ndash70ndash50

Pow

er (k

W)

The upper limit of virtual energy storage output power at 195 degCThe upper limit of virtual energy storage output power at 205 degCThe upper limit of virtual energy storage output power at 215 degC

Figure 16 Comparison of the maximum output power of virtual energy storage at different set temperatures

000 300 600 900 1200 1500 1800 2100 2400Time

0

150

300

450

600

750

900

Pow

er (k

W)

Total power of photovoltaic power generationTotal power of wind generation

Figure 17 -e total power of the wind turbine and photovoltaic power generation of the constant temperature small high-rise building innumber 1 residential area

Table 2 Maintenance cost table for wind turbine and photovoltaicpower generation

Parameter (CNYkWh) ValueWind turbine maintenance cost 011PV maintenance cost 008

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400500600

Pow

er (k

W)

Figure 15 Chart of power range of virtual energy storage with electric vehicle participation

12 Complexity

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

000 300 600 900 1200 1500 1800 2100 2400Time

1516171819202122232425262728293031323334353637

Tem

pera

ture

(degC)

Outdoor temperatureIndoor temperature after virtual energy storage with air conditioning participation

Figure 13 Comparison of indoor and outdoor temperature change curves

300 600 900 1200 1500 1800 2100 2400Time

050

100150200250

Pow

er (k

W) Natural loss power of virtual energy storage with air conditioning participation

ndash2000

200400600800

Pow

er (k

W) Virtual energy storage power with air conditioning participation

Air conditioning output power

300600900

1200

Pow

er (k

W)

Figure 14 Comparison chart of the natural power consumption of the virtual energy storage with air conditioning participation airconditioning power and virtual power of virtual energy storage

ndash30ndash20ndash10

01020304050

Qua

ntity

of E

V

Distribution of arrival and departure times of electric vehicles

Number of EV arrived

Number of EV le

Virtual energy storage power

1200 1500 1800 2100 2400 300 600 900 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400

Pow

er (k

W)

Virtual energy storage remaining power S

10002000300040005000

Elec

tric

ity q

uant

ity(k

Wh)

Figure 12 Comparison chart of electric vehiclersquos space-time distribution remaining power and power

Complexity 11

-e total load demand curve of the residents is shown inFigure 18

-is environment corresponds to four scenesrespectively

Scenario 1 Electric vehicle and air conditioner jointlyparticipate in virtual energy storage

000 300 600 900 1200 1500 1800 2100 2400Time

ndash350ndash330ndash310ndash290ndash270ndash250ndash230ndash210ndash190ndash170ndash150ndash130ndash110

ndash90ndash70ndash50

Pow

er (k

W)

The upper limit of virtual energy storage output power at 195 degCThe upper limit of virtual energy storage output power at 205 degCThe upper limit of virtual energy storage output power at 215 degC

Figure 16 Comparison of the maximum output power of virtual energy storage at different set temperatures

000 300 600 900 1200 1500 1800 2100 2400Time

0

150

300

450

600

750

900

Pow

er (k

W)

Total power of photovoltaic power generationTotal power of wind generation

Figure 17 -e total power of the wind turbine and photovoltaic power generation of the constant temperature small high-rise building innumber 1 residential area

Table 2 Maintenance cost table for wind turbine and photovoltaicpower generation

Parameter (CNYkWh) ValueWind turbine maintenance cost 011PV maintenance cost 008

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400500600

Pow

er (k

W)

Figure 15 Chart of power range of virtual energy storage with electric vehicle participation

12 Complexity

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

-e total load demand curve of the residents is shown inFigure 18

-is environment corresponds to four scenesrespectively

Scenario 1 Electric vehicle and air conditioner jointlyparticipate in virtual energy storage

000 300 600 900 1200 1500 1800 2100 2400Time

ndash350ndash330ndash310ndash290ndash270ndash250ndash230ndash210ndash190ndash170ndash150ndash130ndash110

ndash90ndash70ndash50

Pow

er (k

W)

The upper limit of virtual energy storage output power at 195 degCThe upper limit of virtual energy storage output power at 205 degCThe upper limit of virtual energy storage output power at 215 degC

Figure 16 Comparison of the maximum output power of virtual energy storage at different set temperatures

000 300 600 900 1200 1500 1800 2100 2400Time

0

150

300

450

600

750

900

Pow

er (k

W)

Total power of photovoltaic power generationTotal power of wind generation

Figure 17 -e total power of the wind turbine and photovoltaic power generation of the constant temperature small high-rise building innumber 1 residential area

Table 2 Maintenance cost table for wind turbine and photovoltaicpower generation

Parameter (CNYkWh) ValueWind turbine maintenance cost 011PV maintenance cost 008

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash400ndash300ndash200ndash100

0100200300400500600

Pow

er (k

W)

Figure 15 Chart of power range of virtual energy storage with electric vehicle participation

12 Complexity

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

Scenario 2 Electric vehicle participates in virtual energystorage

Scenario 3 Air conditioner participates in virtual energystorage

Scenario 4 Virtual energy storage is not called-e economics of these four scenarios are compared as

followsIn Scenario1 the results obtained by air conditioning

and electric vehicles participating in virtual energy storageoptimization scheduling and the results of using electricvehicles or air conditioning alone to participate in virtualenergy storage are shown in Figure 19

In Scenario2 the results obtained by air conditionersindependently participating in virtual energy storage opti-mization scheduling are shown in Figure 20

In Scenario3 the results of electric vehicles indepen-dently participating in virtual energy storage optimizationscheduling are shown in Figure 21

In the above four scenarios the comparison results of thetotal daily electricity charges in the residential area areshown in Table 3

From the above comparative analysis the followingconclusions can be drawn

(1) When the joint virtual energy storage of air condi-tioners and electric vehicles is adopted the total costof electricity charges in residential areas can be re-duced by 10

(2) -e photovoltaic power generation in residentialareas is highly compatible with the operating time ofair conditioners -erefore when participating invirtual energy storage alone the effect of air con-ditioning participating in virtual energy storage isbetter than electric vehicles participating in virtualenergy storage

(3) Analyze the reasons for the different total elec-tricity costs in residential areas under differentscenarios on a certain day mainly because airconditioning and electric vehicles can store theelectrical energy generated by new energy powergeneration equipment which reduces the phe-nomenon of wind and heat rejection realizes theefficient utilization of new energy power genera-tion equipment and also reduces the cost ofpurchasing electricity from the power grid-erefore it has also proved that the joint

000 300 600 900 1200 1500 1800 2100 2400Time

200250300350400450500550

Pow

er (k

W)

Figure 18 Daily load curve in residential area number 1

ndash500ndash300ndash100

100300500700900

11001300

Pow

er (k

W) Total power of virtual energy storage

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Virtual energy storage power with air conditioning participationndash400ndash300ndash200ndash100

0100200300400500

Pow

er (k

W)

Virtual energy storage power with EV participation

Figure 19 Optimized power of combined virtual energy storage in Scenario1

Complexity 13

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

participation of electric vehicles and air condi-tioning in virtual energy storage can improve theutilization rate of distributed new energy powergeneration equipment and improve the economicsof electricity consumption

6 Summary

-is paper proposes the use of air conditioning and electricvehicles to jointly participate in virtual energy storage torealize the economic dispatch of energy local area SmartGrid in view of the current status of the controllable load ofair conditioning and the load growth of electric vehicles

Firstly the virtual energy storage model of thermo-electric conversion with the participation of air conditioningload and the electric energy transfer virtual energy storagemodel with electric vehicle participation are establishedBesides the rolling optimization idea is introduced to re-strict the input and output power of the virtual energystorage with air conditioning and electric vehicleparticipation

Secondly a joint virtual energy storage power optimi-zation model is constructed and for the solution of themodel in the initialization process of decision variables dueto the condition that dimensional disaster occurred and theinitial feasible solution cannot be obtained a continuousrolling optimization method is proposed for the feasiblesolution of the high-dimensional complex constraint opti-mization problem so that the virtual energy storage powercan simultaneously meet the local and global constraints

under rolling optimization during the initialization processand thus improve the initialization efficiency

Finally the capacity and economy of joint virtual energystorage in residential areas are calculated -e results provethat air conditioning and electric vehicles have the ability tojointly participate in virtual energy storage and the com-parison proves that joint virtual energy storage can effec-tively improve the economics of electricity consumption-erefore the conclusion is that the joint virtual energystorage with the participation of electric vehicles and airconditioning helps improve the economics of consumerelectricity consumption

Data Availability

-edata used in this paper comes from the statistics of urbantravel data which has not been published publicly -ispaper only takes this data as an example to prove the ef-fectiveness of the proposed method

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

Authorsrsquo Contributions

Rui-Cheng Dai and Xiao-di Zhang participated in the al-gorithm simulation and draft writing Bi Zhao and Xiao-diZhang participated in the concept design interpretationand commenting on the manuscript and the critical revision

1200 1330 1500 1630 1800 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash500ndash300ndash100

100300500

Pow

er (k

W)

Figure 21 Output power of virtual energy storage with independent participation of electric vehicles in Scenario3

Table 3 Comparison of the total electricity cost within one day for the constant temperature building in residential area number 1 underfour scenarios

Scenario Total electricity cost Electricity saving percentageJoint virtual energy storage 65327 minus 96Air conditioning virtual energy storage 66722 minus 76Electric vehicles virtual energy storage 67187 minus 7Without virtual energy storage scheduling 72276 mdash

1200 1330 1500 1630 1900 1930 2100 2230 2400 130 300 430 600 730 900 1030 1200Time

ndash300ndash100

100300500700900

Pow

er (k

W)

Figure 20 Output power of virtual energy storage with independent participation of air conditioning in Scenario2

14 Complexity

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15

of this paper Jun-Wei Yu Bo Fan and Biao Liu participatedin the data collection and analysis of the paper

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant nos 51909199 and 51709215)and the Fundamental Research Funds for the CentralUniversities (WUT 2020IVB012)

References

[1] S Pawan and K Baseem ldquoSmart microgrid energy man-agement using a novel artificial shark optimizationrdquo Com-plexity vol 2017 Article ID 2158926 22 pages 2017

[2] Y Zou Y Chen and Y Zou ldquoSteady-state analysis and outputvoltage minimization based control strategy for electricsprings in the smart grid with multiple renewable energysourcesrdquo Complexity vol 2019 Article ID 5376360 12 pages2019

[3] L Xi Y Y Li and J L ChenLu ldquoA novel automatic gen-eration control method based on the ecological populationcooperative control for the islanded smart gridrdquo Complexityvol 2018 Article ID 2456936 17 pages 2018

[4] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[5] J Lai and X Lu ldquoNonlinear mean-square power sharingcontrol for ac microgrids under distributed event detectionrdquoIEEE Transactions on Industrial Informatics p 1 2020

[6] D Choi A J Crawford V Viswanathan et al ldquoLifecyclecomparison and degradation mechanisms of Li-ion batterychemistries under grid and electric vehicle duty cycle com-binationsrdquo e Electrochemical Society vol 1 p 26 2018

[7] K Mai L Yin and Z Li ldquoEnergy optimization managementof grid-connected wind-solar-battery domestic micro-gridbased on virtual energy storagerdquo Distribution amp Utilizationvol 34 no 4 pp 12ndash18 2017

[8] X Jin Y Mu H Jia J Wu T Jiang and X Yu ldquoDynamiceconomic dispatch of a hybrid energy microgrid consideringbuilding based virtual energy storage systemrdquo Applied Energyvol 194 pp 386ndash398 2017

[9] X Zhan Y Mu and H Jia ldquoOptimal scheduling method for acombined cooling heating and power building microgridconsidering virtual storage system at demand siderdquo in Pro-ceedings of the CSEE vol 37 no 2 pp 581ndash590 BarcelonaSpain April 2017

[10] X Ai Y Zhao and S Zhou ldquoStudy on virtual energy storagefeatures of air conditioning load direct load controlrdquo Pro-ceedings of the CSEE vol 36 no 6 pp 1596ndash1603 2016

[11] C Gao Q Li and Y Li ldquoBi-level optimal dispatch and controlstrategy for air-conditioning load based on direct load con-trolrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 34 no 10 pp 1546ndash1555 2014

[12] O Erdinccedil A Tascikaraoglu N G Paterakis Y Eren andJ P S Catalao ldquoEnd-user comfort oriented day-aheadplanning for responsive residential HVAC demand aggre-gation considering weather forecastsrdquo IEEE Transactions onSmart Grid vol 8 no 1 pp 362ndash372 2017

[13] C H Wai M Beaudin H Zareipour A Schellenberg andN Lu ldquoCooling devices in demand response a comparison ofcontrol methodsrdquo IEEE Transactions on Smart Grid vol 6no 1 pp 249ndash260 2015

[14] J Peppanen M J Reno and S Grijalva ldquo-ermal energystorage for air conditioning as an enabler of residential de-mand responserdquo in Proceedings of the 2014 North AmericanPower Symposium (NAPS) pp 1ndash6 Pullman WA USASeptember 2014

[15] J Lai X Lu X Yu and A Monti ldquoCluster-oriented dis-tributed cooperative control for multiple ac microgridsrdquo IEEETransactions on Industrial Informatics vol 15 no 11pp 5906ndash5918 2019

[16] J Lai X Lu X Yu and A Monti ldquoStochastic distributedsecondary control for ac microgrids via event-triggeredcommunicationrdquo IEEE Transactions on Smart Grid vol 11no 4 pp 2746ndash2759 2020

[17] L Xin L Jingang and T Ruoli ldquoA hybrid constraintshandling strategy for multiconstrained multiobjective opti-mization problem of microgrid economicalenvironmentaldispatchrdquo Complexity vol 2017 Article ID 6249432 12 pages2017

[18] G Xiong J Zhang X Yuan et al ldquoA novel method foreconomic dispatch with across neighborhood search a casestudy in a provincial power grid Chinardquo Complexityvol 2018 Article ID 2591341 18 pages 2018

[19] W-C Yeh M-F He C-L Huang et al ldquoNew genetic al-gorithm for economic dispatch of stand-alone three-modularmicrogrid in DongAo Islandrdquo Applied Energy vol 263 2020

[20] G Ruan H Zhong J Wang Q Xia and C Kang ldquoNeural-network-based Lagrange multiplier selection for distributeddemand response in smart gridrdquo Applied Energy vol 264Article ID 114636 2020

[21] F Pallonetto M De Rosa F Milano and D P Finn ldquoDe-mand response algorithms for smart-grid ready residentialbuildings using machine learning modelsrdquo Applied Energyvol 239 pp 1265ndash1282 2019

[22] W Zhang J Lian C-Y Chang and K Kalsi ldquoAggregatedmodeling and control of air conditioning loads for demandresponserdquo IEEE Transactions on Power Systems vol 28 no 4pp 4655ndash4664 2013

[23] N Ruiz I Cobelo and J Oyarzabal ldquoA direct load controlmodel for virtual power plant managementrdquo IEEE Transac-tions on Power Systems vol 24 no 2 pp 959ndash966 2009

[24] J Lai H Zhou and W Hu ldquoSynchronization of hybridmicrogrids with communication latencyrdquo MathematicalProblems in Engineering vol 2015 Article ID 58626010 pages 2015

Complexity 15