Research ArticleOptimal Model for Complementary Operation of aPhotovoltaic-Wind-Pumped Storage System

Jinjin Gao1 Yuan Zheng 2 Jianming Li1 Xiaoming Zhu1 and Kan Kan 1

1College of Water Conservancy and Hydropower Engineering Hohai University Nanjing 210098 China2College of Energy and Electric Engineering Hohai University Nanjing 210000 China

Correspondence should be addressed to Yuan Zheng zhengyuanhhueducn

Received 25 September 2018 Revised 17 November 2018 Accepted 2 December 2018 Published 26 December 2018

Academic Editor Oliver Schutze

Copyright copy 2018 Jinjin Gao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

An optimization model for the complementary operation of a photovoltaic-wind-pumped storage system is built to make full useof solar and wind energy Apart from ensuring the maximum economic benefit which is normally used as the only objectivethe stable objectives of minimizing the output fluctuation and variation of load and output difference are added to form themultiobjective problems because of lack of study on access capacity of photovoltaic and wind power The model aims to increasethe power benefit and reduce the output fluctuation and variation of load and output difference under the constraints of stationoutput balance and transmission limitation In a case study four schemes including single-objective independent operation single-objective complementary operation and multiobjective complementary operation are compared to discuss the effect of pumpedstorage station on economic objective and stable objectives Furthermore the opposite trend of the two objectives is proved and acompromise optimal solution is given The results indicate that the pumped storage station can effectively increase power benefitand access capacity of photovoltaic and wind power The study can provide references to the complementary optimization of thepumped storage station and the intermittent renewable energy

1 Introduction

Solar and wind energy are attracting increasing attentionrecently because they are pollution-free abundant andrenewable However the high fluctuation and randomnesscharacteristics of solar and wind energy have a great influ-ence on the stability of power system [1 2] Uncontrolledabsorption of large photovoltaic and wind power may resultin violent power fluctuation of the whole power system in acertain period Therefore in consideration of the operationeconomy of photovoltaic and wind power it is significantto maximize the consumption of photovoltaic and windpower without affecting the system An efficient method toovercome the problem is to combine the pumped storagestation with intermittent renewable energy [3ndash5] for thereason that pumped storage plant is a relatively mature wayto store energy and the cost of investment is low whichcan make full use of the excess energy and ensure smoothoperation of the system

In recent years there are many studies on modelling andoptimizing for complementary operation of pumped storage-wind [6 7] or photovoltaic-wind-pumped storage [8 9]systems Increasing the profit and reducing the fluctuationvariance [10] are the primary optimal objectives Because thesolar and wind energy is instable [1 2] as more power benefitis obtained the output fluctuation increasesThus the changeof economic benefit and output fluctuation show an oppositetrend This contradiction can be alleviated by studying theoptimal scheduling and complementary mechanism [11]ThePareto relationship between the two has been found whenstudying the combined operation of pumped storage andwind power [12ndash14] Nevertheless the benefit objective func-tion was given without considering the operating cost of thepumped storage plant and as the output fluctuation objectivethe fluctuation variance function is not very comprehensiveand accurate Also the complementary mechanism has notbeen deeply discussed yet

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 5346253 9 pageshttpsdoiorg10115520185346253

2 Mathematical Problems in Engineering

PV array

Wind turbine

Inverter

Control stationEnd-useLower Reservoir

Upper Reservoir

Pumping

Generating

Figure 1 A photovoltaic-wind-pumped storage system

The constraints are mainly divided into three typesstation type [11] output balance type [12] and transmissionlimitation type [13] Since pumped storage station has manyoperating conditions and its combined operation with pho-tovoltaic andwind power is very complicated the station typehas become a limitation for complementary operation

Although progress has been made some problemsremain to be solved Firstly the objective functions andconstraints have not been defined properly Secondly therelationship between economic and stable objectives has notbeen studied sufficiently Thirdly the role of pumped storagestation in complementary operation of hybrid power systemhas not been well-considered

An optimization model with multiple objectives mul-tiple constraints and high dimension photovoltaic-wind-pumped storage system has been built The economicobjective and stable objective of the model are to maxi-mize the benefit of power generation and to minimize theoutput fluctuation respectively In the case study single-objective independent operation single-objective comple-mentary operation and multiobjective complementary oper-ation are compared and the complementary mechanismof the system is discussed Then the Pareto noninferiorsolution front of power benefit and output fluctuation inmultiobjective cooperative operation is obtained and theinteraction between the two is analyzed Overall improvingthe power benefit and access capacity of photovoltaic andwind power are considered at the same time The resultsprovide a reliable theoretical reference for the study of com-plementary operation between hydropower and renewableenergy

2 Multiobjective Model for a Photovoltaic-Wind-Pumped Storage System

The photovoltaic-wind-pumped storage complementaryoperation system is illustrated in Figure 1 The solar andwind energy have the property of natural temporal andspatial complementarity and the pumped storage plant hasthe characteristics of energy storage peak load regulationand frequency modulation [15 16] which make the systemoperate If the photovoltaic and wind power are unableto be full output the excess solar and wind power will beavailable to pump the lower reservoir for stored gravitationalpotential energy If the power generation of wind farmsand photovoltaic power stations cannot meet the loadrequirements the water from the upper reservoir will beused to drive the turbine to generate power

The principle of complementary operation is that thephotovoltaic and wind power operate in full load accordingto the pre-day power forecast and the output fluctuationand intermittence are mainly regulated by pumped storagestation [17] Namely while a pumped storage plant is includedin the system as the solar and wind energy are fully usedand the operation benefit of photovoltaic and wind power isimproved the output fluctuation of complementary opera-tion system will be smoothed

It is assumed that the initial power output of the photo-voltaic and wind power when the pumped storage system isnot configured and the capacity of the hydroelectric unit afterthe pumped storage system is configured is all determinedThe objective functions include the power benefit maxi-mization the output fluctuation minimization and variationof load and output difference minimization Constraints

Mathematical Problems in Engineering 3

include station constraints output balance constraint andtransmission constraint

21 Objective Function

211 Power Benefit A benefit maximization model is setup to study how to optimize the output of wind turbinephotovoltaic cell board and pump-turbine unit in eachperiod to obtain maximum power benefit under the premiseof certain wind energy resources and solar energy resourcesPower benefit maximization is an economic objective

max1198651 =119879

sum119894=1

119862119894119875119908119900119906119905119894 + 119862119894119875119901V119900119906119905119894 + 119862119894119875ℎ119894 minus 119862119901119894119875

119901119894 minus 119862ℎ (1)

where 1198651 is the power benefit of the system 119879 is thescheduling period 119875119908119900119906119905119894 119875119901V119900119906119905119894 and 119875ℎ119894 are the outputof photovoltaic wind and pumped storage power directlytransported to the load in the 119894119905ℎ period 119875119901119894 is the pumpingpower of the pumped storage plant in the 119894119905ℎ period 119862119894 is thefeed-in tariff in the 119894119905ℎ period 119862119901119894 is the pumping tariff of thepumped storage station in the 119894119905ℎ period 119862ℎ is the start andstop cost of the pumped storage plant

212 Output Fluctuation To minimize the output fluctu-ation of the complementary operation model the outputfluctuation is calculated by quantifying the fluctuation degreeof the process line based on the quantity dimension and theshape dimension [18] Output fluctuation minimization is astable objective

min1198652 =119879

sum119894=1

10038161003816100381610038161003816119875119891 (119894) minus 11987511989110038161003816100381610038161003816119879

sum119894=1

120579119894 (2)

120579119894

=

arctan 10038161003816100381610038161198961198941003816100381610038161003816 (119894 = 1 119879)

1003816100381610038161003816arctan 119896119894 minus arctan 119896119894minus11003816100381610038161003816 (119896119894119896119894minus1 ge 0 2 le 119894 le 119879 minus 1)

arctan 10038161003816100381610038161198961198941003816100381610038161003816 + arctan

1003816100381610038161003816119896119894minus11003816100381610038161003816 (119896119894119896119894minus1 lt 0 2 le 119894 le 119879 minus 1)

(3)

119896119894 =

119875119891 (119894 + 1) minus 119875119891 (119894)119905 (119894 + 1) minus 119905 (119894) (1 le 119894 le 119879 minus 1) 119875119891 (119879) minus 119875119891 (119879 minus 1)119905 (119879) minus 119905 (119879 minus 1) ) (119894 = 119879)

(4)

119875119891 (119894) = 119875119908119900119906119905119894 + 119875119901V119900119906119905119894 + 119875ℎ119894 (5)

where 1198652 is the output fluctuation value of the system119875119891(119894) is the output of the whole complementary operationsystem in the 119894119905ℎ period 120579119894 is the angle of the two adjacentline segments 119896119894 is the slope of the 119894119905ℎ line segments

213 Variation of Load and Output Difference Consideringthe power demand is time-variant in power grid the sumof squares of load and output difference at each moment inthe scheduling period is calculated to minimize the influenceto the power grid when the pumped storage plant is added

Variation of load and output difference minimization is alsoa stable objective

min1198653 =119879

sum119894=1

(119875119891 (119894) minus 119875119903 (i))2

(6)

where 1198653 is the variation of load and output difference ofthe system 119875119903(i) is the load forecasting value in the 119894119905ℎ period

22 Constraints

221 Station Constraints

(1) Pumped Storage Plant Constraints

119864119906min le 119864119906119894 le 119864119906m119886119909119864119897min le 119864119897119894 le 119864119897m119886119909

(7)

where 119864119906119894 is the reservoir energy of the upper reservoirin the 119894119905ℎ period 119864119897119894 is the reservoir energy of the lowerreservoir in the 119894119905ℎ period 119864119906min and 119864119906m119886119909 are the minimumand maximum reservoir energy of the upper reservoirrespectively 119864119897min and 119864119897m119886119909 are the minimum and maximumreservoir energy of the lower reservoir respectively

The constraint of reservoir energy variation can bedivided into two situations

When 119875ℎ119894 gt 0 the reservoir energy variation of the upperand lower reservoirs is respectively as follows

119864119906119894+1 = 119864119906119894 minus(Δ119894119875ℎ119894 )1205781

119864119897119894+1 = 119864119897119894 +(Δ119894119875ℎ119894 )1205781

(8)

When 119875119901119894 gt 0 the reservoir energy variation of the upperand lower reservoirs is respectively

119864119906119894+1 = 119864119906119894 +(Δ119894119875119901119894 )1205782

119864119897119894+1 = 119864119897119894 minus(Δ119894119875119901119894 )1205782

(9)

where 1205781 and 1205782 are the pumping and generating effi-ciency of pumped storage station Δ119894 is the temporal lengthof a single period

minus120583119864119906max le 1198641199060 minus 119864119906119879 le 120583119864119906max

minus120583119864119897max le 1198641198970 minus 119864119897119879 le 120583119864119897max

(10)

where 1198641199060 and 119864119906119879 are the initial reservoir energy and finalreservoir energy of upper reservoir respectively 1198641198970 and 119864119897119879are the he initial reservoir energy and final reservoir energyof lower reservoir respectively 120583 is the maximum allowable

4 Mathematical Problems in Engineering

storage energy coefficient of the upper and lower reservoirsduring the whole scheduling period

119875ℎmin le 119875ℎ119894 le 119875ℎmax

119875119901min le 119875119901119894 le 119875119901max

(11)

where 119875ℎmin and 119875ℎmax are the minimum and maximumoutput of pumped storage plant 119875119901min and 119875119901max are theminimumandmaximumpumping output of pumped storageplant

(2) Wind Power Generation Constraint119875119908min le 119875119908119894 le 119875119908m119886119909 (12)

where 119875119908min and 119875119908m119886119909 are the minimum and maximumoutput of wind power

(3) Photovoltaic Power Generation Constraint119875119901Vmin le 119875119901V119894 le 119875119901Vm119886119909 (13)

where 119875119901Vmin and 119875119901Vm119886119909 are the minimum and maximumoutput of wind power

222 Output Balance Constraint

119875119908119894 + 119875119901V119894 = 119875119908119900119906119905119894 + 119875

119901V119900119906119905119894 + 119875

119901119894

(14)

where119875119908119894 and119875119901V119894 are the output of photovoltaic andwind

power in 119894119905ℎ period

223 Transmission Limitation Constraint

119875119892min le 119875119908119900119906119905119894 + 119875119901V119900119906119905119894 + 119875119901119894 le 119875119892max (15)

where 119875119892min and 119875119892max are the transmission power limits

23 Research Scheme To discuss the multiobjective opti-mization problem of the complementary operation of thephotovoltaic-wind-pumped storage system the four schemesin application of the above models are compared and ana-lyzed In scheme 1 the objective is the maximization ofthe power benefit and four kinds of power station areindependently supplied that is if the wind and photovoltaicpower is fully connected into the power grid this resultcan be used as the benchmark for the optimization for thecomplementary operation of the photovoltaic-wind-pumpedstorage system In scheme 2 the objective is the maximiza-tion of the power benefits by utilizing the complementaryoperation of the photovoltaic-wind-pumped storage systemIn scheme 3 the objectives are the maximization of theeconomic benefits of photovoltaic and wind power stationsand suppression of the output fluctuation with utilizationof the complementary operation system In scheme 4 theobjectives are the maximization of the economic benefits ofphotovoltaic and wind power stations and minimization ofthe variation of load and output difference by utilizing of thecomplementary operation system

Table 1 Model parameters of the system

Parameter value1198641199060 (119872119882 sdot ℎ) 12119864119906min (119872119882 sdot ℎ) 4119864119906max (119872119882 sdot ℎ) 24119875ℎmax (119872119882) 31198641198970 (119872119882 sdot ℎ) 16119864119897min (119872119882 sdot ℎ) 4119864119897max (119872119882 sdot ℎ) 24119875119901max (119872119882) 3119875119892max (119872119882) 121205781 () 93751205782 () 80

3 Model Decomposition

The model needs to obtain the 24 moments of 119875119908119900119906119905119894 119875119901V119900119906119905119894 119875119901119894 and 119875ℎ119894 4lowast24 dimensions namely 96 dimensions whichis a high-dimensional dynamic multiconstrained and mul-tiobjective nonlinear optimization problem

Elite and fast nonmainstream sorting genetic algorithm(NSGA-II) [19 20] is widely used to the multiobjectiveproblems because of its fast convergence In this study theoptimal scheduling of complementary power generation sys-tem is determined by NSGA-II and the Pareto noninferiorityrelationship between power benefit and output fluctuation isobtained The solution has following steps

Step 1 Use NSGA-II toolbox to randomly generate calcula-tion results to form the first population

Step 2 Judge the fitness of the calculation resultsCompute the expected outputs of hydropower photo-

voltaic wind and pumping power according to the stationconstraints

Correct the output with the output balance and thetransmission constraint once the power grid access is limited

Compute the fitness value according to the target functionvalue of the corrected output

Step 3 If the terminal condition is met then export the finaloptimal complementary operation result otherwise proceed

Step 4 Apply crossovermutation and selection to update thepopulation using the NSGA-II Then go to Step 2

The flow chart of the model is illustrated in Figure 2

4 Case Study

41 Data The system of 12MW wind power 3MW pumpedstorage power and 5MW photovoltaic power is simulatedand analyzed to prove the applicability of the model Thescheduling period is set to 24 hours The basic modelparameters are shown in Table 1

Mathematical Problems in Engineering 5

Calculate the expected hydropower output the

expected pumping power output the expected

wind output and the expected photovoltaic output

No

Is the stop condition satisfied

Generate the first population

yes

Generate the objectivessuch as the power benefit

and output fluctuation andreturn the fitness of

population

Start

No

Export the final optimal complementary operation

result

Mutation

Selection

Crossover

Create the offspring population

Input data and set the parameters of NSGA-II

Is the network accesslimited

Yes

Stop

Amend the hydropower output pumping power

output the wind output and the photovoltaic output according to constraints

Figure 2 Flow chart of the model

Consulting [12 21] to the peak-valley feed-in tariffs policyat home and abroad and combining with the actual situationthe feed-in tariffs of the complementary system are set asshown in Table 2

42 Results and Discussion

421 Optimal Results of Scheme 1 In scheme 1 only thepower benefit is taken into account with the three stationsoperating independently When the total amount of photo-voltaic power and wind is connected into the power grid

Table 2 Feed-in tariffs in different periods

Period (h) 119862119894 (yen119896119882ℎ) 119862119901119894 (yen119896119882ℎ)0 le 119894 lt 8 054 0251198621198948 le 119894 lt 22 10384 02511986211989422 le 119894 lt 24 054 025119862119894

the power benefit and output fluctuation are yen87800 and1586MW respectively

6 Mathematical Problems in Engineering

0 5 10 15 20 250

2

4

6

8

10

12

Out

put (

MW

)

Time (h)

Output of only wind and photovoltaic powerOutput of the whole complementary operation systemOutput of pumped storage stationPumping power of the pumped storage station

Figure 3 Single-objective optimization results of scheme 2

422 Optimization Results of Scheme 2 Similar to scheme1 only power benefit is considered but optimizing with thecomplementary operation in scheme 2The genetic algorithmis used to solve the single-objective optimization problemThe energy dispatch within one day of three power supplycomplementsrsquo operation is shown in Figure 3

It can be seen from Figure 3 that if only the maximumpower benefit is optimized as a single objective obviously thepower benefit is the greatest Under the circumstances theoutput of complementary operation system is concentrated inthe peak and middle peak feed-in tariff period while less inthe low valley feed-in tariff period with the output fluctuationof complementary operation system of the whole dispatchingperiod being more intense

423 Optimization Results of Scheme 3 In contrast scheme 3is a multiobjective optimization problem aimed at obtainingthemaximumpower benefit and theminimumoutput fluctu-ation and the NSGA-II algorithm is applied to simulate andanalyze the optimal scheduling model of the complementaryoperation system

According to the above algorithm steps and parametersettings the Pareto noninferior solution sets are obtained forthe optimization problems of scheme 3 as shown in Figure 4

The output fluctuation of complementary operation sys-tem increases with the power benefit as shown in Figure 4For the reason that the objective 1198651 is to obtain the maximumpower benefit and the objective 1198652 is to obtain the minimumoutput fluctuation which means the objective functions 1198651and 1198652 cannot be maximal simultaneously Thus choose acompromise point in the solution set namely the inflectionpoint in Figure 4

The power benefit of the complementary operation sys-tem is yen121 440 per day and the output fluctuation is

112000 114000 116000 118000 120000 122000 12400016

14

12

10

8

6

4

2

0

Out

put fl

uctu

atio

n (M

W)

Power benefit (yen)

Inflection point

Figure 4 Noninferior solution of multiobjective optimizationmodel of scheme 3

0 5 10 15 20 250

2

4

6

8

10

12

Out

put (

MW

)

Time (h)

Output of only wind and photovoltaic power Output of the whole complementary operation system Output of pumped storage station Pumping power of the pumped storage station

Figure 5 Multiobjective optimization results of scheme 3

1125MWThe hourly energy dispatch value corresponding to1 day is shown in Figure 5

According to Figure 5 in the low feed-in tariff periodoutput of some of the available solar and wind power isused to meet the load and the rest is for pumping andstoring energy Instead in the high feed-in tariff period theoutput of wind and the photovoltaic is relatively small whichmeans that the solar and wind power cannot meet the loadrequirements the pumped storage station will run in thecondition of power generation to supplement the remainingpart so that the larger power benefit is obtained and theoutput fluctuation is reduced

424 Optimization Results of Scheme 4 Similar to scheme3 scheme 4 is also a multiobjective optimization problemfor obtaining the maximum power benefit and the minimumvariation of load and output difference by using NSGA-II

Mathematical Problems in Engineering 7

Table 3 Results of comparison of the four schemes

Scheme Power benefit (yen) Output fluctuation(MW)

Variation of load andoutput difference (MW2)

The maximum peak-valleydifference (MW)

1 87800 1586 7733 802 125600 2362 9348 753 121440 1125 mdash 404 123200 mdash 1665 46

112000 114000 116000 118000 120000 122000 124000 12600025

20

15

10

5

0

Varia

tion

of lo

ad an

d ou

tput

diff

eren

ce (M

W2 )

Power Benefit (yen)

Inflection point

Figure 6 Noninferior solution of multiobjective optimizationmodel of scheme 4

algorithm The Pareto noninferior solution sets are obtainedfor scheme 4 as shown in Figure 6

It can be seen from Figure 6 that the results are alsosimilar to scheme 3 the objective functions 1198651 and 1198653 cannotbe maximal simultaneously Therefore choose the inflectionpoint in Figure 6 The power benefit of the system is yen123200 per day and the variation of load and output difference is1665MW2 The hourly energy dispatch value correspondingto 1 day is shown in Figure 7

In Figure 7 in the low feed-in tariff period and the highfeed-in tariff period the hourly energy dispatch value has thesame distribution laws in Figure 5

425 Comparison of the Schemes The comparison results ofthe four schemes are illustrated in Table 3

Combined with data analysis in Figures 3 4 5 6 and 7and Table 1 the following is shown

(1) Scheme 1 and Schemes 3 4 The output fluctuation and thevariation of load and output difference of the power grid arevery intense and the maximum peak-valley difference evenreaches 8 MW as the wind farm and the photovoltaic powerstation operate independently Also in the peak feed-in tariffperiod of 0700-1100 and middle peak feed-in tariff period of1100-1500 the wind farm and the photovoltaic power stationare less productive and obviously the operation benefit is nothigh

But after the pumped storage plant is added the outputfluctuation and variation of load and output difference

0 5 10 15 20 250

2

4

6

8

10

12

Output of only wind and photovoltaic powerOutput of the whole complementary operation systemOutput of pumped storage stationPumping power of the pumped storage station

Out

put (

MW

)

Time (h)

Figure 7 Multiobjective optimization results of scheme 4

of the complementary operation of the photovoltaic-wind-pumped storage system are remarkably reduced The outputfluctuation of the complementary operation system is only71 of the single operation of the photovoltaic and windpower the variation of load and output difference is only215 of the single operation of the photovoltaic and windpower and the maximum peak-valley difference is only 50of the single wind and the photovoltaic power In the peakfeed-in tariff period of 0700-1100 17 00-2100 and so onthe photovoltaic and wind power are less productive and theoperation benefit is considerably improved

(2) Scheme 2 and Schemes 3 4 With the maximum powerbenefit of the complementary operation system regardedas a single objective clearly the benefit is biggest In thesituation the output of the complementary operation systemis concentrated in the peak and middle peak feed-in tariffperiod and the low valley feed-in tariff period is less whichmakes the output fluctuation and the variation of load andoutput difference of the complementary operation systemmore intense in the whole scheduling period

In contrast as can be seen from the results of Scheme 3and Scheme 4 in Table 3 each objective hasmade certain con-cessions and achieved the optimal result of the whole benefit

8 Mathematical Problems in Engineering

which means complementary operation of the photovoltaic-wind-pumped storage system can achieve optimal outputpower in different periods by multiobjective optimization

(2) Scheme 3 and Scheme 4 In both scheme 3 and scheme4 there are economic objectives and stable objectives Theeconomic objectives of the two schemes are all power benefitbut the stable objectives are different

The results of scheme 3 reveal that the power benefitmaximization and output fluctuation minimization cannotbe achieved at the same time In contrast scheme4 is aimed atincreasing the power benefit and decreasing the variation ofload and output difference and the results not only verify therelationship between economic objective and stable objectivein scheme 3 but also reflect the power demand time-variantin the real power system

5 Conclusions

To improve the power benefit and the access capacity of pho-tovoltaic and wind power the storage function of the pumpedstorage station is used to balance the maximum benefit andthe minimum output fluctuation of the photovoltaic-wind-pumped storage system

The optimization model is established after properlydefining the economic and stable objectives and constraintsBy comparing and analyzing the four schemes the role of thepumped storage energy in the complementary operation andthe relationship of the three objectives are studied The mainresults are as follows

(i) After the pumped storage plant is added the outputfluctuation the variation of load and output differ-ence and the maximum peak-valley difference of thecomplementary operation system is only 71 2155and 50 of the single operation of the photovoltaicand wind power respectively which means that thepumped storage station can suppress the output fluc-tuation and reduce the variation of load and outputdifference of the photovoltaic-wind-pumped storagesystem

(ii) In the peak feed-in tariff period of 0700-1100 1700-2100 and so on the power benefit is notablyimproved as the pumped storage station is addedindicating that the pumped storage plant can improvethe benefit of photovoltaic and wind power

(iii) The output fluctuation and variation of load and out-put difference increase with the power benefit whichproves the interaction and competition relationshipbetween the economic and stable objectives Then acompromise point in the Pareto optimal solution setis chosen to obtain the optimal result of the wholebenefit of the system

(iv) Comparing the four schemes it is clear that thepumped storage plant has the advantage of improvingthe benefit and the access capacity of photovoltaic andwind power

At last the accuracy and the availability of the multiob-jective optimization model are proved To conclude a hybridenergy system has been modelled and the complementarymechanism of the system has been deeply discussed in thispaper

Data Availability

Theparameter data of wind farm photovoltaic power stationand pumped storage station used to support the findings ofthis study have not been made available because it is from animportant project which involves issues of confidentiality

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work has been partially supported by the Fundamen-tal Research Funds for Central Universities (Grant No2018B625X14) the Postgraduate Research amp Practice Innova-tion Program of Jiangsu Province (Grant No KYCX18 0594)the National Natural Science Foundation of China (GrantNos 51579080 51339005) the Anhui Provincial NaturalScience Foundation (Grant No 1608085ME119) and thePriority Academic Program Development of Jiangsu HigherEducation Institutions (Grant No YS11001)

References

[1] L Hirth ldquoThe benefits of flexibility The value of wind energywith hydropowerrdquo Applied Energy vol 181 pp 210ndash223 2016

[2] T Ma H Yang L Lu and J Peng ldquoPumped storage-basedstandalone photovoltaic power generation system Modelingand techno-economic optimizationrdquo Applied Energy vol 137no 1 pp 649ndash659 2015

[3] J K Kaldellis and D Zafirakis ldquoOptimum energy storagetechniques for the improvement of renewable energy sources-based electricity generation economic efficiencyrdquo Energy vol32 no 12 pp 2295ndash2305 2007

[4] A Ghasemi and M Enayatzare ldquoOptimal energy managementof a renewable-based isolated microgrid with pumped-storageunit and demand responserdquo Journal of Renewable Energy vol123 pp 460ndash474 2018

[5] H M Jiang Y Yuan X S Zhang and Z X Fu ldquoApplicationof energy storage system in mitigating the flicker resulted fromintegrated wind power generationrdquo Proceedings of the CSU-EPSA vol 25 no 2 pp 7ndash12 2013

[6] R Segurado J Madeira M Costa N Duic and M CarvalholdquoOptimization of a wind powered desalination and pumpedhydro storage systemrdquo Applied Energy vol 177 pp 487ndash4992016

[7] S V Papaefthymiou and S A Papathanassiou ldquoOptimumsizing of wind-pumped-storage hybrid power stations in islandsystemsrdquo Journal of Renewable Energy vol 64 pp 187ndash196 2014

[8] Y Luo and R H Zhang ldquoResearch of optimal scheduling ofhybridPVandwindpower systemrdquoActa Energiae Solaris Sinicavol 36 no 10 pp 2492ndash2498 2015

[9] J Schmidt R Cancella and A O Pereira ldquoAn optimal mix ofsolar PV wind and hydro power for a low-carbon electricity

Mathematical Problems in Engineering 9

supply in Brazilrdquo Journal of Renewable Energy vol 85 pp 137ndash147 2016

[10] H K Abbas R M Zablotowicz and H A Bruns ldquoModelingthe colonization of maize by toxigenic and non-toxigenicAspergillus flavus strains implications for biological controlrdquoWorld Mycotoxin Journal vol 1 no 3 pp 333ndash340 2008

[11] X Wang Y Mei Y Kong Y Lin and H Wang ldquoImprovedmulti-objective model and analysis of the coordinated opera-tion of a hydro-wind-photovoltaic systemrdquo Energy vol 134 pp813ndash839 2017

[12] N Sears ldquo5 Strategies for physician engagementrdquo HealthcareFinancial Management vol 65 no 1 pp 78ndash82 2011

[13] Z C Hu H J Ding and T Kong ldquoA joint daily operationoptimizationmodel forwindpower andpumped-storage plantrdquoAutomation of Electric Power Systems vol 36 no 2 pp 36ndash41+57 2012

[14] M G Zhang and Y Hu ldquoJoint dispatch of wind powergeneration and pumped storage with the appliance of FMOEArdquoActa Energiae Solaris Sinica vol 35 no 9 pp 1803ndash1809 2014

[15] G NottonDMistrushi L Stoyanov and P Berberi ldquoOperationof a photovoltaic-wind plant with a hydro pumping-storage forelectricity peak-shaving in an island contextrdquo Solar Energy vol157 pp 20ndash34 2017

[16] J I Perez-Dıaz and J Jimenez ldquoContribution of a pumped-storage hydropower plant to reduce the scheduling costs ofan isolated power system with high wind power penetrationrdquoEnergy vol 109 pp 92ndash104 2016

[17] N Destro M Korpas and J F Sauterleute ldquoSmoothing ofOffshore Wind Power Variations with Norwegian PumpedHydro Case Studyrdquo Energy Procedia vol 87 pp 61ndash68 2016

[18] X Wang Y Mei H Cai and X Cong ldquoA New FluctuationIndex Characteristics and Application to Hydro-Wind Sys-temsrdquo Energies vol 9 no 2 p 114 2016

[19] K Deb S Agrawal A Pratap and T Meyarivan ldquoA fast elitistnon-dominated sorting genetic algorithm for multi-objectiveoptimizationNSGA-IIrdquo inParallel Problem Solving fromNaturePPSN VI vol 1917 of Lecture Notes in Computer Science pp849ndash858 Springer Berlin Germany 2000

[20] L Chen X P Gu and JH Jia ldquoMulti-objective extended black-start schemes optimization based on virus evolution improvedNSGA-II algorithmrdquo Power System Protection and Control vol2 pp 35ndash42 2014

[21] Q Li Y Yuan Z J Li W S Wang and H Y Lu ldquoResearchon energy shifting benefits of hybrid wind power and pumpedhydro storage system considering peak-valley electricity pricerdquoPower System Technology vol 66 no 6 pp 13ndash18 2009

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 3

include station constraints output balance constraint andtransmission constraint

21 Objective Function

211 Power Benefit A benefit maximization model is setup to study how to optimize the output of wind turbinephotovoltaic cell board and pump-turbine unit in eachperiod to obtain maximum power benefit under the premiseof certain wind energy resources and solar energy resourcesPower benefit maximization is an economic objective

max1198651 =119879

sum119894=1

119862119894119875119908119900119906119905119894 + 119862119894119875119901V119900119906119905119894 + 119862119894119875ℎ119894 minus 119862119901119894119875

119901119894 minus 119862ℎ (1)

where 1198651 is the power benefit of the system 119879 is thescheduling period 119875119908119900119906119905119894 119875119901V119900119906119905119894 and 119875ℎ119894 are the outputof photovoltaic wind and pumped storage power directlytransported to the load in the 119894119905ℎ period 119875119901119894 is the pumpingpower of the pumped storage plant in the 119894119905ℎ period 119862119894 is thefeed-in tariff in the 119894119905ℎ period 119862119901119894 is the pumping tariff of thepumped storage station in the 119894119905ℎ period 119862ℎ is the start andstop cost of the pumped storage plant

212 Output Fluctuation To minimize the output fluctu-ation of the complementary operation model the outputfluctuation is calculated by quantifying the fluctuation degreeof the process line based on the quantity dimension and theshape dimension [18] Output fluctuation minimization is astable objective

min1198652 =119879

sum119894=1

10038161003816100381610038161003816119875119891 (119894) minus 11987511989110038161003816100381610038161003816119879

sum119894=1

120579119894 (2)

120579119894

=

arctan 10038161003816100381610038161198961198941003816100381610038161003816 (119894 = 1 119879)

1003816100381610038161003816arctan 119896119894 minus arctan 119896119894minus11003816100381610038161003816 (119896119894119896119894minus1 ge 0 2 le 119894 le 119879 minus 1)

arctan 10038161003816100381610038161198961198941003816100381610038161003816 + arctan

1003816100381610038161003816119896119894minus11003816100381610038161003816 (119896119894119896119894minus1 lt 0 2 le 119894 le 119879 minus 1)

(3)

119896119894 =

119875119891 (119894 + 1) minus 119875119891 (119894)119905 (119894 + 1) minus 119905 (119894) (1 le 119894 le 119879 minus 1) 119875119891 (119879) minus 119875119891 (119879 minus 1)119905 (119879) minus 119905 (119879 minus 1) ) (119894 = 119879)

(4)

119875119891 (119894) = 119875119908119900119906119905119894 + 119875119901V119900119906119905119894 + 119875ℎ119894 (5)

where 1198652 is the output fluctuation value of the system119875119891(119894) is the output of the whole complementary operationsystem in the 119894119905ℎ period 120579119894 is the angle of the two adjacentline segments 119896119894 is the slope of the 119894119905ℎ line segments

213 Variation of Load and Output Difference Consideringthe power demand is time-variant in power grid the sumof squares of load and output difference at each moment inthe scheduling period is calculated to minimize the influenceto the power grid when the pumped storage plant is added

Variation of load and output difference minimization is alsoa stable objective

min1198653 =119879

sum119894=1

(119875119891 (119894) minus 119875119903 (i))2

(6)

where 1198653 is the variation of load and output difference ofthe system 119875119903(i) is the load forecasting value in the 119894119905ℎ period

22 Constraints

221 Station Constraints

(1) Pumped Storage Plant Constraints

119864119906min le 119864119906119894 le 119864119906m119886119909119864119897min le 119864119897119894 le 119864119897m119886119909

(7)

where 119864119906119894 is the reservoir energy of the upper reservoirin the 119894119905ℎ period 119864119897119894 is the reservoir energy of the lowerreservoir in the 119894119905ℎ period 119864119906min and 119864119906m119886119909 are the minimumand maximum reservoir energy of the upper reservoirrespectively 119864119897min and 119864119897m119886119909 are the minimum and maximumreservoir energy of the lower reservoir respectively

The constraint of reservoir energy variation can bedivided into two situations

When 119875ℎ119894 gt 0 the reservoir energy variation of the upperand lower reservoirs is respectively as follows

119864119906119894+1 = 119864119906119894 minus(Δ119894119875ℎ119894 )1205781

119864119897119894+1 = 119864119897119894 +(Δ119894119875ℎ119894 )1205781

(8)

When 119875119901119894 gt 0 the reservoir energy variation of the upperand lower reservoirs is respectively

119864119906119894+1 = 119864119906119894 +(Δ119894119875119901119894 )1205782

119864119897119894+1 = 119864119897119894 minus(Δ119894119875119901119894 )1205782

(9)

where 1205781 and 1205782 are the pumping and generating effi-ciency of pumped storage station Δ119894 is the temporal lengthof a single period

minus120583119864119906max le 1198641199060 minus 119864119906119879 le 120583119864119906max

minus120583119864119897max le 1198641198970 minus 119864119897119879 le 120583119864119897max

(10)

where 1198641199060 and 119864119906119879 are the initial reservoir energy and finalreservoir energy of upper reservoir respectively 1198641198970 and 119864119897119879are the he initial reservoir energy and final reservoir energyof lower reservoir respectively 120583 is the maximum allowable

4 Mathematical Problems in Engineering

storage energy coefficient of the upper and lower reservoirsduring the whole scheduling period

119875ℎmin le 119875ℎ119894 le 119875ℎmax

119875119901min le 119875119901119894 le 119875119901max

(11)

where 119875ℎmin and 119875ℎmax are the minimum and maximumoutput of pumped storage plant 119875119901min and 119875119901max are theminimumandmaximumpumping output of pumped storageplant

(2) Wind Power Generation Constraint119875119908min le 119875119908119894 le 119875119908m119886119909 (12)

where 119875119908min and 119875119908m119886119909 are the minimum and maximumoutput of wind power

(3) Photovoltaic Power Generation Constraint119875119901Vmin le 119875119901V119894 le 119875119901Vm119886119909 (13)

where 119875119901Vmin and 119875119901Vm119886119909 are the minimum and maximumoutput of wind power

222 Output Balance Constraint

119875119908119894 + 119875119901V119894 = 119875119908119900119906119905119894 + 119875

119901V119900119906119905119894 + 119875

119901119894

(14)

where119875119908119894 and119875119901V119894 are the output of photovoltaic andwind

power in 119894119905ℎ period

223 Transmission Limitation Constraint

119875119892min le 119875119908119900119906119905119894 + 119875119901V119900119906119905119894 + 119875119901119894 le 119875119892max (15)

where 119875119892min and 119875119892max are the transmission power limits

23 Research Scheme To discuss the multiobjective opti-mization problem of the complementary operation of thephotovoltaic-wind-pumped storage system the four schemesin application of the above models are compared and ana-lyzed In scheme 1 the objective is the maximization ofthe power benefit and four kinds of power station areindependently supplied that is if the wind and photovoltaicpower is fully connected into the power grid this resultcan be used as the benchmark for the optimization for thecomplementary operation of the photovoltaic-wind-pumpedstorage system In scheme 2 the objective is the maximiza-tion of the power benefits by utilizing the complementaryoperation of the photovoltaic-wind-pumped storage systemIn scheme 3 the objectives are the maximization of theeconomic benefits of photovoltaic and wind power stationsand suppression of the output fluctuation with utilizationof the complementary operation system In scheme 4 theobjectives are the maximization of the economic benefits ofphotovoltaic and wind power stations and minimization ofthe variation of load and output difference by utilizing of thecomplementary operation system

Table 1 Model parameters of the system

Parameter value1198641199060 (119872119882 sdot ℎ) 12119864119906min (119872119882 sdot ℎ) 4119864119906max (119872119882 sdot ℎ) 24119875ℎmax (119872119882) 31198641198970 (119872119882 sdot ℎ) 16119864119897min (119872119882 sdot ℎ) 4119864119897max (119872119882 sdot ℎ) 24119875119901max (119872119882) 3119875119892max (119872119882) 121205781 () 93751205782 () 80

3 Model Decomposition

The model needs to obtain the 24 moments of 119875119908119900119906119905119894 119875119901V119900119906119905119894 119875119901119894 and 119875ℎ119894 4lowast24 dimensions namely 96 dimensions whichis a high-dimensional dynamic multiconstrained and mul-tiobjective nonlinear optimization problem

Elite and fast nonmainstream sorting genetic algorithm(NSGA-II) [19 20] is widely used to the multiobjectiveproblems because of its fast convergence In this study theoptimal scheduling of complementary power generation sys-tem is determined by NSGA-II and the Pareto noninferiorityrelationship between power benefit and output fluctuation isobtained The solution has following steps

Step 1 Use NSGA-II toolbox to randomly generate calcula-tion results to form the first population

Step 2 Judge the fitness of the calculation resultsCompute the expected outputs of hydropower photo-

voltaic wind and pumping power according to the stationconstraints

Correct the output with the output balance and thetransmission constraint once the power grid access is limited

Compute the fitness value according to the target functionvalue of the corrected output

Step 3 If the terminal condition is met then export the finaloptimal complementary operation result otherwise proceed

Step 4 Apply crossovermutation and selection to update thepopulation using the NSGA-II Then go to Step 2

The flow chart of the model is illustrated in Figure 2

4 Case Study

41 Data The system of 12MW wind power 3MW pumpedstorage power and 5MW photovoltaic power is simulatedand analyzed to prove the applicability of the model Thescheduling period is set to 24 hours The basic modelparameters are shown in Table 1

Mathematical Problems in Engineering 5

Calculate the expected hydropower output the

expected pumping power output the expected

wind output and the expected photovoltaic output

No

Is the stop condition satisfied

Generate the first population

yes

Generate the objectivessuch as the power benefit

and output fluctuation andreturn the fitness of

population

Start

No

Export the final optimal complementary operation

result

Mutation

Selection

Crossover

Create the offspring population

Input data and set the parameters of NSGA-II

Is the network accesslimited

Yes

Stop

Amend the hydropower output pumping power

output the wind output and the photovoltaic output according to constraints

Figure 2 Flow chart of the model

Consulting [12 21] to the peak-valley feed-in tariffs policyat home and abroad and combining with the actual situationthe feed-in tariffs of the complementary system are set asshown in Table 2

42 Results and Discussion

421 Optimal Results of Scheme 1 In scheme 1 only thepower benefit is taken into account with the three stationsoperating independently When the total amount of photo-voltaic power and wind is connected into the power grid

Table 2 Feed-in tariffs in different periods

Period (h) 119862119894 (yen119896119882ℎ) 119862119901119894 (yen119896119882ℎ)0 le 119894 lt 8 054 0251198621198948 le 119894 lt 22 10384 02511986211989422 le 119894 lt 24 054 025119862119894

the power benefit and output fluctuation are yen87800 and1586MW respectively

6 Mathematical Problems in Engineering

0 5 10 15 20 250

2

4

6

8

10

12

Out

put (

MW

)

Time (h)

Output of only wind and photovoltaic powerOutput of the whole complementary operation systemOutput of pumped storage stationPumping power of the pumped storage station

Figure 3 Single-objective optimization results of scheme 2

422 Optimization Results of Scheme 2 Similar to scheme1 only power benefit is considered but optimizing with thecomplementary operation in scheme 2The genetic algorithmis used to solve the single-objective optimization problemThe energy dispatch within one day of three power supplycomplementsrsquo operation is shown in Figure 3

It can be seen from Figure 3 that if only the maximumpower benefit is optimized as a single objective obviously thepower benefit is the greatest Under the circumstances theoutput of complementary operation system is concentrated inthe peak and middle peak feed-in tariff period while less inthe low valley feed-in tariff period with the output fluctuationof complementary operation system of the whole dispatchingperiod being more intense

423 Optimization Results of Scheme 3 In contrast scheme 3is a multiobjective optimization problem aimed at obtainingthemaximumpower benefit and theminimumoutput fluctu-ation and the NSGA-II algorithm is applied to simulate andanalyze the optimal scheduling model of the complementaryoperation system

According to the above algorithm steps and parametersettings the Pareto noninferior solution sets are obtained forthe optimization problems of scheme 3 as shown in Figure 4

The output fluctuation of complementary operation sys-tem increases with the power benefit as shown in Figure 4For the reason that the objective 1198651 is to obtain the maximumpower benefit and the objective 1198652 is to obtain the minimumoutput fluctuation which means the objective functions 1198651and 1198652 cannot be maximal simultaneously Thus choose acompromise point in the solution set namely the inflectionpoint in Figure 4

The power benefit of the complementary operation sys-tem is yen121 440 per day and the output fluctuation is

112000 114000 116000 118000 120000 122000 12400016

14

12

10

8

6

4

2

0

Out

put fl

uctu

atio

n (M

W)

Power benefit (yen)

Inflection point

Figure 4 Noninferior solution of multiobjective optimizationmodel of scheme 3

0 5 10 15 20 250

2

4

6

8

10

12

Out

put (

MW

)

Time (h)

Output of only wind and photovoltaic power Output of the whole complementary operation system Output of pumped storage station Pumping power of the pumped storage station

Figure 5 Multiobjective optimization results of scheme 3

1125MWThe hourly energy dispatch value corresponding to1 day is shown in Figure 5

According to Figure 5 in the low feed-in tariff periodoutput of some of the available solar and wind power isused to meet the load and the rest is for pumping andstoring energy Instead in the high feed-in tariff period theoutput of wind and the photovoltaic is relatively small whichmeans that the solar and wind power cannot meet the loadrequirements the pumped storage station will run in thecondition of power generation to supplement the remainingpart so that the larger power benefit is obtained and theoutput fluctuation is reduced

424 Optimization Results of Scheme 4 Similar to scheme3 scheme 4 is also a multiobjective optimization problemfor obtaining the maximum power benefit and the minimumvariation of load and output difference by using NSGA-II

Mathematical Problems in Engineering 7

Table 3 Results of comparison of the four schemes

Scheme Power benefit (yen) Output fluctuation(MW)

Variation of load andoutput difference (MW2)

The maximum peak-valleydifference (MW)

1 87800 1586 7733 802 125600 2362 9348 753 121440 1125 mdash 404 123200 mdash 1665 46

112000 114000 116000 118000 120000 122000 124000 12600025

20

15

10

5

0

Varia

tion

of lo

ad an

d ou

tput

diff

eren

ce (M

W2 )

Power Benefit (yen)

Inflection point

Figure 6 Noninferior solution of multiobjective optimizationmodel of scheme 4

algorithm The Pareto noninferior solution sets are obtainedfor scheme 4 as shown in Figure 6

It can be seen from Figure 6 that the results are alsosimilar to scheme 3 the objective functions 1198651 and 1198653 cannotbe maximal simultaneously Therefore choose the inflectionpoint in Figure 6 The power benefit of the system is yen123200 per day and the variation of load and output difference is1665MW2 The hourly energy dispatch value correspondingto 1 day is shown in Figure 7

In Figure 7 in the low feed-in tariff period and the highfeed-in tariff period the hourly energy dispatch value has thesame distribution laws in Figure 5

425 Comparison of the Schemes The comparison results ofthe four schemes are illustrated in Table 3

Combined with data analysis in Figures 3 4 5 6 and 7and Table 1 the following is shown

(1) Scheme 1 and Schemes 3 4 The output fluctuation and thevariation of load and output difference of the power grid arevery intense and the maximum peak-valley difference evenreaches 8 MW as the wind farm and the photovoltaic powerstation operate independently Also in the peak feed-in tariffperiod of 0700-1100 and middle peak feed-in tariff period of1100-1500 the wind farm and the photovoltaic power stationare less productive and obviously the operation benefit is nothigh

But after the pumped storage plant is added the outputfluctuation and variation of load and output difference

0 5 10 15 20 250

2

4

6

8

10

12

Output of only wind and photovoltaic powerOutput of the whole complementary operation systemOutput of pumped storage stationPumping power of the pumped storage station

Out

put (

MW

)

Time (h)

Figure 7 Multiobjective optimization results of scheme 4

of the complementary operation of the photovoltaic-wind-pumped storage system are remarkably reduced The outputfluctuation of the complementary operation system is only71 of the single operation of the photovoltaic and windpower the variation of load and output difference is only215 of the single operation of the photovoltaic and windpower and the maximum peak-valley difference is only 50of the single wind and the photovoltaic power In the peakfeed-in tariff period of 0700-1100 17 00-2100 and so onthe photovoltaic and wind power are less productive and theoperation benefit is considerably improved

(2) Scheme 2 and Schemes 3 4 With the maximum powerbenefit of the complementary operation system regardedas a single objective clearly the benefit is biggest In thesituation the output of the complementary operation systemis concentrated in the peak and middle peak feed-in tariffperiod and the low valley feed-in tariff period is less whichmakes the output fluctuation and the variation of load andoutput difference of the complementary operation systemmore intense in the whole scheduling period

In contrast as can be seen from the results of Scheme 3and Scheme 4 in Table 3 each objective hasmade certain con-cessions and achieved the optimal result of the whole benefit

8 Mathematical Problems in Engineering

which means complementary operation of the photovoltaic-wind-pumped storage system can achieve optimal outputpower in different periods by multiobjective optimization

(2) Scheme 3 and Scheme 4 In both scheme 3 and scheme4 there are economic objectives and stable objectives Theeconomic objectives of the two schemes are all power benefitbut the stable objectives are different

The results of scheme 3 reveal that the power benefitmaximization and output fluctuation minimization cannotbe achieved at the same time In contrast scheme4 is aimed atincreasing the power benefit and decreasing the variation ofload and output difference and the results not only verify therelationship between economic objective and stable objectivein scheme 3 but also reflect the power demand time-variantin the real power system

5 Conclusions

To improve the power benefit and the access capacity of pho-tovoltaic and wind power the storage function of the pumpedstorage station is used to balance the maximum benefit andthe minimum output fluctuation of the photovoltaic-wind-pumped storage system

The optimization model is established after properlydefining the economic and stable objectives and constraintsBy comparing and analyzing the four schemes the role of thepumped storage energy in the complementary operation andthe relationship of the three objectives are studied The mainresults are as follows

(i) After the pumped storage plant is added the outputfluctuation the variation of load and output differ-ence and the maximum peak-valley difference of thecomplementary operation system is only 71 2155and 50 of the single operation of the photovoltaicand wind power respectively which means that thepumped storage station can suppress the output fluc-tuation and reduce the variation of load and outputdifference of the photovoltaic-wind-pumped storagesystem

(ii) In the peak feed-in tariff period of 0700-1100 1700-2100 and so on the power benefit is notablyimproved as the pumped storage station is addedindicating that the pumped storage plant can improvethe benefit of photovoltaic and wind power

(iii) The output fluctuation and variation of load and out-put difference increase with the power benefit whichproves the interaction and competition relationshipbetween the economic and stable objectives Then acompromise point in the Pareto optimal solution setis chosen to obtain the optimal result of the wholebenefit of the system

(iv) Comparing the four schemes it is clear that thepumped storage plant has the advantage of improvingthe benefit and the access capacity of photovoltaic andwind power

At last the accuracy and the availability of the multiob-jective optimization model are proved To conclude a hybridenergy system has been modelled and the complementarymechanism of the system has been deeply discussed in thispaper

Data Availability

Theparameter data of wind farm photovoltaic power stationand pumped storage station used to support the findings ofthis study have not been made available because it is from animportant project which involves issues of confidentiality

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work has been partially supported by the Fundamen-tal Research Funds for Central Universities (Grant No2018B625X14) the Postgraduate Research amp Practice Innova-tion Program of Jiangsu Province (Grant No KYCX18 0594)the National Natural Science Foundation of China (GrantNos 51579080 51339005) the Anhui Provincial NaturalScience Foundation (Grant No 1608085ME119) and thePriority Academic Program Development of Jiangsu HigherEducation Institutions (Grant No YS11001)

References

[1] L Hirth ldquoThe benefits of flexibility The value of wind energywith hydropowerrdquo Applied Energy vol 181 pp 210ndash223 2016

[2] T Ma H Yang L Lu and J Peng ldquoPumped storage-basedstandalone photovoltaic power generation system Modelingand techno-economic optimizationrdquo Applied Energy vol 137no 1 pp 649ndash659 2015

[3] J K Kaldellis and D Zafirakis ldquoOptimum energy storagetechniques for the improvement of renewable energy sources-based electricity generation economic efficiencyrdquo Energy vol32 no 12 pp 2295ndash2305 2007

[4] A Ghasemi and M Enayatzare ldquoOptimal energy managementof a renewable-based isolated microgrid with pumped-storageunit and demand responserdquo Journal of Renewable Energy vol123 pp 460ndash474 2018

[5] H M Jiang Y Yuan X S Zhang and Z X Fu ldquoApplicationof energy storage system in mitigating the flicker resulted fromintegrated wind power generationrdquo Proceedings of the CSU-EPSA vol 25 no 2 pp 7ndash12 2013

[6] R Segurado J Madeira M Costa N Duic and M CarvalholdquoOptimization of a wind powered desalination and pumpedhydro storage systemrdquo Applied Energy vol 177 pp 487ndash4992016

[7] S V Papaefthymiou and S A Papathanassiou ldquoOptimumsizing of wind-pumped-storage hybrid power stations in islandsystemsrdquo Journal of Renewable Energy vol 64 pp 187ndash196 2014

[8] Y Luo and R H Zhang ldquoResearch of optimal scheduling ofhybridPVandwindpower systemrdquoActa Energiae Solaris Sinicavol 36 no 10 pp 2492ndash2498 2015

[9] J Schmidt R Cancella and A O Pereira ldquoAn optimal mix ofsolar PV wind and hydro power for a low-carbon electricity

Mathematical Problems in Engineering 9

supply in Brazilrdquo Journal of Renewable Energy vol 85 pp 137ndash147 2016

[10] H K Abbas R M Zablotowicz and H A Bruns ldquoModelingthe colonization of maize by toxigenic and non-toxigenicAspergillus flavus strains implications for biological controlrdquoWorld Mycotoxin Journal vol 1 no 3 pp 333ndash340 2008

[11] X Wang Y Mei Y Kong Y Lin and H Wang ldquoImprovedmulti-objective model and analysis of the coordinated opera-tion of a hydro-wind-photovoltaic systemrdquo Energy vol 134 pp813ndash839 2017

[12] N Sears ldquo5 Strategies for physician engagementrdquo HealthcareFinancial Management vol 65 no 1 pp 78ndash82 2011

[13] Z C Hu H J Ding and T Kong ldquoA joint daily operationoptimizationmodel forwindpower andpumped-storage plantrdquoAutomation of Electric Power Systems vol 36 no 2 pp 36ndash41+57 2012

[14] M G Zhang and Y Hu ldquoJoint dispatch of wind powergeneration and pumped storage with the appliance of FMOEArdquoActa Energiae Solaris Sinica vol 35 no 9 pp 1803ndash1809 2014

[15] G NottonDMistrushi L Stoyanov and P Berberi ldquoOperationof a photovoltaic-wind plant with a hydro pumping-storage forelectricity peak-shaving in an island contextrdquo Solar Energy vol157 pp 20ndash34 2017

[16] J I Perez-Dıaz and J Jimenez ldquoContribution of a pumped-storage hydropower plant to reduce the scheduling costs ofan isolated power system with high wind power penetrationrdquoEnergy vol 109 pp 92ndash104 2016

[17] N Destro M Korpas and J F Sauterleute ldquoSmoothing ofOffshore Wind Power Variations with Norwegian PumpedHydro Case Studyrdquo Energy Procedia vol 87 pp 61ndash68 2016

[18] X Wang Y Mei H Cai and X Cong ldquoA New FluctuationIndex Characteristics and Application to Hydro-Wind Sys-temsrdquo Energies vol 9 no 2 p 114 2016

[19] K Deb S Agrawal A Pratap and T Meyarivan ldquoA fast elitistnon-dominated sorting genetic algorithm for multi-objectiveoptimizationNSGA-IIrdquo inParallel Problem Solving fromNaturePPSN VI vol 1917 of Lecture Notes in Computer Science pp849ndash858 Springer Berlin Germany 2000

[20] L Chen X P Gu and JH Jia ldquoMulti-objective extended black-start schemes optimization based on virus evolution improvedNSGA-II algorithmrdquo Power System Protection and Control vol2 pp 35ndash42 2014

[21] Q Li Y Yuan Z J Li W S Wang and H Y Lu ldquoResearchon energy shifting benefits of hybrid wind power and pumpedhydro storage system considering peak-valley electricity pricerdquoPower System Technology vol 66 no 6 pp 13ndash18 2009

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

4 Mathematical Problems in Engineering

storage energy coefficient of the upper and lower reservoirsduring the whole scheduling period

119875ℎmin le 119875ℎ119894 le 119875ℎmax

119875119901min le 119875119901119894 le 119875119901max

(11)

where 119875ℎmin and 119875ℎmax are the minimum and maximumoutput of pumped storage plant 119875119901min and 119875119901max are theminimumandmaximumpumping output of pumped storageplant

(2) Wind Power Generation Constraint119875119908min le 119875119908119894 le 119875119908m119886119909 (12)

where 119875119908min and 119875119908m119886119909 are the minimum and maximumoutput of wind power

(3) Photovoltaic Power Generation Constraint119875119901Vmin le 119875119901V119894 le 119875119901Vm119886119909 (13)

where 119875119901Vmin and 119875119901Vm119886119909 are the minimum and maximumoutput of wind power

222 Output Balance Constraint

119875119908119894 + 119875119901V119894 = 119875119908119900119906119905119894 + 119875

119901V119900119906119905119894 + 119875

119901119894

(14)

where119875119908119894 and119875119901V119894 are the output of photovoltaic andwind

power in 119894119905ℎ period

223 Transmission Limitation Constraint

119875119892min le 119875119908119900119906119905119894 + 119875119901V119900119906119905119894 + 119875119901119894 le 119875119892max (15)

where 119875119892min and 119875119892max are the transmission power limits

23 Research Scheme To discuss the multiobjective opti-mization problem of the complementary operation of thephotovoltaic-wind-pumped storage system the four schemesin application of the above models are compared and ana-lyzed In scheme 1 the objective is the maximization ofthe power benefit and four kinds of power station areindependently supplied that is if the wind and photovoltaicpower is fully connected into the power grid this resultcan be used as the benchmark for the optimization for thecomplementary operation of the photovoltaic-wind-pumpedstorage system In scheme 2 the objective is the maximiza-tion of the power benefits by utilizing the complementaryoperation of the photovoltaic-wind-pumped storage systemIn scheme 3 the objectives are the maximization of theeconomic benefits of photovoltaic and wind power stationsand suppression of the output fluctuation with utilizationof the complementary operation system In scheme 4 theobjectives are the maximization of the economic benefits ofphotovoltaic and wind power stations and minimization ofthe variation of load and output difference by utilizing of thecomplementary operation system

Table 1 Model parameters of the system

Parameter value1198641199060 (119872119882 sdot ℎ) 12119864119906min (119872119882 sdot ℎ) 4119864119906max (119872119882 sdot ℎ) 24119875ℎmax (119872119882) 31198641198970 (119872119882 sdot ℎ) 16119864119897min (119872119882 sdot ℎ) 4119864119897max (119872119882 sdot ℎ) 24119875119901max (119872119882) 3119875119892max (119872119882) 121205781 () 93751205782 () 80

3 Model Decomposition

The model needs to obtain the 24 moments of 119875119908119900119906119905119894 119875119901V119900119906119905119894 119875119901119894 and 119875ℎ119894 4lowast24 dimensions namely 96 dimensions whichis a high-dimensional dynamic multiconstrained and mul-tiobjective nonlinear optimization problem

Elite and fast nonmainstream sorting genetic algorithm(NSGA-II) [19 20] is widely used to the multiobjectiveproblems because of its fast convergence In this study theoptimal scheduling of complementary power generation sys-tem is determined by NSGA-II and the Pareto noninferiorityrelationship between power benefit and output fluctuation isobtained The solution has following steps

Step 1 Use NSGA-II toolbox to randomly generate calcula-tion results to form the first population

Step 2 Judge the fitness of the calculation resultsCompute the expected outputs of hydropower photo-

voltaic wind and pumping power according to the stationconstraints

Correct the output with the output balance and thetransmission constraint once the power grid access is limited

Compute the fitness value according to the target functionvalue of the corrected output

Step 3 If the terminal condition is met then export the finaloptimal complementary operation result otherwise proceed

Step 4 Apply crossovermutation and selection to update thepopulation using the NSGA-II Then go to Step 2

The flow chart of the model is illustrated in Figure 2

4 Case Study

41 Data The system of 12MW wind power 3MW pumpedstorage power and 5MW photovoltaic power is simulatedand analyzed to prove the applicability of the model Thescheduling period is set to 24 hours The basic modelparameters are shown in Table 1

Mathematical Problems in Engineering 5

Calculate the expected hydropower output the

expected pumping power output the expected

wind output and the expected photovoltaic output

No

Is the stop condition satisfied

Generate the first population

yes

Generate the objectivessuch as the power benefit

and output fluctuation andreturn the fitness of

population

Start

No

Export the final optimal complementary operation

result

Mutation

Selection

Crossover

Create the offspring population

Input data and set the parameters of NSGA-II

Is the network accesslimited

Yes

Stop

Amend the hydropower output pumping power

output the wind output and the photovoltaic output according to constraints

Figure 2 Flow chart of the model

Consulting [12 21] to the peak-valley feed-in tariffs policyat home and abroad and combining with the actual situationthe feed-in tariffs of the complementary system are set asshown in Table 2

42 Results and Discussion

421 Optimal Results of Scheme 1 In scheme 1 only thepower benefit is taken into account with the three stationsoperating independently When the total amount of photo-voltaic power and wind is connected into the power grid

Table 2 Feed-in tariffs in different periods

Period (h) 119862119894 (yen119896119882ℎ) 119862119901119894 (yen119896119882ℎ)0 le 119894 lt 8 054 0251198621198948 le 119894 lt 22 10384 02511986211989422 le 119894 lt 24 054 025119862119894

the power benefit and output fluctuation are yen87800 and1586MW respectively

6 Mathematical Problems in Engineering

0 5 10 15 20 250

2

4

6

8

10

12

Out

put (

MW

)

Time (h)

Output of only wind and photovoltaic powerOutput of the whole complementary operation systemOutput of pumped storage stationPumping power of the pumped storage station

Figure 3 Single-objective optimization results of scheme 2

422 Optimization Results of Scheme 2 Similar to scheme1 only power benefit is considered but optimizing with thecomplementary operation in scheme 2The genetic algorithmis used to solve the single-objective optimization problemThe energy dispatch within one day of three power supplycomplementsrsquo operation is shown in Figure 3

It can be seen from Figure 3 that if only the maximumpower benefit is optimized as a single objective obviously thepower benefit is the greatest Under the circumstances theoutput of complementary operation system is concentrated inthe peak and middle peak feed-in tariff period while less inthe low valley feed-in tariff period with the output fluctuationof complementary operation system of the whole dispatchingperiod being more intense

423 Optimization Results of Scheme 3 In contrast scheme 3is a multiobjective optimization problem aimed at obtainingthemaximumpower benefit and theminimumoutput fluctu-ation and the NSGA-II algorithm is applied to simulate andanalyze the optimal scheduling model of the complementaryoperation system

According to the above algorithm steps and parametersettings the Pareto noninferior solution sets are obtained forthe optimization problems of scheme 3 as shown in Figure 4

The output fluctuation of complementary operation sys-tem increases with the power benefit as shown in Figure 4For the reason that the objective 1198651 is to obtain the maximumpower benefit and the objective 1198652 is to obtain the minimumoutput fluctuation which means the objective functions 1198651and 1198652 cannot be maximal simultaneously Thus choose acompromise point in the solution set namely the inflectionpoint in Figure 4

The power benefit of the complementary operation sys-tem is yen121 440 per day and the output fluctuation is

112000 114000 116000 118000 120000 122000 12400016

14

12

10

8

6

4

2

0

Out

put fl

uctu

atio

n (M

W)

Power benefit (yen)

Inflection point

Figure 4 Noninferior solution of multiobjective optimizationmodel of scheme 3

0 5 10 15 20 250

2

4

6

8

10

12

Out

put (

MW

)

Time (h)

Output of only wind and photovoltaic power Output of the whole complementary operation system Output of pumped storage station Pumping power of the pumped storage station

Figure 5 Multiobjective optimization results of scheme 3

1125MWThe hourly energy dispatch value corresponding to1 day is shown in Figure 5

According to Figure 5 in the low feed-in tariff periodoutput of some of the available solar and wind power isused to meet the load and the rest is for pumping andstoring energy Instead in the high feed-in tariff period theoutput of wind and the photovoltaic is relatively small whichmeans that the solar and wind power cannot meet the loadrequirements the pumped storage station will run in thecondition of power generation to supplement the remainingpart so that the larger power benefit is obtained and theoutput fluctuation is reduced

424 Optimization Results of Scheme 4 Similar to scheme3 scheme 4 is also a multiobjective optimization problemfor obtaining the maximum power benefit and the minimumvariation of load and output difference by using NSGA-II

Mathematical Problems in Engineering 7

Table 3 Results of comparison of the four schemes

Scheme Power benefit (yen) Output fluctuation(MW)

Variation of load andoutput difference (MW2)

The maximum peak-valleydifference (MW)

1 87800 1586 7733 802 125600 2362 9348 753 121440 1125 mdash 404 123200 mdash 1665 46

112000 114000 116000 118000 120000 122000 124000 12600025

20

15

10

5

0

Varia

tion

of lo

ad an

d ou

tput

diff

eren

ce (M

W2 )

Power Benefit (yen)

Inflection point

Figure 6 Noninferior solution of multiobjective optimizationmodel of scheme 4

algorithm The Pareto noninferior solution sets are obtainedfor scheme 4 as shown in Figure 6

It can be seen from Figure 6 that the results are alsosimilar to scheme 3 the objective functions 1198651 and 1198653 cannotbe maximal simultaneously Therefore choose the inflectionpoint in Figure 6 The power benefit of the system is yen123200 per day and the variation of load and output difference is1665MW2 The hourly energy dispatch value correspondingto 1 day is shown in Figure 7

In Figure 7 in the low feed-in tariff period and the highfeed-in tariff period the hourly energy dispatch value has thesame distribution laws in Figure 5

425 Comparison of the Schemes The comparison results ofthe four schemes are illustrated in Table 3

Combined with data analysis in Figures 3 4 5 6 and 7and Table 1 the following is shown

(1) Scheme 1 and Schemes 3 4 The output fluctuation and thevariation of load and output difference of the power grid arevery intense and the maximum peak-valley difference evenreaches 8 MW as the wind farm and the photovoltaic powerstation operate independently Also in the peak feed-in tariffperiod of 0700-1100 and middle peak feed-in tariff period of1100-1500 the wind farm and the photovoltaic power stationare less productive and obviously the operation benefit is nothigh

But after the pumped storage plant is added the outputfluctuation and variation of load and output difference

0 5 10 15 20 250

2

4

6

8

10

12

Output of only wind and photovoltaic powerOutput of the whole complementary operation systemOutput of pumped storage stationPumping power of the pumped storage station

Out

put (

MW

)

Time (h)

Figure 7 Multiobjective optimization results of scheme 4

of the complementary operation of the photovoltaic-wind-pumped storage system are remarkably reduced The outputfluctuation of the complementary operation system is only71 of the single operation of the photovoltaic and windpower the variation of load and output difference is only215 of the single operation of the photovoltaic and windpower and the maximum peak-valley difference is only 50of the single wind and the photovoltaic power In the peakfeed-in tariff period of 0700-1100 17 00-2100 and so onthe photovoltaic and wind power are less productive and theoperation benefit is considerably improved

(2) Scheme 2 and Schemes 3 4 With the maximum powerbenefit of the complementary operation system regardedas a single objective clearly the benefit is biggest In thesituation the output of the complementary operation systemis concentrated in the peak and middle peak feed-in tariffperiod and the low valley feed-in tariff period is less whichmakes the output fluctuation and the variation of load andoutput difference of the complementary operation systemmore intense in the whole scheduling period

In contrast as can be seen from the results of Scheme 3and Scheme 4 in Table 3 each objective hasmade certain con-cessions and achieved the optimal result of the whole benefit

8 Mathematical Problems in Engineering

which means complementary operation of the photovoltaic-wind-pumped storage system can achieve optimal outputpower in different periods by multiobjective optimization

(2) Scheme 3 and Scheme 4 In both scheme 3 and scheme4 there are economic objectives and stable objectives Theeconomic objectives of the two schemes are all power benefitbut the stable objectives are different

The results of scheme 3 reveal that the power benefitmaximization and output fluctuation minimization cannotbe achieved at the same time In contrast scheme4 is aimed atincreasing the power benefit and decreasing the variation ofload and output difference and the results not only verify therelationship between economic objective and stable objectivein scheme 3 but also reflect the power demand time-variantin the real power system

5 Conclusions

To improve the power benefit and the access capacity of pho-tovoltaic and wind power the storage function of the pumpedstorage station is used to balance the maximum benefit andthe minimum output fluctuation of the photovoltaic-wind-pumped storage system

The optimization model is established after properlydefining the economic and stable objectives and constraintsBy comparing and analyzing the four schemes the role of thepumped storage energy in the complementary operation andthe relationship of the three objectives are studied The mainresults are as follows

(i) After the pumped storage plant is added the outputfluctuation the variation of load and output differ-ence and the maximum peak-valley difference of thecomplementary operation system is only 71 2155and 50 of the single operation of the photovoltaicand wind power respectively which means that thepumped storage station can suppress the output fluc-tuation and reduce the variation of load and outputdifference of the photovoltaic-wind-pumped storagesystem

(ii) In the peak feed-in tariff period of 0700-1100 1700-2100 and so on the power benefit is notablyimproved as the pumped storage station is addedindicating that the pumped storage plant can improvethe benefit of photovoltaic and wind power

(iii) The output fluctuation and variation of load and out-put difference increase with the power benefit whichproves the interaction and competition relationshipbetween the economic and stable objectives Then acompromise point in the Pareto optimal solution setis chosen to obtain the optimal result of the wholebenefit of the system

(iv) Comparing the four schemes it is clear that thepumped storage plant has the advantage of improvingthe benefit and the access capacity of photovoltaic andwind power

At last the accuracy and the availability of the multiob-jective optimization model are proved To conclude a hybridenergy system has been modelled and the complementarymechanism of the system has been deeply discussed in thispaper

Data Availability

Theparameter data of wind farm photovoltaic power stationand pumped storage station used to support the findings ofthis study have not been made available because it is from animportant project which involves issues of confidentiality

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work has been partially supported by the Fundamen-tal Research Funds for Central Universities (Grant No2018B625X14) the Postgraduate Research amp Practice Innova-tion Program of Jiangsu Province (Grant No KYCX18 0594)the National Natural Science Foundation of China (GrantNos 51579080 51339005) the Anhui Provincial NaturalScience Foundation (Grant No 1608085ME119) and thePriority Academic Program Development of Jiangsu HigherEducation Institutions (Grant No YS11001)

References

[1] L Hirth ldquoThe benefits of flexibility The value of wind energywith hydropowerrdquo Applied Energy vol 181 pp 210ndash223 2016

[2] T Ma H Yang L Lu and J Peng ldquoPumped storage-basedstandalone photovoltaic power generation system Modelingand techno-economic optimizationrdquo Applied Energy vol 137no 1 pp 649ndash659 2015

[3] J K Kaldellis and D Zafirakis ldquoOptimum energy storagetechniques for the improvement of renewable energy sources-based electricity generation economic efficiencyrdquo Energy vol32 no 12 pp 2295ndash2305 2007

[4] A Ghasemi and M Enayatzare ldquoOptimal energy managementof a renewable-based isolated microgrid with pumped-storageunit and demand responserdquo Journal of Renewable Energy vol123 pp 460ndash474 2018

[5] H M Jiang Y Yuan X S Zhang and Z X Fu ldquoApplicationof energy storage system in mitigating the flicker resulted fromintegrated wind power generationrdquo Proceedings of the CSU-EPSA vol 25 no 2 pp 7ndash12 2013

[6] R Segurado J Madeira M Costa N Duic and M CarvalholdquoOptimization of a wind powered desalination and pumpedhydro storage systemrdquo Applied Energy vol 177 pp 487ndash4992016

[7] S V Papaefthymiou and S A Papathanassiou ldquoOptimumsizing of wind-pumped-storage hybrid power stations in islandsystemsrdquo Journal of Renewable Energy vol 64 pp 187ndash196 2014

[8] Y Luo and R H Zhang ldquoResearch of optimal scheduling ofhybridPVandwindpower systemrdquoActa Energiae Solaris Sinicavol 36 no 10 pp 2492ndash2498 2015

[9] J Schmidt R Cancella and A O Pereira ldquoAn optimal mix ofsolar PV wind and hydro power for a low-carbon electricity

Mathematical Problems in Engineering 9

supply in Brazilrdquo Journal of Renewable Energy vol 85 pp 137ndash147 2016

[10] H K Abbas R M Zablotowicz and H A Bruns ldquoModelingthe colonization of maize by toxigenic and non-toxigenicAspergillus flavus strains implications for biological controlrdquoWorld Mycotoxin Journal vol 1 no 3 pp 333ndash340 2008

[11] X Wang Y Mei Y Kong Y Lin and H Wang ldquoImprovedmulti-objective model and analysis of the coordinated opera-tion of a hydro-wind-photovoltaic systemrdquo Energy vol 134 pp813ndash839 2017

[12] N Sears ldquo5 Strategies for physician engagementrdquo HealthcareFinancial Management vol 65 no 1 pp 78ndash82 2011

[13] Z C Hu H J Ding and T Kong ldquoA joint daily operationoptimizationmodel forwindpower andpumped-storage plantrdquoAutomation of Electric Power Systems vol 36 no 2 pp 36ndash41+57 2012

[14] M G Zhang and Y Hu ldquoJoint dispatch of wind powergeneration and pumped storage with the appliance of FMOEArdquoActa Energiae Solaris Sinica vol 35 no 9 pp 1803ndash1809 2014

[15] G NottonDMistrushi L Stoyanov and P Berberi ldquoOperationof a photovoltaic-wind plant with a hydro pumping-storage forelectricity peak-shaving in an island contextrdquo Solar Energy vol157 pp 20ndash34 2017

[16] J I Perez-Dıaz and J Jimenez ldquoContribution of a pumped-storage hydropower plant to reduce the scheduling costs ofan isolated power system with high wind power penetrationrdquoEnergy vol 109 pp 92ndash104 2016

[17] N Destro M Korpas and J F Sauterleute ldquoSmoothing ofOffshore Wind Power Variations with Norwegian PumpedHydro Case Studyrdquo Energy Procedia vol 87 pp 61ndash68 2016

[18] X Wang Y Mei H Cai and X Cong ldquoA New FluctuationIndex Characteristics and Application to Hydro-Wind Sys-temsrdquo Energies vol 9 no 2 p 114 2016

[19] K Deb S Agrawal A Pratap and T Meyarivan ldquoA fast elitistnon-dominated sorting genetic algorithm for multi-objectiveoptimizationNSGA-IIrdquo inParallel Problem Solving fromNaturePPSN VI vol 1917 of Lecture Notes in Computer Science pp849ndash858 Springer Berlin Germany 2000

[20] L Chen X P Gu and JH Jia ldquoMulti-objective extended black-start schemes optimization based on virus evolution improvedNSGA-II algorithmrdquo Power System Protection and Control vol2 pp 35ndash42 2014

[21] Q Li Y Yuan Z J Li W S Wang and H Y Lu ldquoResearchon energy shifting benefits of hybrid wind power and pumpedhydro storage system considering peak-valley electricity pricerdquoPower System Technology vol 66 no 6 pp 13ndash18 2009

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Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 5

Calculate the expected hydropower output the

expected pumping power output the expected

wind output and the expected photovoltaic output

No

Is the stop condition satisfied

Generate the first population

yes

Generate the objectivessuch as the power benefit

and output fluctuation andreturn the fitness of

population

Start

No

Export the final optimal complementary operation

result

Mutation

Selection

Crossover

Create the offspring population

Input data and set the parameters of NSGA-II

Is the network accesslimited

Yes

Stop

Amend the hydropower output pumping power

output the wind output and the photovoltaic output according to constraints

Figure 2 Flow chart of the model

Consulting [12 21] to the peak-valley feed-in tariffs policyat home and abroad and combining with the actual situationthe feed-in tariffs of the complementary system are set asshown in Table 2

42 Results and Discussion

421 Optimal Results of Scheme 1 In scheme 1 only thepower benefit is taken into account with the three stationsoperating independently When the total amount of photo-voltaic power and wind is connected into the power grid

Table 2 Feed-in tariffs in different periods

Period (h) 119862119894 (yen119896119882ℎ) 119862119901119894 (yen119896119882ℎ)0 le 119894 lt 8 054 0251198621198948 le 119894 lt 22 10384 02511986211989422 le 119894 lt 24 054 025119862119894

the power benefit and output fluctuation are yen87800 and1586MW respectively

6 Mathematical Problems in Engineering

0 5 10 15 20 250

2

4

6

8

10

12

Out

put (

MW

)

Time (h)

Output of only wind and photovoltaic powerOutput of the whole complementary operation systemOutput of pumped storage stationPumping power of the pumped storage station

Figure 3 Single-objective optimization results of scheme 2

422 Optimization Results of Scheme 2 Similar to scheme1 only power benefit is considered but optimizing with thecomplementary operation in scheme 2The genetic algorithmis used to solve the single-objective optimization problemThe energy dispatch within one day of three power supplycomplementsrsquo operation is shown in Figure 3

It can be seen from Figure 3 that if only the maximumpower benefit is optimized as a single objective obviously thepower benefit is the greatest Under the circumstances theoutput of complementary operation system is concentrated inthe peak and middle peak feed-in tariff period while less inthe low valley feed-in tariff period with the output fluctuationof complementary operation system of the whole dispatchingperiod being more intense

423 Optimization Results of Scheme 3 In contrast scheme 3is a multiobjective optimization problem aimed at obtainingthemaximumpower benefit and theminimumoutput fluctu-ation and the NSGA-II algorithm is applied to simulate andanalyze the optimal scheduling model of the complementaryoperation system

According to the above algorithm steps and parametersettings the Pareto noninferior solution sets are obtained forthe optimization problems of scheme 3 as shown in Figure 4

The output fluctuation of complementary operation sys-tem increases with the power benefit as shown in Figure 4For the reason that the objective 1198651 is to obtain the maximumpower benefit and the objective 1198652 is to obtain the minimumoutput fluctuation which means the objective functions 1198651and 1198652 cannot be maximal simultaneously Thus choose acompromise point in the solution set namely the inflectionpoint in Figure 4

The power benefit of the complementary operation sys-tem is yen121 440 per day and the output fluctuation is

112000 114000 116000 118000 120000 122000 12400016

14

12

10

8

6

4

2

0

Out

put fl

uctu

atio

n (M

W)

Power benefit (yen)

Inflection point

Figure 4 Noninferior solution of multiobjective optimizationmodel of scheme 3

0 5 10 15 20 250

2

4

6

8

10

12

Out

put (

MW

)

Time (h)

Output of only wind and photovoltaic power Output of the whole complementary operation system Output of pumped storage station Pumping power of the pumped storage station

Figure 5 Multiobjective optimization results of scheme 3

1125MWThe hourly energy dispatch value corresponding to1 day is shown in Figure 5

According to Figure 5 in the low feed-in tariff periodoutput of some of the available solar and wind power isused to meet the load and the rest is for pumping andstoring energy Instead in the high feed-in tariff period theoutput of wind and the photovoltaic is relatively small whichmeans that the solar and wind power cannot meet the loadrequirements the pumped storage station will run in thecondition of power generation to supplement the remainingpart so that the larger power benefit is obtained and theoutput fluctuation is reduced

424 Optimization Results of Scheme 4 Similar to scheme3 scheme 4 is also a multiobjective optimization problemfor obtaining the maximum power benefit and the minimumvariation of load and output difference by using NSGA-II

Mathematical Problems in Engineering 7

Table 3 Results of comparison of the four schemes

Scheme Power benefit (yen) Output fluctuation(MW)

Variation of load andoutput difference (MW2)

The maximum peak-valleydifference (MW)

1 87800 1586 7733 802 125600 2362 9348 753 121440 1125 mdash 404 123200 mdash 1665 46

112000 114000 116000 118000 120000 122000 124000 12600025

20

15

10

5

0

Varia

tion

of lo

ad an

d ou

tput

diff

eren

ce (M

W2 )

Power Benefit (yen)

Inflection point

Figure 6 Noninferior solution of multiobjective optimizationmodel of scheme 4

algorithm The Pareto noninferior solution sets are obtainedfor scheme 4 as shown in Figure 6

It can be seen from Figure 6 that the results are alsosimilar to scheme 3 the objective functions 1198651 and 1198653 cannotbe maximal simultaneously Therefore choose the inflectionpoint in Figure 6 The power benefit of the system is yen123200 per day and the variation of load and output difference is1665MW2 The hourly energy dispatch value correspondingto 1 day is shown in Figure 7

In Figure 7 in the low feed-in tariff period and the highfeed-in tariff period the hourly energy dispatch value has thesame distribution laws in Figure 5

425 Comparison of the Schemes The comparison results ofthe four schemes are illustrated in Table 3

Combined with data analysis in Figures 3 4 5 6 and 7and Table 1 the following is shown

(1) Scheme 1 and Schemes 3 4 The output fluctuation and thevariation of load and output difference of the power grid arevery intense and the maximum peak-valley difference evenreaches 8 MW as the wind farm and the photovoltaic powerstation operate independently Also in the peak feed-in tariffperiod of 0700-1100 and middle peak feed-in tariff period of1100-1500 the wind farm and the photovoltaic power stationare less productive and obviously the operation benefit is nothigh

But after the pumped storage plant is added the outputfluctuation and variation of load and output difference

0 5 10 15 20 250

2

4

6

8

10

12

Output of only wind and photovoltaic powerOutput of the whole complementary operation systemOutput of pumped storage stationPumping power of the pumped storage station

Out

put (

MW

)

Time (h)

Figure 7 Multiobjective optimization results of scheme 4

of the complementary operation of the photovoltaic-wind-pumped storage system are remarkably reduced The outputfluctuation of the complementary operation system is only71 of the single operation of the photovoltaic and windpower the variation of load and output difference is only215 of the single operation of the photovoltaic and windpower and the maximum peak-valley difference is only 50of the single wind and the photovoltaic power In the peakfeed-in tariff period of 0700-1100 17 00-2100 and so onthe photovoltaic and wind power are less productive and theoperation benefit is considerably improved

(2) Scheme 2 and Schemes 3 4 With the maximum powerbenefit of the complementary operation system regardedas a single objective clearly the benefit is biggest In thesituation the output of the complementary operation systemis concentrated in the peak and middle peak feed-in tariffperiod and the low valley feed-in tariff period is less whichmakes the output fluctuation and the variation of load andoutput difference of the complementary operation systemmore intense in the whole scheduling period

In contrast as can be seen from the results of Scheme 3and Scheme 4 in Table 3 each objective hasmade certain con-cessions and achieved the optimal result of the whole benefit

8 Mathematical Problems in Engineering

which means complementary operation of the photovoltaic-wind-pumped storage system can achieve optimal outputpower in different periods by multiobjective optimization

(2) Scheme 3 and Scheme 4 In both scheme 3 and scheme4 there are economic objectives and stable objectives Theeconomic objectives of the two schemes are all power benefitbut the stable objectives are different

The results of scheme 3 reveal that the power benefitmaximization and output fluctuation minimization cannotbe achieved at the same time In contrast scheme4 is aimed atincreasing the power benefit and decreasing the variation ofload and output difference and the results not only verify therelationship between economic objective and stable objectivein scheme 3 but also reflect the power demand time-variantin the real power system

5 Conclusions

To improve the power benefit and the access capacity of pho-tovoltaic and wind power the storage function of the pumpedstorage station is used to balance the maximum benefit andthe minimum output fluctuation of the photovoltaic-wind-pumped storage system

The optimization model is established after properlydefining the economic and stable objectives and constraintsBy comparing and analyzing the four schemes the role of thepumped storage energy in the complementary operation andthe relationship of the three objectives are studied The mainresults are as follows

(i) After the pumped storage plant is added the outputfluctuation the variation of load and output differ-ence and the maximum peak-valley difference of thecomplementary operation system is only 71 2155and 50 of the single operation of the photovoltaicand wind power respectively which means that thepumped storage station can suppress the output fluc-tuation and reduce the variation of load and outputdifference of the photovoltaic-wind-pumped storagesystem

(ii) In the peak feed-in tariff period of 0700-1100 1700-2100 and so on the power benefit is notablyimproved as the pumped storage station is addedindicating that the pumped storage plant can improvethe benefit of photovoltaic and wind power

(iii) The output fluctuation and variation of load and out-put difference increase with the power benefit whichproves the interaction and competition relationshipbetween the economic and stable objectives Then acompromise point in the Pareto optimal solution setis chosen to obtain the optimal result of the wholebenefit of the system

(iv) Comparing the four schemes it is clear that thepumped storage plant has the advantage of improvingthe benefit and the access capacity of photovoltaic andwind power

At last the accuracy and the availability of the multiob-jective optimization model are proved To conclude a hybridenergy system has been modelled and the complementarymechanism of the system has been deeply discussed in thispaper

Data Availability

Theparameter data of wind farm photovoltaic power stationand pumped storage station used to support the findings ofthis study have not been made available because it is from animportant project which involves issues of confidentiality

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work has been partially supported by the Fundamen-tal Research Funds for Central Universities (Grant No2018B625X14) the Postgraduate Research amp Practice Innova-tion Program of Jiangsu Province (Grant No KYCX18 0594)the National Natural Science Foundation of China (GrantNos 51579080 51339005) the Anhui Provincial NaturalScience Foundation (Grant No 1608085ME119) and thePriority Academic Program Development of Jiangsu HigherEducation Institutions (Grant No YS11001)

References

[1] L Hirth ldquoThe benefits of flexibility The value of wind energywith hydropowerrdquo Applied Energy vol 181 pp 210ndash223 2016

[2] T Ma H Yang L Lu and J Peng ldquoPumped storage-basedstandalone photovoltaic power generation system Modelingand techno-economic optimizationrdquo Applied Energy vol 137no 1 pp 649ndash659 2015

[3] J K Kaldellis and D Zafirakis ldquoOptimum energy storagetechniques for the improvement of renewable energy sources-based electricity generation economic efficiencyrdquo Energy vol32 no 12 pp 2295ndash2305 2007

[4] A Ghasemi and M Enayatzare ldquoOptimal energy managementof a renewable-based isolated microgrid with pumped-storageunit and demand responserdquo Journal of Renewable Energy vol123 pp 460ndash474 2018

[5] H M Jiang Y Yuan X S Zhang and Z X Fu ldquoApplicationof energy storage system in mitigating the flicker resulted fromintegrated wind power generationrdquo Proceedings of the CSU-EPSA vol 25 no 2 pp 7ndash12 2013

[6] R Segurado J Madeira M Costa N Duic and M CarvalholdquoOptimization of a wind powered desalination and pumpedhydro storage systemrdquo Applied Energy vol 177 pp 487ndash4992016

[7] S V Papaefthymiou and S A Papathanassiou ldquoOptimumsizing of wind-pumped-storage hybrid power stations in islandsystemsrdquo Journal of Renewable Energy vol 64 pp 187ndash196 2014

[8] Y Luo and R H Zhang ldquoResearch of optimal scheduling ofhybridPVandwindpower systemrdquoActa Energiae Solaris Sinicavol 36 no 10 pp 2492ndash2498 2015

[9] J Schmidt R Cancella and A O Pereira ldquoAn optimal mix ofsolar PV wind and hydro power for a low-carbon electricity

Mathematical Problems in Engineering 9

supply in Brazilrdquo Journal of Renewable Energy vol 85 pp 137ndash147 2016

[10] H K Abbas R M Zablotowicz and H A Bruns ldquoModelingthe colonization of maize by toxigenic and non-toxigenicAspergillus flavus strains implications for biological controlrdquoWorld Mycotoxin Journal vol 1 no 3 pp 333ndash340 2008

[11] X Wang Y Mei Y Kong Y Lin and H Wang ldquoImprovedmulti-objective model and analysis of the coordinated opera-tion of a hydro-wind-photovoltaic systemrdquo Energy vol 134 pp813ndash839 2017

[12] N Sears ldquo5 Strategies for physician engagementrdquo HealthcareFinancial Management vol 65 no 1 pp 78ndash82 2011

[13] Z C Hu H J Ding and T Kong ldquoA joint daily operationoptimizationmodel forwindpower andpumped-storage plantrdquoAutomation of Electric Power Systems vol 36 no 2 pp 36ndash41+57 2012

[14] M G Zhang and Y Hu ldquoJoint dispatch of wind powergeneration and pumped storage with the appliance of FMOEArdquoActa Energiae Solaris Sinica vol 35 no 9 pp 1803ndash1809 2014

[15] G NottonDMistrushi L Stoyanov and P Berberi ldquoOperationof a photovoltaic-wind plant with a hydro pumping-storage forelectricity peak-shaving in an island contextrdquo Solar Energy vol157 pp 20ndash34 2017

[16] J I Perez-Dıaz and J Jimenez ldquoContribution of a pumped-storage hydropower plant to reduce the scheduling costs ofan isolated power system with high wind power penetrationrdquoEnergy vol 109 pp 92ndash104 2016

[17] N Destro M Korpas and J F Sauterleute ldquoSmoothing ofOffshore Wind Power Variations with Norwegian PumpedHydro Case Studyrdquo Energy Procedia vol 87 pp 61ndash68 2016

[18] X Wang Y Mei H Cai and X Cong ldquoA New FluctuationIndex Characteristics and Application to Hydro-Wind Sys-temsrdquo Energies vol 9 no 2 p 114 2016

[19] K Deb S Agrawal A Pratap and T Meyarivan ldquoA fast elitistnon-dominated sorting genetic algorithm for multi-objectiveoptimizationNSGA-IIrdquo inParallel Problem Solving fromNaturePPSN VI vol 1917 of Lecture Notes in Computer Science pp849ndash858 Springer Berlin Germany 2000

[20] L Chen X P Gu and JH Jia ldquoMulti-objective extended black-start schemes optimization based on virus evolution improvedNSGA-II algorithmrdquo Power System Protection and Control vol2 pp 35ndash42 2014

[21] Q Li Y Yuan Z J Li W S Wang and H Y Lu ldquoResearchon energy shifting benefits of hybrid wind power and pumpedhydro storage system considering peak-valley electricity pricerdquoPower System Technology vol 66 no 6 pp 13ndash18 2009

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

6 Mathematical Problems in Engineering

0 5 10 15 20 250

2

4

6

8

10

12

Out

put (

MW

)

Time (h)

Output of only wind and photovoltaic powerOutput of the whole complementary operation systemOutput of pumped storage stationPumping power of the pumped storage station

Figure 3 Single-objective optimization results of scheme 2

422 Optimization Results of Scheme 2 Similar to scheme1 only power benefit is considered but optimizing with thecomplementary operation in scheme 2The genetic algorithmis used to solve the single-objective optimization problemThe energy dispatch within one day of three power supplycomplementsrsquo operation is shown in Figure 3

It can be seen from Figure 3 that if only the maximumpower benefit is optimized as a single objective obviously thepower benefit is the greatest Under the circumstances theoutput of complementary operation system is concentrated inthe peak and middle peak feed-in tariff period while less inthe low valley feed-in tariff period with the output fluctuationof complementary operation system of the whole dispatchingperiod being more intense

423 Optimization Results of Scheme 3 In contrast scheme 3is a multiobjective optimization problem aimed at obtainingthemaximumpower benefit and theminimumoutput fluctu-ation and the NSGA-II algorithm is applied to simulate andanalyze the optimal scheduling model of the complementaryoperation system

According to the above algorithm steps and parametersettings the Pareto noninferior solution sets are obtained forthe optimization problems of scheme 3 as shown in Figure 4

The output fluctuation of complementary operation sys-tem increases with the power benefit as shown in Figure 4For the reason that the objective 1198651 is to obtain the maximumpower benefit and the objective 1198652 is to obtain the minimumoutput fluctuation which means the objective functions 1198651and 1198652 cannot be maximal simultaneously Thus choose acompromise point in the solution set namely the inflectionpoint in Figure 4

The power benefit of the complementary operation sys-tem is yen121 440 per day and the output fluctuation is

112000 114000 116000 118000 120000 122000 12400016

14

12

10

8

6

4

2

0

Out

put fl

uctu

atio

n (M

W)

Power benefit (yen)

Inflection point

Figure 4 Noninferior solution of multiobjective optimizationmodel of scheme 3

0 5 10 15 20 250

2

4

6

8

10

12

Out

put (

MW

)

Time (h)

Output of only wind and photovoltaic power Output of the whole complementary operation system Output of pumped storage station Pumping power of the pumped storage station

Figure 5 Multiobjective optimization results of scheme 3

1125MWThe hourly energy dispatch value corresponding to1 day is shown in Figure 5

According to Figure 5 in the low feed-in tariff periodoutput of some of the available solar and wind power isused to meet the load and the rest is for pumping andstoring energy Instead in the high feed-in tariff period theoutput of wind and the photovoltaic is relatively small whichmeans that the solar and wind power cannot meet the loadrequirements the pumped storage station will run in thecondition of power generation to supplement the remainingpart so that the larger power benefit is obtained and theoutput fluctuation is reduced

424 Optimization Results of Scheme 4 Similar to scheme3 scheme 4 is also a multiobjective optimization problemfor obtaining the maximum power benefit and the minimumvariation of load and output difference by using NSGA-II

Mathematical Problems in Engineering 7

Table 3 Results of comparison of the four schemes

Scheme Power benefit (yen) Output fluctuation(MW)

Variation of load andoutput difference (MW2)

The maximum peak-valleydifference (MW)

1 87800 1586 7733 802 125600 2362 9348 753 121440 1125 mdash 404 123200 mdash 1665 46

112000 114000 116000 118000 120000 122000 124000 12600025

20

15

10

5

0

Varia

tion

of lo

ad an

d ou

tput

diff

eren

ce (M

W2 )

Power Benefit (yen)

Inflection point

Figure 6 Noninferior solution of multiobjective optimizationmodel of scheme 4

algorithm The Pareto noninferior solution sets are obtainedfor scheme 4 as shown in Figure 6

It can be seen from Figure 6 that the results are alsosimilar to scheme 3 the objective functions 1198651 and 1198653 cannotbe maximal simultaneously Therefore choose the inflectionpoint in Figure 6 The power benefit of the system is yen123200 per day and the variation of load and output difference is1665MW2 The hourly energy dispatch value correspondingto 1 day is shown in Figure 7

In Figure 7 in the low feed-in tariff period and the highfeed-in tariff period the hourly energy dispatch value has thesame distribution laws in Figure 5

425 Comparison of the Schemes The comparison results ofthe four schemes are illustrated in Table 3

Combined with data analysis in Figures 3 4 5 6 and 7and Table 1 the following is shown

(1) Scheme 1 and Schemes 3 4 The output fluctuation and thevariation of load and output difference of the power grid arevery intense and the maximum peak-valley difference evenreaches 8 MW as the wind farm and the photovoltaic powerstation operate independently Also in the peak feed-in tariffperiod of 0700-1100 and middle peak feed-in tariff period of1100-1500 the wind farm and the photovoltaic power stationare less productive and obviously the operation benefit is nothigh

But after the pumped storage plant is added the outputfluctuation and variation of load and output difference

0 5 10 15 20 250

2

4

6

8

10

12

Output of only wind and photovoltaic powerOutput of the whole complementary operation systemOutput of pumped storage stationPumping power of the pumped storage station

Out

put (

MW

)

Time (h)

Figure 7 Multiobjective optimization results of scheme 4

of the complementary operation of the photovoltaic-wind-pumped storage system are remarkably reduced The outputfluctuation of the complementary operation system is only71 of the single operation of the photovoltaic and windpower the variation of load and output difference is only215 of the single operation of the photovoltaic and windpower and the maximum peak-valley difference is only 50of the single wind and the photovoltaic power In the peakfeed-in tariff period of 0700-1100 17 00-2100 and so onthe photovoltaic and wind power are less productive and theoperation benefit is considerably improved

(2) Scheme 2 and Schemes 3 4 With the maximum powerbenefit of the complementary operation system regardedas a single objective clearly the benefit is biggest In thesituation the output of the complementary operation systemis concentrated in the peak and middle peak feed-in tariffperiod and the low valley feed-in tariff period is less whichmakes the output fluctuation and the variation of load andoutput difference of the complementary operation systemmore intense in the whole scheduling period

In contrast as can be seen from the results of Scheme 3and Scheme 4 in Table 3 each objective hasmade certain con-cessions and achieved the optimal result of the whole benefit

8 Mathematical Problems in Engineering

which means complementary operation of the photovoltaic-wind-pumped storage system can achieve optimal outputpower in different periods by multiobjective optimization

(2) Scheme 3 and Scheme 4 In both scheme 3 and scheme4 there are economic objectives and stable objectives Theeconomic objectives of the two schemes are all power benefitbut the stable objectives are different

The results of scheme 3 reveal that the power benefitmaximization and output fluctuation minimization cannotbe achieved at the same time In contrast scheme4 is aimed atincreasing the power benefit and decreasing the variation ofload and output difference and the results not only verify therelationship between economic objective and stable objectivein scheme 3 but also reflect the power demand time-variantin the real power system

5 Conclusions

To improve the power benefit and the access capacity of pho-tovoltaic and wind power the storage function of the pumpedstorage station is used to balance the maximum benefit andthe minimum output fluctuation of the photovoltaic-wind-pumped storage system

The optimization model is established after properlydefining the economic and stable objectives and constraintsBy comparing and analyzing the four schemes the role of thepumped storage energy in the complementary operation andthe relationship of the three objectives are studied The mainresults are as follows

(i) After the pumped storage plant is added the outputfluctuation the variation of load and output differ-ence and the maximum peak-valley difference of thecomplementary operation system is only 71 2155and 50 of the single operation of the photovoltaicand wind power respectively which means that thepumped storage station can suppress the output fluc-tuation and reduce the variation of load and outputdifference of the photovoltaic-wind-pumped storagesystem

(ii) In the peak feed-in tariff period of 0700-1100 1700-2100 and so on the power benefit is notablyimproved as the pumped storage station is addedindicating that the pumped storage plant can improvethe benefit of photovoltaic and wind power

(iii) The output fluctuation and variation of load and out-put difference increase with the power benefit whichproves the interaction and competition relationshipbetween the economic and stable objectives Then acompromise point in the Pareto optimal solution setis chosen to obtain the optimal result of the wholebenefit of the system

(iv) Comparing the four schemes it is clear that thepumped storage plant has the advantage of improvingthe benefit and the access capacity of photovoltaic andwind power

At last the accuracy and the availability of the multiob-jective optimization model are proved To conclude a hybridenergy system has been modelled and the complementarymechanism of the system has been deeply discussed in thispaper

Data Availability

Theparameter data of wind farm photovoltaic power stationand pumped storage station used to support the findings ofthis study have not been made available because it is from animportant project which involves issues of confidentiality

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work has been partially supported by the Fundamen-tal Research Funds for Central Universities (Grant No2018B625X14) the Postgraduate Research amp Practice Innova-tion Program of Jiangsu Province (Grant No KYCX18 0594)the National Natural Science Foundation of China (GrantNos 51579080 51339005) the Anhui Provincial NaturalScience Foundation (Grant No 1608085ME119) and thePriority Academic Program Development of Jiangsu HigherEducation Institutions (Grant No YS11001)

References

[1] L Hirth ldquoThe benefits of flexibility The value of wind energywith hydropowerrdquo Applied Energy vol 181 pp 210ndash223 2016

[2] T Ma H Yang L Lu and J Peng ldquoPumped storage-basedstandalone photovoltaic power generation system Modelingand techno-economic optimizationrdquo Applied Energy vol 137no 1 pp 649ndash659 2015

[3] J K Kaldellis and D Zafirakis ldquoOptimum energy storagetechniques for the improvement of renewable energy sources-based electricity generation economic efficiencyrdquo Energy vol32 no 12 pp 2295ndash2305 2007

[4] A Ghasemi and M Enayatzare ldquoOptimal energy managementof a renewable-based isolated microgrid with pumped-storageunit and demand responserdquo Journal of Renewable Energy vol123 pp 460ndash474 2018

[5] H M Jiang Y Yuan X S Zhang and Z X Fu ldquoApplicationof energy storage system in mitigating the flicker resulted fromintegrated wind power generationrdquo Proceedings of the CSU-EPSA vol 25 no 2 pp 7ndash12 2013

[6] R Segurado J Madeira M Costa N Duic and M CarvalholdquoOptimization of a wind powered desalination and pumpedhydro storage systemrdquo Applied Energy vol 177 pp 487ndash4992016

[7] S V Papaefthymiou and S A Papathanassiou ldquoOptimumsizing of wind-pumped-storage hybrid power stations in islandsystemsrdquo Journal of Renewable Energy vol 64 pp 187ndash196 2014

[8] Y Luo and R H Zhang ldquoResearch of optimal scheduling ofhybridPVandwindpower systemrdquoActa Energiae Solaris Sinicavol 36 no 10 pp 2492ndash2498 2015

[9] J Schmidt R Cancella and A O Pereira ldquoAn optimal mix ofsolar PV wind and hydro power for a low-carbon electricity

Mathematical Problems in Engineering 9

supply in Brazilrdquo Journal of Renewable Energy vol 85 pp 137ndash147 2016

[10] H K Abbas R M Zablotowicz and H A Bruns ldquoModelingthe colonization of maize by toxigenic and non-toxigenicAspergillus flavus strains implications for biological controlrdquoWorld Mycotoxin Journal vol 1 no 3 pp 333ndash340 2008

[11] X Wang Y Mei Y Kong Y Lin and H Wang ldquoImprovedmulti-objective model and analysis of the coordinated opera-tion of a hydro-wind-photovoltaic systemrdquo Energy vol 134 pp813ndash839 2017

[12] N Sears ldquo5 Strategies for physician engagementrdquo HealthcareFinancial Management vol 65 no 1 pp 78ndash82 2011

[13] Z C Hu H J Ding and T Kong ldquoA joint daily operationoptimizationmodel forwindpower andpumped-storage plantrdquoAutomation of Electric Power Systems vol 36 no 2 pp 36ndash41+57 2012

[14] M G Zhang and Y Hu ldquoJoint dispatch of wind powergeneration and pumped storage with the appliance of FMOEArdquoActa Energiae Solaris Sinica vol 35 no 9 pp 1803ndash1809 2014

[15] G NottonDMistrushi L Stoyanov and P Berberi ldquoOperationof a photovoltaic-wind plant with a hydro pumping-storage forelectricity peak-shaving in an island contextrdquo Solar Energy vol157 pp 20ndash34 2017

[16] J I Perez-Dıaz and J Jimenez ldquoContribution of a pumped-storage hydropower plant to reduce the scheduling costs ofan isolated power system with high wind power penetrationrdquoEnergy vol 109 pp 92ndash104 2016

[17] N Destro M Korpas and J F Sauterleute ldquoSmoothing ofOffshore Wind Power Variations with Norwegian PumpedHydro Case Studyrdquo Energy Procedia vol 87 pp 61ndash68 2016

[18] X Wang Y Mei H Cai and X Cong ldquoA New FluctuationIndex Characteristics and Application to Hydro-Wind Sys-temsrdquo Energies vol 9 no 2 p 114 2016

[19] K Deb S Agrawal A Pratap and T Meyarivan ldquoA fast elitistnon-dominated sorting genetic algorithm for multi-objectiveoptimizationNSGA-IIrdquo inParallel Problem Solving fromNaturePPSN VI vol 1917 of Lecture Notes in Computer Science pp849ndash858 Springer Berlin Germany 2000

[20] L Chen X P Gu and JH Jia ldquoMulti-objective extended black-start schemes optimization based on virus evolution improvedNSGA-II algorithmrdquo Power System Protection and Control vol2 pp 35ndash42 2014

[21] Q Li Y Yuan Z J Li W S Wang and H Y Lu ldquoResearchon energy shifting benefits of hybrid wind power and pumpedhydro storage system considering peak-valley electricity pricerdquoPower System Technology vol 66 no 6 pp 13ndash18 2009

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 7

Table 3 Results of comparison of the four schemes

Scheme Power benefit (yen) Output fluctuation(MW)

Variation of load andoutput difference (MW2)

The maximum peak-valleydifference (MW)

1 87800 1586 7733 802 125600 2362 9348 753 121440 1125 mdash 404 123200 mdash 1665 46

112000 114000 116000 118000 120000 122000 124000 12600025

20

15

10

5

0

Varia

tion

of lo

ad an

d ou

tput

diff

eren

ce (M

W2 )

Power Benefit (yen)

Inflection point

Figure 6 Noninferior solution of multiobjective optimizationmodel of scheme 4

algorithm The Pareto noninferior solution sets are obtainedfor scheme 4 as shown in Figure 6

It can be seen from Figure 6 that the results are alsosimilar to scheme 3 the objective functions 1198651 and 1198653 cannotbe maximal simultaneously Therefore choose the inflectionpoint in Figure 6 The power benefit of the system is yen123200 per day and the variation of load and output difference is1665MW2 The hourly energy dispatch value correspondingto 1 day is shown in Figure 7

In Figure 7 in the low feed-in tariff period and the highfeed-in tariff period the hourly energy dispatch value has thesame distribution laws in Figure 5

425 Comparison of the Schemes The comparison results ofthe four schemes are illustrated in Table 3

Combined with data analysis in Figures 3 4 5 6 and 7and Table 1 the following is shown

(1) Scheme 1 and Schemes 3 4 The output fluctuation and thevariation of load and output difference of the power grid arevery intense and the maximum peak-valley difference evenreaches 8 MW as the wind farm and the photovoltaic powerstation operate independently Also in the peak feed-in tariffperiod of 0700-1100 and middle peak feed-in tariff period of1100-1500 the wind farm and the photovoltaic power stationare less productive and obviously the operation benefit is nothigh

But after the pumped storage plant is added the outputfluctuation and variation of load and output difference

0 5 10 15 20 250

2

4

6

8

10

12

Output of only wind and photovoltaic powerOutput of the whole complementary operation systemOutput of pumped storage stationPumping power of the pumped storage station

Out

put (

MW

)

Time (h)

Figure 7 Multiobjective optimization results of scheme 4

of the complementary operation of the photovoltaic-wind-pumped storage system are remarkably reduced The outputfluctuation of the complementary operation system is only71 of the single operation of the photovoltaic and windpower the variation of load and output difference is only215 of the single operation of the photovoltaic and windpower and the maximum peak-valley difference is only 50of the single wind and the photovoltaic power In the peakfeed-in tariff period of 0700-1100 17 00-2100 and so onthe photovoltaic and wind power are less productive and theoperation benefit is considerably improved

(2) Scheme 2 and Schemes 3 4 With the maximum powerbenefit of the complementary operation system regardedas a single objective clearly the benefit is biggest In thesituation the output of the complementary operation systemis concentrated in the peak and middle peak feed-in tariffperiod and the low valley feed-in tariff period is less whichmakes the output fluctuation and the variation of load andoutput difference of the complementary operation systemmore intense in the whole scheduling period

In contrast as can be seen from the results of Scheme 3and Scheme 4 in Table 3 each objective hasmade certain con-cessions and achieved the optimal result of the whole benefit

8 Mathematical Problems in Engineering

which means complementary operation of the photovoltaic-wind-pumped storage system can achieve optimal outputpower in different periods by multiobjective optimization

(2) Scheme 3 and Scheme 4 In both scheme 3 and scheme4 there are economic objectives and stable objectives Theeconomic objectives of the two schemes are all power benefitbut the stable objectives are different

The results of scheme 3 reveal that the power benefitmaximization and output fluctuation minimization cannotbe achieved at the same time In contrast scheme4 is aimed atincreasing the power benefit and decreasing the variation ofload and output difference and the results not only verify therelationship between economic objective and stable objectivein scheme 3 but also reflect the power demand time-variantin the real power system

5 Conclusions

To improve the power benefit and the access capacity of pho-tovoltaic and wind power the storage function of the pumpedstorage station is used to balance the maximum benefit andthe minimum output fluctuation of the photovoltaic-wind-pumped storage system

The optimization model is established after properlydefining the economic and stable objectives and constraintsBy comparing and analyzing the four schemes the role of thepumped storage energy in the complementary operation andthe relationship of the three objectives are studied The mainresults are as follows

(i) After the pumped storage plant is added the outputfluctuation the variation of load and output differ-ence and the maximum peak-valley difference of thecomplementary operation system is only 71 2155and 50 of the single operation of the photovoltaicand wind power respectively which means that thepumped storage station can suppress the output fluc-tuation and reduce the variation of load and outputdifference of the photovoltaic-wind-pumped storagesystem

(ii) In the peak feed-in tariff period of 0700-1100 1700-2100 and so on the power benefit is notablyimproved as the pumped storage station is addedindicating that the pumped storage plant can improvethe benefit of photovoltaic and wind power

(iii) The output fluctuation and variation of load and out-put difference increase with the power benefit whichproves the interaction and competition relationshipbetween the economic and stable objectives Then acompromise point in the Pareto optimal solution setis chosen to obtain the optimal result of the wholebenefit of the system

(iv) Comparing the four schemes it is clear that thepumped storage plant has the advantage of improvingthe benefit and the access capacity of photovoltaic andwind power

At last the accuracy and the availability of the multiob-jective optimization model are proved To conclude a hybridenergy system has been modelled and the complementarymechanism of the system has been deeply discussed in thispaper

Data Availability

Theparameter data of wind farm photovoltaic power stationand pumped storage station used to support the findings ofthis study have not been made available because it is from animportant project which involves issues of confidentiality

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work has been partially supported by the Fundamen-tal Research Funds for Central Universities (Grant No2018B625X14) the Postgraduate Research amp Practice Innova-tion Program of Jiangsu Province (Grant No KYCX18 0594)the National Natural Science Foundation of China (GrantNos 51579080 51339005) the Anhui Provincial NaturalScience Foundation (Grant No 1608085ME119) and thePriority Academic Program Development of Jiangsu HigherEducation Institutions (Grant No YS11001)

References

[1] L Hirth ldquoThe benefits of flexibility The value of wind energywith hydropowerrdquo Applied Energy vol 181 pp 210ndash223 2016

[2] T Ma H Yang L Lu and J Peng ldquoPumped storage-basedstandalone photovoltaic power generation system Modelingand techno-economic optimizationrdquo Applied Energy vol 137no 1 pp 649ndash659 2015

[3] J K Kaldellis and D Zafirakis ldquoOptimum energy storagetechniques for the improvement of renewable energy sources-based electricity generation economic efficiencyrdquo Energy vol32 no 12 pp 2295ndash2305 2007

[4] A Ghasemi and M Enayatzare ldquoOptimal energy managementof a renewable-based isolated microgrid with pumped-storageunit and demand responserdquo Journal of Renewable Energy vol123 pp 460ndash474 2018

[5] H M Jiang Y Yuan X S Zhang and Z X Fu ldquoApplicationof energy storage system in mitigating the flicker resulted fromintegrated wind power generationrdquo Proceedings of the CSU-EPSA vol 25 no 2 pp 7ndash12 2013

[6] R Segurado J Madeira M Costa N Duic and M CarvalholdquoOptimization of a wind powered desalination and pumpedhydro storage systemrdquo Applied Energy vol 177 pp 487ndash4992016

[7] S V Papaefthymiou and S A Papathanassiou ldquoOptimumsizing of wind-pumped-storage hybrid power stations in islandsystemsrdquo Journal of Renewable Energy vol 64 pp 187ndash196 2014

[8] Y Luo and R H Zhang ldquoResearch of optimal scheduling ofhybridPVandwindpower systemrdquoActa Energiae Solaris Sinicavol 36 no 10 pp 2492ndash2498 2015

[9] J Schmidt R Cancella and A O Pereira ldquoAn optimal mix ofsolar PV wind and hydro power for a low-carbon electricity

Mathematical Problems in Engineering 9

supply in Brazilrdquo Journal of Renewable Energy vol 85 pp 137ndash147 2016

[10] H K Abbas R M Zablotowicz and H A Bruns ldquoModelingthe colonization of maize by toxigenic and non-toxigenicAspergillus flavus strains implications for biological controlrdquoWorld Mycotoxin Journal vol 1 no 3 pp 333ndash340 2008

[11] X Wang Y Mei Y Kong Y Lin and H Wang ldquoImprovedmulti-objective model and analysis of the coordinated opera-tion of a hydro-wind-photovoltaic systemrdquo Energy vol 134 pp813ndash839 2017

[12] N Sears ldquo5 Strategies for physician engagementrdquo HealthcareFinancial Management vol 65 no 1 pp 78ndash82 2011

[13] Z C Hu H J Ding and T Kong ldquoA joint daily operationoptimizationmodel forwindpower andpumped-storage plantrdquoAutomation of Electric Power Systems vol 36 no 2 pp 36ndash41+57 2012

[14] M G Zhang and Y Hu ldquoJoint dispatch of wind powergeneration and pumped storage with the appliance of FMOEArdquoActa Energiae Solaris Sinica vol 35 no 9 pp 1803ndash1809 2014

[15] G NottonDMistrushi L Stoyanov and P Berberi ldquoOperationof a photovoltaic-wind plant with a hydro pumping-storage forelectricity peak-shaving in an island contextrdquo Solar Energy vol157 pp 20ndash34 2017

[16] J I Perez-Dıaz and J Jimenez ldquoContribution of a pumped-storage hydropower plant to reduce the scheduling costs ofan isolated power system with high wind power penetrationrdquoEnergy vol 109 pp 92ndash104 2016

[17] N Destro M Korpas and J F Sauterleute ldquoSmoothing ofOffshore Wind Power Variations with Norwegian PumpedHydro Case Studyrdquo Energy Procedia vol 87 pp 61ndash68 2016

[18] X Wang Y Mei H Cai and X Cong ldquoA New FluctuationIndex Characteristics and Application to Hydro-Wind Sys-temsrdquo Energies vol 9 no 2 p 114 2016

[19] K Deb S Agrawal A Pratap and T Meyarivan ldquoA fast elitistnon-dominated sorting genetic algorithm for multi-objectiveoptimizationNSGA-IIrdquo inParallel Problem Solving fromNaturePPSN VI vol 1917 of Lecture Notes in Computer Science pp849ndash858 Springer Berlin Germany 2000

[20] L Chen X P Gu and JH Jia ldquoMulti-objective extended black-start schemes optimization based on virus evolution improvedNSGA-II algorithmrdquo Power System Protection and Control vol2 pp 35ndash42 2014

[21] Q Li Y Yuan Z J Li W S Wang and H Y Lu ldquoResearchon energy shifting benefits of hybrid wind power and pumpedhydro storage system considering peak-valley electricity pricerdquoPower System Technology vol 66 no 6 pp 13ndash18 2009

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

8 Mathematical Problems in Engineering

which means complementary operation of the photovoltaic-wind-pumped storage system can achieve optimal outputpower in different periods by multiobjective optimization

(2) Scheme 3 and Scheme 4 In both scheme 3 and scheme4 there are economic objectives and stable objectives Theeconomic objectives of the two schemes are all power benefitbut the stable objectives are different

The results of scheme 3 reveal that the power benefitmaximization and output fluctuation minimization cannotbe achieved at the same time In contrast scheme4 is aimed atincreasing the power benefit and decreasing the variation ofload and output difference and the results not only verify therelationship between economic objective and stable objectivein scheme 3 but also reflect the power demand time-variantin the real power system

5 Conclusions

To improve the power benefit and the access capacity of pho-tovoltaic and wind power the storage function of the pumpedstorage station is used to balance the maximum benefit andthe minimum output fluctuation of the photovoltaic-wind-pumped storage system

The optimization model is established after properlydefining the economic and stable objectives and constraintsBy comparing and analyzing the four schemes the role of thepumped storage energy in the complementary operation andthe relationship of the three objectives are studied The mainresults are as follows

(i) After the pumped storage plant is added the outputfluctuation the variation of load and output differ-ence and the maximum peak-valley difference of thecomplementary operation system is only 71 2155and 50 of the single operation of the photovoltaicand wind power respectively which means that thepumped storage station can suppress the output fluc-tuation and reduce the variation of load and outputdifference of the photovoltaic-wind-pumped storagesystem

(ii) In the peak feed-in tariff period of 0700-1100 1700-2100 and so on the power benefit is notablyimproved as the pumped storage station is addedindicating that the pumped storage plant can improvethe benefit of photovoltaic and wind power

(iii) The output fluctuation and variation of load and out-put difference increase with the power benefit whichproves the interaction and competition relationshipbetween the economic and stable objectives Then acompromise point in the Pareto optimal solution setis chosen to obtain the optimal result of the wholebenefit of the system

(iv) Comparing the four schemes it is clear that thepumped storage plant has the advantage of improvingthe benefit and the access capacity of photovoltaic andwind power

At last the accuracy and the availability of the multiob-jective optimization model are proved To conclude a hybridenergy system has been modelled and the complementarymechanism of the system has been deeply discussed in thispaper

Data Availability

Theparameter data of wind farm photovoltaic power stationand pumped storage station used to support the findings ofthis study have not been made available because it is from animportant project which involves issues of confidentiality

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work has been partially supported by the Fundamen-tal Research Funds for Central Universities (Grant No2018B625X14) the Postgraduate Research amp Practice Innova-tion Program of Jiangsu Province (Grant No KYCX18 0594)the National Natural Science Foundation of China (GrantNos 51579080 51339005) the Anhui Provincial NaturalScience Foundation (Grant No 1608085ME119) and thePriority Academic Program Development of Jiangsu HigherEducation Institutions (Grant No YS11001)

References

[1] L Hirth ldquoThe benefits of flexibility The value of wind energywith hydropowerrdquo Applied Energy vol 181 pp 210ndash223 2016

[2] T Ma H Yang L Lu and J Peng ldquoPumped storage-basedstandalone photovoltaic power generation system Modelingand techno-economic optimizationrdquo Applied Energy vol 137no 1 pp 649ndash659 2015

[3] J K Kaldellis and D Zafirakis ldquoOptimum energy storagetechniques for the improvement of renewable energy sources-based electricity generation economic efficiencyrdquo Energy vol32 no 12 pp 2295ndash2305 2007

[4] A Ghasemi and M Enayatzare ldquoOptimal energy managementof a renewable-based isolated microgrid with pumped-storageunit and demand responserdquo Journal of Renewable Energy vol123 pp 460ndash474 2018

[5] H M Jiang Y Yuan X S Zhang and Z X Fu ldquoApplicationof energy storage system in mitigating the flicker resulted fromintegrated wind power generationrdquo Proceedings of the CSU-EPSA vol 25 no 2 pp 7ndash12 2013

[6] R Segurado J Madeira M Costa N Duic and M CarvalholdquoOptimization of a wind powered desalination and pumpedhydro storage systemrdquo Applied Energy vol 177 pp 487ndash4992016

[7] S V Papaefthymiou and S A Papathanassiou ldquoOptimumsizing of wind-pumped-storage hybrid power stations in islandsystemsrdquo Journal of Renewable Energy vol 64 pp 187ndash196 2014

[8] Y Luo and R H Zhang ldquoResearch of optimal scheduling ofhybridPVandwindpower systemrdquoActa Energiae Solaris Sinicavol 36 no 10 pp 2492ndash2498 2015

[9] J Schmidt R Cancella and A O Pereira ldquoAn optimal mix ofsolar PV wind and hydro power for a low-carbon electricity

Mathematical Problems in Engineering 9

supply in Brazilrdquo Journal of Renewable Energy vol 85 pp 137ndash147 2016

[10] H K Abbas R M Zablotowicz and H A Bruns ldquoModelingthe colonization of maize by toxigenic and non-toxigenicAspergillus flavus strains implications for biological controlrdquoWorld Mycotoxin Journal vol 1 no 3 pp 333ndash340 2008

[11] X Wang Y Mei Y Kong Y Lin and H Wang ldquoImprovedmulti-objective model and analysis of the coordinated opera-tion of a hydro-wind-photovoltaic systemrdquo Energy vol 134 pp813ndash839 2017

[12] N Sears ldquo5 Strategies for physician engagementrdquo HealthcareFinancial Management vol 65 no 1 pp 78ndash82 2011

[13] Z C Hu H J Ding and T Kong ldquoA joint daily operationoptimizationmodel forwindpower andpumped-storage plantrdquoAutomation of Electric Power Systems vol 36 no 2 pp 36ndash41+57 2012

[14] M G Zhang and Y Hu ldquoJoint dispatch of wind powergeneration and pumped storage with the appliance of FMOEArdquoActa Energiae Solaris Sinica vol 35 no 9 pp 1803ndash1809 2014

[15] G NottonDMistrushi L Stoyanov and P Berberi ldquoOperationof a photovoltaic-wind plant with a hydro pumping-storage forelectricity peak-shaving in an island contextrdquo Solar Energy vol157 pp 20ndash34 2017

[16] J I Perez-Dıaz and J Jimenez ldquoContribution of a pumped-storage hydropower plant to reduce the scheduling costs ofan isolated power system with high wind power penetrationrdquoEnergy vol 109 pp 92ndash104 2016

[17] N Destro M Korpas and J F Sauterleute ldquoSmoothing ofOffshore Wind Power Variations with Norwegian PumpedHydro Case Studyrdquo Energy Procedia vol 87 pp 61ndash68 2016

[18] X Wang Y Mei H Cai and X Cong ldquoA New FluctuationIndex Characteristics and Application to Hydro-Wind Sys-temsrdquo Energies vol 9 no 2 p 114 2016

[19] K Deb S Agrawal A Pratap and T Meyarivan ldquoA fast elitistnon-dominated sorting genetic algorithm for multi-objectiveoptimizationNSGA-IIrdquo inParallel Problem Solving fromNaturePPSN VI vol 1917 of Lecture Notes in Computer Science pp849ndash858 Springer Berlin Germany 2000

[20] L Chen X P Gu and JH Jia ldquoMulti-objective extended black-start schemes optimization based on virus evolution improvedNSGA-II algorithmrdquo Power System Protection and Control vol2 pp 35ndash42 2014

[21] Q Li Y Yuan Z J Li W S Wang and H Y Lu ldquoResearchon energy shifting benefits of hybrid wind power and pumpedhydro storage system considering peak-valley electricity pricerdquoPower System Technology vol 66 no 6 pp 13ndash18 2009

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 9

supply in Brazilrdquo Journal of Renewable Energy vol 85 pp 137ndash147 2016

[10] H K Abbas R M Zablotowicz and H A Bruns ldquoModelingthe colonization of maize by toxigenic and non-toxigenicAspergillus flavus strains implications for biological controlrdquoWorld Mycotoxin Journal vol 1 no 3 pp 333ndash340 2008

[11] X Wang Y Mei Y Kong Y Lin and H Wang ldquoImprovedmulti-objective model and analysis of the coordinated opera-tion of a hydro-wind-photovoltaic systemrdquo Energy vol 134 pp813ndash839 2017

[12] N Sears ldquo5 Strategies for physician engagementrdquo HealthcareFinancial Management vol 65 no 1 pp 78ndash82 2011

[13] Z C Hu H J Ding and T Kong ldquoA joint daily operationoptimizationmodel forwindpower andpumped-storage plantrdquoAutomation of Electric Power Systems vol 36 no 2 pp 36ndash41+57 2012

[14] M G Zhang and Y Hu ldquoJoint dispatch of wind powergeneration and pumped storage with the appliance of FMOEArdquoActa Energiae Solaris Sinica vol 35 no 9 pp 1803ndash1809 2014

[15] G NottonDMistrushi L Stoyanov and P Berberi ldquoOperationof a photovoltaic-wind plant with a hydro pumping-storage forelectricity peak-shaving in an island contextrdquo Solar Energy vol157 pp 20ndash34 2017

[16] J I Perez-Dıaz and J Jimenez ldquoContribution of a pumped-storage hydropower plant to reduce the scheduling costs ofan isolated power system with high wind power penetrationrdquoEnergy vol 109 pp 92ndash104 2016

[17] N Destro M Korpas and J F Sauterleute ldquoSmoothing ofOffshore Wind Power Variations with Norwegian PumpedHydro Case Studyrdquo Energy Procedia vol 87 pp 61ndash68 2016

[18] X Wang Y Mei H Cai and X Cong ldquoA New FluctuationIndex Characteristics and Application to Hydro-Wind Sys-temsrdquo Energies vol 9 no 2 p 114 2016

[19] K Deb S Agrawal A Pratap and T Meyarivan ldquoA fast elitistnon-dominated sorting genetic algorithm for multi-objectiveoptimizationNSGA-IIrdquo inParallel Problem Solving fromNaturePPSN VI vol 1917 of Lecture Notes in Computer Science pp849ndash858 Springer Berlin Germany 2000

[20] L Chen X P Gu and JH Jia ldquoMulti-objective extended black-start schemes optimization based on virus evolution improvedNSGA-II algorithmrdquo Power System Protection and Control vol2 pp 35ndash42 2014

[21] Q Li Y Yuan Z J Li W S Wang and H Y Lu ldquoResearchon energy shifting benefits of hybrid wind power and pumpedhydro storage system considering peak-valley electricity pricerdquoPower System Technology vol 66 no 6 pp 13ndash18 2009

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom