Research ArticleA Hybrid Dynamical Modelling and Control Approach forEnergy Saving of Central Air Conditioning

Yan Zhang 12 Yongqiang Liu 1 and Yang Liu 1

1School of Electric Power South China University of Technology Guangzhou Guangdong China2Faculty of Development and Educational Technology Centre Guangdong University of Finance and EconomicsGuangzhou Guangdong China

Correspondence should be addressed to Yang Liu ly96mailscuteducn

Received 1 February 2018 Revised 7 June 2018 Accepted 14 June 2018 Published 8 July 2018

Academic Editor Bin Jiang

Copyright copy 2018 Yan Zhang 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

Currently in China energy conservation and emission reduction are important initiatives for society Because of its largeproportion of building energy consumption several methods for building energy conservation have been introduced for centralair conditioning This paper presents a hybrid system for a modelling and control approach By analysing the cooling capacitytransfer process and the electromagnetic properties of pumps the modelling is performed in a hybrid system frameworkPumps are classified as fixed-frequency pumps variable-frequency pumps and switchable pumps a switch control strategyis used in the chilled water system for supplying cooling capacity In order to adjust indoor temperature and save electricalenergy the cooling capacity allocation and average temperature methods are presented which satisfy the goal of optimalcontrol of real-time energy consumption As a numerical example the temperature variation and cold regulation processesare simulated Three rooms are the control objects that lower the setting points and pumps waste as little electrical energy aspossible The results show 494 of water pump power consumption when compared with constant water volume technologyThe modelling and control approach is more advantageous in ensuring the success of reconstruction projects for central airconditioning

1 Introduction

Currently China is facing a series of ecological problemssuch as climate change environmental degradation andincreases in energy consumption According to the ldquoChinaStatistical Yearbook 2015rdquo the levels of energy utilizationand features of energy consumption remain in a backwardpredicament of high energy consumption low efficiencyand serious waste In 2013 for example the average powerconsumption was 1485 million kWh every day and thetransfer efficiency was 4312 [1] These statistical data showthe extensive form of Chinese development which is fardifferent from that of developed countries Recently theChinese government has made unflinching efforts to buildan environmentally friendly society certainly the concepts ofenergy conservation and emission reduction have informedpolicy orientation

Central air conditioning accounts for a great proportionof building energy consumption and has considerable oppor-tunities for energy conservation and emission reductionThus research on energy savings for central air conditioninghas a significant impact There are several methods forbuilding energy conservation manual dispatching basedon management view optimized control schemes based onsample statistics and technical renovation based on variablewaterair volume In the perspective of management Lianget al [2] pointed out the ldquoreasonable energy consumptionstandardrdquo and ldquodifferentiation of buildingsrdquo The conceptsof ldquopriority buildingsrdquo and ldquobenchmarking buildingsrdquo wereproposed By evaluation and supervision an operating planis made for saving energy Fong et al [3] used an approachof evolutionary programming for energy management Theexisting operational settings can be improved by suggestingoptimized information Kecebas and Yabanova [4] studied

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 6389438 12 pageshttpsdoiorg10115520186389438

2 Mathematical Problems in Engineering

exergy efficiencies of district heating systems by using anartificial neural network technique Using average weeklydata the performance and characteristics are predicted Inaddition ambient temperature and flow rates are the mainfactors in thermal optimizationThese are extensivemeasureswith conspicuous disadvantages Manual dispatching relieson the experience and subjectivity of operators and lacksaccuracy According to the day season climatic characteris-tics and other factors the method of the optimized controlscheme satisfies the requirements to some extent but is notsuited for changes of some random loads and thus lacks in-time adjustment

Because of uncertain cold loading variable waterairvolume has the advantages of instantaneous adjustment ofcooling capacity and energy consumption Compared withbuilding a new system technical innovation avoids massivecost and long projects Moreover in the air conditioningsystem up to 70 of the power consumption is due to pumpsand fans [5] Obviously in renewal projects pumps and fanshave great potential for energy savings

Many investigation reports in the literature show thatvariable water volume technology is a current focus inour research There are several optimization methods thatcan effectively address these problems These methods arethe analytical approach [6ndash9] direct search method [10]linear quadratic programming [11] nonlinear programmingmethod [12] heuristic optimization algorithm [3 13 14] andartificial neural networks [15] Kaya et al [6] analysed theinfluence factors of the effectiveness in pumps and presentedan approach for improvement By using measured datathe potential energy saving opportunities investment costsand payback periods are calculated Lu et al [7] providedsome formulation and analysis based on global optimizationtechnologies towards overall heating ventilation and airconditioning (HVAC) systems For new urban developmentChow et al [8] predicted thermal demands and outlinedan energy modelling methodology and decision approachto derive the most desirable scheme for a given projectSheng and Duanmu [9] presented electricity consumptionand economic analyses Lu et al [13] andNassif et al [14] useda genetic algorithm to optimize the models of components inHVAC systems Fong et al [3] adopted a robust evolutionaryalgorithm for system optimization

Control strategies include temperature difference andpressure difference control methods Wang and Burnett [16]developed an online control strategy to optimize the speed ofvariable-speed condenser cooling water pumps by adjustingthe pressure set point The adaptive strategy is used toidentify the parameters with sampling at each step Zhao etal [5] focused on extreme value analysis for parallel variable-frequency hydraulic pumps in central air conditioning sys-tems He used a variable differential pressure set point controlstrategy to respond to fast load variations and exploredthe optimal number of operating units of parallel variable-frequency pumps This method obtains electricity savingsof 158 and 4 compared with a single-pump operationscheme and dual-pump operation scheme respectively

Moreover some experimental and applicable results showadvantages towards the method of technical renovation

Anderson et al [17] built an experimental system for HVACcontrol and obtained some ideal results Qu et al [18]proposed a multilayer feed-forward artificial neural networkbased on a Back Propagation (BP) algorithm and used MAT-LAB implements to design and train an energy consumptionprediction model of a micro urban building Lu et al [19]proposed an optimization plan in building sections Forengineering applications there are persuasive architectures inHong Kong [20 21] and Da Lian [22]

In these studies pure continuous or discrete controlsystems are used for the control of the entire air conditioningsystem However the constant frequency pumps variable-frequency pumps and switching pumps in the chilled watersystem constitute a hybrid systemThe frequency conversionoperation and switching action of the pumps reflect thecontinuous and discrete dynamics respectively Thereforethe methods can hardly reflect the accuracy and applicabilityof the system structure and control process nor an idealenergy saving effect In addition the electromagnetic prop-erties of pumps are elided normally although the hydraulicand thermodynamic characteristics are considered Becausethe mathematical model of a pump motor is a high-ordernonlinear multivariable system with strong coupling effectsthe variable-frequency quadratic regression empirical for-mulas or simple proportional expressions cannot reflect thedynamics of motor appropriately Compared with the pres-sure difference control strategy the temperature differencecontrol method is superior in energy saving

In this paper a hybrid model was used in the modellingof the chilled water system in a central air conditioningsystem Variable-frequency pumps and switchable pumpsdenote continuous and discrete control inputs respectivelyBased on the model a hybrid dynamical control strategywas proposed for variable volume control and better energysaving performance This model reflects the actual work-ing conditions of central air conditioning water systemsespecially in aspects of pump movement and water flowchange characteristics Problems such as time variabilitymultivariable nonlinearity and uncertainty are consideredand the energy saving performance of the proposed controlmethod is exhibited

The modelling and controlling of the system are shownas follows first an optimized pump model of speed adjust-ment based on vector control was developed which preferselectromagnetic properties and the torque response effect Inaddition considering the load characteristics of thewater sys-tem we regulate the water volume of pumps by vector controlinstantaneously Second the cooling capacity transfer processis described with thermodynamic properties throughout theframework The measure of constant temperature differenceis used in the model Third we use switching controlstrategy cooling capacity allocation and average temperaturemethods in order to obtain the hybrid dynamical propertyby volume adjusting and pump switching (onoff) Thuswe not only realise variable volume control but also satisfythe energy saving requirement Finally a numerical exampleillustrates the control process and situation of energy savings

This paper is organized as follows In Section 2 themathematical description of hybrid system is presented

Mathematical Problems in Engineering 3

fresh air

cold air

room(temperature

Inside)

latentheat

Inside

M

M

evaporator

pumps

air conditioningunit

chilledwaterCycle

mixed air

random heat of occupantsand equipment

Chilled water system Air system

heat transferfrom building structure

Figure 1 Cooling capacity transfer and temperature change processes

In Section 3 hybrid system modelling of cooling capacitytransfer process between water system and wind system isexpressed In Section 4 the hybrid dynamical control strategyused in energy saving for chilled water system is presentedIn Section 5 a simulation example is given to illustrate themodelling and control processes Section 6 concludes thepaper

2 Mathematical Description of Hybrid System

The hybrid system is described by

120590119894(120591) = 119860 119894119909 (120591) + 119861119894119906 (120591) + 119891119894 (1a)

119910119894 = 119862119894119909 (120591) (1b)

for

[119909119894119906119894] isin 119883119894 (2)

where 119909119894 isin 119877119899 denotes state variables 119906119894 isin 119877119898 denotescontrol variables f i denotes constant vector and 119910119894 denotesoutput Ai and Ci are state matrices Bi is input matrix⋃119899119894=0119883119894 are convex polyhedra in the input+state space and119883119894 cap 119883119895 = denotes possibly being unbounded by each

other119883119894 implies the ith subsystem and 119894 = 0 1 119873 implies119873 + 1 subsystems ⋃119899119894=0119883119894 = 119883 implies that all subsystems

constitute the whole system 120590119894(120591) 120591 isin [0 +infin) denotesthe switching law of the hybrid system Several differentialor difference equations as subsystems constitute a hybridsystem and they obey the switching law The law decidesthe key issues such as switching time switching state andswitching orientation The system switches among the119873 + 1subsystems and selects only one at any time

3 Modelling the Framework ofthe Cooling Capacity Transfer andTemperature Change Processes

In the air conditioning system the cooling capacity transfersfrom chiller unit to chilled water system by evaporator Thepumps drive water as cycle in the chilled water system andsend cooling capacity to air condition unit for exchangingfrom chilled water system to air system After mixing withfresh air the cold air is sent to air conditioning room todrop the temperature In the process of temperature changein air conditioning room the heat balance is influencedby several aspects cold air random heat of occupants andequipment latent heat inside and heat transfer from buildingstructure The processes of the cooling capacity transfer andtemperature change is shown in Figure 1

This paper uses constant air volume and variable watervolumeconstant temperature differencemeasures to transfercooling capacity In chilled water system switching andvariable-frequency behaviours of pumps adjust the flow forsaving energy which denote the discrete and continuous timeprocess respectively So we give an equation to show the heatbalance as follows

119862119886119898119886

119889120579119889120591 = minus120576119862119908Δ120579 (119902119887 + 119902119866 + 119896119902119904119908)

minus (1 minus 119877119903) 119902119904119886119862119886120579 + (1 minus 119877119903) 119902119904119886119862119886120579119900119906119905+ 119876119903119889 + 119876119902119903 minussum119870119895119860119895120579 +sum119870119895119860119895120579119895

(3)

On the left side of the equation 119862119886119898119886(119889120579119889120591) means thetime differential of the heat capacity of a room On the leftside of the equation minus120576119862119908Δ120579(119902119887 + 119902119866 + 119896119902119904119908) means thecooling capacity for chilled water system minus(1 minus 119877119903)119902119904119886119862119886120579and (1 minus 119877119903)119902119904119886119862119886120579119900119906119905 mean the cooling capacity from returnand fresh air systems respectively 119876119903119889 means random heatof occupants and equipment 119876119902119903 means latent heat inside

4 Mathematical Problems in Engineering

minussum119870119895119860119895120579 + sum119870119895119860119895120579119895 means heat transfer from buildingstructure

The description of the symbol can be seen in the subse-quent chapters and in Nomenclature

Towards motor model of variable-frequency pump weuse a direct torque control model to build and designthe closed-loop control of torque and flux linkage but forconstant frequency pump we use constant to describe it Bybuilding relationship of torquewithwater flowvolumewe getequations of state space for the whole process of the model atlast

31 Modelling the Cooling Capacity Transfer Process It isknown that the cold load of central air conditioning isaffected by factors such as the structure and materials ofa building outdoor weather parameters indoor lightingradiating equipment and number of occupants In order todescribe the dynamic process we consider the area 119860 119894 andtemperature 120579119894 of walls windows and roof according to thedifferent materials and use the heat transfer coefficient 119870119894accordingly We use 119876119903119889 to indicate the random changingheat by equipment and people The supply air carries coolingcapacity inside the building to balance the heat

The dynamic thermal balance equation in a room is

119862119886119898119886

119889120579119889120591 = 119902sa119862119886 (120579119904119886 minus 120579) +sum119870119895119860119895 (120579119895 minus 120579) + 119876119903119889 (4)

where119862119886 is the specific heat of air 120579 is the temperature inside119898119886 is the mass inside 119902119904119886 is the sending air volume and 120579119904119886 isthe sending air temperature

In the cooling capacity transfer process some of the coldis lost we set the transfer efficiency as 120576 fromwater system119876119908to air system119876119886 (0 le 120576 le 1) so we easily obtain the equation120576119876119908 = 119876119886 In view of the factors of latent heat load 119876119902119903 andsensible heat load 119876119909119903 we obtain

120576119876119908 = 119876119886 = 119876119902119903 + 119876119909119903 (5)

The media of the water system and air system are water andair respectively by the temperature differenceΔ120579 the coolingcapacity is transferred Thus the equation becomes

120576119902119908119862119908Δ120579 = 119902119904119886119862119886 (120579 minus 120579119904119886) + 119876119902119903 (6)

where 119862119908 is the specific heat of water and 119902119908 is the watervolume

Because of the return air rate 119877119903 the fresh rate obviouslyis 1minus119877119903 hereby the air volume of the test room is divided intoreturn air volume 119902119903119905 and fresh air volume 119902119891 The equationbecomes

120576119902119908119862119908Δ120579 = (1 minus 119877119903) 119902119904119886119862119886 (120579119891 minus 120579119904119886)+ 119877119903119902119904119886119862119886 (120579 minus 120579119904119886) + 119876119902119903

(7)

The equation can be rewritten as

120579119904119886 = 120579119891 (1 minus 119877119903) + 120579119877119903 minus 119862119908119902119908Δ120579119902119904119886119862119886 + 119876119902119903119902119904119886119862119886 (8)

Substituting (8) into (4) obtains

119862119886119898119886

119889120579119889120591 = minus120576119902119908119862119908Δ120579

+ [(119877119903 minus 1) 119902119904119886119862119886 minussum119870119895119860119895] 120579+ (1 minus 119877119903) 119902119904119886119862119886120579119891 +sum119870119895119860119895120579119895 + 119876119903119889+ 119876119902119903

(9)

In the chilled water system we use the variable flow volumeand constant temperature difference measures With regardto variable flow volume we should notice that the minimumvolume is not lower than 40 of the rated value otherwisethe energy efficiency of the pump would decay sharply Thuswhatever kinds of pumps are operating the whole water flowvolume should be between 40 and 100 In the system thepumps are divided into three kinds fixed pumps variable-frequency pumps and switchable pumps The fixed pumpsand variable-frequency pumps always operate the switchablepumps either operate or not because of the cold loading Bothfixed pumps and switchable pumps are fixed-frequency todistinguish them they are simply called fixed pumps andswitchable pumps respectively

According to the three kinds of pumps the water flowvolume is expressed as

119902119908 = 119902119892 + 119902119887 + 119896119902119904119908 (10)

Here 119902119892 is a constant that indicates the flow volume of allthe fixed pumps 119902119887 is a state variable that indicates the flowvolume of the variable-frequency pumps 119902119904119908 is a constantthat indicates the flow volume of a switchable pump and 119896is the number of operating switchable pumps Therefore wesubstitute (10) into (9) to obtain (3)

32 Motor Model of Variable-Frequency Pump Mostvariable-frequency pumps are asynchronous AC motors inair conditioning systems We use a stator flux-oriented directtorque control-space vector pulse width modulation (DTC-SVPWM) model to build and design the closed-loop controlof torque and flux linkage The features of DTC-SVPWMare that the controller computes the suitable stator voltagevector and the method of SVPWM modulation generatesthe voltage vector to control torque and flux linkage Thestructure is shown in Figure 2

The M-T coordinate system is a synchronous revolutionaccording to the stator flux orientation the direction ofthe M-axis is the same as that of the stator flux linkageand we use 119906lowast119904119872 which is output from the flux linkage PIadjuster to control the amplitude of the stator flux linkageΨ119904 The direction of the T-axis is perpendicular to statorflux linkage we use 119906lowast119904119879 which is output from the torquePI adjuster to control the rotational speed of the statorflux linkage and then electromagnetic torque Te We obtain119906lowast119904 from the transformation of coordinates and input it tothe SPVWM to control the motor Via double closed-loopfeedback control flux linkage and electromagnetic torque arecomparedwith the setting values and accurately adjustedThe

Mathematical Problems in Engineering 5

M-T

ATRSVPWM

Voltage estimation

module

stator flux linkagetorque

estimator

Ψlowasts

Tlowaste

Te

ulowastsM

ulowasts

ulowastsT

-

ss

AΨR

us

SABC

uDC

is

Figure 2 Motor model

voltage estimation module estimates the actual stator voltagevector according to switch status signal 119878119860119861119862 and measuredbusbar voltage 119906119863119862

The simplified equations of stator voltage and torque are

119889Ψ119904119889120591 = 119906119904119872 minus 119903119904119894119904119872 (11a)

119879119890 = 1119903119904 119899119901Ψ119904 (119906119904119879 minus 120596119904Ψ119904) (11b)

It is apparent that the input variables and output variableshave coupling relationships so we cannot use 119906119904119872 and 119906119904119879to achieve independent control with Ψ119904 and 119879119890 respectivelyTherefore a new variable 119906Ψ must be introduced for decou-pling Let

119906Ψ = 119906119904119872 minus 119903119904119894119904119872 (12a)

119906119879 = Ψ119904 (119906119904119879 minus 120596119904Ψ119904) (12b)

After decoupling the transfer function is a proportionalcomponent from 119906119879 to 119879119890 the transfer function is

119866119879 (119904) = 119879119890 (119904)119906119879 (119904) =119899119901119903119904 (13)

The dynamic structure of the torque control loop is shown inFigure 3 In the figure there is an inertial component and aproportional component The filter time constant 119879119891119879 is thesame as the feedback smoothing time constant the integraltime constant of the torque controller is 119879119894119879

We use an integral controller for torque adjustment

119866119860119879119877 (119904) = 1119904119879119894119879 (14)

Thus the torque control loop is simplified as

119866119879minus0 (119904) = 119899119901119904119879119894119879 (1 + 119904119879119891119879) 119903119904 (15)

33 Building the Relationship of Torque with Water FlowVolume of a Variable-Frequency Pump In general the watervolume 119902 is in proportion to speed 119899 of a pump in a water

ATR TeTlowaste

1

TfTs + 1

1

TfTs + 1

uT 1

rsnp

Figure 3 Torque control loop

system so it is obvious that 1199021199020 = 1198991198990 where 1199020 is therated water volume and 1198990 is the rated speed Using motionequation where 119869 is the rotational inertia 119879119890 is the torqueand 119879119871 is the load torque the torque is obtained by

119879119890 = 119879119871 + 11986911989901199020 119889119902119889120591 (16)

In addition the load of the pumps conforms to a quadraticproportion where 1198791198710 is the rated load torque As anequation

1198791198711198791198710 =119899211989920 (17)

Thus the relationship from torque to water flow volume isbuilt Combining (17) with (10) we build the state spaceequation to show the whole control process of the pumpsHere with 1199091 = 120579 as the inside temperature and 1199092 = 119902119887as water flow volume of the variable-frequency pump 1199091 and1199092 are state variablesWith 119906 = 119879119890 as a control variable we set119910 = 1199091 as the output variable Figure 4 shows the state space

Thus the coefficients of the state space equation are

119860 = (119908 minus 1) 119902119899119888119886 minus sum119870119894119860119862119911119861 = minus120576119888119908Δ120579119862119911119864= (1 minus 119908) 119902119904119886119888119886120579119900119906119905 + sum119870119894119860 119894120579119894 + 119876 + 119876119902119903 minus 119902119866120576119888119908Δ120579

119862119911

6 Mathematical Problems in Engineering

u

x1x2 x1x2

H

G

E F

B

Ax2

yintint

Figure 4 State space

119865119894 = minus119896119902119873120576119888119908Δ120579119862119911 [119896 = 1 2 119899]119866 = 1119869

11990201198990119867 = 119879119871011989920

1119869 11990201198990

(18)

Combining these equations and coefficients we get theequations of state space

= ( 11986001198610 )119909 + (

0119867)119909

2 + (0119866)119906 + (119864 + 1198650 ) (19a)

119910 = (10)119909 (19b)

34 Mathematical Power Models of Pumps According to theelectromagnetic property of a variable-frequency pump theoutput mechanical power of the pump is

119875119900119901 = 120578119887119879119890120596 = 1205781198871198791198901198999550 (20)

120578119887 is the factor converted from motor power into outputmechanical power 0 le 120578119887 le 1 and 120596 is angular velocity

The power of a fixed pump is 119875119892 and the power ofswitchable pumps is 119875119904119908 Both of these kinds of pumpsoperate at constant frequency so we consider them operatingat constant power Thus we get the total power of the pumps

119875119905119900119905119886119897 = 119866119875119892 + 119875119887 + 119896119875119904119908 (21)

G is the total number of fixed pumps and k is the number ofoperating switching pumps

4 Hybrid Dynamical Control Strategy

41 Target of Optimal Hybrid Control for Central Air Con-ditioning The goal of optimal control for central air con-ditioning is to minimise the power of the chilled pumps

further the inside temperature 120579 should be close to the settingtemperature 120579119904119890119905 We obtain the target function

min 119869 = int1205911198911205910

119875119905119900119905119886119897119889120591120590119894(120591)

= int12059111205910

1198751199051199001199051198861198971198891205911205901(120591)

+ int12059121205911

1198751199051199001199051198861198971198891205911205902(120591)

+

+ int120591119891120591119899minus1

119875119905119900119905119886119897119889120591120590119899(120591)

= 119899minus1sum119894=0

int1205911+1198941205910+119894

119875119905119900119905119886119897119889120591120590119894+1(120591)

(22)

where 120591119891 = 120591119899 Due to the switching behaviours the systemis divided into some subsystems in different time intervalsnamely [1205910 1205911] [1205911 1205912][120591119899-1 120591f] The switching sequence isproduced at switching time 120591i and the switching law 120590i and120591i are one-to-one correspondence

Equation (22) means that (i) the target function is to findtheminimumvalue of energy consumption of pumps on timeinterval [1205910 120591f] (ii) the function is divided into several partsandwe calculate the integration on each time interval (iii) thesum of all integration terms is the minimum of the objectivefunction

Remarks 1

(1) i is finite(2) Switching law is state-independent so the length of

each time interval is not the same(3) We simply consider the requirement of energy saving

and the humidity is not concerned in this work

42 Developing the Switching Control Strategy Variable waterflow is realised by variable-frequency regulation of variable-frequency pumps and switching control of switchable pumpsFor the water flow volume of the variable-frequency pumpthe feedback closed loop can be used in the system foraccurate adjustment For the switching pumps we proposean algorithm for deployment According to the changingcold load we set the switching condition and orientationThe switching law is a simple and economic mode inreconstruction engineering that avoids complex processesand computing time It is shown in Figure 5

The switching strategy is based on state dependence Theswitching behaviour occurs simply by satisfying the state

Mathematical Problems in Engineering 7

Y

Y

YN N

N

N

initialize set k=N

After a sampling period obtaintemperature inside

k=k

k=N k=0

k=k-1k=0k=k+1k=N

Y

-set ⩾H

-set⩾H

Figure 5 Control strategy of switching pumps

judgement In other words once the real-time sampling valueis beyond the setting threshold value |119867| the system willswitch At the initial time k is set to the maximum value NAfter each sampling period (constant) the system obtains theinside temperature 120579 and compares |120579 minus 120579119904119890119905| with |119867| If thevalue is in the setting range the systemwill stay in the currentsubsystem Otherwise we will calculate |120579 minus 120579119904119890119905| One way is119896 + 1 because of 120579 minus 120579119904119890119905 ge 119867 unless k is the maximum theother is k-1 because of 120579minus120579119904119890119905 le minus119867 unless k is theminimum

Remarks 2

(1) 120579119904119890119905 is the inside temperature setting and 120579 is the real-time inside temperature

(2) k is the number of operating switching pumps(3) Themaximum number of switching pumps isN If all

the switching pumps are operating the system is closeto full capacity

(4) The minimum number of switching pumps is 0 If anonswitching pump is operating the system is closeto optimal energy saving

(5) Whether switching is on or off the system obeys onepump at a timeThe switching behaviour triggers onlyone pump

43 Cooling Capacity Allocation and Average TemperatureMethods For a whole building the framework is modelledwith a switching control strategy In real system with manyrooms with different areas the cooling capacity requirementand temperature setting need an adaptive method to matchFor allocation of cooling capacity we adopt a weighting

factor according to the proportion of thermal capacity in eachroom This is a quantitative criterion on the demand sideon the supply side there is a measure to balance differentinside temperatures The average temperature difference as afeedback signal is used to control the pumps The switchingcondition |120579 minus 120579119904119890119905| can be modified as

1003816100381610038161003816120579 minus 1205791199041198901199051003816100381610038161003816 =119873sum1

1003816100381610038161003816120579119894 minus 120579119904119890119905minus1198941003816100381610038161003816119873 (23)

The weighting factor is

119865119894 = 119862119885minus119894sum1198731 119862119885minus119894 (24)

The schematic diagram is shown in Figure 6

Remarks 3

(1) |120579 minus 120579119904119890119905| is the average temperature difference of thebuilding

(2) 120579119894 is the real-time temperature inside the 119894th room120579119904119890119905minus119894 is the setting temperature inside the 119894th roomThere are N rooms operating by using cooling capac-ity

(3) 119865119894 is the weighting factor of the 119894th room for coolingcapacity allocation119862119885minus119894 is the thermal capacity of the119894th room

(4) sum1198731 119862119885minus119894 is the total thermal capacity of the rooms byusing cooling capacity

(5) Obviously these are based on the quantitative crite-rion whatever the average temperature difference orweighting factor

(6) In view of allocating cooling capacity by weightingfactor the computing method of average temperaturedifference actually involves the average temperatureper cubic meter

(7) Heat capacity 119862119885 is equal to 119862119886119898119886 for each room

5 Numerical Example and Simulation Results

In this section we present numerical results from simulationsof the chilled water system Three different rooms are thesimulation objects the cold air is sent to the rooms forreducing the inside temperaturesThe supply side uses pumpsfor sending cold water to the air system by the switchingcontrol strategy and cooling capacity allocation method Weuse one variable-frequency pump four switching pumps andtwo fixed pumps to transfer chilled water and adjust coolingcapacityThe cooling capacity transfermode of variable watervolume and constant air volume is presented The purposeof the variable water volume is accuracy control and energysaving via our model and control strategy The parametersare listed in Table 1

Simulink 2007 was used for simulating the whole processwhere the simulation time was 5000 s The switching sampletime 119879119871 of the system was set to 60 s the system checksthe real-time inside temperature each 119879119871 and decides the

8 Mathematical Problems in Engineering

Table 1 Thermal parameters

Parameter Value Remark119898119886 (kg) 67725 903 158025 Rooms A B and C respectively119902119887 (kgs) 002119902119904119908 (kgs) 0013119902119904119886 (kgs) 0655 0655 0655 Rooms A B and C respectively119902119892 (kgs) 0025119860 119894 (m

2) 36 8 0 Room A119860 119894 (m

2) 52 9 0 Room B119860 119894 (m

2) 66 12 6 Room C119862119886 (Jkglowastk) 1010119862119908 (Jkglowastk) 4180119865 0214 0286 05 Rooms A B and C respectively119867 (∘119862) 02119870119891119887 00037 0286 00026 Rooms A B and C respectively119870119891119887119905 -0061 Whole system119870119895 (Wm2lowastk) 0049 0051 005119876119902119903 (J) 19 28 31 Rooms A B and C respectively119877119903 082Δ120579 (∘119862) 5120576 086120579119894119899119894 (∘119862) 30 30 30 Rooms A B and C respectively120579119891 (∘119862) 25 25 25 Rooms A B and C respectively120579119895 (∘119862) 35 35 36 Room A120579119895 (∘119862) 35 35 36 Room B120579119895 (∘119862) 35 35 36 Room CΘ119904119890119905 (

∘119862) 258 261 259 Rooms A B and C respectively

Fixed pump 1M

Fixed pump n

M

Variable frequency pump

M

Switching pump 1

M

Switching pump n

M

Always working

Always working

Not always working(switching onoff)Control

strategy

CoolingCapacityallocation

Room 1heat exchanger

Room 2heat exchanger

Room nheat exchanger

WeightingFactor

calculatIon

Factor 1

Factor 2

Factor n

average temperature

difference Calculation

Figure 6 Cooling capacity allocation and average temperature methods

Mathematical Problems in Engineering 9

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

255

26

265

27

275

28

285

29

295

30

tem

pera

ture

insid

e(∘ C)

Figure 7 Inside temperature

switching behaviour Feedback control is used in the threerooms and the whole system which adjusts the insidetemperatures and water flow volume respectively

The inside temperatures of the three rooms started at30∘C and the system began at full capacity in other words allpumps were operating at rated power at the very start Somecurves were introduced into rooms as inside random coldloads the surface temperatures of thewall space window androof are set at constant valuesThe sending air volumewas thesame as the three rooms and was constant

Figure 7 shows that the inside temperatures declinerapidly by the sending air At approximately 120591 =1000 s thetemperatures stabilise near the setting values although therandom cold loads disturb the system (Figure 8) and the totaltemperature difference is close to zero all for the three rooms(Figure 9) In addition because of the lower cooling capacityrequirements after 1000 s the total water flow volume fallswhich is operating near the lowest flow volume (approx-imately 40) in other words the water system realises alarge potential space for energy saving (Figure 10) In thecontrol process the variable-frequency pump changes speedto alter the water volume in real-time by feedback controlIn the first 1000 s the pump is operating at rated powerin the last approximately 2000 s the pump is operating ina fine adjustment status because of the real-time changingof cooling capacity requirements In the middle period thepump is operating at half the rated power Switching pumpsobey the control strategy and cooling capacity allocationmethods which adjust the number of operating switchablepumps (Figure 10) We set the threshold value |119867| = 02and the total temperature difference leads to the switchingsituation shown in Figure 10

Considering the electromagnetic properties the speed ofa pump starts from zero to a stable value with a smooth

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

30

35

40

45

50

55

rand

om Q

(W)

Figure 8 Random cold loads

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

minus2

0

2

4

6

8

10

12

14

delta

T(∘

C)

Figure 9 Total temperature difference

curve (Figure 11) otherwise it exhibits simply a horizontalline with a constant value The torque responds accordingto the equation of motion which shows the electromagneticspeed regulation process (Figure 12) otherwise it exhibits ahorizontal line as well Considering the load characteristicin (17) the actual speed and torque responses do not showsimple information Figure 12 shows that the torque curvehas acceleration and callback processes after 02 s the torquestabilises at 196119873sdot1198982 which is less than the rated load torqueof 22 119873 sdot 1198982 The speed stabilises at 1273 119903119886119889119898 somewhatless than the rated speed of 1350 119903119886119889119898 The electromagneticparameters are shown in Table 2

By the power models of the pumps the energy con-sumption was simulated (Figure 13) because of the variable

10 Mathematical Problems in Engineering

Table 2 Electromagnetic parameters

Parameter Value Remark119899119901 2 variable-frequency pump119903119904 (Ω) 25 variable-frequency pumpJ (kgm2) 00012 variable-frequency pump1198751198870 (KW) 28 variable-frequency pump119875119892 (KW) 15119875119904119908 (KW) 161198791198710 (Nm2) 22 variable-frequency pump119866 2120578119887 09 variable-frequency pump

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000t (seconds)

switchable pumpsvariable frequency pump

fixed frequency pumpstotal pumps

0

001

002

003

004

005

006

007

008

009

01

wat

er fl

ow v

olum

e (kg

s)

Figure 10 Water flow volume

01 02 03 04 05 06 07 08 09 10t (seconds)

0

200

400

600

800

1000

1200

1400

spee

d (r

ads

)

Figure 11 Speed of pump

0

5

10

15

20

25

torq

ue (N

lowastm

)

01 02 03 04 05 06 07 08 09 10t (seconds)

Figure 12 Electromagnetic torque

water volume technology the energy savings were calculated(Figure 14) It is obvious that in the first 1000 s less energysavings is realised because of the cooling demand howeverafter 1000 s large energy savings are shown according tothe stabilised inside temperature None of the switchablepumps operates after approximately 120591 =1000 s thus thepower consumption remains near 2 KWh This is the sameas the variable-frequency pump which has a favourableadjustment due to the variable water flow Figures 8 and10 show that even though some interference causes volumechanges the variable-frequency pump adjusts the water flowvolume to play the roles of accuracy control and energysaving After 5000 s the total energy consumption of thepumps is approximately 86 KWh

The performance of systems controlled by hybriddynamic control strategy and constant water volumetechnology (all the pumps work at rated power and thechilled water system works without using our controlstrategy) respectively is shown in Figure 14 For constantwater volume control technology the total volume is alwaysat 0097 kgs the total power is always at 107 KW and

Mathematical Problems in Engineering 11

switchable pumpsfixed frequency pumpvariable frequency pumps

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

05

1

15

2

25

3

35

4

45

pow

er co

nsum

ptio

n (K

Wh)

Figure 13 Power consumption

variable water volumeconstant water volume

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

2

4

6

8

10

12

14

16

18

pow

er co

nsum

ptio

n (K

Wh)

Figure 14 Power consumption comparison

the whole energy consumption is up to approximately 17KWh Compared with the results of the system controlledby the hybrid dynamic control strategy it can be foundthat the energy saving potential of the pumps has notbeen excavated in the constant water volume technique Incontrast when the low cooling load level of the system is lowthe pumps may reduce frequency or quit working for energysaving as presented in Figures 10 and 13 Consequentlythe total energy consumption of the system control by thehybrid dynamical control method is approximately 86KWh The system exhibits 494 energy saving in 5000 s

compared with that controlled by constant water volumescheme

6 Conclusions

A hybrid dynamical approach to modelling and control isused in central air conditioning which is a suitable approachfor energy saving reconstruction in contemporary ChinaBy analysing the cooling capacity transfer process from thechilled water system to the air system the framework is builtBy involving a direct torque control measure the electromag-netic property is considered For optimal hybrid control theswitching control strategy is developed the cooling capacityallocation and average temperature methods are presentedOn the basis of mathematical power models of pumpsthe goal of accurate control and energy saving is realisedBy simulation a numeral example shows a hybrid controlprocess and situation of energy savings The approach saves494 of water pump power consumption when comparedwith constant water volume technology The modelling andcontrol of multihybrid systems and their applications inrefrigeration systems will be investigated in future works

Nomenclature

119894 Current119896 Amount119898 Mass119899 Speed119899119901 Number of pole-pairs119902 Flow volume119877 Resistance119906 Voltage119860 Area119862 Specific heat119862119885 Thermal capacityF Factor of cooling capacity allocationG Amount119867 Constant119869 Rotating inertia119870119891119887 Feedback coefficient (a room)119870119891119887119905 Feedback coefficient (total system)119870119894 Heat transfer coefficient119875 Power119876 Heat119877119903 Returned air rate119878119860119861119862 Switch status signal119879119890 Electromagnetic torque119879119871 Load torque

Greek symbols

120576 Heat transfer efficiency120578 FactorΔ120579 Temperature difference120579 Temperature120579119895 Surface temperatureΨ Flux linkage120596 Angular speed

12 Mathematical Problems in Engineering

Subscript

0 Rated119860 Air119861 Variable-frequency pump119865 Fresh air119891119879 Filter time119866 Fixed-frequency pump119894119899119894 Initial119894119879 Integral time119895 Surface (wall space window and roof)119902119903 Latent heat119903119889 Random119903119905 Return119904 Stator119904119886 Sending air119904119890119905 Setting value119904119908 Switchable pump119904119872 M-axis of stator flux-oriented119904119879 T-axis of stator flux-oriented119908 Water119905119905 Totalxr Sensible heatDC Busbar120595 Flux linkage

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the National Natural ScienceFoundation of China (no 40761104181)

References

[1] China Statistical Yearbook China Statistical Publishing HouseBeijing China 2015

[2] J Liang B Li Y Wu and R Yao ldquoAn investigation of theexisting situation and trends in building energy efficiencymanagement in Chinardquo Energy and Buildings vol 39 no 10 pp1098ndash1106 2007

[3] K F Fong V I Hanby and T T Chow ldquoHVAC systemoptimization for energymanagement by evolutionary program-mingrdquo Energy and Buildings vol 38 no 3 pp 220ndash231 2006

[4] A Kecebas and I Yabanova ldquoThermal monitoring and opti-mization of geothermal district heating systems using artificialneural network A case studyrdquo Energy and Buildings vol 50 pp339ndash346 2012

[5] T Y Zhao J L Zhang and L D Ma ldquoOn-line optimizationcontrol method based on extreme value analysis for parallelvariable-frequency hydraulic pumps in central air-conditioningsystemsrdquo Building and Environment vol 47 pp 330ndash338 2012

[6] D Kaya E A Yagmur K S Yigit F C Kilic A S Eren andC Celik ldquoEnergy efficiency in pumpsrdquo Energy Conversion andManagement vol 49 no 6 pp 1662ndash1673 2008

[7] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[8] T T Chow K F Fong A L S Chan R Yau W H Au andV Cheng ldquoEnergy modelling of district cooling system for newurban developmentrdquo Energy and Buildings vol 36 no 11 pp1153ndash1162 2004

[9] X Sheng and L Duanmu ldquoElectricity consumption and eco-nomic analyses of district heating system with distributedvariable speed pumpsrdquo Energy and Buildings vol 118 pp 291ndash300 2016

[10] R M Lewis V Torczon and M W Trosset ldquoDirect searchmethods then and nowrdquo Journal of Computational and AppliedMathematics vol 124 no 1-2 pp 191ndash207 2000

[11] J Sun and A Reddy ldquoOptimal control of building HVACampRsystems using complete simulation-based sequential quadraticprogramming (CSB-SQP)rdquo Building and Environment vol 40no 5 pp 657ndash669 2005

[12] M Zaheer-Uddin and G R Zheng ldquoOptimal control of time-scheduled heating ventilating and air conditioning processesin buildingsrdquo Energy Conversion and Management vol 41 no1 pp 49ndash60 2000

[13] L Lu W Cai Y C Soh L Xie and S Li ldquoHVAC systemoptimization - Condenser water looprdquo Energy Conversion andManagement vol 45 no 4 pp 613ndash630 2004

[14] N Nassif S Moujaes and M Zaheeruddin ldquoSelf-tuningdynamic models of HVAC system componentsrdquo Energy andBuildings vol 40 no 9 pp 1709ndash1720 2008

[15] I-H Yang M-S Yeo and K-W Kim ldquoApplication of artificialneural network to predict the optimal start time for heatingsystem in buildingrdquo Energy Conversion and Management vol44 no 17 pp 2791ndash2809 2003

[16] S Wang and J Burnett ldquoOnline adaptive control for optimizingvariable-speed pumps of indirect water-cooled chilling sys-temsrdquoAppliedThermal Engineering vol 21 no 11 pp 1083ndash11032001

[17] M Anderson M Buehner P Young et al ldquoAn experimentalsystem for advanced heating ventilating and air conditioning(HVAC) controlrdquo Energy and Buildings vol 39 no 2 pp 136ndash147 2007

[18] S Qu Z Sun H Fan and K Li ldquoBP neural network for theprediction of urban building energy consumption based onMatlab and its applicationrdquo in Second International Conferenceon Computer Modeling and Simulation pp 263ndash267 IEEESanya Hainan China 2010

[19] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[20] Z Ma and S Wang ldquoAn optimal control strategy for complexbuilding central chilled water systems for practical and real-time applicationsrdquo Building and Environment vol 44 no 6 pp1188ndash1198 2009

[21] D-C Gao S Wang and Y Sun ldquoA fault-tolerant and energyefficient control strategy for primary-secondary chilled watersystems in buildingsrdquo Energy and Buildings vol 43 no 12 pp3646ndash3656 2011

[22] X Sheng andD Lin ldquoEnergy saving analyses on the reconstruc-tion project in district heating system with distributed variablespeed pumpsrdquo Applied Thermal Engineering vol 101 pp 432ndash445 2016

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Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 3

fresh air

cold air

room(temperature

Inside)

latentheat

Inside

M

M

evaporator

pumps

air conditioningunit

chilledwaterCycle

mixed air

random heat of occupantsand equipment

Chilled water system Air system

heat transferfrom building structure

Figure 1 Cooling capacity transfer and temperature change processes

In Section 3 hybrid system modelling of cooling capacitytransfer process between water system and wind system isexpressed In Section 4 the hybrid dynamical control strategyused in energy saving for chilled water system is presentedIn Section 5 a simulation example is given to illustrate themodelling and control processes Section 6 concludes thepaper

2 Mathematical Description of Hybrid System

The hybrid system is described by

120590119894(120591) = 119860 119894119909 (120591) + 119861119894119906 (120591) + 119891119894 (1a)

119910119894 = 119862119894119909 (120591) (1b)

for

[119909119894119906119894] isin 119883119894 (2)

where 119909119894 isin 119877119899 denotes state variables 119906119894 isin 119877119898 denotescontrol variables f i denotes constant vector and 119910119894 denotesoutput Ai and Ci are state matrices Bi is input matrix⋃119899119894=0119883119894 are convex polyhedra in the input+state space and119883119894 cap 119883119895 = denotes possibly being unbounded by each

other119883119894 implies the ith subsystem and 119894 = 0 1 119873 implies119873 + 1 subsystems ⋃119899119894=0119883119894 = 119883 implies that all subsystems

constitute the whole system 120590119894(120591) 120591 isin [0 +infin) denotesthe switching law of the hybrid system Several differentialor difference equations as subsystems constitute a hybridsystem and they obey the switching law The law decidesthe key issues such as switching time switching state andswitching orientation The system switches among the119873 + 1subsystems and selects only one at any time

3 Modelling the Framework ofthe Cooling Capacity Transfer andTemperature Change Processes

In the air conditioning system the cooling capacity transfersfrom chiller unit to chilled water system by evaporator Thepumps drive water as cycle in the chilled water system andsend cooling capacity to air condition unit for exchangingfrom chilled water system to air system After mixing withfresh air the cold air is sent to air conditioning room todrop the temperature In the process of temperature changein air conditioning room the heat balance is influencedby several aspects cold air random heat of occupants andequipment latent heat inside and heat transfer from buildingstructure The processes of the cooling capacity transfer andtemperature change is shown in Figure 1

This paper uses constant air volume and variable watervolumeconstant temperature differencemeasures to transfercooling capacity In chilled water system switching andvariable-frequency behaviours of pumps adjust the flow forsaving energy which denote the discrete and continuous timeprocess respectively So we give an equation to show the heatbalance as follows

119862119886119898119886

119889120579119889120591 = minus120576119862119908Δ120579 (119902119887 + 119902119866 + 119896119902119904119908)

minus (1 minus 119877119903) 119902119904119886119862119886120579 + (1 minus 119877119903) 119902119904119886119862119886120579119900119906119905+ 119876119903119889 + 119876119902119903 minussum119870119895119860119895120579 +sum119870119895119860119895120579119895

(3)

On the left side of the equation 119862119886119898119886(119889120579119889120591) means thetime differential of the heat capacity of a room On the leftside of the equation minus120576119862119908Δ120579(119902119887 + 119902119866 + 119896119902119904119908) means thecooling capacity for chilled water system minus(1 minus 119877119903)119902119904119886119862119886120579and (1 minus 119877119903)119902119904119886119862119886120579119900119906119905 mean the cooling capacity from returnand fresh air systems respectively 119876119903119889 means random heatof occupants and equipment 119876119902119903 means latent heat inside

4 Mathematical Problems in Engineering

minussum119870119895119860119895120579 + sum119870119895119860119895120579119895 means heat transfer from buildingstructure

The description of the symbol can be seen in the subse-quent chapters and in Nomenclature

Towards motor model of variable-frequency pump weuse a direct torque control model to build and designthe closed-loop control of torque and flux linkage but forconstant frequency pump we use constant to describe it Bybuilding relationship of torquewithwater flowvolumewe getequations of state space for the whole process of the model atlast

31 Modelling the Cooling Capacity Transfer Process It isknown that the cold load of central air conditioning isaffected by factors such as the structure and materials ofa building outdoor weather parameters indoor lightingradiating equipment and number of occupants In order todescribe the dynamic process we consider the area 119860 119894 andtemperature 120579119894 of walls windows and roof according to thedifferent materials and use the heat transfer coefficient 119870119894accordingly We use 119876119903119889 to indicate the random changingheat by equipment and people The supply air carries coolingcapacity inside the building to balance the heat

The dynamic thermal balance equation in a room is

119862119886119898119886

119889120579119889120591 = 119902sa119862119886 (120579119904119886 minus 120579) +sum119870119895119860119895 (120579119895 minus 120579) + 119876119903119889 (4)

where119862119886 is the specific heat of air 120579 is the temperature inside119898119886 is the mass inside 119902119904119886 is the sending air volume and 120579119904119886 isthe sending air temperature

In the cooling capacity transfer process some of the coldis lost we set the transfer efficiency as 120576 fromwater system119876119908to air system119876119886 (0 le 120576 le 1) so we easily obtain the equation120576119876119908 = 119876119886 In view of the factors of latent heat load 119876119902119903 andsensible heat load 119876119909119903 we obtain

120576119876119908 = 119876119886 = 119876119902119903 + 119876119909119903 (5)

The media of the water system and air system are water andair respectively by the temperature differenceΔ120579 the coolingcapacity is transferred Thus the equation becomes

120576119902119908119862119908Δ120579 = 119902119904119886119862119886 (120579 minus 120579119904119886) + 119876119902119903 (6)

where 119862119908 is the specific heat of water and 119902119908 is the watervolume

Because of the return air rate 119877119903 the fresh rate obviouslyis 1minus119877119903 hereby the air volume of the test room is divided intoreturn air volume 119902119903119905 and fresh air volume 119902119891 The equationbecomes

120576119902119908119862119908Δ120579 = (1 minus 119877119903) 119902119904119886119862119886 (120579119891 minus 120579119904119886)+ 119877119903119902119904119886119862119886 (120579 minus 120579119904119886) + 119876119902119903

(7)

The equation can be rewritten as

120579119904119886 = 120579119891 (1 minus 119877119903) + 120579119877119903 minus 119862119908119902119908Δ120579119902119904119886119862119886 + 119876119902119903119902119904119886119862119886 (8)

Substituting (8) into (4) obtains

119862119886119898119886

119889120579119889120591 = minus120576119902119908119862119908Δ120579

+ [(119877119903 minus 1) 119902119904119886119862119886 minussum119870119895119860119895] 120579+ (1 minus 119877119903) 119902119904119886119862119886120579119891 +sum119870119895119860119895120579119895 + 119876119903119889+ 119876119902119903

(9)

In the chilled water system we use the variable flow volumeand constant temperature difference measures With regardto variable flow volume we should notice that the minimumvolume is not lower than 40 of the rated value otherwisethe energy efficiency of the pump would decay sharply Thuswhatever kinds of pumps are operating the whole water flowvolume should be between 40 and 100 In the system thepumps are divided into three kinds fixed pumps variable-frequency pumps and switchable pumps The fixed pumpsand variable-frequency pumps always operate the switchablepumps either operate or not because of the cold loading Bothfixed pumps and switchable pumps are fixed-frequency todistinguish them they are simply called fixed pumps andswitchable pumps respectively

According to the three kinds of pumps the water flowvolume is expressed as

119902119908 = 119902119892 + 119902119887 + 119896119902119904119908 (10)

Here 119902119892 is a constant that indicates the flow volume of allthe fixed pumps 119902119887 is a state variable that indicates the flowvolume of the variable-frequency pumps 119902119904119908 is a constantthat indicates the flow volume of a switchable pump and 119896is the number of operating switchable pumps Therefore wesubstitute (10) into (9) to obtain (3)

32 Motor Model of Variable-Frequency Pump Mostvariable-frequency pumps are asynchronous AC motors inair conditioning systems We use a stator flux-oriented directtorque control-space vector pulse width modulation (DTC-SVPWM) model to build and design the closed-loop controlof torque and flux linkage The features of DTC-SVPWMare that the controller computes the suitable stator voltagevector and the method of SVPWM modulation generatesthe voltage vector to control torque and flux linkage Thestructure is shown in Figure 2

The M-T coordinate system is a synchronous revolutionaccording to the stator flux orientation the direction ofthe M-axis is the same as that of the stator flux linkageand we use 119906lowast119904119872 which is output from the flux linkage PIadjuster to control the amplitude of the stator flux linkageΨ119904 The direction of the T-axis is perpendicular to statorflux linkage we use 119906lowast119904119879 which is output from the torquePI adjuster to control the rotational speed of the statorflux linkage and then electromagnetic torque Te We obtain119906lowast119904 from the transformation of coordinates and input it tothe SPVWM to control the motor Via double closed-loopfeedback control flux linkage and electromagnetic torque arecomparedwith the setting values and accurately adjustedThe

Mathematical Problems in Engineering 5

M-T

ATRSVPWM

Voltage estimation

module

stator flux linkagetorque

estimator

Ψlowasts

Tlowaste

Te

ulowastsM

ulowasts

ulowastsT

-

ss

AΨR

us

SABC

uDC

is

Figure 2 Motor model

voltage estimation module estimates the actual stator voltagevector according to switch status signal 119878119860119861119862 and measuredbusbar voltage 119906119863119862

The simplified equations of stator voltage and torque are

119889Ψ119904119889120591 = 119906119904119872 minus 119903119904119894119904119872 (11a)

119879119890 = 1119903119904 119899119901Ψ119904 (119906119904119879 minus 120596119904Ψ119904) (11b)

It is apparent that the input variables and output variableshave coupling relationships so we cannot use 119906119904119872 and 119906119904119879to achieve independent control with Ψ119904 and 119879119890 respectivelyTherefore a new variable 119906Ψ must be introduced for decou-pling Let

119906Ψ = 119906119904119872 minus 119903119904119894119904119872 (12a)

119906119879 = Ψ119904 (119906119904119879 minus 120596119904Ψ119904) (12b)

After decoupling the transfer function is a proportionalcomponent from 119906119879 to 119879119890 the transfer function is

119866119879 (119904) = 119879119890 (119904)119906119879 (119904) =119899119901119903119904 (13)

The dynamic structure of the torque control loop is shown inFigure 3 In the figure there is an inertial component and aproportional component The filter time constant 119879119891119879 is thesame as the feedback smoothing time constant the integraltime constant of the torque controller is 119879119894119879

We use an integral controller for torque adjustment

119866119860119879119877 (119904) = 1119904119879119894119879 (14)

Thus the torque control loop is simplified as

119866119879minus0 (119904) = 119899119901119904119879119894119879 (1 + 119904119879119891119879) 119903119904 (15)

33 Building the Relationship of Torque with Water FlowVolume of a Variable-Frequency Pump In general the watervolume 119902 is in proportion to speed 119899 of a pump in a water

ATR TeTlowaste

1

TfTs + 1

1

TfTs + 1

uT 1

rsnp

Figure 3 Torque control loop

system so it is obvious that 1199021199020 = 1198991198990 where 1199020 is therated water volume and 1198990 is the rated speed Using motionequation where 119869 is the rotational inertia 119879119890 is the torqueand 119879119871 is the load torque the torque is obtained by

119879119890 = 119879119871 + 11986911989901199020 119889119902119889120591 (16)

In addition the load of the pumps conforms to a quadraticproportion where 1198791198710 is the rated load torque As anequation

1198791198711198791198710 =119899211989920 (17)

Thus the relationship from torque to water flow volume isbuilt Combining (17) with (10) we build the state spaceequation to show the whole control process of the pumpsHere with 1199091 = 120579 as the inside temperature and 1199092 = 119902119887as water flow volume of the variable-frequency pump 1199091 and1199092 are state variablesWith 119906 = 119879119890 as a control variable we set119910 = 1199091 as the output variable Figure 4 shows the state space

Thus the coefficients of the state space equation are

119860 = (119908 minus 1) 119902119899119888119886 minus sum119870119894119860119862119911119861 = minus120576119888119908Δ120579119862119911119864= (1 minus 119908) 119902119904119886119888119886120579119900119906119905 + sum119870119894119860 119894120579119894 + 119876 + 119876119902119903 minus 119902119866120576119888119908Δ120579

119862119911

6 Mathematical Problems in Engineering

u

x1x2 x1x2

H

G

E F

B

Ax2

yintint

Figure 4 State space

119865119894 = minus119896119902119873120576119888119908Δ120579119862119911 [119896 = 1 2 119899]119866 = 1119869

11990201198990119867 = 119879119871011989920

1119869 11990201198990

(18)

Combining these equations and coefficients we get theequations of state space

= ( 11986001198610 )119909 + (

0119867)119909

2 + (0119866)119906 + (119864 + 1198650 ) (19a)

119910 = (10)119909 (19b)

34 Mathematical Power Models of Pumps According to theelectromagnetic property of a variable-frequency pump theoutput mechanical power of the pump is

119875119900119901 = 120578119887119879119890120596 = 1205781198871198791198901198999550 (20)

120578119887 is the factor converted from motor power into outputmechanical power 0 le 120578119887 le 1 and 120596 is angular velocity

The power of a fixed pump is 119875119892 and the power ofswitchable pumps is 119875119904119908 Both of these kinds of pumpsoperate at constant frequency so we consider them operatingat constant power Thus we get the total power of the pumps

119875119905119900119905119886119897 = 119866119875119892 + 119875119887 + 119896119875119904119908 (21)

G is the total number of fixed pumps and k is the number ofoperating switching pumps

4 Hybrid Dynamical Control Strategy

41 Target of Optimal Hybrid Control for Central Air Con-ditioning The goal of optimal control for central air con-ditioning is to minimise the power of the chilled pumps

further the inside temperature 120579 should be close to the settingtemperature 120579119904119890119905 We obtain the target function

min 119869 = int1205911198911205910

119875119905119900119905119886119897119889120591120590119894(120591)

= int12059111205910

1198751199051199001199051198861198971198891205911205901(120591)

+ int12059121205911

1198751199051199001199051198861198971198891205911205902(120591)

+

+ int120591119891120591119899minus1

119875119905119900119905119886119897119889120591120590119899(120591)

= 119899minus1sum119894=0

int1205911+1198941205910+119894

119875119905119900119905119886119897119889120591120590119894+1(120591)

(22)

where 120591119891 = 120591119899 Due to the switching behaviours the systemis divided into some subsystems in different time intervalsnamely [1205910 1205911] [1205911 1205912][120591119899-1 120591f] The switching sequence isproduced at switching time 120591i and the switching law 120590i and120591i are one-to-one correspondence

Equation (22) means that (i) the target function is to findtheminimumvalue of energy consumption of pumps on timeinterval [1205910 120591f] (ii) the function is divided into several partsandwe calculate the integration on each time interval (iii) thesum of all integration terms is the minimum of the objectivefunction

Remarks 1

(1) i is finite(2) Switching law is state-independent so the length of

each time interval is not the same(3) We simply consider the requirement of energy saving

and the humidity is not concerned in this work

42 Developing the Switching Control Strategy Variable waterflow is realised by variable-frequency regulation of variable-frequency pumps and switching control of switchable pumpsFor the water flow volume of the variable-frequency pumpthe feedback closed loop can be used in the system foraccurate adjustment For the switching pumps we proposean algorithm for deployment According to the changingcold load we set the switching condition and orientationThe switching law is a simple and economic mode inreconstruction engineering that avoids complex processesand computing time It is shown in Figure 5

The switching strategy is based on state dependence Theswitching behaviour occurs simply by satisfying the state

Mathematical Problems in Engineering 7

Y

Y

YN N

N

N

initialize set k=N

After a sampling period obtaintemperature inside

k=k

k=N k=0

k=k-1k=0k=k+1k=N

Y

-set ⩾H

-set⩾H

Figure 5 Control strategy of switching pumps

judgement In other words once the real-time sampling valueis beyond the setting threshold value |119867| the system willswitch At the initial time k is set to the maximum value NAfter each sampling period (constant) the system obtains theinside temperature 120579 and compares |120579 minus 120579119904119890119905| with |119867| If thevalue is in the setting range the systemwill stay in the currentsubsystem Otherwise we will calculate |120579 minus 120579119904119890119905| One way is119896 + 1 because of 120579 minus 120579119904119890119905 ge 119867 unless k is the maximum theother is k-1 because of 120579minus120579119904119890119905 le minus119867 unless k is theminimum

Remarks 2

(1) 120579119904119890119905 is the inside temperature setting and 120579 is the real-time inside temperature

(2) k is the number of operating switching pumps(3) Themaximum number of switching pumps isN If all

the switching pumps are operating the system is closeto full capacity

(4) The minimum number of switching pumps is 0 If anonswitching pump is operating the system is closeto optimal energy saving

(5) Whether switching is on or off the system obeys onepump at a timeThe switching behaviour triggers onlyone pump

43 Cooling Capacity Allocation and Average TemperatureMethods For a whole building the framework is modelledwith a switching control strategy In real system with manyrooms with different areas the cooling capacity requirementand temperature setting need an adaptive method to matchFor allocation of cooling capacity we adopt a weighting

factor according to the proportion of thermal capacity in eachroom This is a quantitative criterion on the demand sideon the supply side there is a measure to balance differentinside temperatures The average temperature difference as afeedback signal is used to control the pumps The switchingcondition |120579 minus 120579119904119890119905| can be modified as

1003816100381610038161003816120579 minus 1205791199041198901199051003816100381610038161003816 =119873sum1

1003816100381610038161003816120579119894 minus 120579119904119890119905minus1198941003816100381610038161003816119873 (23)

The weighting factor is

119865119894 = 119862119885minus119894sum1198731 119862119885minus119894 (24)

The schematic diagram is shown in Figure 6

Remarks 3

(1) |120579 minus 120579119904119890119905| is the average temperature difference of thebuilding

(2) 120579119894 is the real-time temperature inside the 119894th room120579119904119890119905minus119894 is the setting temperature inside the 119894th roomThere are N rooms operating by using cooling capac-ity

(3) 119865119894 is the weighting factor of the 119894th room for coolingcapacity allocation119862119885minus119894 is the thermal capacity of the119894th room

(4) sum1198731 119862119885minus119894 is the total thermal capacity of the rooms byusing cooling capacity

(5) Obviously these are based on the quantitative crite-rion whatever the average temperature difference orweighting factor

(6) In view of allocating cooling capacity by weightingfactor the computing method of average temperaturedifference actually involves the average temperatureper cubic meter

(7) Heat capacity 119862119885 is equal to 119862119886119898119886 for each room

5 Numerical Example and Simulation Results

In this section we present numerical results from simulationsof the chilled water system Three different rooms are thesimulation objects the cold air is sent to the rooms forreducing the inside temperaturesThe supply side uses pumpsfor sending cold water to the air system by the switchingcontrol strategy and cooling capacity allocation method Weuse one variable-frequency pump four switching pumps andtwo fixed pumps to transfer chilled water and adjust coolingcapacityThe cooling capacity transfermode of variable watervolume and constant air volume is presented The purposeof the variable water volume is accuracy control and energysaving via our model and control strategy The parametersare listed in Table 1

Simulink 2007 was used for simulating the whole processwhere the simulation time was 5000 s The switching sampletime 119879119871 of the system was set to 60 s the system checksthe real-time inside temperature each 119879119871 and decides the

8 Mathematical Problems in Engineering

Table 1 Thermal parameters

Parameter Value Remark119898119886 (kg) 67725 903 158025 Rooms A B and C respectively119902119887 (kgs) 002119902119904119908 (kgs) 0013119902119904119886 (kgs) 0655 0655 0655 Rooms A B and C respectively119902119892 (kgs) 0025119860 119894 (m

2) 36 8 0 Room A119860 119894 (m

2) 52 9 0 Room B119860 119894 (m

2) 66 12 6 Room C119862119886 (Jkglowastk) 1010119862119908 (Jkglowastk) 4180119865 0214 0286 05 Rooms A B and C respectively119867 (∘119862) 02119870119891119887 00037 0286 00026 Rooms A B and C respectively119870119891119887119905 -0061 Whole system119870119895 (Wm2lowastk) 0049 0051 005119876119902119903 (J) 19 28 31 Rooms A B and C respectively119877119903 082Δ120579 (∘119862) 5120576 086120579119894119899119894 (∘119862) 30 30 30 Rooms A B and C respectively120579119891 (∘119862) 25 25 25 Rooms A B and C respectively120579119895 (∘119862) 35 35 36 Room A120579119895 (∘119862) 35 35 36 Room B120579119895 (∘119862) 35 35 36 Room CΘ119904119890119905 (

∘119862) 258 261 259 Rooms A B and C respectively

Fixed pump 1M

Fixed pump n

M

Variable frequency pump

M

Switching pump 1

M

Switching pump n

M

Always working

Always working

Not always working(switching onoff)Control

strategy

CoolingCapacityallocation

Room 1heat exchanger

Room 2heat exchanger

Room nheat exchanger

WeightingFactor

calculatIon

Factor 1

Factor 2

Factor n

average temperature

difference Calculation

Figure 6 Cooling capacity allocation and average temperature methods

Mathematical Problems in Engineering 9

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

255

26

265

27

275

28

285

29

295

30

tem

pera

ture

insid

e(∘ C)

Figure 7 Inside temperature

switching behaviour Feedback control is used in the threerooms and the whole system which adjusts the insidetemperatures and water flow volume respectively

The inside temperatures of the three rooms started at30∘C and the system began at full capacity in other words allpumps were operating at rated power at the very start Somecurves were introduced into rooms as inside random coldloads the surface temperatures of thewall space window androof are set at constant valuesThe sending air volumewas thesame as the three rooms and was constant

Figure 7 shows that the inside temperatures declinerapidly by the sending air At approximately 120591 =1000 s thetemperatures stabilise near the setting values although therandom cold loads disturb the system (Figure 8) and the totaltemperature difference is close to zero all for the three rooms(Figure 9) In addition because of the lower cooling capacityrequirements after 1000 s the total water flow volume fallswhich is operating near the lowest flow volume (approx-imately 40) in other words the water system realises alarge potential space for energy saving (Figure 10) In thecontrol process the variable-frequency pump changes speedto alter the water volume in real-time by feedback controlIn the first 1000 s the pump is operating at rated powerin the last approximately 2000 s the pump is operating ina fine adjustment status because of the real-time changingof cooling capacity requirements In the middle period thepump is operating at half the rated power Switching pumpsobey the control strategy and cooling capacity allocationmethods which adjust the number of operating switchablepumps (Figure 10) We set the threshold value |119867| = 02and the total temperature difference leads to the switchingsituation shown in Figure 10

Considering the electromagnetic properties the speed ofa pump starts from zero to a stable value with a smooth

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

30

35

40

45

50

55

rand

om Q

(W)

Figure 8 Random cold loads

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

minus2

0

2

4

6

8

10

12

14

delta

T(∘

C)

Figure 9 Total temperature difference

curve (Figure 11) otherwise it exhibits simply a horizontalline with a constant value The torque responds accordingto the equation of motion which shows the electromagneticspeed regulation process (Figure 12) otherwise it exhibits ahorizontal line as well Considering the load characteristicin (17) the actual speed and torque responses do not showsimple information Figure 12 shows that the torque curvehas acceleration and callback processes after 02 s the torquestabilises at 196119873sdot1198982 which is less than the rated load torqueof 22 119873 sdot 1198982 The speed stabilises at 1273 119903119886119889119898 somewhatless than the rated speed of 1350 119903119886119889119898 The electromagneticparameters are shown in Table 2

By the power models of the pumps the energy con-sumption was simulated (Figure 13) because of the variable

10 Mathematical Problems in Engineering

Table 2 Electromagnetic parameters

Parameter Value Remark119899119901 2 variable-frequency pump119903119904 (Ω) 25 variable-frequency pumpJ (kgm2) 00012 variable-frequency pump1198751198870 (KW) 28 variable-frequency pump119875119892 (KW) 15119875119904119908 (KW) 161198791198710 (Nm2) 22 variable-frequency pump119866 2120578119887 09 variable-frequency pump

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000t (seconds)

switchable pumpsvariable frequency pump

fixed frequency pumpstotal pumps

0

001

002

003

004

005

006

007

008

009

01

wat

er fl

ow v

olum

e (kg

s)

Figure 10 Water flow volume

01 02 03 04 05 06 07 08 09 10t (seconds)

0

200

400

600

800

1000

1200

1400

spee

d (r

ads

)

Figure 11 Speed of pump

0

5

10

15

20

25

torq

ue (N

lowastm

)

01 02 03 04 05 06 07 08 09 10t (seconds)

Figure 12 Electromagnetic torque

water volume technology the energy savings were calculated(Figure 14) It is obvious that in the first 1000 s less energysavings is realised because of the cooling demand howeverafter 1000 s large energy savings are shown according tothe stabilised inside temperature None of the switchablepumps operates after approximately 120591 =1000 s thus thepower consumption remains near 2 KWh This is the sameas the variable-frequency pump which has a favourableadjustment due to the variable water flow Figures 8 and10 show that even though some interference causes volumechanges the variable-frequency pump adjusts the water flowvolume to play the roles of accuracy control and energysaving After 5000 s the total energy consumption of thepumps is approximately 86 KWh

The performance of systems controlled by hybriddynamic control strategy and constant water volumetechnology (all the pumps work at rated power and thechilled water system works without using our controlstrategy) respectively is shown in Figure 14 For constantwater volume control technology the total volume is alwaysat 0097 kgs the total power is always at 107 KW and

Mathematical Problems in Engineering 11

switchable pumpsfixed frequency pumpvariable frequency pumps

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

05

1

15

2

25

3

35

4

45

pow

er co

nsum

ptio

n (K

Wh)

Figure 13 Power consumption

variable water volumeconstant water volume

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

2

4

6

8

10

12

14

16

18

pow

er co

nsum

ptio

n (K

Wh)

Figure 14 Power consumption comparison

the whole energy consumption is up to approximately 17KWh Compared with the results of the system controlledby the hybrid dynamic control strategy it can be foundthat the energy saving potential of the pumps has notbeen excavated in the constant water volume technique Incontrast when the low cooling load level of the system is lowthe pumps may reduce frequency or quit working for energysaving as presented in Figures 10 and 13 Consequentlythe total energy consumption of the system control by thehybrid dynamical control method is approximately 86KWh The system exhibits 494 energy saving in 5000 s

compared with that controlled by constant water volumescheme

6 Conclusions

A hybrid dynamical approach to modelling and control isused in central air conditioning which is a suitable approachfor energy saving reconstruction in contemporary ChinaBy analysing the cooling capacity transfer process from thechilled water system to the air system the framework is builtBy involving a direct torque control measure the electromag-netic property is considered For optimal hybrid control theswitching control strategy is developed the cooling capacityallocation and average temperature methods are presentedOn the basis of mathematical power models of pumpsthe goal of accurate control and energy saving is realisedBy simulation a numeral example shows a hybrid controlprocess and situation of energy savings The approach saves494 of water pump power consumption when comparedwith constant water volume technology The modelling andcontrol of multihybrid systems and their applications inrefrigeration systems will be investigated in future works

Nomenclature

119894 Current119896 Amount119898 Mass119899 Speed119899119901 Number of pole-pairs119902 Flow volume119877 Resistance119906 Voltage119860 Area119862 Specific heat119862119885 Thermal capacityF Factor of cooling capacity allocationG Amount119867 Constant119869 Rotating inertia119870119891119887 Feedback coefficient (a room)119870119891119887119905 Feedback coefficient (total system)119870119894 Heat transfer coefficient119875 Power119876 Heat119877119903 Returned air rate119878119860119861119862 Switch status signal119879119890 Electromagnetic torque119879119871 Load torque

Greek symbols

120576 Heat transfer efficiency120578 FactorΔ120579 Temperature difference120579 Temperature120579119895 Surface temperatureΨ Flux linkage120596 Angular speed

12 Mathematical Problems in Engineering

Subscript

0 Rated119860 Air119861 Variable-frequency pump119865 Fresh air119891119879 Filter time119866 Fixed-frequency pump119894119899119894 Initial119894119879 Integral time119895 Surface (wall space window and roof)119902119903 Latent heat119903119889 Random119903119905 Return119904 Stator119904119886 Sending air119904119890119905 Setting value119904119908 Switchable pump119904119872 M-axis of stator flux-oriented119904119879 T-axis of stator flux-oriented119908 Water119905119905 Totalxr Sensible heatDC Busbar120595 Flux linkage

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the National Natural ScienceFoundation of China (no 40761104181)

References

[1] China Statistical Yearbook China Statistical Publishing HouseBeijing China 2015

[2] J Liang B Li Y Wu and R Yao ldquoAn investigation of theexisting situation and trends in building energy efficiencymanagement in Chinardquo Energy and Buildings vol 39 no 10 pp1098ndash1106 2007

[3] K F Fong V I Hanby and T T Chow ldquoHVAC systemoptimization for energymanagement by evolutionary program-mingrdquo Energy and Buildings vol 38 no 3 pp 220ndash231 2006

[4] A Kecebas and I Yabanova ldquoThermal monitoring and opti-mization of geothermal district heating systems using artificialneural network A case studyrdquo Energy and Buildings vol 50 pp339ndash346 2012

[5] T Y Zhao J L Zhang and L D Ma ldquoOn-line optimizationcontrol method based on extreme value analysis for parallelvariable-frequency hydraulic pumps in central air-conditioningsystemsrdquo Building and Environment vol 47 pp 330ndash338 2012

[6] D Kaya E A Yagmur K S Yigit F C Kilic A S Eren andC Celik ldquoEnergy efficiency in pumpsrdquo Energy Conversion andManagement vol 49 no 6 pp 1662ndash1673 2008

[7] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[8] T T Chow K F Fong A L S Chan R Yau W H Au andV Cheng ldquoEnergy modelling of district cooling system for newurban developmentrdquo Energy and Buildings vol 36 no 11 pp1153ndash1162 2004

[9] X Sheng and L Duanmu ldquoElectricity consumption and eco-nomic analyses of district heating system with distributedvariable speed pumpsrdquo Energy and Buildings vol 118 pp 291ndash300 2016

[10] R M Lewis V Torczon and M W Trosset ldquoDirect searchmethods then and nowrdquo Journal of Computational and AppliedMathematics vol 124 no 1-2 pp 191ndash207 2000

[11] J Sun and A Reddy ldquoOptimal control of building HVACampRsystems using complete simulation-based sequential quadraticprogramming (CSB-SQP)rdquo Building and Environment vol 40no 5 pp 657ndash669 2005

[12] M Zaheer-Uddin and G R Zheng ldquoOptimal control of time-scheduled heating ventilating and air conditioning processesin buildingsrdquo Energy Conversion and Management vol 41 no1 pp 49ndash60 2000

[13] L Lu W Cai Y C Soh L Xie and S Li ldquoHVAC systemoptimization - Condenser water looprdquo Energy Conversion andManagement vol 45 no 4 pp 613ndash630 2004

[14] N Nassif S Moujaes and M Zaheeruddin ldquoSelf-tuningdynamic models of HVAC system componentsrdquo Energy andBuildings vol 40 no 9 pp 1709ndash1720 2008

[15] I-H Yang M-S Yeo and K-W Kim ldquoApplication of artificialneural network to predict the optimal start time for heatingsystem in buildingrdquo Energy Conversion and Management vol44 no 17 pp 2791ndash2809 2003

[16] S Wang and J Burnett ldquoOnline adaptive control for optimizingvariable-speed pumps of indirect water-cooled chilling sys-temsrdquoAppliedThermal Engineering vol 21 no 11 pp 1083ndash11032001

[17] M Anderson M Buehner P Young et al ldquoAn experimentalsystem for advanced heating ventilating and air conditioning(HVAC) controlrdquo Energy and Buildings vol 39 no 2 pp 136ndash147 2007

[18] S Qu Z Sun H Fan and K Li ldquoBP neural network for theprediction of urban building energy consumption based onMatlab and its applicationrdquo in Second International Conferenceon Computer Modeling and Simulation pp 263ndash267 IEEESanya Hainan China 2010

[19] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[20] Z Ma and S Wang ldquoAn optimal control strategy for complexbuilding central chilled water systems for practical and real-time applicationsrdquo Building and Environment vol 44 no 6 pp1188ndash1198 2009

[21] D-C Gao S Wang and Y Sun ldquoA fault-tolerant and energyefficient control strategy for primary-secondary chilled watersystems in buildingsrdquo Energy and Buildings vol 43 no 12 pp3646ndash3656 2011

[22] X Sheng andD Lin ldquoEnergy saving analyses on the reconstruc-tion project in district heating system with distributed variablespeed pumpsrdquo Applied Thermal Engineering vol 101 pp 432ndash445 2016

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4 Mathematical Problems in Engineering

minussum119870119895119860119895120579 + sum119870119895119860119895120579119895 means heat transfer from buildingstructure

The description of the symbol can be seen in the subse-quent chapters and in Nomenclature

Towards motor model of variable-frequency pump weuse a direct torque control model to build and designthe closed-loop control of torque and flux linkage but forconstant frequency pump we use constant to describe it Bybuilding relationship of torquewithwater flowvolumewe getequations of state space for the whole process of the model atlast

31 Modelling the Cooling Capacity Transfer Process It isknown that the cold load of central air conditioning isaffected by factors such as the structure and materials ofa building outdoor weather parameters indoor lightingradiating equipment and number of occupants In order todescribe the dynamic process we consider the area 119860 119894 andtemperature 120579119894 of walls windows and roof according to thedifferent materials and use the heat transfer coefficient 119870119894accordingly We use 119876119903119889 to indicate the random changingheat by equipment and people The supply air carries coolingcapacity inside the building to balance the heat

The dynamic thermal balance equation in a room is

119862119886119898119886

119889120579119889120591 = 119902sa119862119886 (120579119904119886 minus 120579) +sum119870119895119860119895 (120579119895 minus 120579) + 119876119903119889 (4)

where119862119886 is the specific heat of air 120579 is the temperature inside119898119886 is the mass inside 119902119904119886 is the sending air volume and 120579119904119886 isthe sending air temperature

In the cooling capacity transfer process some of the coldis lost we set the transfer efficiency as 120576 fromwater system119876119908to air system119876119886 (0 le 120576 le 1) so we easily obtain the equation120576119876119908 = 119876119886 In view of the factors of latent heat load 119876119902119903 andsensible heat load 119876119909119903 we obtain

120576119876119908 = 119876119886 = 119876119902119903 + 119876119909119903 (5)

The media of the water system and air system are water andair respectively by the temperature differenceΔ120579 the coolingcapacity is transferred Thus the equation becomes

120576119902119908119862119908Δ120579 = 119902119904119886119862119886 (120579 minus 120579119904119886) + 119876119902119903 (6)

where 119862119908 is the specific heat of water and 119902119908 is the watervolume

Because of the return air rate 119877119903 the fresh rate obviouslyis 1minus119877119903 hereby the air volume of the test room is divided intoreturn air volume 119902119903119905 and fresh air volume 119902119891 The equationbecomes

120576119902119908119862119908Δ120579 = (1 minus 119877119903) 119902119904119886119862119886 (120579119891 minus 120579119904119886)+ 119877119903119902119904119886119862119886 (120579 minus 120579119904119886) + 119876119902119903

(7)

The equation can be rewritten as

120579119904119886 = 120579119891 (1 minus 119877119903) + 120579119877119903 minus 119862119908119902119908Δ120579119902119904119886119862119886 + 119876119902119903119902119904119886119862119886 (8)

Substituting (8) into (4) obtains

119862119886119898119886

119889120579119889120591 = minus120576119902119908119862119908Δ120579

+ [(119877119903 minus 1) 119902119904119886119862119886 minussum119870119895119860119895] 120579+ (1 minus 119877119903) 119902119904119886119862119886120579119891 +sum119870119895119860119895120579119895 + 119876119903119889+ 119876119902119903

(9)

In the chilled water system we use the variable flow volumeand constant temperature difference measures With regardto variable flow volume we should notice that the minimumvolume is not lower than 40 of the rated value otherwisethe energy efficiency of the pump would decay sharply Thuswhatever kinds of pumps are operating the whole water flowvolume should be between 40 and 100 In the system thepumps are divided into three kinds fixed pumps variable-frequency pumps and switchable pumps The fixed pumpsand variable-frequency pumps always operate the switchablepumps either operate or not because of the cold loading Bothfixed pumps and switchable pumps are fixed-frequency todistinguish them they are simply called fixed pumps andswitchable pumps respectively

According to the three kinds of pumps the water flowvolume is expressed as

119902119908 = 119902119892 + 119902119887 + 119896119902119904119908 (10)

Here 119902119892 is a constant that indicates the flow volume of allthe fixed pumps 119902119887 is a state variable that indicates the flowvolume of the variable-frequency pumps 119902119904119908 is a constantthat indicates the flow volume of a switchable pump and 119896is the number of operating switchable pumps Therefore wesubstitute (10) into (9) to obtain (3)

32 Motor Model of Variable-Frequency Pump Mostvariable-frequency pumps are asynchronous AC motors inair conditioning systems We use a stator flux-oriented directtorque control-space vector pulse width modulation (DTC-SVPWM) model to build and design the closed-loop controlof torque and flux linkage The features of DTC-SVPWMare that the controller computes the suitable stator voltagevector and the method of SVPWM modulation generatesthe voltage vector to control torque and flux linkage Thestructure is shown in Figure 2

The M-T coordinate system is a synchronous revolutionaccording to the stator flux orientation the direction ofthe M-axis is the same as that of the stator flux linkageand we use 119906lowast119904119872 which is output from the flux linkage PIadjuster to control the amplitude of the stator flux linkageΨ119904 The direction of the T-axis is perpendicular to statorflux linkage we use 119906lowast119904119879 which is output from the torquePI adjuster to control the rotational speed of the statorflux linkage and then electromagnetic torque Te We obtain119906lowast119904 from the transformation of coordinates and input it tothe SPVWM to control the motor Via double closed-loopfeedback control flux linkage and electromagnetic torque arecomparedwith the setting values and accurately adjustedThe

Mathematical Problems in Engineering 5

M-T

ATRSVPWM

Voltage estimation

module

stator flux linkagetorque

estimator

Ψlowasts

Tlowaste

Te

ulowastsM

ulowasts

ulowastsT

-

ss

AΨR

us

SABC

uDC

is

Figure 2 Motor model

voltage estimation module estimates the actual stator voltagevector according to switch status signal 119878119860119861119862 and measuredbusbar voltage 119906119863119862

The simplified equations of stator voltage and torque are

119889Ψ119904119889120591 = 119906119904119872 minus 119903119904119894119904119872 (11a)

119879119890 = 1119903119904 119899119901Ψ119904 (119906119904119879 minus 120596119904Ψ119904) (11b)

It is apparent that the input variables and output variableshave coupling relationships so we cannot use 119906119904119872 and 119906119904119879to achieve independent control with Ψ119904 and 119879119890 respectivelyTherefore a new variable 119906Ψ must be introduced for decou-pling Let

119906Ψ = 119906119904119872 minus 119903119904119894119904119872 (12a)

119906119879 = Ψ119904 (119906119904119879 minus 120596119904Ψ119904) (12b)

After decoupling the transfer function is a proportionalcomponent from 119906119879 to 119879119890 the transfer function is

119866119879 (119904) = 119879119890 (119904)119906119879 (119904) =119899119901119903119904 (13)

The dynamic structure of the torque control loop is shown inFigure 3 In the figure there is an inertial component and aproportional component The filter time constant 119879119891119879 is thesame as the feedback smoothing time constant the integraltime constant of the torque controller is 119879119894119879

We use an integral controller for torque adjustment

119866119860119879119877 (119904) = 1119904119879119894119879 (14)

Thus the torque control loop is simplified as

119866119879minus0 (119904) = 119899119901119904119879119894119879 (1 + 119904119879119891119879) 119903119904 (15)

33 Building the Relationship of Torque with Water FlowVolume of a Variable-Frequency Pump In general the watervolume 119902 is in proportion to speed 119899 of a pump in a water

ATR TeTlowaste

1

TfTs + 1

1

TfTs + 1

uT 1

rsnp

Figure 3 Torque control loop

system so it is obvious that 1199021199020 = 1198991198990 where 1199020 is therated water volume and 1198990 is the rated speed Using motionequation where 119869 is the rotational inertia 119879119890 is the torqueand 119879119871 is the load torque the torque is obtained by

119879119890 = 119879119871 + 11986911989901199020 119889119902119889120591 (16)

In addition the load of the pumps conforms to a quadraticproportion where 1198791198710 is the rated load torque As anequation

1198791198711198791198710 =119899211989920 (17)

Thus the relationship from torque to water flow volume isbuilt Combining (17) with (10) we build the state spaceequation to show the whole control process of the pumpsHere with 1199091 = 120579 as the inside temperature and 1199092 = 119902119887as water flow volume of the variable-frequency pump 1199091 and1199092 are state variablesWith 119906 = 119879119890 as a control variable we set119910 = 1199091 as the output variable Figure 4 shows the state space

Thus the coefficients of the state space equation are

119860 = (119908 minus 1) 119902119899119888119886 minus sum119870119894119860119862119911119861 = minus120576119888119908Δ120579119862119911119864= (1 minus 119908) 119902119904119886119888119886120579119900119906119905 + sum119870119894119860 119894120579119894 + 119876 + 119876119902119903 minus 119902119866120576119888119908Δ120579

119862119911

6 Mathematical Problems in Engineering

u

x1x2 x1x2

H

G

E F

B

Ax2

yintint

Figure 4 State space

119865119894 = minus119896119902119873120576119888119908Δ120579119862119911 [119896 = 1 2 119899]119866 = 1119869

11990201198990119867 = 119879119871011989920

1119869 11990201198990

(18)

Combining these equations and coefficients we get theequations of state space

= ( 11986001198610 )119909 + (

0119867)119909

2 + (0119866)119906 + (119864 + 1198650 ) (19a)

119910 = (10)119909 (19b)

34 Mathematical Power Models of Pumps According to theelectromagnetic property of a variable-frequency pump theoutput mechanical power of the pump is

119875119900119901 = 120578119887119879119890120596 = 1205781198871198791198901198999550 (20)

120578119887 is the factor converted from motor power into outputmechanical power 0 le 120578119887 le 1 and 120596 is angular velocity

The power of a fixed pump is 119875119892 and the power ofswitchable pumps is 119875119904119908 Both of these kinds of pumpsoperate at constant frequency so we consider them operatingat constant power Thus we get the total power of the pumps

119875119905119900119905119886119897 = 119866119875119892 + 119875119887 + 119896119875119904119908 (21)

G is the total number of fixed pumps and k is the number ofoperating switching pumps

4 Hybrid Dynamical Control Strategy

41 Target of Optimal Hybrid Control for Central Air Con-ditioning The goal of optimal control for central air con-ditioning is to minimise the power of the chilled pumps

further the inside temperature 120579 should be close to the settingtemperature 120579119904119890119905 We obtain the target function

min 119869 = int1205911198911205910

119875119905119900119905119886119897119889120591120590119894(120591)

= int12059111205910

1198751199051199001199051198861198971198891205911205901(120591)

+ int12059121205911

1198751199051199001199051198861198971198891205911205902(120591)

+

+ int120591119891120591119899minus1

119875119905119900119905119886119897119889120591120590119899(120591)

= 119899minus1sum119894=0

int1205911+1198941205910+119894

119875119905119900119905119886119897119889120591120590119894+1(120591)

(22)

where 120591119891 = 120591119899 Due to the switching behaviours the systemis divided into some subsystems in different time intervalsnamely [1205910 1205911] [1205911 1205912][120591119899-1 120591f] The switching sequence isproduced at switching time 120591i and the switching law 120590i and120591i are one-to-one correspondence

Equation (22) means that (i) the target function is to findtheminimumvalue of energy consumption of pumps on timeinterval [1205910 120591f] (ii) the function is divided into several partsandwe calculate the integration on each time interval (iii) thesum of all integration terms is the minimum of the objectivefunction

Remarks 1

(1) i is finite(2) Switching law is state-independent so the length of

each time interval is not the same(3) We simply consider the requirement of energy saving

and the humidity is not concerned in this work

42 Developing the Switching Control Strategy Variable waterflow is realised by variable-frequency regulation of variable-frequency pumps and switching control of switchable pumpsFor the water flow volume of the variable-frequency pumpthe feedback closed loop can be used in the system foraccurate adjustment For the switching pumps we proposean algorithm for deployment According to the changingcold load we set the switching condition and orientationThe switching law is a simple and economic mode inreconstruction engineering that avoids complex processesand computing time It is shown in Figure 5

The switching strategy is based on state dependence Theswitching behaviour occurs simply by satisfying the state

Mathematical Problems in Engineering 7

Y

Y

YN N

N

N

initialize set k=N

After a sampling period obtaintemperature inside

k=k

k=N k=0

k=k-1k=0k=k+1k=N

Y

-set ⩾H

-set⩾H

Figure 5 Control strategy of switching pumps

judgement In other words once the real-time sampling valueis beyond the setting threshold value |119867| the system willswitch At the initial time k is set to the maximum value NAfter each sampling period (constant) the system obtains theinside temperature 120579 and compares |120579 minus 120579119904119890119905| with |119867| If thevalue is in the setting range the systemwill stay in the currentsubsystem Otherwise we will calculate |120579 minus 120579119904119890119905| One way is119896 + 1 because of 120579 minus 120579119904119890119905 ge 119867 unless k is the maximum theother is k-1 because of 120579minus120579119904119890119905 le minus119867 unless k is theminimum

Remarks 2

(1) 120579119904119890119905 is the inside temperature setting and 120579 is the real-time inside temperature

(2) k is the number of operating switching pumps(3) Themaximum number of switching pumps isN If all

the switching pumps are operating the system is closeto full capacity

(4) The minimum number of switching pumps is 0 If anonswitching pump is operating the system is closeto optimal energy saving

(5) Whether switching is on or off the system obeys onepump at a timeThe switching behaviour triggers onlyone pump

43 Cooling Capacity Allocation and Average TemperatureMethods For a whole building the framework is modelledwith a switching control strategy In real system with manyrooms with different areas the cooling capacity requirementand temperature setting need an adaptive method to matchFor allocation of cooling capacity we adopt a weighting

factor according to the proportion of thermal capacity in eachroom This is a quantitative criterion on the demand sideon the supply side there is a measure to balance differentinside temperatures The average temperature difference as afeedback signal is used to control the pumps The switchingcondition |120579 minus 120579119904119890119905| can be modified as

1003816100381610038161003816120579 minus 1205791199041198901199051003816100381610038161003816 =119873sum1

1003816100381610038161003816120579119894 minus 120579119904119890119905minus1198941003816100381610038161003816119873 (23)

The weighting factor is

119865119894 = 119862119885minus119894sum1198731 119862119885minus119894 (24)

The schematic diagram is shown in Figure 6

Remarks 3

(1) |120579 minus 120579119904119890119905| is the average temperature difference of thebuilding

(2) 120579119894 is the real-time temperature inside the 119894th room120579119904119890119905minus119894 is the setting temperature inside the 119894th roomThere are N rooms operating by using cooling capac-ity

(3) 119865119894 is the weighting factor of the 119894th room for coolingcapacity allocation119862119885minus119894 is the thermal capacity of the119894th room

(4) sum1198731 119862119885minus119894 is the total thermal capacity of the rooms byusing cooling capacity

(5) Obviously these are based on the quantitative crite-rion whatever the average temperature difference orweighting factor

(6) In view of allocating cooling capacity by weightingfactor the computing method of average temperaturedifference actually involves the average temperatureper cubic meter

(7) Heat capacity 119862119885 is equal to 119862119886119898119886 for each room

5 Numerical Example and Simulation Results

In this section we present numerical results from simulationsof the chilled water system Three different rooms are thesimulation objects the cold air is sent to the rooms forreducing the inside temperaturesThe supply side uses pumpsfor sending cold water to the air system by the switchingcontrol strategy and cooling capacity allocation method Weuse one variable-frequency pump four switching pumps andtwo fixed pumps to transfer chilled water and adjust coolingcapacityThe cooling capacity transfermode of variable watervolume and constant air volume is presented The purposeof the variable water volume is accuracy control and energysaving via our model and control strategy The parametersare listed in Table 1

Simulink 2007 was used for simulating the whole processwhere the simulation time was 5000 s The switching sampletime 119879119871 of the system was set to 60 s the system checksthe real-time inside temperature each 119879119871 and decides the

8 Mathematical Problems in Engineering

Table 1 Thermal parameters

Parameter Value Remark119898119886 (kg) 67725 903 158025 Rooms A B and C respectively119902119887 (kgs) 002119902119904119908 (kgs) 0013119902119904119886 (kgs) 0655 0655 0655 Rooms A B and C respectively119902119892 (kgs) 0025119860 119894 (m

2) 36 8 0 Room A119860 119894 (m

2) 52 9 0 Room B119860 119894 (m

2) 66 12 6 Room C119862119886 (Jkglowastk) 1010119862119908 (Jkglowastk) 4180119865 0214 0286 05 Rooms A B and C respectively119867 (∘119862) 02119870119891119887 00037 0286 00026 Rooms A B and C respectively119870119891119887119905 -0061 Whole system119870119895 (Wm2lowastk) 0049 0051 005119876119902119903 (J) 19 28 31 Rooms A B and C respectively119877119903 082Δ120579 (∘119862) 5120576 086120579119894119899119894 (∘119862) 30 30 30 Rooms A B and C respectively120579119891 (∘119862) 25 25 25 Rooms A B and C respectively120579119895 (∘119862) 35 35 36 Room A120579119895 (∘119862) 35 35 36 Room B120579119895 (∘119862) 35 35 36 Room CΘ119904119890119905 (

∘119862) 258 261 259 Rooms A B and C respectively

Fixed pump 1M

Fixed pump n

M

Variable frequency pump

M

Switching pump 1

M

Switching pump n

M

Always working

Always working

Not always working(switching onoff)Control

strategy

CoolingCapacityallocation

Room 1heat exchanger

Room 2heat exchanger

Room nheat exchanger

WeightingFactor

calculatIon

Factor 1

Factor 2

Factor n

average temperature

difference Calculation

Figure 6 Cooling capacity allocation and average temperature methods

Mathematical Problems in Engineering 9

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

255

26

265

27

275

28

285

29

295

30

tem

pera

ture

insid

e(∘ C)

Figure 7 Inside temperature

switching behaviour Feedback control is used in the threerooms and the whole system which adjusts the insidetemperatures and water flow volume respectively

The inside temperatures of the three rooms started at30∘C and the system began at full capacity in other words allpumps were operating at rated power at the very start Somecurves were introduced into rooms as inside random coldloads the surface temperatures of thewall space window androof are set at constant valuesThe sending air volumewas thesame as the three rooms and was constant

Figure 7 shows that the inside temperatures declinerapidly by the sending air At approximately 120591 =1000 s thetemperatures stabilise near the setting values although therandom cold loads disturb the system (Figure 8) and the totaltemperature difference is close to zero all for the three rooms(Figure 9) In addition because of the lower cooling capacityrequirements after 1000 s the total water flow volume fallswhich is operating near the lowest flow volume (approx-imately 40) in other words the water system realises alarge potential space for energy saving (Figure 10) In thecontrol process the variable-frequency pump changes speedto alter the water volume in real-time by feedback controlIn the first 1000 s the pump is operating at rated powerin the last approximately 2000 s the pump is operating ina fine adjustment status because of the real-time changingof cooling capacity requirements In the middle period thepump is operating at half the rated power Switching pumpsobey the control strategy and cooling capacity allocationmethods which adjust the number of operating switchablepumps (Figure 10) We set the threshold value |119867| = 02and the total temperature difference leads to the switchingsituation shown in Figure 10

Considering the electromagnetic properties the speed ofa pump starts from zero to a stable value with a smooth

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

30

35

40

45

50

55

rand

om Q

(W)

Figure 8 Random cold loads

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

minus2

0

2

4

6

8

10

12

14

delta

T(∘

C)

Figure 9 Total temperature difference

curve (Figure 11) otherwise it exhibits simply a horizontalline with a constant value The torque responds accordingto the equation of motion which shows the electromagneticspeed regulation process (Figure 12) otherwise it exhibits ahorizontal line as well Considering the load characteristicin (17) the actual speed and torque responses do not showsimple information Figure 12 shows that the torque curvehas acceleration and callback processes after 02 s the torquestabilises at 196119873sdot1198982 which is less than the rated load torqueof 22 119873 sdot 1198982 The speed stabilises at 1273 119903119886119889119898 somewhatless than the rated speed of 1350 119903119886119889119898 The electromagneticparameters are shown in Table 2

By the power models of the pumps the energy con-sumption was simulated (Figure 13) because of the variable

10 Mathematical Problems in Engineering

Table 2 Electromagnetic parameters

Parameter Value Remark119899119901 2 variable-frequency pump119903119904 (Ω) 25 variable-frequency pumpJ (kgm2) 00012 variable-frequency pump1198751198870 (KW) 28 variable-frequency pump119875119892 (KW) 15119875119904119908 (KW) 161198791198710 (Nm2) 22 variable-frequency pump119866 2120578119887 09 variable-frequency pump

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000t (seconds)

switchable pumpsvariable frequency pump

fixed frequency pumpstotal pumps

0

001

002

003

004

005

006

007

008

009

01

wat

er fl

ow v

olum

e (kg

s)

Figure 10 Water flow volume

01 02 03 04 05 06 07 08 09 10t (seconds)

0

200

400

600

800

1000

1200

1400

spee

d (r

ads

)

Figure 11 Speed of pump

0

5

10

15

20

25

torq

ue (N

lowastm

)

01 02 03 04 05 06 07 08 09 10t (seconds)

Figure 12 Electromagnetic torque

water volume technology the energy savings were calculated(Figure 14) It is obvious that in the first 1000 s less energysavings is realised because of the cooling demand howeverafter 1000 s large energy savings are shown according tothe stabilised inside temperature None of the switchablepumps operates after approximately 120591 =1000 s thus thepower consumption remains near 2 KWh This is the sameas the variable-frequency pump which has a favourableadjustment due to the variable water flow Figures 8 and10 show that even though some interference causes volumechanges the variable-frequency pump adjusts the water flowvolume to play the roles of accuracy control and energysaving After 5000 s the total energy consumption of thepumps is approximately 86 KWh

The performance of systems controlled by hybriddynamic control strategy and constant water volumetechnology (all the pumps work at rated power and thechilled water system works without using our controlstrategy) respectively is shown in Figure 14 For constantwater volume control technology the total volume is alwaysat 0097 kgs the total power is always at 107 KW and

Mathematical Problems in Engineering 11

switchable pumpsfixed frequency pumpvariable frequency pumps

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

05

1

15

2

25

3

35

4

45

pow

er co

nsum

ptio

n (K

Wh)

Figure 13 Power consumption

variable water volumeconstant water volume

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

2

4

6

8

10

12

14

16

18

pow

er co

nsum

ptio

n (K

Wh)

Figure 14 Power consumption comparison

the whole energy consumption is up to approximately 17KWh Compared with the results of the system controlledby the hybrid dynamic control strategy it can be foundthat the energy saving potential of the pumps has notbeen excavated in the constant water volume technique Incontrast when the low cooling load level of the system is lowthe pumps may reduce frequency or quit working for energysaving as presented in Figures 10 and 13 Consequentlythe total energy consumption of the system control by thehybrid dynamical control method is approximately 86KWh The system exhibits 494 energy saving in 5000 s

compared with that controlled by constant water volumescheme

6 Conclusions

A hybrid dynamical approach to modelling and control isused in central air conditioning which is a suitable approachfor energy saving reconstruction in contemporary ChinaBy analysing the cooling capacity transfer process from thechilled water system to the air system the framework is builtBy involving a direct torque control measure the electromag-netic property is considered For optimal hybrid control theswitching control strategy is developed the cooling capacityallocation and average temperature methods are presentedOn the basis of mathematical power models of pumpsthe goal of accurate control and energy saving is realisedBy simulation a numeral example shows a hybrid controlprocess and situation of energy savings The approach saves494 of water pump power consumption when comparedwith constant water volume technology The modelling andcontrol of multihybrid systems and their applications inrefrigeration systems will be investigated in future works

Nomenclature

119894 Current119896 Amount119898 Mass119899 Speed119899119901 Number of pole-pairs119902 Flow volume119877 Resistance119906 Voltage119860 Area119862 Specific heat119862119885 Thermal capacityF Factor of cooling capacity allocationG Amount119867 Constant119869 Rotating inertia119870119891119887 Feedback coefficient (a room)119870119891119887119905 Feedback coefficient (total system)119870119894 Heat transfer coefficient119875 Power119876 Heat119877119903 Returned air rate119878119860119861119862 Switch status signal119879119890 Electromagnetic torque119879119871 Load torque

Greek symbols

120576 Heat transfer efficiency120578 FactorΔ120579 Temperature difference120579 Temperature120579119895 Surface temperatureΨ Flux linkage120596 Angular speed

12 Mathematical Problems in Engineering

Subscript

0 Rated119860 Air119861 Variable-frequency pump119865 Fresh air119891119879 Filter time119866 Fixed-frequency pump119894119899119894 Initial119894119879 Integral time119895 Surface (wall space window and roof)119902119903 Latent heat119903119889 Random119903119905 Return119904 Stator119904119886 Sending air119904119890119905 Setting value119904119908 Switchable pump119904119872 M-axis of stator flux-oriented119904119879 T-axis of stator flux-oriented119908 Water119905119905 Totalxr Sensible heatDC Busbar120595 Flux linkage

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the National Natural ScienceFoundation of China (no 40761104181)

References

[1] China Statistical Yearbook China Statistical Publishing HouseBeijing China 2015

[2] J Liang B Li Y Wu and R Yao ldquoAn investigation of theexisting situation and trends in building energy efficiencymanagement in Chinardquo Energy and Buildings vol 39 no 10 pp1098ndash1106 2007

[3] K F Fong V I Hanby and T T Chow ldquoHVAC systemoptimization for energymanagement by evolutionary program-mingrdquo Energy and Buildings vol 38 no 3 pp 220ndash231 2006

[4] A Kecebas and I Yabanova ldquoThermal monitoring and opti-mization of geothermal district heating systems using artificialneural network A case studyrdquo Energy and Buildings vol 50 pp339ndash346 2012

[5] T Y Zhao J L Zhang and L D Ma ldquoOn-line optimizationcontrol method based on extreme value analysis for parallelvariable-frequency hydraulic pumps in central air-conditioningsystemsrdquo Building and Environment vol 47 pp 330ndash338 2012

[6] D Kaya E A Yagmur K S Yigit F C Kilic A S Eren andC Celik ldquoEnergy efficiency in pumpsrdquo Energy Conversion andManagement vol 49 no 6 pp 1662ndash1673 2008

[7] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[8] T T Chow K F Fong A L S Chan R Yau W H Au andV Cheng ldquoEnergy modelling of district cooling system for newurban developmentrdquo Energy and Buildings vol 36 no 11 pp1153ndash1162 2004

[9] X Sheng and L Duanmu ldquoElectricity consumption and eco-nomic analyses of district heating system with distributedvariable speed pumpsrdquo Energy and Buildings vol 118 pp 291ndash300 2016

[10] R M Lewis V Torczon and M W Trosset ldquoDirect searchmethods then and nowrdquo Journal of Computational and AppliedMathematics vol 124 no 1-2 pp 191ndash207 2000

[11] J Sun and A Reddy ldquoOptimal control of building HVACampRsystems using complete simulation-based sequential quadraticprogramming (CSB-SQP)rdquo Building and Environment vol 40no 5 pp 657ndash669 2005

[12] M Zaheer-Uddin and G R Zheng ldquoOptimal control of time-scheduled heating ventilating and air conditioning processesin buildingsrdquo Energy Conversion and Management vol 41 no1 pp 49ndash60 2000

[13] L Lu W Cai Y C Soh L Xie and S Li ldquoHVAC systemoptimization - Condenser water looprdquo Energy Conversion andManagement vol 45 no 4 pp 613ndash630 2004

[14] N Nassif S Moujaes and M Zaheeruddin ldquoSelf-tuningdynamic models of HVAC system componentsrdquo Energy andBuildings vol 40 no 9 pp 1709ndash1720 2008

[15] I-H Yang M-S Yeo and K-W Kim ldquoApplication of artificialneural network to predict the optimal start time for heatingsystem in buildingrdquo Energy Conversion and Management vol44 no 17 pp 2791ndash2809 2003

[16] S Wang and J Burnett ldquoOnline adaptive control for optimizingvariable-speed pumps of indirect water-cooled chilling sys-temsrdquoAppliedThermal Engineering vol 21 no 11 pp 1083ndash11032001

[17] M Anderson M Buehner P Young et al ldquoAn experimentalsystem for advanced heating ventilating and air conditioning(HVAC) controlrdquo Energy and Buildings vol 39 no 2 pp 136ndash147 2007

[18] S Qu Z Sun H Fan and K Li ldquoBP neural network for theprediction of urban building energy consumption based onMatlab and its applicationrdquo in Second International Conferenceon Computer Modeling and Simulation pp 263ndash267 IEEESanya Hainan China 2010

[19] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[20] Z Ma and S Wang ldquoAn optimal control strategy for complexbuilding central chilled water systems for practical and real-time applicationsrdquo Building and Environment vol 44 no 6 pp1188ndash1198 2009

[21] D-C Gao S Wang and Y Sun ldquoA fault-tolerant and energyefficient control strategy for primary-secondary chilled watersystems in buildingsrdquo Energy and Buildings vol 43 no 12 pp3646ndash3656 2011

[22] X Sheng andD Lin ldquoEnergy saving analyses on the reconstruc-tion project in district heating system with distributed variablespeed pumpsrdquo Applied Thermal Engineering vol 101 pp 432ndash445 2016

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Mathematical Problems in Engineering 5

M-T

ATRSVPWM

Voltage estimation

module

stator flux linkagetorque

estimator

Ψlowasts

Tlowaste

Te

ulowastsM

ulowasts

ulowastsT

-

ss

AΨR

us

SABC

uDC

is

Figure 2 Motor model

voltage estimation module estimates the actual stator voltagevector according to switch status signal 119878119860119861119862 and measuredbusbar voltage 119906119863119862

The simplified equations of stator voltage and torque are

119889Ψ119904119889120591 = 119906119904119872 minus 119903119904119894119904119872 (11a)

119879119890 = 1119903119904 119899119901Ψ119904 (119906119904119879 minus 120596119904Ψ119904) (11b)

It is apparent that the input variables and output variableshave coupling relationships so we cannot use 119906119904119872 and 119906119904119879to achieve independent control with Ψ119904 and 119879119890 respectivelyTherefore a new variable 119906Ψ must be introduced for decou-pling Let

119906Ψ = 119906119904119872 minus 119903119904119894119904119872 (12a)

119906119879 = Ψ119904 (119906119904119879 minus 120596119904Ψ119904) (12b)

After decoupling the transfer function is a proportionalcomponent from 119906119879 to 119879119890 the transfer function is

119866119879 (119904) = 119879119890 (119904)119906119879 (119904) =119899119901119903119904 (13)

The dynamic structure of the torque control loop is shown inFigure 3 In the figure there is an inertial component and aproportional component The filter time constant 119879119891119879 is thesame as the feedback smoothing time constant the integraltime constant of the torque controller is 119879119894119879

We use an integral controller for torque adjustment

119866119860119879119877 (119904) = 1119904119879119894119879 (14)

Thus the torque control loop is simplified as

119866119879minus0 (119904) = 119899119901119904119879119894119879 (1 + 119904119879119891119879) 119903119904 (15)

33 Building the Relationship of Torque with Water FlowVolume of a Variable-Frequency Pump In general the watervolume 119902 is in proportion to speed 119899 of a pump in a water

ATR TeTlowaste

1

TfTs + 1

1

TfTs + 1

uT 1

rsnp

Figure 3 Torque control loop

system so it is obvious that 1199021199020 = 1198991198990 where 1199020 is therated water volume and 1198990 is the rated speed Using motionequation where 119869 is the rotational inertia 119879119890 is the torqueand 119879119871 is the load torque the torque is obtained by

119879119890 = 119879119871 + 11986911989901199020 119889119902119889120591 (16)

In addition the load of the pumps conforms to a quadraticproportion where 1198791198710 is the rated load torque As anequation

1198791198711198791198710 =119899211989920 (17)

Thus the relationship from torque to water flow volume isbuilt Combining (17) with (10) we build the state spaceequation to show the whole control process of the pumpsHere with 1199091 = 120579 as the inside temperature and 1199092 = 119902119887as water flow volume of the variable-frequency pump 1199091 and1199092 are state variablesWith 119906 = 119879119890 as a control variable we set119910 = 1199091 as the output variable Figure 4 shows the state space

Thus the coefficients of the state space equation are

119860 = (119908 minus 1) 119902119899119888119886 minus sum119870119894119860119862119911119861 = minus120576119888119908Δ120579119862119911119864= (1 minus 119908) 119902119904119886119888119886120579119900119906119905 + sum119870119894119860 119894120579119894 + 119876 + 119876119902119903 minus 119902119866120576119888119908Δ120579

119862119911

6 Mathematical Problems in Engineering

u

x1x2 x1x2

H

G

E F

B

Ax2

yintint

Figure 4 State space

119865119894 = minus119896119902119873120576119888119908Δ120579119862119911 [119896 = 1 2 119899]119866 = 1119869

11990201198990119867 = 119879119871011989920

1119869 11990201198990

(18)

Combining these equations and coefficients we get theequations of state space

= ( 11986001198610 )119909 + (

0119867)119909

2 + (0119866)119906 + (119864 + 1198650 ) (19a)

119910 = (10)119909 (19b)

34 Mathematical Power Models of Pumps According to theelectromagnetic property of a variable-frequency pump theoutput mechanical power of the pump is

119875119900119901 = 120578119887119879119890120596 = 1205781198871198791198901198999550 (20)

120578119887 is the factor converted from motor power into outputmechanical power 0 le 120578119887 le 1 and 120596 is angular velocity

The power of a fixed pump is 119875119892 and the power ofswitchable pumps is 119875119904119908 Both of these kinds of pumpsoperate at constant frequency so we consider them operatingat constant power Thus we get the total power of the pumps

119875119905119900119905119886119897 = 119866119875119892 + 119875119887 + 119896119875119904119908 (21)

G is the total number of fixed pumps and k is the number ofoperating switching pumps

4 Hybrid Dynamical Control Strategy

41 Target of Optimal Hybrid Control for Central Air Con-ditioning The goal of optimal control for central air con-ditioning is to minimise the power of the chilled pumps

further the inside temperature 120579 should be close to the settingtemperature 120579119904119890119905 We obtain the target function

min 119869 = int1205911198911205910

119875119905119900119905119886119897119889120591120590119894(120591)

= int12059111205910

1198751199051199001199051198861198971198891205911205901(120591)

+ int12059121205911

1198751199051199001199051198861198971198891205911205902(120591)

+

+ int120591119891120591119899minus1

119875119905119900119905119886119897119889120591120590119899(120591)

= 119899minus1sum119894=0

int1205911+1198941205910+119894

119875119905119900119905119886119897119889120591120590119894+1(120591)

(22)

where 120591119891 = 120591119899 Due to the switching behaviours the systemis divided into some subsystems in different time intervalsnamely [1205910 1205911] [1205911 1205912][120591119899-1 120591f] The switching sequence isproduced at switching time 120591i and the switching law 120590i and120591i are one-to-one correspondence

Equation (22) means that (i) the target function is to findtheminimumvalue of energy consumption of pumps on timeinterval [1205910 120591f] (ii) the function is divided into several partsandwe calculate the integration on each time interval (iii) thesum of all integration terms is the minimum of the objectivefunction

Remarks 1

(1) i is finite(2) Switching law is state-independent so the length of

each time interval is not the same(3) We simply consider the requirement of energy saving

and the humidity is not concerned in this work

42 Developing the Switching Control Strategy Variable waterflow is realised by variable-frequency regulation of variable-frequency pumps and switching control of switchable pumpsFor the water flow volume of the variable-frequency pumpthe feedback closed loop can be used in the system foraccurate adjustment For the switching pumps we proposean algorithm for deployment According to the changingcold load we set the switching condition and orientationThe switching law is a simple and economic mode inreconstruction engineering that avoids complex processesand computing time It is shown in Figure 5

The switching strategy is based on state dependence Theswitching behaviour occurs simply by satisfying the state

Mathematical Problems in Engineering 7

Y

Y

YN N

N

N

initialize set k=N

After a sampling period obtaintemperature inside

k=k

k=N k=0

k=k-1k=0k=k+1k=N

Y

-set ⩾H

-set⩾H

Figure 5 Control strategy of switching pumps

judgement In other words once the real-time sampling valueis beyond the setting threshold value |119867| the system willswitch At the initial time k is set to the maximum value NAfter each sampling period (constant) the system obtains theinside temperature 120579 and compares |120579 minus 120579119904119890119905| with |119867| If thevalue is in the setting range the systemwill stay in the currentsubsystem Otherwise we will calculate |120579 minus 120579119904119890119905| One way is119896 + 1 because of 120579 minus 120579119904119890119905 ge 119867 unless k is the maximum theother is k-1 because of 120579minus120579119904119890119905 le minus119867 unless k is theminimum

Remarks 2

(1) 120579119904119890119905 is the inside temperature setting and 120579 is the real-time inside temperature

(2) k is the number of operating switching pumps(3) Themaximum number of switching pumps isN If all

the switching pumps are operating the system is closeto full capacity

(4) The minimum number of switching pumps is 0 If anonswitching pump is operating the system is closeto optimal energy saving

(5) Whether switching is on or off the system obeys onepump at a timeThe switching behaviour triggers onlyone pump

43 Cooling Capacity Allocation and Average TemperatureMethods For a whole building the framework is modelledwith a switching control strategy In real system with manyrooms with different areas the cooling capacity requirementand temperature setting need an adaptive method to matchFor allocation of cooling capacity we adopt a weighting

factor according to the proportion of thermal capacity in eachroom This is a quantitative criterion on the demand sideon the supply side there is a measure to balance differentinside temperatures The average temperature difference as afeedback signal is used to control the pumps The switchingcondition |120579 minus 120579119904119890119905| can be modified as

1003816100381610038161003816120579 minus 1205791199041198901199051003816100381610038161003816 =119873sum1

1003816100381610038161003816120579119894 minus 120579119904119890119905minus1198941003816100381610038161003816119873 (23)

The weighting factor is

119865119894 = 119862119885minus119894sum1198731 119862119885minus119894 (24)

The schematic diagram is shown in Figure 6

Remarks 3

(1) |120579 minus 120579119904119890119905| is the average temperature difference of thebuilding

(2) 120579119894 is the real-time temperature inside the 119894th room120579119904119890119905minus119894 is the setting temperature inside the 119894th roomThere are N rooms operating by using cooling capac-ity

(3) 119865119894 is the weighting factor of the 119894th room for coolingcapacity allocation119862119885minus119894 is the thermal capacity of the119894th room

(4) sum1198731 119862119885minus119894 is the total thermal capacity of the rooms byusing cooling capacity

(5) Obviously these are based on the quantitative crite-rion whatever the average temperature difference orweighting factor

(6) In view of allocating cooling capacity by weightingfactor the computing method of average temperaturedifference actually involves the average temperatureper cubic meter

(7) Heat capacity 119862119885 is equal to 119862119886119898119886 for each room

5 Numerical Example and Simulation Results

In this section we present numerical results from simulationsof the chilled water system Three different rooms are thesimulation objects the cold air is sent to the rooms forreducing the inside temperaturesThe supply side uses pumpsfor sending cold water to the air system by the switchingcontrol strategy and cooling capacity allocation method Weuse one variable-frequency pump four switching pumps andtwo fixed pumps to transfer chilled water and adjust coolingcapacityThe cooling capacity transfermode of variable watervolume and constant air volume is presented The purposeof the variable water volume is accuracy control and energysaving via our model and control strategy The parametersare listed in Table 1

Simulink 2007 was used for simulating the whole processwhere the simulation time was 5000 s The switching sampletime 119879119871 of the system was set to 60 s the system checksthe real-time inside temperature each 119879119871 and decides the

8 Mathematical Problems in Engineering

Table 1 Thermal parameters

Parameter Value Remark119898119886 (kg) 67725 903 158025 Rooms A B and C respectively119902119887 (kgs) 002119902119904119908 (kgs) 0013119902119904119886 (kgs) 0655 0655 0655 Rooms A B and C respectively119902119892 (kgs) 0025119860 119894 (m

2) 36 8 0 Room A119860 119894 (m

2) 52 9 0 Room B119860 119894 (m

2) 66 12 6 Room C119862119886 (Jkglowastk) 1010119862119908 (Jkglowastk) 4180119865 0214 0286 05 Rooms A B and C respectively119867 (∘119862) 02119870119891119887 00037 0286 00026 Rooms A B and C respectively119870119891119887119905 -0061 Whole system119870119895 (Wm2lowastk) 0049 0051 005119876119902119903 (J) 19 28 31 Rooms A B and C respectively119877119903 082Δ120579 (∘119862) 5120576 086120579119894119899119894 (∘119862) 30 30 30 Rooms A B and C respectively120579119891 (∘119862) 25 25 25 Rooms A B and C respectively120579119895 (∘119862) 35 35 36 Room A120579119895 (∘119862) 35 35 36 Room B120579119895 (∘119862) 35 35 36 Room CΘ119904119890119905 (

∘119862) 258 261 259 Rooms A B and C respectively

Fixed pump 1M

Fixed pump n

M

Variable frequency pump

M

Switching pump 1

M

Switching pump n

M

Always working

Always working

Not always working(switching onoff)Control

strategy

CoolingCapacityallocation

Room 1heat exchanger

Room 2heat exchanger

Room nheat exchanger

WeightingFactor

calculatIon

Factor 1

Factor 2

Factor n

average temperature

difference Calculation

Figure 6 Cooling capacity allocation and average temperature methods

Mathematical Problems in Engineering 9

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

255

26

265

27

275

28

285

29

295

30

tem

pera

ture

insid

e(∘ C)

Figure 7 Inside temperature

switching behaviour Feedback control is used in the threerooms and the whole system which adjusts the insidetemperatures and water flow volume respectively

The inside temperatures of the three rooms started at30∘C and the system began at full capacity in other words allpumps were operating at rated power at the very start Somecurves were introduced into rooms as inside random coldloads the surface temperatures of thewall space window androof are set at constant valuesThe sending air volumewas thesame as the three rooms and was constant

Figure 7 shows that the inside temperatures declinerapidly by the sending air At approximately 120591 =1000 s thetemperatures stabilise near the setting values although therandom cold loads disturb the system (Figure 8) and the totaltemperature difference is close to zero all for the three rooms(Figure 9) In addition because of the lower cooling capacityrequirements after 1000 s the total water flow volume fallswhich is operating near the lowest flow volume (approx-imately 40) in other words the water system realises alarge potential space for energy saving (Figure 10) In thecontrol process the variable-frequency pump changes speedto alter the water volume in real-time by feedback controlIn the first 1000 s the pump is operating at rated powerin the last approximately 2000 s the pump is operating ina fine adjustment status because of the real-time changingof cooling capacity requirements In the middle period thepump is operating at half the rated power Switching pumpsobey the control strategy and cooling capacity allocationmethods which adjust the number of operating switchablepumps (Figure 10) We set the threshold value |119867| = 02and the total temperature difference leads to the switchingsituation shown in Figure 10

Considering the electromagnetic properties the speed ofa pump starts from zero to a stable value with a smooth

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

30

35

40

45

50

55

rand

om Q

(W)

Figure 8 Random cold loads

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

minus2

0

2

4

6

8

10

12

14

delta

T(∘

C)

Figure 9 Total temperature difference

curve (Figure 11) otherwise it exhibits simply a horizontalline with a constant value The torque responds accordingto the equation of motion which shows the electromagneticspeed regulation process (Figure 12) otherwise it exhibits ahorizontal line as well Considering the load characteristicin (17) the actual speed and torque responses do not showsimple information Figure 12 shows that the torque curvehas acceleration and callback processes after 02 s the torquestabilises at 196119873sdot1198982 which is less than the rated load torqueof 22 119873 sdot 1198982 The speed stabilises at 1273 119903119886119889119898 somewhatless than the rated speed of 1350 119903119886119889119898 The electromagneticparameters are shown in Table 2

By the power models of the pumps the energy con-sumption was simulated (Figure 13) because of the variable

10 Mathematical Problems in Engineering

Table 2 Electromagnetic parameters

Parameter Value Remark119899119901 2 variable-frequency pump119903119904 (Ω) 25 variable-frequency pumpJ (kgm2) 00012 variable-frequency pump1198751198870 (KW) 28 variable-frequency pump119875119892 (KW) 15119875119904119908 (KW) 161198791198710 (Nm2) 22 variable-frequency pump119866 2120578119887 09 variable-frequency pump

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000t (seconds)

switchable pumpsvariable frequency pump

fixed frequency pumpstotal pumps

0

001

002

003

004

005

006

007

008

009

01

wat

er fl

ow v

olum

e (kg

s)

Figure 10 Water flow volume

01 02 03 04 05 06 07 08 09 10t (seconds)

0

200

400

600

800

1000

1200

1400

spee

d (r

ads

)

Figure 11 Speed of pump

0

5

10

15

20

25

torq

ue (N

lowastm

)

01 02 03 04 05 06 07 08 09 10t (seconds)

Figure 12 Electromagnetic torque

water volume technology the energy savings were calculated(Figure 14) It is obvious that in the first 1000 s less energysavings is realised because of the cooling demand howeverafter 1000 s large energy savings are shown according tothe stabilised inside temperature None of the switchablepumps operates after approximately 120591 =1000 s thus thepower consumption remains near 2 KWh This is the sameas the variable-frequency pump which has a favourableadjustment due to the variable water flow Figures 8 and10 show that even though some interference causes volumechanges the variable-frequency pump adjusts the water flowvolume to play the roles of accuracy control and energysaving After 5000 s the total energy consumption of thepumps is approximately 86 KWh

The performance of systems controlled by hybriddynamic control strategy and constant water volumetechnology (all the pumps work at rated power and thechilled water system works without using our controlstrategy) respectively is shown in Figure 14 For constantwater volume control technology the total volume is alwaysat 0097 kgs the total power is always at 107 KW and

Mathematical Problems in Engineering 11

switchable pumpsfixed frequency pumpvariable frequency pumps

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

05

1

15

2

25

3

35

4

45

pow

er co

nsum

ptio

n (K

Wh)

Figure 13 Power consumption

variable water volumeconstant water volume

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

2

4

6

8

10

12

14

16

18

pow

er co

nsum

ptio

n (K

Wh)

Figure 14 Power consumption comparison

the whole energy consumption is up to approximately 17KWh Compared with the results of the system controlledby the hybrid dynamic control strategy it can be foundthat the energy saving potential of the pumps has notbeen excavated in the constant water volume technique Incontrast when the low cooling load level of the system is lowthe pumps may reduce frequency or quit working for energysaving as presented in Figures 10 and 13 Consequentlythe total energy consumption of the system control by thehybrid dynamical control method is approximately 86KWh The system exhibits 494 energy saving in 5000 s

compared with that controlled by constant water volumescheme

6 Conclusions

A hybrid dynamical approach to modelling and control isused in central air conditioning which is a suitable approachfor energy saving reconstruction in contemporary ChinaBy analysing the cooling capacity transfer process from thechilled water system to the air system the framework is builtBy involving a direct torque control measure the electromag-netic property is considered For optimal hybrid control theswitching control strategy is developed the cooling capacityallocation and average temperature methods are presentedOn the basis of mathematical power models of pumpsthe goal of accurate control and energy saving is realisedBy simulation a numeral example shows a hybrid controlprocess and situation of energy savings The approach saves494 of water pump power consumption when comparedwith constant water volume technology The modelling andcontrol of multihybrid systems and their applications inrefrigeration systems will be investigated in future works

Nomenclature

119894 Current119896 Amount119898 Mass119899 Speed119899119901 Number of pole-pairs119902 Flow volume119877 Resistance119906 Voltage119860 Area119862 Specific heat119862119885 Thermal capacityF Factor of cooling capacity allocationG Amount119867 Constant119869 Rotating inertia119870119891119887 Feedback coefficient (a room)119870119891119887119905 Feedback coefficient (total system)119870119894 Heat transfer coefficient119875 Power119876 Heat119877119903 Returned air rate119878119860119861119862 Switch status signal119879119890 Electromagnetic torque119879119871 Load torque

Greek symbols

120576 Heat transfer efficiency120578 FactorΔ120579 Temperature difference120579 Temperature120579119895 Surface temperatureΨ Flux linkage120596 Angular speed

12 Mathematical Problems in Engineering

Subscript

0 Rated119860 Air119861 Variable-frequency pump119865 Fresh air119891119879 Filter time119866 Fixed-frequency pump119894119899119894 Initial119894119879 Integral time119895 Surface (wall space window and roof)119902119903 Latent heat119903119889 Random119903119905 Return119904 Stator119904119886 Sending air119904119890119905 Setting value119904119908 Switchable pump119904119872 M-axis of stator flux-oriented119904119879 T-axis of stator flux-oriented119908 Water119905119905 Totalxr Sensible heatDC Busbar120595 Flux linkage

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the National Natural ScienceFoundation of China (no 40761104181)

References

[1] China Statistical Yearbook China Statistical Publishing HouseBeijing China 2015

[2] J Liang B Li Y Wu and R Yao ldquoAn investigation of theexisting situation and trends in building energy efficiencymanagement in Chinardquo Energy and Buildings vol 39 no 10 pp1098ndash1106 2007

[3] K F Fong V I Hanby and T T Chow ldquoHVAC systemoptimization for energymanagement by evolutionary program-mingrdquo Energy and Buildings vol 38 no 3 pp 220ndash231 2006

[4] A Kecebas and I Yabanova ldquoThermal monitoring and opti-mization of geothermal district heating systems using artificialneural network A case studyrdquo Energy and Buildings vol 50 pp339ndash346 2012

[5] T Y Zhao J L Zhang and L D Ma ldquoOn-line optimizationcontrol method based on extreme value analysis for parallelvariable-frequency hydraulic pumps in central air-conditioningsystemsrdquo Building and Environment vol 47 pp 330ndash338 2012

[6] D Kaya E A Yagmur K S Yigit F C Kilic A S Eren andC Celik ldquoEnergy efficiency in pumpsrdquo Energy Conversion andManagement vol 49 no 6 pp 1662ndash1673 2008

[7] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[8] T T Chow K F Fong A L S Chan R Yau W H Au andV Cheng ldquoEnergy modelling of district cooling system for newurban developmentrdquo Energy and Buildings vol 36 no 11 pp1153ndash1162 2004

[9] X Sheng and L Duanmu ldquoElectricity consumption and eco-nomic analyses of district heating system with distributedvariable speed pumpsrdquo Energy and Buildings vol 118 pp 291ndash300 2016

[10] R M Lewis V Torczon and M W Trosset ldquoDirect searchmethods then and nowrdquo Journal of Computational and AppliedMathematics vol 124 no 1-2 pp 191ndash207 2000

[11] J Sun and A Reddy ldquoOptimal control of building HVACampRsystems using complete simulation-based sequential quadraticprogramming (CSB-SQP)rdquo Building and Environment vol 40no 5 pp 657ndash669 2005

[12] M Zaheer-Uddin and G R Zheng ldquoOptimal control of time-scheduled heating ventilating and air conditioning processesin buildingsrdquo Energy Conversion and Management vol 41 no1 pp 49ndash60 2000

[13] L Lu W Cai Y C Soh L Xie and S Li ldquoHVAC systemoptimization - Condenser water looprdquo Energy Conversion andManagement vol 45 no 4 pp 613ndash630 2004

[14] N Nassif S Moujaes and M Zaheeruddin ldquoSelf-tuningdynamic models of HVAC system componentsrdquo Energy andBuildings vol 40 no 9 pp 1709ndash1720 2008

[15] I-H Yang M-S Yeo and K-W Kim ldquoApplication of artificialneural network to predict the optimal start time for heatingsystem in buildingrdquo Energy Conversion and Management vol44 no 17 pp 2791ndash2809 2003

[16] S Wang and J Burnett ldquoOnline adaptive control for optimizingvariable-speed pumps of indirect water-cooled chilling sys-temsrdquoAppliedThermal Engineering vol 21 no 11 pp 1083ndash11032001

[17] M Anderson M Buehner P Young et al ldquoAn experimentalsystem for advanced heating ventilating and air conditioning(HVAC) controlrdquo Energy and Buildings vol 39 no 2 pp 136ndash147 2007

[18] S Qu Z Sun H Fan and K Li ldquoBP neural network for theprediction of urban building energy consumption based onMatlab and its applicationrdquo in Second International Conferenceon Computer Modeling and Simulation pp 263ndash267 IEEESanya Hainan China 2010

[19] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[20] Z Ma and S Wang ldquoAn optimal control strategy for complexbuilding central chilled water systems for practical and real-time applicationsrdquo Building and Environment vol 44 no 6 pp1188ndash1198 2009

[21] D-C Gao S Wang and Y Sun ldquoA fault-tolerant and energyefficient control strategy for primary-secondary chilled watersystems in buildingsrdquo Energy and Buildings vol 43 no 12 pp3646ndash3656 2011

[22] X Sheng andD Lin ldquoEnergy saving analyses on the reconstruc-tion project in district heating system with distributed variablespeed pumpsrdquo Applied Thermal Engineering vol 101 pp 432ndash445 2016

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Submit your manuscripts atwwwhindawicom

6 Mathematical Problems in Engineering

u

x1x2 x1x2

H

G

E F

B

Ax2

yintint

Figure 4 State space

119865119894 = minus119896119902119873120576119888119908Δ120579119862119911 [119896 = 1 2 119899]119866 = 1119869

11990201198990119867 = 119879119871011989920

1119869 11990201198990

(18)

Combining these equations and coefficients we get theequations of state space

= ( 11986001198610 )119909 + (

0119867)119909

2 + (0119866)119906 + (119864 + 1198650 ) (19a)

119910 = (10)119909 (19b)

34 Mathematical Power Models of Pumps According to theelectromagnetic property of a variable-frequency pump theoutput mechanical power of the pump is

119875119900119901 = 120578119887119879119890120596 = 1205781198871198791198901198999550 (20)

120578119887 is the factor converted from motor power into outputmechanical power 0 le 120578119887 le 1 and 120596 is angular velocity

The power of a fixed pump is 119875119892 and the power ofswitchable pumps is 119875119904119908 Both of these kinds of pumpsoperate at constant frequency so we consider them operatingat constant power Thus we get the total power of the pumps

119875119905119900119905119886119897 = 119866119875119892 + 119875119887 + 119896119875119904119908 (21)

G is the total number of fixed pumps and k is the number ofoperating switching pumps

4 Hybrid Dynamical Control Strategy

41 Target of Optimal Hybrid Control for Central Air Con-ditioning The goal of optimal control for central air con-ditioning is to minimise the power of the chilled pumps

further the inside temperature 120579 should be close to the settingtemperature 120579119904119890119905 We obtain the target function

min 119869 = int1205911198911205910

119875119905119900119905119886119897119889120591120590119894(120591)

= int12059111205910

1198751199051199001199051198861198971198891205911205901(120591)

+ int12059121205911

1198751199051199001199051198861198971198891205911205902(120591)

+

+ int120591119891120591119899minus1

119875119905119900119905119886119897119889120591120590119899(120591)

= 119899minus1sum119894=0

int1205911+1198941205910+119894

119875119905119900119905119886119897119889120591120590119894+1(120591)

(22)

where 120591119891 = 120591119899 Due to the switching behaviours the systemis divided into some subsystems in different time intervalsnamely [1205910 1205911] [1205911 1205912][120591119899-1 120591f] The switching sequence isproduced at switching time 120591i and the switching law 120590i and120591i are one-to-one correspondence

Equation (22) means that (i) the target function is to findtheminimumvalue of energy consumption of pumps on timeinterval [1205910 120591f] (ii) the function is divided into several partsandwe calculate the integration on each time interval (iii) thesum of all integration terms is the minimum of the objectivefunction

Remarks 1

(1) i is finite(2) Switching law is state-independent so the length of

each time interval is not the same(3) We simply consider the requirement of energy saving

and the humidity is not concerned in this work

42 Developing the Switching Control Strategy Variable waterflow is realised by variable-frequency regulation of variable-frequency pumps and switching control of switchable pumpsFor the water flow volume of the variable-frequency pumpthe feedback closed loop can be used in the system foraccurate adjustment For the switching pumps we proposean algorithm for deployment According to the changingcold load we set the switching condition and orientationThe switching law is a simple and economic mode inreconstruction engineering that avoids complex processesand computing time It is shown in Figure 5

The switching strategy is based on state dependence Theswitching behaviour occurs simply by satisfying the state

Mathematical Problems in Engineering 7

Y

Y

YN N

N

N

initialize set k=N

After a sampling period obtaintemperature inside

k=k

k=N k=0

k=k-1k=0k=k+1k=N

Y

-set ⩾H

-set⩾H

Figure 5 Control strategy of switching pumps

judgement In other words once the real-time sampling valueis beyond the setting threshold value |119867| the system willswitch At the initial time k is set to the maximum value NAfter each sampling period (constant) the system obtains theinside temperature 120579 and compares |120579 minus 120579119904119890119905| with |119867| If thevalue is in the setting range the systemwill stay in the currentsubsystem Otherwise we will calculate |120579 minus 120579119904119890119905| One way is119896 + 1 because of 120579 minus 120579119904119890119905 ge 119867 unless k is the maximum theother is k-1 because of 120579minus120579119904119890119905 le minus119867 unless k is theminimum

Remarks 2

(1) 120579119904119890119905 is the inside temperature setting and 120579 is the real-time inside temperature

(2) k is the number of operating switching pumps(3) Themaximum number of switching pumps isN If all

the switching pumps are operating the system is closeto full capacity

(4) The minimum number of switching pumps is 0 If anonswitching pump is operating the system is closeto optimal energy saving

(5) Whether switching is on or off the system obeys onepump at a timeThe switching behaviour triggers onlyone pump

43 Cooling Capacity Allocation and Average TemperatureMethods For a whole building the framework is modelledwith a switching control strategy In real system with manyrooms with different areas the cooling capacity requirementand temperature setting need an adaptive method to matchFor allocation of cooling capacity we adopt a weighting

factor according to the proportion of thermal capacity in eachroom This is a quantitative criterion on the demand sideon the supply side there is a measure to balance differentinside temperatures The average temperature difference as afeedback signal is used to control the pumps The switchingcondition |120579 minus 120579119904119890119905| can be modified as

1003816100381610038161003816120579 minus 1205791199041198901199051003816100381610038161003816 =119873sum1

1003816100381610038161003816120579119894 minus 120579119904119890119905minus1198941003816100381610038161003816119873 (23)

The weighting factor is

119865119894 = 119862119885minus119894sum1198731 119862119885minus119894 (24)

The schematic diagram is shown in Figure 6

Remarks 3

(1) |120579 minus 120579119904119890119905| is the average temperature difference of thebuilding

(2) 120579119894 is the real-time temperature inside the 119894th room120579119904119890119905minus119894 is the setting temperature inside the 119894th roomThere are N rooms operating by using cooling capac-ity

(3) 119865119894 is the weighting factor of the 119894th room for coolingcapacity allocation119862119885minus119894 is the thermal capacity of the119894th room

(4) sum1198731 119862119885minus119894 is the total thermal capacity of the rooms byusing cooling capacity

(5) Obviously these are based on the quantitative crite-rion whatever the average temperature difference orweighting factor

(6) In view of allocating cooling capacity by weightingfactor the computing method of average temperaturedifference actually involves the average temperatureper cubic meter

(7) Heat capacity 119862119885 is equal to 119862119886119898119886 for each room

5 Numerical Example and Simulation Results

In this section we present numerical results from simulationsof the chilled water system Three different rooms are thesimulation objects the cold air is sent to the rooms forreducing the inside temperaturesThe supply side uses pumpsfor sending cold water to the air system by the switchingcontrol strategy and cooling capacity allocation method Weuse one variable-frequency pump four switching pumps andtwo fixed pumps to transfer chilled water and adjust coolingcapacityThe cooling capacity transfermode of variable watervolume and constant air volume is presented The purposeof the variable water volume is accuracy control and energysaving via our model and control strategy The parametersare listed in Table 1

Simulink 2007 was used for simulating the whole processwhere the simulation time was 5000 s The switching sampletime 119879119871 of the system was set to 60 s the system checksthe real-time inside temperature each 119879119871 and decides the

8 Mathematical Problems in Engineering

Table 1 Thermal parameters

Parameter Value Remark119898119886 (kg) 67725 903 158025 Rooms A B and C respectively119902119887 (kgs) 002119902119904119908 (kgs) 0013119902119904119886 (kgs) 0655 0655 0655 Rooms A B and C respectively119902119892 (kgs) 0025119860 119894 (m

2) 36 8 0 Room A119860 119894 (m

2) 52 9 0 Room B119860 119894 (m

2) 66 12 6 Room C119862119886 (Jkglowastk) 1010119862119908 (Jkglowastk) 4180119865 0214 0286 05 Rooms A B and C respectively119867 (∘119862) 02119870119891119887 00037 0286 00026 Rooms A B and C respectively119870119891119887119905 -0061 Whole system119870119895 (Wm2lowastk) 0049 0051 005119876119902119903 (J) 19 28 31 Rooms A B and C respectively119877119903 082Δ120579 (∘119862) 5120576 086120579119894119899119894 (∘119862) 30 30 30 Rooms A B and C respectively120579119891 (∘119862) 25 25 25 Rooms A B and C respectively120579119895 (∘119862) 35 35 36 Room A120579119895 (∘119862) 35 35 36 Room B120579119895 (∘119862) 35 35 36 Room CΘ119904119890119905 (

∘119862) 258 261 259 Rooms A B and C respectively

Fixed pump 1M

Fixed pump n

M

Variable frequency pump

M

Switching pump 1

M

Switching pump n

M

Always working

Always working

Not always working(switching onoff)Control

strategy

CoolingCapacityallocation

Room 1heat exchanger

Room 2heat exchanger

Room nheat exchanger

WeightingFactor

calculatIon

Factor 1

Factor 2

Factor n

average temperature

difference Calculation

Figure 6 Cooling capacity allocation and average temperature methods

Mathematical Problems in Engineering 9

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

255

26

265

27

275

28

285

29

295

30

tem

pera

ture

insid

e(∘ C)

Figure 7 Inside temperature

switching behaviour Feedback control is used in the threerooms and the whole system which adjusts the insidetemperatures and water flow volume respectively

The inside temperatures of the three rooms started at30∘C and the system began at full capacity in other words allpumps were operating at rated power at the very start Somecurves were introduced into rooms as inside random coldloads the surface temperatures of thewall space window androof are set at constant valuesThe sending air volumewas thesame as the three rooms and was constant

Figure 7 shows that the inside temperatures declinerapidly by the sending air At approximately 120591 =1000 s thetemperatures stabilise near the setting values although therandom cold loads disturb the system (Figure 8) and the totaltemperature difference is close to zero all for the three rooms(Figure 9) In addition because of the lower cooling capacityrequirements after 1000 s the total water flow volume fallswhich is operating near the lowest flow volume (approx-imately 40) in other words the water system realises alarge potential space for energy saving (Figure 10) In thecontrol process the variable-frequency pump changes speedto alter the water volume in real-time by feedback controlIn the first 1000 s the pump is operating at rated powerin the last approximately 2000 s the pump is operating ina fine adjustment status because of the real-time changingof cooling capacity requirements In the middle period thepump is operating at half the rated power Switching pumpsobey the control strategy and cooling capacity allocationmethods which adjust the number of operating switchablepumps (Figure 10) We set the threshold value |119867| = 02and the total temperature difference leads to the switchingsituation shown in Figure 10

Considering the electromagnetic properties the speed ofa pump starts from zero to a stable value with a smooth

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

30

35

40

45

50

55

rand

om Q

(W)

Figure 8 Random cold loads

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

minus2

0

2

4

6

8

10

12

14

delta

T(∘

C)

Figure 9 Total temperature difference

curve (Figure 11) otherwise it exhibits simply a horizontalline with a constant value The torque responds accordingto the equation of motion which shows the electromagneticspeed regulation process (Figure 12) otherwise it exhibits ahorizontal line as well Considering the load characteristicin (17) the actual speed and torque responses do not showsimple information Figure 12 shows that the torque curvehas acceleration and callback processes after 02 s the torquestabilises at 196119873sdot1198982 which is less than the rated load torqueof 22 119873 sdot 1198982 The speed stabilises at 1273 119903119886119889119898 somewhatless than the rated speed of 1350 119903119886119889119898 The electromagneticparameters are shown in Table 2

By the power models of the pumps the energy con-sumption was simulated (Figure 13) because of the variable

10 Mathematical Problems in Engineering

Table 2 Electromagnetic parameters

Parameter Value Remark119899119901 2 variable-frequency pump119903119904 (Ω) 25 variable-frequency pumpJ (kgm2) 00012 variable-frequency pump1198751198870 (KW) 28 variable-frequency pump119875119892 (KW) 15119875119904119908 (KW) 161198791198710 (Nm2) 22 variable-frequency pump119866 2120578119887 09 variable-frequency pump

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000t (seconds)

switchable pumpsvariable frequency pump

fixed frequency pumpstotal pumps

0

001

002

003

004

005

006

007

008

009

01

wat

er fl

ow v

olum

e (kg

s)

Figure 10 Water flow volume

01 02 03 04 05 06 07 08 09 10t (seconds)

0

200

400

600

800

1000

1200

1400

spee

d (r

ads

)

Figure 11 Speed of pump

0

5

10

15

20

25

torq

ue (N

lowastm

)

01 02 03 04 05 06 07 08 09 10t (seconds)

Figure 12 Electromagnetic torque

water volume technology the energy savings were calculated(Figure 14) It is obvious that in the first 1000 s less energysavings is realised because of the cooling demand howeverafter 1000 s large energy savings are shown according tothe stabilised inside temperature None of the switchablepumps operates after approximately 120591 =1000 s thus thepower consumption remains near 2 KWh This is the sameas the variable-frequency pump which has a favourableadjustment due to the variable water flow Figures 8 and10 show that even though some interference causes volumechanges the variable-frequency pump adjusts the water flowvolume to play the roles of accuracy control and energysaving After 5000 s the total energy consumption of thepumps is approximately 86 KWh

The performance of systems controlled by hybriddynamic control strategy and constant water volumetechnology (all the pumps work at rated power and thechilled water system works without using our controlstrategy) respectively is shown in Figure 14 For constantwater volume control technology the total volume is alwaysat 0097 kgs the total power is always at 107 KW and

Mathematical Problems in Engineering 11

switchable pumpsfixed frequency pumpvariable frequency pumps

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

05

1

15

2

25

3

35

4

45

pow

er co

nsum

ptio

n (K

Wh)

Figure 13 Power consumption

variable water volumeconstant water volume

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

2

4

6

8

10

12

14

16

18

pow

er co

nsum

ptio

n (K

Wh)

Figure 14 Power consumption comparison

the whole energy consumption is up to approximately 17KWh Compared with the results of the system controlledby the hybrid dynamic control strategy it can be foundthat the energy saving potential of the pumps has notbeen excavated in the constant water volume technique Incontrast when the low cooling load level of the system is lowthe pumps may reduce frequency or quit working for energysaving as presented in Figures 10 and 13 Consequentlythe total energy consumption of the system control by thehybrid dynamical control method is approximately 86KWh The system exhibits 494 energy saving in 5000 s

compared with that controlled by constant water volumescheme

6 Conclusions

A hybrid dynamical approach to modelling and control isused in central air conditioning which is a suitable approachfor energy saving reconstruction in contemporary ChinaBy analysing the cooling capacity transfer process from thechilled water system to the air system the framework is builtBy involving a direct torque control measure the electromag-netic property is considered For optimal hybrid control theswitching control strategy is developed the cooling capacityallocation and average temperature methods are presentedOn the basis of mathematical power models of pumpsthe goal of accurate control and energy saving is realisedBy simulation a numeral example shows a hybrid controlprocess and situation of energy savings The approach saves494 of water pump power consumption when comparedwith constant water volume technology The modelling andcontrol of multihybrid systems and their applications inrefrigeration systems will be investigated in future works

Nomenclature

119894 Current119896 Amount119898 Mass119899 Speed119899119901 Number of pole-pairs119902 Flow volume119877 Resistance119906 Voltage119860 Area119862 Specific heat119862119885 Thermal capacityF Factor of cooling capacity allocationG Amount119867 Constant119869 Rotating inertia119870119891119887 Feedback coefficient (a room)119870119891119887119905 Feedback coefficient (total system)119870119894 Heat transfer coefficient119875 Power119876 Heat119877119903 Returned air rate119878119860119861119862 Switch status signal119879119890 Electromagnetic torque119879119871 Load torque

Greek symbols

120576 Heat transfer efficiency120578 FactorΔ120579 Temperature difference120579 Temperature120579119895 Surface temperatureΨ Flux linkage120596 Angular speed

12 Mathematical Problems in Engineering

Subscript

0 Rated119860 Air119861 Variable-frequency pump119865 Fresh air119891119879 Filter time119866 Fixed-frequency pump119894119899119894 Initial119894119879 Integral time119895 Surface (wall space window and roof)119902119903 Latent heat119903119889 Random119903119905 Return119904 Stator119904119886 Sending air119904119890119905 Setting value119904119908 Switchable pump119904119872 M-axis of stator flux-oriented119904119879 T-axis of stator flux-oriented119908 Water119905119905 Totalxr Sensible heatDC Busbar120595 Flux linkage

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the National Natural ScienceFoundation of China (no 40761104181)

References

[1] China Statistical Yearbook China Statistical Publishing HouseBeijing China 2015

[2] J Liang B Li Y Wu and R Yao ldquoAn investigation of theexisting situation and trends in building energy efficiencymanagement in Chinardquo Energy and Buildings vol 39 no 10 pp1098ndash1106 2007

[3] K F Fong V I Hanby and T T Chow ldquoHVAC systemoptimization for energymanagement by evolutionary program-mingrdquo Energy and Buildings vol 38 no 3 pp 220ndash231 2006

[4] A Kecebas and I Yabanova ldquoThermal monitoring and opti-mization of geothermal district heating systems using artificialneural network A case studyrdquo Energy and Buildings vol 50 pp339ndash346 2012

[5] T Y Zhao J L Zhang and L D Ma ldquoOn-line optimizationcontrol method based on extreme value analysis for parallelvariable-frequency hydraulic pumps in central air-conditioningsystemsrdquo Building and Environment vol 47 pp 330ndash338 2012

[6] D Kaya E A Yagmur K S Yigit F C Kilic A S Eren andC Celik ldquoEnergy efficiency in pumpsrdquo Energy Conversion andManagement vol 49 no 6 pp 1662ndash1673 2008

[7] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[8] T T Chow K F Fong A L S Chan R Yau W H Au andV Cheng ldquoEnergy modelling of district cooling system for newurban developmentrdquo Energy and Buildings vol 36 no 11 pp1153ndash1162 2004

[9] X Sheng and L Duanmu ldquoElectricity consumption and eco-nomic analyses of district heating system with distributedvariable speed pumpsrdquo Energy and Buildings vol 118 pp 291ndash300 2016

[10] R M Lewis V Torczon and M W Trosset ldquoDirect searchmethods then and nowrdquo Journal of Computational and AppliedMathematics vol 124 no 1-2 pp 191ndash207 2000

[11] J Sun and A Reddy ldquoOptimal control of building HVACampRsystems using complete simulation-based sequential quadraticprogramming (CSB-SQP)rdquo Building and Environment vol 40no 5 pp 657ndash669 2005

[12] M Zaheer-Uddin and G R Zheng ldquoOptimal control of time-scheduled heating ventilating and air conditioning processesin buildingsrdquo Energy Conversion and Management vol 41 no1 pp 49ndash60 2000

[13] L Lu W Cai Y C Soh L Xie and S Li ldquoHVAC systemoptimization - Condenser water looprdquo Energy Conversion andManagement vol 45 no 4 pp 613ndash630 2004

[14] N Nassif S Moujaes and M Zaheeruddin ldquoSelf-tuningdynamic models of HVAC system componentsrdquo Energy andBuildings vol 40 no 9 pp 1709ndash1720 2008

[15] I-H Yang M-S Yeo and K-W Kim ldquoApplication of artificialneural network to predict the optimal start time for heatingsystem in buildingrdquo Energy Conversion and Management vol44 no 17 pp 2791ndash2809 2003

[16] S Wang and J Burnett ldquoOnline adaptive control for optimizingvariable-speed pumps of indirect water-cooled chilling sys-temsrdquoAppliedThermal Engineering vol 21 no 11 pp 1083ndash11032001

[17] M Anderson M Buehner P Young et al ldquoAn experimentalsystem for advanced heating ventilating and air conditioning(HVAC) controlrdquo Energy and Buildings vol 39 no 2 pp 136ndash147 2007

[18] S Qu Z Sun H Fan and K Li ldquoBP neural network for theprediction of urban building energy consumption based onMatlab and its applicationrdquo in Second International Conferenceon Computer Modeling and Simulation pp 263ndash267 IEEESanya Hainan China 2010

[19] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[20] Z Ma and S Wang ldquoAn optimal control strategy for complexbuilding central chilled water systems for practical and real-time applicationsrdquo Building and Environment vol 44 no 6 pp1188ndash1198 2009

[21] D-C Gao S Wang and Y Sun ldquoA fault-tolerant and energyefficient control strategy for primary-secondary chilled watersystems in buildingsrdquo Energy and Buildings vol 43 no 12 pp3646ndash3656 2011

[22] X Sheng andD Lin ldquoEnergy saving analyses on the reconstruc-tion project in district heating system with distributed variablespeed pumpsrdquo Applied Thermal Engineering vol 101 pp 432ndash445 2016

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Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 7

Y

Y

YN N

N

N

initialize set k=N

After a sampling period obtaintemperature inside

k=k

k=N k=0

k=k-1k=0k=k+1k=N

Y

-set ⩾H

-set⩾H

Figure 5 Control strategy of switching pumps

judgement In other words once the real-time sampling valueis beyond the setting threshold value |119867| the system willswitch At the initial time k is set to the maximum value NAfter each sampling period (constant) the system obtains theinside temperature 120579 and compares |120579 minus 120579119904119890119905| with |119867| If thevalue is in the setting range the systemwill stay in the currentsubsystem Otherwise we will calculate |120579 minus 120579119904119890119905| One way is119896 + 1 because of 120579 minus 120579119904119890119905 ge 119867 unless k is the maximum theother is k-1 because of 120579minus120579119904119890119905 le minus119867 unless k is theminimum

Remarks 2

(1) 120579119904119890119905 is the inside temperature setting and 120579 is the real-time inside temperature

(2) k is the number of operating switching pumps(3) Themaximum number of switching pumps isN If all

the switching pumps are operating the system is closeto full capacity

(4) The minimum number of switching pumps is 0 If anonswitching pump is operating the system is closeto optimal energy saving

(5) Whether switching is on or off the system obeys onepump at a timeThe switching behaviour triggers onlyone pump

43 Cooling Capacity Allocation and Average TemperatureMethods For a whole building the framework is modelledwith a switching control strategy In real system with manyrooms with different areas the cooling capacity requirementand temperature setting need an adaptive method to matchFor allocation of cooling capacity we adopt a weighting

factor according to the proportion of thermal capacity in eachroom This is a quantitative criterion on the demand sideon the supply side there is a measure to balance differentinside temperatures The average temperature difference as afeedback signal is used to control the pumps The switchingcondition |120579 minus 120579119904119890119905| can be modified as

1003816100381610038161003816120579 minus 1205791199041198901199051003816100381610038161003816 =119873sum1

1003816100381610038161003816120579119894 minus 120579119904119890119905minus1198941003816100381610038161003816119873 (23)

The weighting factor is

119865119894 = 119862119885minus119894sum1198731 119862119885minus119894 (24)

The schematic diagram is shown in Figure 6

Remarks 3

(1) |120579 minus 120579119904119890119905| is the average temperature difference of thebuilding

(2) 120579119894 is the real-time temperature inside the 119894th room120579119904119890119905minus119894 is the setting temperature inside the 119894th roomThere are N rooms operating by using cooling capac-ity

(3) 119865119894 is the weighting factor of the 119894th room for coolingcapacity allocation119862119885minus119894 is the thermal capacity of the119894th room

(4) sum1198731 119862119885minus119894 is the total thermal capacity of the rooms byusing cooling capacity

(5) Obviously these are based on the quantitative crite-rion whatever the average temperature difference orweighting factor

(6) In view of allocating cooling capacity by weightingfactor the computing method of average temperaturedifference actually involves the average temperatureper cubic meter

(7) Heat capacity 119862119885 is equal to 119862119886119898119886 for each room

5 Numerical Example and Simulation Results

In this section we present numerical results from simulationsof the chilled water system Three different rooms are thesimulation objects the cold air is sent to the rooms forreducing the inside temperaturesThe supply side uses pumpsfor sending cold water to the air system by the switchingcontrol strategy and cooling capacity allocation method Weuse one variable-frequency pump four switching pumps andtwo fixed pumps to transfer chilled water and adjust coolingcapacityThe cooling capacity transfermode of variable watervolume and constant air volume is presented The purposeof the variable water volume is accuracy control and energysaving via our model and control strategy The parametersare listed in Table 1

Simulink 2007 was used for simulating the whole processwhere the simulation time was 5000 s The switching sampletime 119879119871 of the system was set to 60 s the system checksthe real-time inside temperature each 119879119871 and decides the

8 Mathematical Problems in Engineering

Table 1 Thermal parameters

Parameter Value Remark119898119886 (kg) 67725 903 158025 Rooms A B and C respectively119902119887 (kgs) 002119902119904119908 (kgs) 0013119902119904119886 (kgs) 0655 0655 0655 Rooms A B and C respectively119902119892 (kgs) 0025119860 119894 (m

2) 36 8 0 Room A119860 119894 (m

2) 52 9 0 Room B119860 119894 (m

2) 66 12 6 Room C119862119886 (Jkglowastk) 1010119862119908 (Jkglowastk) 4180119865 0214 0286 05 Rooms A B and C respectively119867 (∘119862) 02119870119891119887 00037 0286 00026 Rooms A B and C respectively119870119891119887119905 -0061 Whole system119870119895 (Wm2lowastk) 0049 0051 005119876119902119903 (J) 19 28 31 Rooms A B and C respectively119877119903 082Δ120579 (∘119862) 5120576 086120579119894119899119894 (∘119862) 30 30 30 Rooms A B and C respectively120579119891 (∘119862) 25 25 25 Rooms A B and C respectively120579119895 (∘119862) 35 35 36 Room A120579119895 (∘119862) 35 35 36 Room B120579119895 (∘119862) 35 35 36 Room CΘ119904119890119905 (

∘119862) 258 261 259 Rooms A B and C respectively

Fixed pump 1M

Fixed pump n

M

Variable frequency pump

M

Switching pump 1

M

Switching pump n

M

Always working

Always working

Not always working(switching onoff)Control

strategy

CoolingCapacityallocation

Room 1heat exchanger

Room 2heat exchanger

Room nheat exchanger

WeightingFactor

calculatIon

Factor 1

Factor 2

Factor n

average temperature

difference Calculation

Figure 6 Cooling capacity allocation and average temperature methods

Mathematical Problems in Engineering 9

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

255

26

265

27

275

28

285

29

295

30

tem

pera

ture

insid

e(∘ C)

Figure 7 Inside temperature

switching behaviour Feedback control is used in the threerooms and the whole system which adjusts the insidetemperatures and water flow volume respectively

The inside temperatures of the three rooms started at30∘C and the system began at full capacity in other words allpumps were operating at rated power at the very start Somecurves were introduced into rooms as inside random coldloads the surface temperatures of thewall space window androof are set at constant valuesThe sending air volumewas thesame as the three rooms and was constant

Figure 7 shows that the inside temperatures declinerapidly by the sending air At approximately 120591 =1000 s thetemperatures stabilise near the setting values although therandom cold loads disturb the system (Figure 8) and the totaltemperature difference is close to zero all for the three rooms(Figure 9) In addition because of the lower cooling capacityrequirements after 1000 s the total water flow volume fallswhich is operating near the lowest flow volume (approx-imately 40) in other words the water system realises alarge potential space for energy saving (Figure 10) In thecontrol process the variable-frequency pump changes speedto alter the water volume in real-time by feedback controlIn the first 1000 s the pump is operating at rated powerin the last approximately 2000 s the pump is operating ina fine adjustment status because of the real-time changingof cooling capacity requirements In the middle period thepump is operating at half the rated power Switching pumpsobey the control strategy and cooling capacity allocationmethods which adjust the number of operating switchablepumps (Figure 10) We set the threshold value |119867| = 02and the total temperature difference leads to the switchingsituation shown in Figure 10

Considering the electromagnetic properties the speed ofa pump starts from zero to a stable value with a smooth

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

30

35

40

45

50

55

rand

om Q

(W)

Figure 8 Random cold loads

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

minus2

0

2

4

6

8

10

12

14

delta

T(∘

C)

Figure 9 Total temperature difference

curve (Figure 11) otherwise it exhibits simply a horizontalline with a constant value The torque responds accordingto the equation of motion which shows the electromagneticspeed regulation process (Figure 12) otherwise it exhibits ahorizontal line as well Considering the load characteristicin (17) the actual speed and torque responses do not showsimple information Figure 12 shows that the torque curvehas acceleration and callback processes after 02 s the torquestabilises at 196119873sdot1198982 which is less than the rated load torqueof 22 119873 sdot 1198982 The speed stabilises at 1273 119903119886119889119898 somewhatless than the rated speed of 1350 119903119886119889119898 The electromagneticparameters are shown in Table 2

By the power models of the pumps the energy con-sumption was simulated (Figure 13) because of the variable

10 Mathematical Problems in Engineering

Table 2 Electromagnetic parameters

Parameter Value Remark119899119901 2 variable-frequency pump119903119904 (Ω) 25 variable-frequency pumpJ (kgm2) 00012 variable-frequency pump1198751198870 (KW) 28 variable-frequency pump119875119892 (KW) 15119875119904119908 (KW) 161198791198710 (Nm2) 22 variable-frequency pump119866 2120578119887 09 variable-frequency pump

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000t (seconds)

switchable pumpsvariable frequency pump

fixed frequency pumpstotal pumps

0

001

002

003

004

005

006

007

008

009

01

wat

er fl

ow v

olum

e (kg

s)

Figure 10 Water flow volume

01 02 03 04 05 06 07 08 09 10t (seconds)

0

200

400

600

800

1000

1200

1400

spee

d (r

ads

)

Figure 11 Speed of pump

0

5

10

15

20

25

torq

ue (N

lowastm

)

01 02 03 04 05 06 07 08 09 10t (seconds)

Figure 12 Electromagnetic torque

water volume technology the energy savings were calculated(Figure 14) It is obvious that in the first 1000 s less energysavings is realised because of the cooling demand howeverafter 1000 s large energy savings are shown according tothe stabilised inside temperature None of the switchablepumps operates after approximately 120591 =1000 s thus thepower consumption remains near 2 KWh This is the sameas the variable-frequency pump which has a favourableadjustment due to the variable water flow Figures 8 and10 show that even though some interference causes volumechanges the variable-frequency pump adjusts the water flowvolume to play the roles of accuracy control and energysaving After 5000 s the total energy consumption of thepumps is approximately 86 KWh

The performance of systems controlled by hybriddynamic control strategy and constant water volumetechnology (all the pumps work at rated power and thechilled water system works without using our controlstrategy) respectively is shown in Figure 14 For constantwater volume control technology the total volume is alwaysat 0097 kgs the total power is always at 107 KW and

Mathematical Problems in Engineering 11

switchable pumpsfixed frequency pumpvariable frequency pumps

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

05

1

15

2

25

3

35

4

45

pow

er co

nsum

ptio

n (K

Wh)

Figure 13 Power consumption

variable water volumeconstant water volume

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

2

4

6

8

10

12

14

16

18

pow

er co

nsum

ptio

n (K

Wh)

Figure 14 Power consumption comparison

the whole energy consumption is up to approximately 17KWh Compared with the results of the system controlledby the hybrid dynamic control strategy it can be foundthat the energy saving potential of the pumps has notbeen excavated in the constant water volume technique Incontrast when the low cooling load level of the system is lowthe pumps may reduce frequency or quit working for energysaving as presented in Figures 10 and 13 Consequentlythe total energy consumption of the system control by thehybrid dynamical control method is approximately 86KWh The system exhibits 494 energy saving in 5000 s

compared with that controlled by constant water volumescheme

6 Conclusions

A hybrid dynamical approach to modelling and control isused in central air conditioning which is a suitable approachfor energy saving reconstruction in contemporary ChinaBy analysing the cooling capacity transfer process from thechilled water system to the air system the framework is builtBy involving a direct torque control measure the electromag-netic property is considered For optimal hybrid control theswitching control strategy is developed the cooling capacityallocation and average temperature methods are presentedOn the basis of mathematical power models of pumpsthe goal of accurate control and energy saving is realisedBy simulation a numeral example shows a hybrid controlprocess and situation of energy savings The approach saves494 of water pump power consumption when comparedwith constant water volume technology The modelling andcontrol of multihybrid systems and their applications inrefrigeration systems will be investigated in future works

Nomenclature

119894 Current119896 Amount119898 Mass119899 Speed119899119901 Number of pole-pairs119902 Flow volume119877 Resistance119906 Voltage119860 Area119862 Specific heat119862119885 Thermal capacityF Factor of cooling capacity allocationG Amount119867 Constant119869 Rotating inertia119870119891119887 Feedback coefficient (a room)119870119891119887119905 Feedback coefficient (total system)119870119894 Heat transfer coefficient119875 Power119876 Heat119877119903 Returned air rate119878119860119861119862 Switch status signal119879119890 Electromagnetic torque119879119871 Load torque

Greek symbols

120576 Heat transfer efficiency120578 FactorΔ120579 Temperature difference120579 Temperature120579119895 Surface temperatureΨ Flux linkage120596 Angular speed

12 Mathematical Problems in Engineering

Subscript

0 Rated119860 Air119861 Variable-frequency pump119865 Fresh air119891119879 Filter time119866 Fixed-frequency pump119894119899119894 Initial119894119879 Integral time119895 Surface (wall space window and roof)119902119903 Latent heat119903119889 Random119903119905 Return119904 Stator119904119886 Sending air119904119890119905 Setting value119904119908 Switchable pump119904119872 M-axis of stator flux-oriented119904119879 T-axis of stator flux-oriented119908 Water119905119905 Totalxr Sensible heatDC Busbar120595 Flux linkage

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the National Natural ScienceFoundation of China (no 40761104181)

References

[1] China Statistical Yearbook China Statistical Publishing HouseBeijing China 2015

[2] J Liang B Li Y Wu and R Yao ldquoAn investigation of theexisting situation and trends in building energy efficiencymanagement in Chinardquo Energy and Buildings vol 39 no 10 pp1098ndash1106 2007

[3] K F Fong V I Hanby and T T Chow ldquoHVAC systemoptimization for energymanagement by evolutionary program-mingrdquo Energy and Buildings vol 38 no 3 pp 220ndash231 2006

[4] A Kecebas and I Yabanova ldquoThermal monitoring and opti-mization of geothermal district heating systems using artificialneural network A case studyrdquo Energy and Buildings vol 50 pp339ndash346 2012

[5] T Y Zhao J L Zhang and L D Ma ldquoOn-line optimizationcontrol method based on extreme value analysis for parallelvariable-frequency hydraulic pumps in central air-conditioningsystemsrdquo Building and Environment vol 47 pp 330ndash338 2012

[6] D Kaya E A Yagmur K S Yigit F C Kilic A S Eren andC Celik ldquoEnergy efficiency in pumpsrdquo Energy Conversion andManagement vol 49 no 6 pp 1662ndash1673 2008

[7] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[8] T T Chow K F Fong A L S Chan R Yau W H Au andV Cheng ldquoEnergy modelling of district cooling system for newurban developmentrdquo Energy and Buildings vol 36 no 11 pp1153ndash1162 2004

[9] X Sheng and L Duanmu ldquoElectricity consumption and eco-nomic analyses of district heating system with distributedvariable speed pumpsrdquo Energy and Buildings vol 118 pp 291ndash300 2016

[10] R M Lewis V Torczon and M W Trosset ldquoDirect searchmethods then and nowrdquo Journal of Computational and AppliedMathematics vol 124 no 1-2 pp 191ndash207 2000

[11] J Sun and A Reddy ldquoOptimal control of building HVACampRsystems using complete simulation-based sequential quadraticprogramming (CSB-SQP)rdquo Building and Environment vol 40no 5 pp 657ndash669 2005

[12] M Zaheer-Uddin and G R Zheng ldquoOptimal control of time-scheduled heating ventilating and air conditioning processesin buildingsrdquo Energy Conversion and Management vol 41 no1 pp 49ndash60 2000

[13] L Lu W Cai Y C Soh L Xie and S Li ldquoHVAC systemoptimization - Condenser water looprdquo Energy Conversion andManagement vol 45 no 4 pp 613ndash630 2004

[14] N Nassif S Moujaes and M Zaheeruddin ldquoSelf-tuningdynamic models of HVAC system componentsrdquo Energy andBuildings vol 40 no 9 pp 1709ndash1720 2008

[15] I-H Yang M-S Yeo and K-W Kim ldquoApplication of artificialneural network to predict the optimal start time for heatingsystem in buildingrdquo Energy Conversion and Management vol44 no 17 pp 2791ndash2809 2003

[16] S Wang and J Burnett ldquoOnline adaptive control for optimizingvariable-speed pumps of indirect water-cooled chilling sys-temsrdquoAppliedThermal Engineering vol 21 no 11 pp 1083ndash11032001

[17] M Anderson M Buehner P Young et al ldquoAn experimentalsystem for advanced heating ventilating and air conditioning(HVAC) controlrdquo Energy and Buildings vol 39 no 2 pp 136ndash147 2007

[18] S Qu Z Sun H Fan and K Li ldquoBP neural network for theprediction of urban building energy consumption based onMatlab and its applicationrdquo in Second International Conferenceon Computer Modeling and Simulation pp 263ndash267 IEEESanya Hainan China 2010

[19] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[20] Z Ma and S Wang ldquoAn optimal control strategy for complexbuilding central chilled water systems for practical and real-time applicationsrdquo Building and Environment vol 44 no 6 pp1188ndash1198 2009

[21] D-C Gao S Wang and Y Sun ldquoA fault-tolerant and energyefficient control strategy for primary-secondary chilled watersystems in buildingsrdquo Energy and Buildings vol 43 no 12 pp3646ndash3656 2011

[22] X Sheng andD Lin ldquoEnergy saving analyses on the reconstruc-tion project in district heating system with distributed variablespeed pumpsrdquo Applied Thermal Engineering vol 101 pp 432ndash445 2016

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

Table 1 Thermal parameters

Parameter Value Remark119898119886 (kg) 67725 903 158025 Rooms A B and C respectively119902119887 (kgs) 002119902119904119908 (kgs) 0013119902119904119886 (kgs) 0655 0655 0655 Rooms A B and C respectively119902119892 (kgs) 0025119860 119894 (m

2) 36 8 0 Room A119860 119894 (m

2) 52 9 0 Room B119860 119894 (m

2) 66 12 6 Room C119862119886 (Jkglowastk) 1010119862119908 (Jkglowastk) 4180119865 0214 0286 05 Rooms A B and C respectively119867 (∘119862) 02119870119891119887 00037 0286 00026 Rooms A B and C respectively119870119891119887119905 -0061 Whole system119870119895 (Wm2lowastk) 0049 0051 005119876119902119903 (J) 19 28 31 Rooms A B and C respectively119877119903 082Δ120579 (∘119862) 5120576 086120579119894119899119894 (∘119862) 30 30 30 Rooms A B and C respectively120579119891 (∘119862) 25 25 25 Rooms A B and C respectively120579119895 (∘119862) 35 35 36 Room A120579119895 (∘119862) 35 35 36 Room B120579119895 (∘119862) 35 35 36 Room CΘ119904119890119905 (

∘119862) 258 261 259 Rooms A B and C respectively

Fixed pump 1M

Fixed pump n

M

Variable frequency pump

M

Switching pump 1

M

Switching pump n

M

Always working

Always working

Not always working(switching onoff)Control

strategy

CoolingCapacityallocation

Room 1heat exchanger

Room 2heat exchanger

Room nheat exchanger

WeightingFactor

calculatIon

Factor 1

Factor 2

Factor n

average temperature

difference Calculation

Figure 6 Cooling capacity allocation and average temperature methods

Mathematical Problems in Engineering 9

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

255

26

265

27

275

28

285

29

295

30

tem

pera

ture

insid

e(∘ C)

Figure 7 Inside temperature

switching behaviour Feedback control is used in the threerooms and the whole system which adjusts the insidetemperatures and water flow volume respectively

The inside temperatures of the three rooms started at30∘C and the system began at full capacity in other words allpumps were operating at rated power at the very start Somecurves were introduced into rooms as inside random coldloads the surface temperatures of thewall space window androof are set at constant valuesThe sending air volumewas thesame as the three rooms and was constant

Figure 7 shows that the inside temperatures declinerapidly by the sending air At approximately 120591 =1000 s thetemperatures stabilise near the setting values although therandom cold loads disturb the system (Figure 8) and the totaltemperature difference is close to zero all for the three rooms(Figure 9) In addition because of the lower cooling capacityrequirements after 1000 s the total water flow volume fallswhich is operating near the lowest flow volume (approx-imately 40) in other words the water system realises alarge potential space for energy saving (Figure 10) In thecontrol process the variable-frequency pump changes speedto alter the water volume in real-time by feedback controlIn the first 1000 s the pump is operating at rated powerin the last approximately 2000 s the pump is operating ina fine adjustment status because of the real-time changingof cooling capacity requirements In the middle period thepump is operating at half the rated power Switching pumpsobey the control strategy and cooling capacity allocationmethods which adjust the number of operating switchablepumps (Figure 10) We set the threshold value |119867| = 02and the total temperature difference leads to the switchingsituation shown in Figure 10

Considering the electromagnetic properties the speed ofa pump starts from zero to a stable value with a smooth

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

30

35

40

45

50

55

rand

om Q

(W)

Figure 8 Random cold loads

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

minus2

0

2

4

6

8

10

12

14

delta

T(∘

C)

Figure 9 Total temperature difference

curve (Figure 11) otherwise it exhibits simply a horizontalline with a constant value The torque responds accordingto the equation of motion which shows the electromagneticspeed regulation process (Figure 12) otherwise it exhibits ahorizontal line as well Considering the load characteristicin (17) the actual speed and torque responses do not showsimple information Figure 12 shows that the torque curvehas acceleration and callback processes after 02 s the torquestabilises at 196119873sdot1198982 which is less than the rated load torqueof 22 119873 sdot 1198982 The speed stabilises at 1273 119903119886119889119898 somewhatless than the rated speed of 1350 119903119886119889119898 The electromagneticparameters are shown in Table 2

By the power models of the pumps the energy con-sumption was simulated (Figure 13) because of the variable

10 Mathematical Problems in Engineering

Table 2 Electromagnetic parameters

Parameter Value Remark119899119901 2 variable-frequency pump119903119904 (Ω) 25 variable-frequency pumpJ (kgm2) 00012 variable-frequency pump1198751198870 (KW) 28 variable-frequency pump119875119892 (KW) 15119875119904119908 (KW) 161198791198710 (Nm2) 22 variable-frequency pump119866 2120578119887 09 variable-frequency pump

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000t (seconds)

switchable pumpsvariable frequency pump

fixed frequency pumpstotal pumps

0

001

002

003

004

005

006

007

008

009

01

wat

er fl

ow v

olum

e (kg

s)

Figure 10 Water flow volume

01 02 03 04 05 06 07 08 09 10t (seconds)

0

200

400

600

800

1000

1200

1400

spee

d (r

ads

)

Figure 11 Speed of pump

0

5

10

15

20

25

torq

ue (N

lowastm

)

01 02 03 04 05 06 07 08 09 10t (seconds)

Figure 12 Electromagnetic torque

water volume technology the energy savings were calculated(Figure 14) It is obvious that in the first 1000 s less energysavings is realised because of the cooling demand howeverafter 1000 s large energy savings are shown according tothe stabilised inside temperature None of the switchablepumps operates after approximately 120591 =1000 s thus thepower consumption remains near 2 KWh This is the sameas the variable-frequency pump which has a favourableadjustment due to the variable water flow Figures 8 and10 show that even though some interference causes volumechanges the variable-frequency pump adjusts the water flowvolume to play the roles of accuracy control and energysaving After 5000 s the total energy consumption of thepumps is approximately 86 KWh

The performance of systems controlled by hybriddynamic control strategy and constant water volumetechnology (all the pumps work at rated power and thechilled water system works without using our controlstrategy) respectively is shown in Figure 14 For constantwater volume control technology the total volume is alwaysat 0097 kgs the total power is always at 107 KW and

Mathematical Problems in Engineering 11

switchable pumpsfixed frequency pumpvariable frequency pumps

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

05

1

15

2

25

3

35

4

45

pow

er co

nsum

ptio

n (K

Wh)

Figure 13 Power consumption

variable water volumeconstant water volume

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

2

4

6

8

10

12

14

16

18

pow

er co

nsum

ptio

n (K

Wh)

Figure 14 Power consumption comparison

the whole energy consumption is up to approximately 17KWh Compared with the results of the system controlledby the hybrid dynamic control strategy it can be foundthat the energy saving potential of the pumps has notbeen excavated in the constant water volume technique Incontrast when the low cooling load level of the system is lowthe pumps may reduce frequency or quit working for energysaving as presented in Figures 10 and 13 Consequentlythe total energy consumption of the system control by thehybrid dynamical control method is approximately 86KWh The system exhibits 494 energy saving in 5000 s

compared with that controlled by constant water volumescheme

6 Conclusions

A hybrid dynamical approach to modelling and control isused in central air conditioning which is a suitable approachfor energy saving reconstruction in contemporary ChinaBy analysing the cooling capacity transfer process from thechilled water system to the air system the framework is builtBy involving a direct torque control measure the electromag-netic property is considered For optimal hybrid control theswitching control strategy is developed the cooling capacityallocation and average temperature methods are presentedOn the basis of mathematical power models of pumpsthe goal of accurate control and energy saving is realisedBy simulation a numeral example shows a hybrid controlprocess and situation of energy savings The approach saves494 of water pump power consumption when comparedwith constant water volume technology The modelling andcontrol of multihybrid systems and their applications inrefrigeration systems will be investigated in future works

Nomenclature

119894 Current119896 Amount119898 Mass119899 Speed119899119901 Number of pole-pairs119902 Flow volume119877 Resistance119906 Voltage119860 Area119862 Specific heat119862119885 Thermal capacityF Factor of cooling capacity allocationG Amount119867 Constant119869 Rotating inertia119870119891119887 Feedback coefficient (a room)119870119891119887119905 Feedback coefficient (total system)119870119894 Heat transfer coefficient119875 Power119876 Heat119877119903 Returned air rate119878119860119861119862 Switch status signal119879119890 Electromagnetic torque119879119871 Load torque

Greek symbols

120576 Heat transfer efficiency120578 FactorΔ120579 Temperature difference120579 Temperature120579119895 Surface temperatureΨ Flux linkage120596 Angular speed

12 Mathematical Problems in Engineering

Subscript

0 Rated119860 Air119861 Variable-frequency pump119865 Fresh air119891119879 Filter time119866 Fixed-frequency pump119894119899119894 Initial119894119879 Integral time119895 Surface (wall space window and roof)119902119903 Latent heat119903119889 Random119903119905 Return119904 Stator119904119886 Sending air119904119890119905 Setting value119904119908 Switchable pump119904119872 M-axis of stator flux-oriented119904119879 T-axis of stator flux-oriented119908 Water119905119905 Totalxr Sensible heatDC Busbar120595 Flux linkage

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the National Natural ScienceFoundation of China (no 40761104181)

References

[1] China Statistical Yearbook China Statistical Publishing HouseBeijing China 2015

[2] J Liang B Li Y Wu and R Yao ldquoAn investigation of theexisting situation and trends in building energy efficiencymanagement in Chinardquo Energy and Buildings vol 39 no 10 pp1098ndash1106 2007

[3] K F Fong V I Hanby and T T Chow ldquoHVAC systemoptimization for energymanagement by evolutionary program-mingrdquo Energy and Buildings vol 38 no 3 pp 220ndash231 2006

[4] A Kecebas and I Yabanova ldquoThermal monitoring and opti-mization of geothermal district heating systems using artificialneural network A case studyrdquo Energy and Buildings vol 50 pp339ndash346 2012

[5] T Y Zhao J L Zhang and L D Ma ldquoOn-line optimizationcontrol method based on extreme value analysis for parallelvariable-frequency hydraulic pumps in central air-conditioningsystemsrdquo Building and Environment vol 47 pp 330ndash338 2012

[6] D Kaya E A Yagmur K S Yigit F C Kilic A S Eren andC Celik ldquoEnergy efficiency in pumpsrdquo Energy Conversion andManagement vol 49 no 6 pp 1662ndash1673 2008

[7] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[8] T T Chow K F Fong A L S Chan R Yau W H Au andV Cheng ldquoEnergy modelling of district cooling system for newurban developmentrdquo Energy and Buildings vol 36 no 11 pp1153ndash1162 2004

[9] X Sheng and L Duanmu ldquoElectricity consumption and eco-nomic analyses of district heating system with distributedvariable speed pumpsrdquo Energy and Buildings vol 118 pp 291ndash300 2016

[10] R M Lewis V Torczon and M W Trosset ldquoDirect searchmethods then and nowrdquo Journal of Computational and AppliedMathematics vol 124 no 1-2 pp 191ndash207 2000

[11] J Sun and A Reddy ldquoOptimal control of building HVACampRsystems using complete simulation-based sequential quadraticprogramming (CSB-SQP)rdquo Building and Environment vol 40no 5 pp 657ndash669 2005

[12] M Zaheer-Uddin and G R Zheng ldquoOptimal control of time-scheduled heating ventilating and air conditioning processesin buildingsrdquo Energy Conversion and Management vol 41 no1 pp 49ndash60 2000

[13] L Lu W Cai Y C Soh L Xie and S Li ldquoHVAC systemoptimization - Condenser water looprdquo Energy Conversion andManagement vol 45 no 4 pp 613ndash630 2004

[14] N Nassif S Moujaes and M Zaheeruddin ldquoSelf-tuningdynamic models of HVAC system componentsrdquo Energy andBuildings vol 40 no 9 pp 1709ndash1720 2008

[15] I-H Yang M-S Yeo and K-W Kim ldquoApplication of artificialneural network to predict the optimal start time for heatingsystem in buildingrdquo Energy Conversion and Management vol44 no 17 pp 2791ndash2809 2003

[16] S Wang and J Burnett ldquoOnline adaptive control for optimizingvariable-speed pumps of indirect water-cooled chilling sys-temsrdquoAppliedThermal Engineering vol 21 no 11 pp 1083ndash11032001

[17] M Anderson M Buehner P Young et al ldquoAn experimentalsystem for advanced heating ventilating and air conditioning(HVAC) controlrdquo Energy and Buildings vol 39 no 2 pp 136ndash147 2007

[18] S Qu Z Sun H Fan and K Li ldquoBP neural network for theprediction of urban building energy consumption based onMatlab and its applicationrdquo in Second International Conferenceon Computer Modeling and Simulation pp 263ndash267 IEEESanya Hainan China 2010

[19] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[20] Z Ma and S Wang ldquoAn optimal control strategy for complexbuilding central chilled water systems for practical and real-time applicationsrdquo Building and Environment vol 44 no 6 pp1188ndash1198 2009

[21] D-C Gao S Wang and Y Sun ldquoA fault-tolerant and energyefficient control strategy for primary-secondary chilled watersystems in buildingsrdquo Energy and Buildings vol 43 no 12 pp3646ndash3656 2011

[22] X Sheng andD Lin ldquoEnergy saving analyses on the reconstruc-tion project in district heating system with distributed variablespeed pumpsrdquo Applied Thermal Engineering vol 101 pp 432ndash445 2016

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

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

255

26

265

27

275

28

285

29

295

30

tem

pera

ture

insid

e(∘ C)

Figure 7 Inside temperature

switching behaviour Feedback control is used in the threerooms and the whole system which adjusts the insidetemperatures and water flow volume respectively

The inside temperatures of the three rooms started at30∘C and the system began at full capacity in other words allpumps were operating at rated power at the very start Somecurves were introduced into rooms as inside random coldloads the surface temperatures of thewall space window androof are set at constant valuesThe sending air volumewas thesame as the three rooms and was constant

Figure 7 shows that the inside temperatures declinerapidly by the sending air At approximately 120591 =1000 s thetemperatures stabilise near the setting values although therandom cold loads disturb the system (Figure 8) and the totaltemperature difference is close to zero all for the three rooms(Figure 9) In addition because of the lower cooling capacityrequirements after 1000 s the total water flow volume fallswhich is operating near the lowest flow volume (approx-imately 40) in other words the water system realises alarge potential space for energy saving (Figure 10) In thecontrol process the variable-frequency pump changes speedto alter the water volume in real-time by feedback controlIn the first 1000 s the pump is operating at rated powerin the last approximately 2000 s the pump is operating ina fine adjustment status because of the real-time changingof cooling capacity requirements In the middle period thepump is operating at half the rated power Switching pumpsobey the control strategy and cooling capacity allocationmethods which adjust the number of operating switchablepumps (Figure 10) We set the threshold value |119867| = 02and the total temperature difference leads to the switchingsituation shown in Figure 10

Considering the electromagnetic properties the speed ofa pump starts from zero to a stable value with a smooth

room Aroom Broom C

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

25

30

35

40

45

50

55

rand

om Q

(W)

Figure 8 Random cold loads

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

minus2

0

2

4

6

8

10

12

14

delta

T(∘

C)

Figure 9 Total temperature difference

curve (Figure 11) otherwise it exhibits simply a horizontalline with a constant value The torque responds accordingto the equation of motion which shows the electromagneticspeed regulation process (Figure 12) otherwise it exhibits ahorizontal line as well Considering the load characteristicin (17) the actual speed and torque responses do not showsimple information Figure 12 shows that the torque curvehas acceleration and callback processes after 02 s the torquestabilises at 196119873sdot1198982 which is less than the rated load torqueof 22 119873 sdot 1198982 The speed stabilises at 1273 119903119886119889119898 somewhatless than the rated speed of 1350 119903119886119889119898 The electromagneticparameters are shown in Table 2

By the power models of the pumps the energy con-sumption was simulated (Figure 13) because of the variable

10 Mathematical Problems in Engineering

Table 2 Electromagnetic parameters

Parameter Value Remark119899119901 2 variable-frequency pump119903119904 (Ω) 25 variable-frequency pumpJ (kgm2) 00012 variable-frequency pump1198751198870 (KW) 28 variable-frequency pump119875119892 (KW) 15119875119904119908 (KW) 161198791198710 (Nm2) 22 variable-frequency pump119866 2120578119887 09 variable-frequency pump

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000t (seconds)

switchable pumpsvariable frequency pump

fixed frequency pumpstotal pumps

0

001

002

003

004

005

006

007

008

009

01

wat

er fl

ow v

olum

e (kg

s)

Figure 10 Water flow volume

01 02 03 04 05 06 07 08 09 10t (seconds)

0

200

400

600

800

1000

1200

1400

spee

d (r

ads

)

Figure 11 Speed of pump

0

5

10

15

20

25

torq

ue (N

lowastm

)

01 02 03 04 05 06 07 08 09 10t (seconds)

Figure 12 Electromagnetic torque

water volume technology the energy savings were calculated(Figure 14) It is obvious that in the first 1000 s less energysavings is realised because of the cooling demand howeverafter 1000 s large energy savings are shown according tothe stabilised inside temperature None of the switchablepumps operates after approximately 120591 =1000 s thus thepower consumption remains near 2 KWh This is the sameas the variable-frequency pump which has a favourableadjustment due to the variable water flow Figures 8 and10 show that even though some interference causes volumechanges the variable-frequency pump adjusts the water flowvolume to play the roles of accuracy control and energysaving After 5000 s the total energy consumption of thepumps is approximately 86 KWh

The performance of systems controlled by hybriddynamic control strategy and constant water volumetechnology (all the pumps work at rated power and thechilled water system works without using our controlstrategy) respectively is shown in Figure 14 For constantwater volume control technology the total volume is alwaysat 0097 kgs the total power is always at 107 KW and

Mathematical Problems in Engineering 11

switchable pumpsfixed frequency pumpvariable frequency pumps

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

05

1

15

2

25

3

35

4

45

pow

er co

nsum

ptio

n (K

Wh)

Figure 13 Power consumption

variable water volumeconstant water volume

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

2

4

6

8

10

12

14

16

18

pow

er co

nsum

ptio

n (K

Wh)

Figure 14 Power consumption comparison

the whole energy consumption is up to approximately 17KWh Compared with the results of the system controlledby the hybrid dynamic control strategy it can be foundthat the energy saving potential of the pumps has notbeen excavated in the constant water volume technique Incontrast when the low cooling load level of the system is lowthe pumps may reduce frequency or quit working for energysaving as presented in Figures 10 and 13 Consequentlythe total energy consumption of the system control by thehybrid dynamical control method is approximately 86KWh The system exhibits 494 energy saving in 5000 s

compared with that controlled by constant water volumescheme

6 Conclusions

A hybrid dynamical approach to modelling and control isused in central air conditioning which is a suitable approachfor energy saving reconstruction in contemporary ChinaBy analysing the cooling capacity transfer process from thechilled water system to the air system the framework is builtBy involving a direct torque control measure the electromag-netic property is considered For optimal hybrid control theswitching control strategy is developed the cooling capacityallocation and average temperature methods are presentedOn the basis of mathematical power models of pumpsthe goal of accurate control and energy saving is realisedBy simulation a numeral example shows a hybrid controlprocess and situation of energy savings The approach saves494 of water pump power consumption when comparedwith constant water volume technology The modelling andcontrol of multihybrid systems and their applications inrefrigeration systems will be investigated in future works

Nomenclature

119894 Current119896 Amount119898 Mass119899 Speed119899119901 Number of pole-pairs119902 Flow volume119877 Resistance119906 Voltage119860 Area119862 Specific heat119862119885 Thermal capacityF Factor of cooling capacity allocationG Amount119867 Constant119869 Rotating inertia119870119891119887 Feedback coefficient (a room)119870119891119887119905 Feedback coefficient (total system)119870119894 Heat transfer coefficient119875 Power119876 Heat119877119903 Returned air rate119878119860119861119862 Switch status signal119879119890 Electromagnetic torque119879119871 Load torque

Greek symbols

120576 Heat transfer efficiency120578 FactorΔ120579 Temperature difference120579 Temperature120579119895 Surface temperatureΨ Flux linkage120596 Angular speed

12 Mathematical Problems in Engineering

Subscript

0 Rated119860 Air119861 Variable-frequency pump119865 Fresh air119891119879 Filter time119866 Fixed-frequency pump119894119899119894 Initial119894119879 Integral time119895 Surface (wall space window and roof)119902119903 Latent heat119903119889 Random119903119905 Return119904 Stator119904119886 Sending air119904119890119905 Setting value119904119908 Switchable pump119904119872 M-axis of stator flux-oriented119904119879 T-axis of stator flux-oriented119908 Water119905119905 Totalxr Sensible heatDC Busbar120595 Flux linkage

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the National Natural ScienceFoundation of China (no 40761104181)

References

[1] China Statistical Yearbook China Statistical Publishing HouseBeijing China 2015

[2] J Liang B Li Y Wu and R Yao ldquoAn investigation of theexisting situation and trends in building energy efficiencymanagement in Chinardquo Energy and Buildings vol 39 no 10 pp1098ndash1106 2007

[3] K F Fong V I Hanby and T T Chow ldquoHVAC systemoptimization for energymanagement by evolutionary program-mingrdquo Energy and Buildings vol 38 no 3 pp 220ndash231 2006

[4] A Kecebas and I Yabanova ldquoThermal monitoring and opti-mization of geothermal district heating systems using artificialneural network A case studyrdquo Energy and Buildings vol 50 pp339ndash346 2012

[5] T Y Zhao J L Zhang and L D Ma ldquoOn-line optimizationcontrol method based on extreme value analysis for parallelvariable-frequency hydraulic pumps in central air-conditioningsystemsrdquo Building and Environment vol 47 pp 330ndash338 2012

[6] D Kaya E A Yagmur K S Yigit F C Kilic A S Eren andC Celik ldquoEnergy efficiency in pumpsrdquo Energy Conversion andManagement vol 49 no 6 pp 1662ndash1673 2008

[7] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[8] T T Chow K F Fong A L S Chan R Yau W H Au andV Cheng ldquoEnergy modelling of district cooling system for newurban developmentrdquo Energy and Buildings vol 36 no 11 pp1153ndash1162 2004

[9] X Sheng and L Duanmu ldquoElectricity consumption and eco-nomic analyses of district heating system with distributedvariable speed pumpsrdquo Energy and Buildings vol 118 pp 291ndash300 2016

[10] R M Lewis V Torczon and M W Trosset ldquoDirect searchmethods then and nowrdquo Journal of Computational and AppliedMathematics vol 124 no 1-2 pp 191ndash207 2000

[11] J Sun and A Reddy ldquoOptimal control of building HVACampRsystems using complete simulation-based sequential quadraticprogramming (CSB-SQP)rdquo Building and Environment vol 40no 5 pp 657ndash669 2005

[12] M Zaheer-Uddin and G R Zheng ldquoOptimal control of time-scheduled heating ventilating and air conditioning processesin buildingsrdquo Energy Conversion and Management vol 41 no1 pp 49ndash60 2000

[13] L Lu W Cai Y C Soh L Xie and S Li ldquoHVAC systemoptimization - Condenser water looprdquo Energy Conversion andManagement vol 45 no 4 pp 613ndash630 2004

[14] N Nassif S Moujaes and M Zaheeruddin ldquoSelf-tuningdynamic models of HVAC system componentsrdquo Energy andBuildings vol 40 no 9 pp 1709ndash1720 2008

[15] I-H Yang M-S Yeo and K-W Kim ldquoApplication of artificialneural network to predict the optimal start time for heatingsystem in buildingrdquo Energy Conversion and Management vol44 no 17 pp 2791ndash2809 2003

[16] S Wang and J Burnett ldquoOnline adaptive control for optimizingvariable-speed pumps of indirect water-cooled chilling sys-temsrdquoAppliedThermal Engineering vol 21 no 11 pp 1083ndash11032001

[17] M Anderson M Buehner P Young et al ldquoAn experimentalsystem for advanced heating ventilating and air conditioning(HVAC) controlrdquo Energy and Buildings vol 39 no 2 pp 136ndash147 2007

[18] S Qu Z Sun H Fan and K Li ldquoBP neural network for theprediction of urban building energy consumption based onMatlab and its applicationrdquo in Second International Conferenceon Computer Modeling and Simulation pp 263ndash267 IEEESanya Hainan China 2010

[19] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[20] Z Ma and S Wang ldquoAn optimal control strategy for complexbuilding central chilled water systems for practical and real-time applicationsrdquo Building and Environment vol 44 no 6 pp1188ndash1198 2009

[21] D-C Gao S Wang and Y Sun ldquoA fault-tolerant and energyefficient control strategy for primary-secondary chilled watersystems in buildingsrdquo Energy and Buildings vol 43 no 12 pp3646ndash3656 2011

[22] X Sheng andD Lin ldquoEnergy saving analyses on the reconstruc-tion project in district heating system with distributed variablespeed pumpsrdquo Applied Thermal Engineering vol 101 pp 432ndash445 2016

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

10 Mathematical Problems in Engineering

Table 2 Electromagnetic parameters

Parameter Value Remark119899119901 2 variable-frequency pump119903119904 (Ω) 25 variable-frequency pumpJ (kgm2) 00012 variable-frequency pump1198751198870 (KW) 28 variable-frequency pump119875119892 (KW) 15119875119904119908 (KW) 161198791198710 (Nm2) 22 variable-frequency pump119866 2120578119887 09 variable-frequency pump

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000t (seconds)

switchable pumpsvariable frequency pump

fixed frequency pumpstotal pumps

0

001

002

003

004

005

006

007

008

009

01

wat

er fl

ow v

olum

e (kg

s)

Figure 10 Water flow volume

01 02 03 04 05 06 07 08 09 10t (seconds)

0

200

400

600

800

1000

1200

1400

spee

d (r

ads

)

Figure 11 Speed of pump

0

5

10

15

20

25

torq

ue (N

lowastm

)

01 02 03 04 05 06 07 08 09 10t (seconds)

Figure 12 Electromagnetic torque

water volume technology the energy savings were calculated(Figure 14) It is obvious that in the first 1000 s less energysavings is realised because of the cooling demand howeverafter 1000 s large energy savings are shown according tothe stabilised inside temperature None of the switchablepumps operates after approximately 120591 =1000 s thus thepower consumption remains near 2 KWh This is the sameas the variable-frequency pump which has a favourableadjustment due to the variable water flow Figures 8 and10 show that even though some interference causes volumechanges the variable-frequency pump adjusts the water flowvolume to play the roles of accuracy control and energysaving After 5000 s the total energy consumption of thepumps is approximately 86 KWh

The performance of systems controlled by hybriddynamic control strategy and constant water volumetechnology (all the pumps work at rated power and thechilled water system works without using our controlstrategy) respectively is shown in Figure 14 For constantwater volume control technology the total volume is alwaysat 0097 kgs the total power is always at 107 KW and

Mathematical Problems in Engineering 11

switchable pumpsfixed frequency pumpvariable frequency pumps

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

05

1

15

2

25

3

35

4

45

pow

er co

nsum

ptio

n (K

Wh)

Figure 13 Power consumption

variable water volumeconstant water volume

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

2

4

6

8

10

12

14

16

18

pow

er co

nsum

ptio

n (K

Wh)

Figure 14 Power consumption comparison

the whole energy consumption is up to approximately 17KWh Compared with the results of the system controlledby the hybrid dynamic control strategy it can be foundthat the energy saving potential of the pumps has notbeen excavated in the constant water volume technique Incontrast when the low cooling load level of the system is lowthe pumps may reduce frequency or quit working for energysaving as presented in Figures 10 and 13 Consequentlythe total energy consumption of the system control by thehybrid dynamical control method is approximately 86KWh The system exhibits 494 energy saving in 5000 s

compared with that controlled by constant water volumescheme

6 Conclusions

A hybrid dynamical approach to modelling and control isused in central air conditioning which is a suitable approachfor energy saving reconstruction in contemporary ChinaBy analysing the cooling capacity transfer process from thechilled water system to the air system the framework is builtBy involving a direct torque control measure the electromag-netic property is considered For optimal hybrid control theswitching control strategy is developed the cooling capacityallocation and average temperature methods are presentedOn the basis of mathematical power models of pumpsthe goal of accurate control and energy saving is realisedBy simulation a numeral example shows a hybrid controlprocess and situation of energy savings The approach saves494 of water pump power consumption when comparedwith constant water volume technology The modelling andcontrol of multihybrid systems and their applications inrefrigeration systems will be investigated in future works

Nomenclature

119894 Current119896 Amount119898 Mass119899 Speed119899119901 Number of pole-pairs119902 Flow volume119877 Resistance119906 Voltage119860 Area119862 Specific heat119862119885 Thermal capacityF Factor of cooling capacity allocationG Amount119867 Constant119869 Rotating inertia119870119891119887 Feedback coefficient (a room)119870119891119887119905 Feedback coefficient (total system)119870119894 Heat transfer coefficient119875 Power119876 Heat119877119903 Returned air rate119878119860119861119862 Switch status signal119879119890 Electromagnetic torque119879119871 Load torque

Greek symbols

120576 Heat transfer efficiency120578 FactorΔ120579 Temperature difference120579 Temperature120579119895 Surface temperatureΨ Flux linkage120596 Angular speed

12 Mathematical Problems in Engineering

Subscript

0 Rated119860 Air119861 Variable-frequency pump119865 Fresh air119891119879 Filter time119866 Fixed-frequency pump119894119899119894 Initial119894119879 Integral time119895 Surface (wall space window and roof)119902119903 Latent heat119903119889 Random119903119905 Return119904 Stator119904119886 Sending air119904119890119905 Setting value119904119908 Switchable pump119904119872 M-axis of stator flux-oriented119904119879 T-axis of stator flux-oriented119908 Water119905119905 Totalxr Sensible heatDC Busbar120595 Flux linkage

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the National Natural ScienceFoundation of China (no 40761104181)

References

[1] China Statistical Yearbook China Statistical Publishing HouseBeijing China 2015

[2] J Liang B Li Y Wu and R Yao ldquoAn investigation of theexisting situation and trends in building energy efficiencymanagement in Chinardquo Energy and Buildings vol 39 no 10 pp1098ndash1106 2007

[3] K F Fong V I Hanby and T T Chow ldquoHVAC systemoptimization for energymanagement by evolutionary program-mingrdquo Energy and Buildings vol 38 no 3 pp 220ndash231 2006

[4] A Kecebas and I Yabanova ldquoThermal monitoring and opti-mization of geothermal district heating systems using artificialneural network A case studyrdquo Energy and Buildings vol 50 pp339ndash346 2012

[5] T Y Zhao J L Zhang and L D Ma ldquoOn-line optimizationcontrol method based on extreme value analysis for parallelvariable-frequency hydraulic pumps in central air-conditioningsystemsrdquo Building and Environment vol 47 pp 330ndash338 2012

[6] D Kaya E A Yagmur K S Yigit F C Kilic A S Eren andC Celik ldquoEnergy efficiency in pumpsrdquo Energy Conversion andManagement vol 49 no 6 pp 1662ndash1673 2008

[7] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[8] T T Chow K F Fong A L S Chan R Yau W H Au andV Cheng ldquoEnergy modelling of district cooling system for newurban developmentrdquo Energy and Buildings vol 36 no 11 pp1153ndash1162 2004

[9] X Sheng and L Duanmu ldquoElectricity consumption and eco-nomic analyses of district heating system with distributedvariable speed pumpsrdquo Energy and Buildings vol 118 pp 291ndash300 2016

[10] R M Lewis V Torczon and M W Trosset ldquoDirect searchmethods then and nowrdquo Journal of Computational and AppliedMathematics vol 124 no 1-2 pp 191ndash207 2000

[11] J Sun and A Reddy ldquoOptimal control of building HVACampRsystems using complete simulation-based sequential quadraticprogramming (CSB-SQP)rdquo Building and Environment vol 40no 5 pp 657ndash669 2005

[12] M Zaheer-Uddin and G R Zheng ldquoOptimal control of time-scheduled heating ventilating and air conditioning processesin buildingsrdquo Energy Conversion and Management vol 41 no1 pp 49ndash60 2000

[13] L Lu W Cai Y C Soh L Xie and S Li ldquoHVAC systemoptimization - Condenser water looprdquo Energy Conversion andManagement vol 45 no 4 pp 613ndash630 2004

[14] N Nassif S Moujaes and M Zaheeruddin ldquoSelf-tuningdynamic models of HVAC system componentsrdquo Energy andBuildings vol 40 no 9 pp 1709ndash1720 2008

[15] I-H Yang M-S Yeo and K-W Kim ldquoApplication of artificialneural network to predict the optimal start time for heatingsystem in buildingrdquo Energy Conversion and Management vol44 no 17 pp 2791ndash2809 2003

[16] S Wang and J Burnett ldquoOnline adaptive control for optimizingvariable-speed pumps of indirect water-cooled chilling sys-temsrdquoAppliedThermal Engineering vol 21 no 11 pp 1083ndash11032001

[17] M Anderson M Buehner P Young et al ldquoAn experimentalsystem for advanced heating ventilating and air conditioning(HVAC) controlrdquo Energy and Buildings vol 39 no 2 pp 136ndash147 2007

[18] S Qu Z Sun H Fan and K Li ldquoBP neural network for theprediction of urban building energy consumption based onMatlab and its applicationrdquo in Second International Conferenceon Computer Modeling and Simulation pp 263ndash267 IEEESanya Hainan China 2010

[19] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[20] Z Ma and S Wang ldquoAn optimal control strategy for complexbuilding central chilled water systems for practical and real-time applicationsrdquo Building and Environment vol 44 no 6 pp1188ndash1198 2009

[21] D-C Gao S Wang and Y Sun ldquoA fault-tolerant and energyefficient control strategy for primary-secondary chilled watersystems in buildingsrdquo Energy and Buildings vol 43 no 12 pp3646ndash3656 2011

[22] X Sheng andD Lin ldquoEnergy saving analyses on the reconstruc-tion project in district heating system with distributed variablespeed pumpsrdquo Applied Thermal Engineering vol 101 pp 432ndash445 2016

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 11

switchable pumpsfixed frequency pumpvariable frequency pumps

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

05

1

15

2

25

3

35

4

45

pow

er co

nsum

ptio

n (K

Wh)

Figure 13 Power consumption

variable water volumeconstant water volume

500 1000 1500 2000 2500 3000 3500 4000 4500 50000t (seconds)

0

2

4

6

8

10

12

14

16

18

pow

er co

nsum

ptio

n (K

Wh)

Figure 14 Power consumption comparison

the whole energy consumption is up to approximately 17KWh Compared with the results of the system controlledby the hybrid dynamic control strategy it can be foundthat the energy saving potential of the pumps has notbeen excavated in the constant water volume technique Incontrast when the low cooling load level of the system is lowthe pumps may reduce frequency or quit working for energysaving as presented in Figures 10 and 13 Consequentlythe total energy consumption of the system control by thehybrid dynamical control method is approximately 86KWh The system exhibits 494 energy saving in 5000 s

compared with that controlled by constant water volumescheme

6 Conclusions

A hybrid dynamical approach to modelling and control isused in central air conditioning which is a suitable approachfor energy saving reconstruction in contemporary ChinaBy analysing the cooling capacity transfer process from thechilled water system to the air system the framework is builtBy involving a direct torque control measure the electromag-netic property is considered For optimal hybrid control theswitching control strategy is developed the cooling capacityallocation and average temperature methods are presentedOn the basis of mathematical power models of pumpsthe goal of accurate control and energy saving is realisedBy simulation a numeral example shows a hybrid controlprocess and situation of energy savings The approach saves494 of water pump power consumption when comparedwith constant water volume technology The modelling andcontrol of multihybrid systems and their applications inrefrigeration systems will be investigated in future works

Nomenclature

119894 Current119896 Amount119898 Mass119899 Speed119899119901 Number of pole-pairs119902 Flow volume119877 Resistance119906 Voltage119860 Area119862 Specific heat119862119885 Thermal capacityF Factor of cooling capacity allocationG Amount119867 Constant119869 Rotating inertia119870119891119887 Feedback coefficient (a room)119870119891119887119905 Feedback coefficient (total system)119870119894 Heat transfer coefficient119875 Power119876 Heat119877119903 Returned air rate119878119860119861119862 Switch status signal119879119890 Electromagnetic torque119879119871 Load torque

Greek symbols

120576 Heat transfer efficiency120578 FactorΔ120579 Temperature difference120579 Temperature120579119895 Surface temperatureΨ Flux linkage120596 Angular speed

12 Mathematical Problems in Engineering

Subscript

0 Rated119860 Air119861 Variable-frequency pump119865 Fresh air119891119879 Filter time119866 Fixed-frequency pump119894119899119894 Initial119894119879 Integral time119895 Surface (wall space window and roof)119902119903 Latent heat119903119889 Random119903119905 Return119904 Stator119904119886 Sending air119904119890119905 Setting value119904119908 Switchable pump119904119872 M-axis of stator flux-oriented119904119879 T-axis of stator flux-oriented119908 Water119905119905 Totalxr Sensible heatDC Busbar120595 Flux linkage

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the National Natural ScienceFoundation of China (no 40761104181)

References

[1] China Statistical Yearbook China Statistical Publishing HouseBeijing China 2015

[2] J Liang B Li Y Wu and R Yao ldquoAn investigation of theexisting situation and trends in building energy efficiencymanagement in Chinardquo Energy and Buildings vol 39 no 10 pp1098ndash1106 2007

[3] K F Fong V I Hanby and T T Chow ldquoHVAC systemoptimization for energymanagement by evolutionary program-mingrdquo Energy and Buildings vol 38 no 3 pp 220ndash231 2006

[4] A Kecebas and I Yabanova ldquoThermal monitoring and opti-mization of geothermal district heating systems using artificialneural network A case studyrdquo Energy and Buildings vol 50 pp339ndash346 2012

[5] T Y Zhao J L Zhang and L D Ma ldquoOn-line optimizationcontrol method based on extreme value analysis for parallelvariable-frequency hydraulic pumps in central air-conditioningsystemsrdquo Building and Environment vol 47 pp 330ndash338 2012

[6] D Kaya E A Yagmur K S Yigit F C Kilic A S Eren andC Celik ldquoEnergy efficiency in pumpsrdquo Energy Conversion andManagement vol 49 no 6 pp 1662ndash1673 2008

[7] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[8] T T Chow K F Fong A L S Chan R Yau W H Au andV Cheng ldquoEnergy modelling of district cooling system for newurban developmentrdquo Energy and Buildings vol 36 no 11 pp1153ndash1162 2004

[9] X Sheng and L Duanmu ldquoElectricity consumption and eco-nomic analyses of district heating system with distributedvariable speed pumpsrdquo Energy and Buildings vol 118 pp 291ndash300 2016

[10] R M Lewis V Torczon and M W Trosset ldquoDirect searchmethods then and nowrdquo Journal of Computational and AppliedMathematics vol 124 no 1-2 pp 191ndash207 2000

[11] J Sun and A Reddy ldquoOptimal control of building HVACampRsystems using complete simulation-based sequential quadraticprogramming (CSB-SQP)rdquo Building and Environment vol 40no 5 pp 657ndash669 2005

[12] M Zaheer-Uddin and G R Zheng ldquoOptimal control of time-scheduled heating ventilating and air conditioning processesin buildingsrdquo Energy Conversion and Management vol 41 no1 pp 49ndash60 2000

[13] L Lu W Cai Y C Soh L Xie and S Li ldquoHVAC systemoptimization - Condenser water looprdquo Energy Conversion andManagement vol 45 no 4 pp 613ndash630 2004

[14] N Nassif S Moujaes and M Zaheeruddin ldquoSelf-tuningdynamic models of HVAC system componentsrdquo Energy andBuildings vol 40 no 9 pp 1709ndash1720 2008

[15] I-H Yang M-S Yeo and K-W Kim ldquoApplication of artificialneural network to predict the optimal start time for heatingsystem in buildingrdquo Energy Conversion and Management vol44 no 17 pp 2791ndash2809 2003

[16] S Wang and J Burnett ldquoOnline adaptive control for optimizingvariable-speed pumps of indirect water-cooled chilling sys-temsrdquoAppliedThermal Engineering vol 21 no 11 pp 1083ndash11032001

[17] M Anderson M Buehner P Young et al ldquoAn experimentalsystem for advanced heating ventilating and air conditioning(HVAC) controlrdquo Energy and Buildings vol 39 no 2 pp 136ndash147 2007

[18] S Qu Z Sun H Fan and K Li ldquoBP neural network for theprediction of urban building energy consumption based onMatlab and its applicationrdquo in Second International Conferenceon Computer Modeling and Simulation pp 263ndash267 IEEESanya Hainan China 2010

[19] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[20] Z Ma and S Wang ldquoAn optimal control strategy for complexbuilding central chilled water systems for practical and real-time applicationsrdquo Building and Environment vol 44 no 6 pp1188ndash1198 2009

[21] D-C Gao S Wang and Y Sun ldquoA fault-tolerant and energyefficient control strategy for primary-secondary chilled watersystems in buildingsrdquo Energy and Buildings vol 43 no 12 pp3646ndash3656 2011

[22] X Sheng andD Lin ldquoEnergy saving analyses on the reconstruc-tion project in district heating system with distributed variablespeed pumpsrdquo Applied Thermal Engineering vol 101 pp 432ndash445 2016

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

12 Mathematical Problems in Engineering

Subscript

0 Rated119860 Air119861 Variable-frequency pump119865 Fresh air119891119879 Filter time119866 Fixed-frequency pump119894119899119894 Initial119894119879 Integral time119895 Surface (wall space window and roof)119902119903 Latent heat119903119889 Random119903119905 Return119904 Stator119904119886 Sending air119904119890119905 Setting value119904119908 Switchable pump119904119872 M-axis of stator flux-oriented119904119879 T-axis of stator flux-oriented119908 Water119905119905 Totalxr Sensible heatDC Busbar120595 Flux linkage

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was supported by the National Natural ScienceFoundation of China (no 40761104181)

References

[1] China Statistical Yearbook China Statistical Publishing HouseBeijing China 2015

[2] J Liang B Li Y Wu and R Yao ldquoAn investigation of theexisting situation and trends in building energy efficiencymanagement in Chinardquo Energy and Buildings vol 39 no 10 pp1098ndash1106 2007

[3] K F Fong V I Hanby and T T Chow ldquoHVAC systemoptimization for energymanagement by evolutionary program-mingrdquo Energy and Buildings vol 38 no 3 pp 220ndash231 2006

[4] A Kecebas and I Yabanova ldquoThermal monitoring and opti-mization of geothermal district heating systems using artificialneural network A case studyrdquo Energy and Buildings vol 50 pp339ndash346 2012

[5] T Y Zhao J L Zhang and L D Ma ldquoOn-line optimizationcontrol method based on extreme value analysis for parallelvariable-frequency hydraulic pumps in central air-conditioningsystemsrdquo Building and Environment vol 47 pp 330ndash338 2012

[6] D Kaya E A Yagmur K S Yigit F C Kilic A S Eren andC Celik ldquoEnergy efficiency in pumpsrdquo Energy Conversion andManagement vol 49 no 6 pp 1662ndash1673 2008

[7] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[8] T T Chow K F Fong A L S Chan R Yau W H Au andV Cheng ldquoEnergy modelling of district cooling system for newurban developmentrdquo Energy and Buildings vol 36 no 11 pp1153ndash1162 2004

[9] X Sheng and L Duanmu ldquoElectricity consumption and eco-nomic analyses of district heating system with distributedvariable speed pumpsrdquo Energy and Buildings vol 118 pp 291ndash300 2016

[10] R M Lewis V Torczon and M W Trosset ldquoDirect searchmethods then and nowrdquo Journal of Computational and AppliedMathematics vol 124 no 1-2 pp 191ndash207 2000

[11] J Sun and A Reddy ldquoOptimal control of building HVACampRsystems using complete simulation-based sequential quadraticprogramming (CSB-SQP)rdquo Building and Environment vol 40no 5 pp 657ndash669 2005

[12] M Zaheer-Uddin and G R Zheng ldquoOptimal control of time-scheduled heating ventilating and air conditioning processesin buildingsrdquo Energy Conversion and Management vol 41 no1 pp 49ndash60 2000

[13] L Lu W Cai Y C Soh L Xie and S Li ldquoHVAC systemoptimization - Condenser water looprdquo Energy Conversion andManagement vol 45 no 4 pp 613ndash630 2004

[14] N Nassif S Moujaes and M Zaheeruddin ldquoSelf-tuningdynamic models of HVAC system componentsrdquo Energy andBuildings vol 40 no 9 pp 1709ndash1720 2008

[15] I-H Yang M-S Yeo and K-W Kim ldquoApplication of artificialneural network to predict the optimal start time for heatingsystem in buildingrdquo Energy Conversion and Management vol44 no 17 pp 2791ndash2809 2003

[16] S Wang and J Burnett ldquoOnline adaptive control for optimizingvariable-speed pumps of indirect water-cooled chilling sys-temsrdquoAppliedThermal Engineering vol 21 no 11 pp 1083ndash11032001

[17] M Anderson M Buehner P Young et al ldquoAn experimentalsystem for advanced heating ventilating and air conditioning(HVAC) controlrdquo Energy and Buildings vol 39 no 2 pp 136ndash147 2007

[18] S Qu Z Sun H Fan and K Li ldquoBP neural network for theprediction of urban building energy consumption based onMatlab and its applicationrdquo in Second International Conferenceon Computer Modeling and Simulation pp 263ndash267 IEEESanya Hainan China 2010

[19] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[20] Z Ma and S Wang ldquoAn optimal control strategy for complexbuilding central chilled water systems for practical and real-time applicationsrdquo Building and Environment vol 44 no 6 pp1188ndash1198 2009

[21] D-C Gao S Wang and Y Sun ldquoA fault-tolerant and energyefficient control strategy for primary-secondary chilled watersystems in buildingsrdquo Energy and Buildings vol 43 no 12 pp3646ndash3656 2011

[22] X Sheng andD Lin ldquoEnergy saving analyses on the reconstruc-tion project in district heating system with distributed variablespeed pumpsrdquo Applied Thermal Engineering vol 101 pp 432ndash445 2016

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