vav terminal control note

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Model-based optimal control of VAV air-conditioning system using genetic algorithm Shengwei Wang*, Xinqiao Jin Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong Received 19 January 1999; accepted 26 May 1999 Abstract A control strategy using a system approach based on predicting the responses of overall system environment and energy performance to the changes of control settings of VAV air-conditioning systems is developed. Incremental dynamic models with ‘self-tuning’ of the VAV system are developed and used. A genetic algorithm is used by the strategy to solve the on-line optimisation problem of multiple parameters. The strategy is tested and evaluated in a simulated ‘living’ environment under various weather conditions. 7 2000 Elsevier Science Ltd. All rights reserved. 1. Introduction Optimal control of HVAC system aims at providing the desired indoor comfort and environment with least energy input under dynamic outdoor conditions and indoor loads. It can be achieved by using suitable local controls of the sub-processes and optimal supervisory controls of the system. The typical local controls in VAV (variable air volume) air-conditioning systems are the indoor temperature control, VAV static press- ure control, AHU (air handling unit) supply air tem- perature control, outdoor ventilation flow control, infiltration (exfiltration) flow control, etc. The set- points of the local controls of these sub-processes strongly aect the indoor comfort, environment and energy consumption. The optimal settings of these set- points vary due to the changes of the outdoor con- ditions and indoor loads. The outdoor air ventilation rate aects both the indoor air quality and the energy consumption. The re- duction of the total ventilation rate under a partial load results in significant saving in VAV fan energy. But a low ventilation rate may cause deficiencies of the system performance, e.g. poor mixing of supply and room air, inadequate room ambient air circulation and dumping [1]. Proper resetting of the AHU supply air temperature allows the VAV system providing ade- quate total ventilation rate with least fan energy con- sumption. The temperature of the chilled water supplied to a building aects the COP of the chillers, the consumption of the water pump in a variable flow system as well as the VAV fan consumption [2]. To optimise the overall system performance, the sys- tem approach was utilised in optimal control strategies in a few studies. After examining the studies prior to 1991 on the optimal control for HVAC and building systems, House and Smith proposed a system approach for optimising multi-zone building systems [3,4]. An optimal control solution is sought, which minimises the system operating costs and eciently uses energy without sacrificing the thermal comfort. In their study, the interactive nature of HVAC com- ponents, the multi-zone building system and their as- sociated variables were of concern. The studies based on system approaches show that an optimal control strategy, in which the multiple control variables are optimised simultaneously, can improve the system re- Building and Environment 35 (2000) 471–487 0360-1323/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S0360-1323(99)00032-3 www.elsevier.com/locate/buildenv * Corresponding author. Tel.: +852-27665859; fax: +852- 27746146. E-mail address: [email protected] (S. Wang).

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Page 1: Vav Terminal Control Note

Model-based optimal control of VAV air-conditioning systemusing genetic algorithm

Shengwei Wang*, Xinqiao Jin

Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong

Received 19 January 1999; accepted 26 May 1999

Abstract

A control strategy using a system approach based on predicting the responses of overall system environment and energy

performance to the changes of control settings of VAV air-conditioning systems is developed. Incremental dynamic models with`self-tuning' of the VAV system are developed and used. A genetic algorithm is used by the strategy to solve the on-lineoptimisation problem of multiple parameters. The strategy is tested and evaluated in a simulated `living' environment undervarious weather conditions. 7 2000 Elsevier Science Ltd. All rights reserved.

1. Introduction

Optimal control of HVAC system aims at providingthe desired indoor comfort and environment with leastenergy input under dynamic outdoor conditions andindoor loads. It can be achieved by using suitable localcontrols of the sub-processes and optimal supervisorycontrols of the system. The typical local controls inVAV (variable air volume) air-conditioning systemsare the indoor temperature control, VAV static press-ure control, AHU (air handling unit) supply air tem-perature control, outdoor ventilation ¯ow control,in®ltration (ex®ltration) ¯ow control, etc. The set-points of the local controls of these sub-processesstrongly a�ect the indoor comfort, environment andenergy consumption. The optimal settings of these set-points vary due to the changes of the outdoor con-ditions and indoor loads.

The outdoor air ventilation rate a�ects both theindoor air quality and the energy consumption. The re-duction of the total ventilation rate under a partialload results in signi®cant saving in VAV fan energy.

But a low ventilation rate may cause de®ciencies of the

system performance, e.g. poor mixing of supply and

room air, inadequate room ambient air circulation and

dumping [1]. Proper resetting of the AHU supply air

temperature allows the VAV system providing ade-

quate total ventilation rate with least fan energy con-

sumption. The temperature of the chilled water

supplied to a building a�ects the COP of the chillers,

the consumption of the water pump in a variable ¯ow

system as well as the VAV fan consumption [2].

To optimise the overall system performance, the sys-

tem approach was utilised in optimal control strategies

in a few studies. After examining the studies prior to

1991 on the optimal control for HVAC and building

systems, House and Smith proposed a system

approach for optimising multi-zone building systems

[3,4]. An optimal control solution is sought, which

minimises the system operating costs and e�ciently

uses energy without sacri®cing the thermal comfort. In

their study, the interactive nature of HVAC com-

ponents, the multi-zone building system and their as-

sociated variables were of concern. The studies based

on system approaches show that an optimal control

strategy, in which the multiple control variables are

optimised simultaneously, can improve the system re-

Building and Environment 35 (2000) 471±487

0360-1323/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved.

PII: S0360-1323(99 )00032 -3

www.elsevier.com/locate/buildenv

* Corresponding author. Tel.: +852-27665859; fax: +852-

27746146.

E-mail address: [email protected] (S. Wang).

Page 2: Vav Terminal Control Note

sponses and reduces energy use compared to the tra-ditional control strategies [5,6].

A foundation of a multiple control variable (set-point) optimisation problem is to predict the responseof a system. Most of the studies based on systemapproaches employ simpli®ed dynamic or static gov-erning equations to evaluate the responses of the sys-tem to the changes of control variables [4±6]. Thereare many parameters that are uncertain to apply theseequations for an on-line control strategy. This mayresult in signi®cant deviations between real values andcomputation values. There are many detailed physicaldynamic models developed to simulate the responsesof the building and HVAC system to the changes ofthe control variables [7,8]. However, many of theseparameters require detailed information on the systemand very high computation power and memory spacemay be required. This makes the use of these modelsin on-line control unfeasible. Recently, identi®ed blackbox models and neural network models are introducedin optimal control applications [9±11]. The accuracy ofthese models depends on the size of data used to trainthe models. Compared with physical models, the re-liability of these models could be a problem when the

models work in the range from where the training datasets lack information.

The use of on-line identi®cation techniques [11]allow the models used to be reasonably simple andself-tuning techniques [12] can be used to reduce theerrors progressively by using the data of actual on-linemeasurements. Based on these techniques, simpli®edadaptive physical models using on-line identi®cationand self-tuning are developed and employed in the on-line optimal control strategy presented in this paper.These simpli®ed physical models predict the responsesof the system with su�cient accuracy in a wide range.The parameters of the models are identi®ed and tunedon-line automatically.

Finding the solution to an optimal problem isanother key issue of system optimal control. Houseand Smith employed a sequential quadratic pro-gramming (SQP) to compute the optimal values.Nizet et al. [13] used a conjugate gradient methodto develop an optimal control method. Both optim-isation methods as well as other conventional op-timisation methods have to start from initial guessesof optimal variables and their convergence speed isa�ected by their initial guesses in most cases. The

Nomenclature

Cc CO2 concentration (ppm)Cv VOCs concentration (mg/m3)cp heat capacity (kJ/kgK)D humidity load (kg/s)E di�erence of temperature (8C)e error (ÿ)F volumetric ¯ow rate (m3/s)G air humidity (kg)h enthalpy (kJ/kg)KP proportional gain (ÿ)Lc CO2 load (10ÿ6 m3/s)Lv VOCs load (mg/s)M mass (kg)m mass ¯ow rate(kg/s)mcond condense water rate (kg/s)Qs heat load (kW)Qsen sensible heat (kW)Qtot total heat (kW)RH relative humidity (ÿ)T temperature (8C)U PID controller output (ÿ)UAw water side heat transfer coe�cient (kJ/K)UAa,T air side sensible heat transfer coe�cient (kJ/

K)UAa,h air side mass transfer coe�cient (kg)V volume (m3)W energy consumption (kW)

Dtsim simulation time step (s)Dtsmp sampling time step (s)Dtpred prediction period (s)

Subscripta airahu air handling unitai air inletao air outletCAV constant air volumechil chillerD derivative termfh outdoor airI integral termi zonein inletout outletP proportional termPID PIDref referencesup supplythld thresholdVAV variable air volumew waterwi water inletwo water outlet

S. Wang, X. Jin / Building and Environment 35 (2000) 471±487472

Page 3: Vav Terminal Control Note

genetic algorithm (GA) is a better optimisationmethod especially when an optimal problem is notperfectly smooth and unimodal, or is not wellunderstood, or the ®tness function (cost function) isnoisy [14]. The genetic algorithm can quickly ®nd asu�ciently good solution (i.e. near optimal solution)and can be applied when a task does not requirean `absolute' optimum. It therefore well ®tsthe characteristic of an on-line optimisation problemsince it requests to ®nd a near optimal solutionquickly and the ®tness function might be noisybecause it is based on the on-line signals of sensorswhich are prone to errors. The conventional optim-isation methods such as simple hill climbing mightbe irrecoverably led astray by noises. GA is thoughtto perform robustly in the presence of smallamounts of noises since it works by accumulating®tness statistics over many generations.

Another equally important issue of optimal con-trol scheme is the selection of the cost function (orperformance index), which has to be minimised ormaximised. Most of the earlier studies in this ®eldonly concerned performances of energy and thermalcomfort of system. Mumma and Bolin [15] pre-sented an optimal strategy to control IAQ (indoorair quality) to satisfy ASHRAE Standard 62-1989[16] in VAV systems while minimising the energyuse. Besides the air pollutant concentrations (i.e.IAQ index), the indoor air humidity and ventilationrate should be concerned to optimise the overallsystem performance.

This paper presents an on-line control strategy ofair-conditioning systems using a system approach,which is suitable to be used in the Building Manage-ment Systems (BMS) with integrated digital controlstations for VAV (variable air volume) terminals,AHUs (air handling units) and central refrigerationsystem. A cost function is formed which concerns theenergy consumption of an entire system including thefan, pump and chiller, the indoor thermal comfort,indoor air quality (CO2 and VOC), indoor air humid-ity and the total ventilation rate. A genetic algorithmis used to search the optimal settings of the multiplevariable process (i.e. AHU supply air temperature,outdoor ventilation rate and chilled water temperatureset-points) by minimising the cost function. The strat-egy predicts the system responses to the variouschanges of the control set-points at actual outdoor andindoor conditions using the simpli®ed adaptive physi-cal models using on-line parameter identi®cation andself-tuning.

The strategy is tested and evaluated under various`real-life' conditions on-line on a centralised VAV air-conditioning system simulated using detailed HVACdynamic models. This paper presents the control strat-egy, simpli®ed adaptive models, the on-line parameter

identi®cation and model `self-tuning', the GA-basedoptimisation approach and evaluation of the controlstrategy.

2. Air-conditioning and control system description

A schematic of the air-conditioning and control sys-tem is shown in Fig. 1. The air-conditioning systemconsists of two AHUs, in which the supply air to VAVterminals and CAV (constant air volume) terminals isconditioned respectively, supply and return fans, ducts,dampers, VAV terminals and CAV terminals, chillersand pumps.

The total ¯oor area is 1166 m2 and divided into 8zones. Four of exterior zones orientating north areequipped with VAV and CAV, others are equippedwith VAV only.

The sub-processes in the system are controlled bythe local digital controllers. The air temperature ineach zone is controlled by a pressure-independentVAV controller. A PID controller moderates the pos-ition of the VAV damper to maintain the supply air¯ow rate at its set-point. This air¯ow rate set-point isreset by a PID temperature controller to maintain adesired space temperature. The supply air temperatureis controlled by moderating the opening of the valveand therefore adjusting the chilled water ¯ow ratethrough the CAV and VAV coils.

Two variable blade angle fans are used as the VAVsupply fan and the return fan. The CAV supply fan isa constant fan. The VAV supply fan is controlled by aPID controller to maintain the supply air static press-ure at its set-point which is reset by a supervisory con-troller. The return fan is controlled by the ex®ltration¯ow controller, which controls the di�erence betweenthe total supply and return air ¯ow rates at certain set-point to maintain a positive pressure by moderatingthe pitch angle of the return fan. The outdoor air¯owrate is controlled by the outdoor air¯ow controller bymoderating the positions of the mixing damper, out-door air damper and exhaust damper. A variable fre-quency pump is used as the secondary chilled waterpump to supply chilled water to the AHUs. It is con-trolled by a PID controller to maintain certain di�er-ential pressure between supply water and return waterby moderating the frequency of the input power to themotor. The supply water temperature is controlled bythe controller of the chillers according to the tempera-ture set-point. The control and sensor signals aredepicted as a dashed line in Fig. 1.

3. Optimal control strategy

A setting of a local control may be optimal when

S. Wang, X. Jin / Building and Environment 35 (2000) 471±487 473

Page 4: Vav Terminal Control Note

concerning certain sub-system or certain system per-formance criteria only, but may not be optimal whenthe entire HVAC system and overall performance ofthe system are of concern. Therefore, the overall per-formances of the entire system should be concernedwhen optimising the settings of the sub-processes. Thestrategy presented below aims at optimising the set-tings of AHU supply air temperature, outdoor venti-lation ¯ow rate and chilled water temperature whichoptimise the overall performance of the system underdynamic conditions.

3.1. On-line optimal control strategy

The on-line optimal control strategy is based on themodel-based prediction and the genetic algorithm op-timisation. It determines the optimal control variablesto minimise the `cost' of the entire system. The optimalcontrol strategy is illustrated in Fig. 2.

At a sampling instant, the optimisation processorfetches the necessary data from the sensors and localcontrollers. The allowed ranges of set-points in the fol-lowing sampling step are provided to the GA optimiserby the constrains and AI rules of the pre-processor.The `AI rules' consist of:

(A) Estimate the possible range of each control vari-able according to the current set-points of con-trolled variable and the set-point change speed. (B)Further narrow the possible range of each con-trolled variable according to the current control sig-nals of the position demands of the VAV dampersand the AHU chilled water valves. For instance, theset-point of the supply air temperature cannot befurther increased or reduced if some positiondemands of the VAV dampers exceed its upper orlower limit. (C) The range of each set-point is®nally set within the range given by the `constrains'.

The `constrains' give the upper and lower limits ofthe three set-points (outdoor air ventilation rate,supply air temperature and chilled water temperature).The limits of the supply air temperature and thechilled water temperature are given by the system de-sign. The upper limit of the outdoor air ventilationrate is set by the current total supply air¯ow rate, thelower limit is set by the ¯ow rate given by the DVCstrategy.

The GA optimiser starts with group of random set-point trails within their allowed ranges at its ®rst gen-eration. At the computation of each generation, eachset-points trail of the group is given to the model-

Fig. 1. Schematic of HVAC and control system.

S. Wang, X. Jin / Building and Environment 35 (2000) 471±487474

Page 5: Vav Terminal Control Note

based predictor. The predictor simulates the responsesof the system within a prediction period (Dtpred), whichis used by the cost estimator to compute the `overallcost' using the cost function. The GA optimiser pro-duces the next generation (a group of set-points trails)according to its rules and the costs at current gener-ation. Through many generations of computation, theGA optimiser ®nds the optimal set-point trail whichminimises the overall cost over the entire predictionperiod. Compromising the control quality (i.e. stab-ility) and `cost' saving, the optimal set-points obtainedby the GA optimiser are further checked by the rule-based supervisor according to cost of the optimal set-points given by the GA optimiser and the cost of thecurrent control settings in the next prediction period.When the `cost' saving is signi®cant, the optimal set-points will be used to update the current set-points.Otherwise, the set-points remain unchanged.

3.2. Component models and on-line parametersestimation

A strategy based on simpli®ed physical models isdeveloped to predict the system response and evaluatethe system's overall performance. The adaptive ®nite-time prediction models of the building, coil, fan, VAVsystem, chilled water network, pump and chiller aredeveloped to predict the energy and environment per-formance of the system. These simpli®ed models simu-late the response of the system accurately in ®nite time

step, since the working conditions of the models haveno noticeable changes in ®nite time step. An on-linelearning and estimation approach is utilised to identifyand update the parameters required by these models toensure the model accuracy when the conditionchanges.

3.2.1. Incremental dynamic building model with `self-tuning'

For each zone, the temperature and humidity can bedescribed as di�erential Eq. (1) and (2).

Micp@Ti

@ t� mVAV, icp�TVAV ÿ Ti � �mCAV, icp�TCAV

ÿ Ti � �Qs, i �1�

Mi@Gi

@ t�mVAV, i�GVAV ÿ Gi � �mCAV, i�GCAV ÿ Gi ��Di �2�

The overall IAQ, i.e. the pollutant (CO2 and VOCs)concentrations, assuming positive pressure in the build-ing, can be described as Eqs. (3) and (4).

V@Cc

@t� Ffh�Cc, fh ÿ Cc� � Lc �3�

V@Cv

@t� Ffh�Cv, fh ÿ Cv� � Lv �4�

Fig. 2. Strategy of on-line optimal control.

S. Wang, X. Jin / Building and Environment 35 (2000) 471±487 475

Page 6: Vav Terminal Control Note

To accurately predict the dynamic responses of processat the end of a prediction period (Dtpred) and withinthe prediction period, the prediction period is simu-lated by dividing the period into N simulation steps ofthe time step Dtsim.

Dtsim � Dtpred

N�5�

During a small simulation time step, supply air ¯owrate and conditions are assumed to be constant.Because of heat load (Qs,i), humidity load (Di) andpollutants load (Lc, Lv) are slowly-varying variables,they are assumed to be constant during a predictionperiod. Therefore, the Eqs. (1)±(4) can be expressedapproximately as below by replacing the derivativeterms approximately with ®nite di�erence terms,

T j�1i � T j

i �"m j

VAV, i

Mi�T j

VAV ÿ T ji �

� m jCAV, i

Mi�T j

CAV ÿ T ji � �

Qs, i

Micp

#Dtsim �6�

G j�1i � G j

i �"m j

VAV, i

Mi�G j

VAV ÿ G ji �

� m jCAV, i

Mi�G j

CAV ÿ G ji � �

Di

Mi

#Dtsim �7�

C j�1c � C j

c ��F j

fh

V�C j

c, fh ÿ C jc � �

Lc

V

�Dtsim �8�

C j�1v � C j

v ��F j

fh

V�C j

v, fh ÿ C jv � �

Lv

V

�Dtsim �9�

Where, the superscript j and j + 1 represent the cur-rent and next simulation time steps respectively.

The CAV air¯ow rate is considered to be constantwithin a prediction period. Neglecting the delay of theVAV air ¯ow control loop in responding to the changeof ¯ow set-point, VAV supply air ¯ow rate �m j

VAV, i �of current simulation time step can be represented bythe prediction of the VAV ¯ow rate set-point as shownby Eq. (10).

m jVAV, i � mVAV, min, i �U j

PID, i�mVAV, max, i

ÿmVAV, min, i � �10�

Where, U jPID, i is the prediction of the PID control

output of the space temperature controller at currentsimulation step. It is computed by Eq. (11).

U jPID, i � U j

P, i �U jI, i �U j

D, i �11�

Where, U jP, i, U j

I, i, and U jD, i are the proportional

term, integral term and derivative term respectively.For a simulation time step, they can be predicted byEqs. (12)±(14), which can be di�erent according to theactual PID algorithm implemented by a manufacturer.Where, Ei is the di�erence between the air temperatureand its set-point of i zone.

U jP, i � KP, iE

ji �12�

U jI, i �

KP, i

tI, i

�E ji � E jÿ1

i �2

Dtsim �U jÿ1I, i �13�

U jD, i �

KP, i�E j

i ÿ E jÿ1i �

Dtsim

tD, i �U jÿ1D, i

2�14�

At each sampling step, the initial values of integralterm and derivative term can be fetched from relevantstorage of the space temperature controllers. The heatload (Qs,i), humidity load (Di) and pollutants load (Lc,Lv) are considered to be constant during a samplingstep (Dtsmp) and can be estimated by Eqs. (16)±(19).

Qks, i �Micp

T ki ÿ T kÿ1

i

Dtsmp

ÿ�mkÿ1

VAV, i �mkVAV, i

2cp�T kÿ1

VAV ÿ T kÿ1i �

� mkÿ1CAV, i �mk

CAV, i

2cp�T kÿ1

CAV ÿ T kÿ1i �

��16�

Dki �Mi

G ki ÿ G kÿ1

i

Dtsmp

ÿ�mkÿ1

VAV, i �mkVAV, i

2�G kÿ1

VAV ÿ G kÿ1i �

� mkÿ1CAV, i �mk

CAV, i

2�G kÿ1

CAV ÿ G kÿ1i �

��17�

Lkc � V

C kc ÿ C kÿ1

c

Dtsmpÿ F kÿ1

fh � F kÿ1fh

2

�C kÿ1c, fh ÿ C kÿ1

c ��18�

Lkv � V

C kv ÿ C kÿ1

v

Dtsmp

ÿ F kÿ1fh � F kÿ1

fh

2

�C kÿ1v, fh ÿ C kÿ1

v ��19�

S. Wang, X. Jin / Building and Environment 35 (2000) 471±487476

Page 7: Vav Terminal Control Note

Where, k and k ÿ 1 represent the current and previoussampling instants respectively.

It is possible that there are derivations between thepredictions and real processes, the model are furthertuned as follows to increase the accuracy.

Y � Y� e �20�Where, Y is an output of the model (i.e. state variablesTi, Di, Cc, and Cv), Y is the output of the modelafter correction, e is the correction factor representingthe estimated error between model prediction and realprocess.

The process of model parameter estimation andmodel `self-tuning' is illustrated in Fig. 3. At asampling instant �tkÿ1�, the required measurementdata are collected to estimate the parameters of themodel. The model predicts the state variables at thenext sampling instant �tk� by the simulation of a fewtime steps. At the next sampling instant, the state vari-ables of the real process are available and the modelprediction errors can be estimated.

To reduce the e�ects of measurement uncertainty, a®lter using forgetting factor is used to stabilise theerror estimation as shown in Eq. (21).

ekest � lekÿ1est � �1ÿ l�ekmes �21�Where eest is the model error estimation, emes is themeasured model error. The superscript k and k ÿ 1 iscurrent and previous sampling instants respectively. lis a forgetting factor.

3.2.2. Incremental coil model with `self-tuning'Given the air inlet and outlet temperatures, humid-

ity, water inlet temperature and the air¯ow rate, thecoil model predicts the required water ¯ow rate andthe air humidity at the coil outlet. It assumes that theLewis number is equal to one approximately. It is truewhen the coil works in the normal temperature range.In this case, the Lewis relation, Eq. (22), exists [17].

UAa, T

UAa, h

� cp �22�

Where, UAa,T is the sensible heat transfer coe�cient,UAa,h is the mass transfer coe�cient (or evaporationcoe�cient).

The sensible heat transfer rate of a coil can be com-puted by Eq. (23) also regarding the Lewis relation.Where, Tb is the equivalent coil surface temperature.The sensible heat balance on the airside can be shownby Eq. (24). The total heat transfer on the airside canbe computed by Eq. (25). hb is the saturated airenthalpy of the equivalent coil surface temperature(Tb). The vapour condensation rate on the coil surfacecan be computed by Eq. (26). Db is the saturated airhumidity at coil surface temperature. The equivalentcoil surface temperature can be obtained by solvingEqs. (23) and (24). Knowing the water condensation,the air outlet humidity can be calculated by Eq. (27).

Qsen � UAa, T�Ta, in ÿ Tb� � UAa, hcp�Ta, in ÿ Tb� �23�

Qsen � macp�Ta, in ÿ Ta, out� �24�

Qtot � UAa, h�ha, in ÿ hb� �25�

mcond � UAa, h�Ga, in ÿ Gb� �26�

Fig. 3. Strategy of on-line parameters estimation and tuning.

S. Wang, X. Jin / Building and Environment 35 (2000) 471±487 477

Page 8: Vav Terminal Control Note

Ga, out � Ga, in ÿ mcond

ma

�27�

The water ¯ow rate is calculated using the heat trans-fer characteristics on water side. The total heat transferon the waterside has the correlation as shown in Eq.(28). The transfer coe�cients on waterside and airsideare the functions of water and air ¯ow rates, whichcan be represented as Eqs. (29) and (30). The water¯ow rate can be obtained by solving the Eqs. (28) and(29).

Qtot � UAw�Tb ÿ Tw, in� �28�

UAw � aw�mw�bw �29�

UAa, h � aa�ma�ba �30�To increase the accuracy of the model prediction, themodel parameters (aa, ba, aw and bw) are assumed tobe constant within a limited working range. Therefore,they are considered to be slowly-varying parameters.They are estimated by using RLS (recursive least-squares) estimation technique with exponential forget-ting using the measured ¯ow rates and heat (mass)transfer coe�cients. The supply air¯ow rate of eachAHU (coil) is measured. The heat (mass) transfer coef-®cients and the chilled water ¯ow rate of each AHUcan not be obtained directly by measurement. Theyare calculated using the measured data as follows.

For the system shown in Fig. 1, the total supplywater ¯ow rate (mw,sup), return water temperature(Tw,out) and the air enthalpy at the inlet and outlet ofeach coil (ha,in, ha,out,CAV and ha,out,VAV) are obtainedfrom measurements directly. The chilled water ¯owrate of each AHU can be calculated by solving thesimultaneous Eq. (31). When there are more than twoAHUs in HVAC system, the chilled water ¯ow rate ofeach coil can be estimated by using the water valveposition demand signal of each controller and supplywater pressure.8>><>>:mw, CAV �mw, VAV � mw, sup

mw, CAVTw, out, CAV �mw, VAVTw, out, VAV � mw, supTw, out

mw, CAVcw�Tw, out, CAV ÿ Tw, in� � mCAV�ha, out, CAV ÿ ha, in�mw, VAVcw�Tw, out, VAV ÿ Tw, in� � mVAV�ha, out, VAV ÿ ha, in�

�31�

Given the air temperature and enthalpy at the coilinlet and outlet, the air ¯ow rate, and the supplychilled water temperature, the mass transfer coe�cientson the air side (UAa,h) and the heat transfer coe�-cients on the water side (UAw) of a coil can be esti-mated by the coil model, i.e. by solving thesimultaneous Eqs. (23)±(28).

Using the heat transfer coe�cients calculated at cur-

rent and former sampling instants, RLS technique isused to estimate and update the parameters of the coilmodel i.e. the coe�cients in Eqs. (29) and (30).

3.2.3. Incremental fan/pump model with `self-tuning'When the change of the fan/pump ¯ow rate is small,

their electricity consumption can be modelled to be ap-proximately proportional to their volumetric ¯ow ratecubed as shown in Eq. (32) [18]. Where o is a coe�-cient that can be assumed to be constant since the ¯owrate change is small in a prediction period.

W � oF 3 �32�Since the energy consumption and ¯ow rate aremeasured, the parameter, o, can be learnt and esti-mated directly by Eq. (33) and updated at eachsampling instant. The same ®lter, which is shown inEq. (21), is used to ®ltrate the e�ects of the measure-ment noises on the parameter estimation.

ok � Wk

�F k�3 �33�

3.2.4. Incremental chiller model with `self-tuning'Assuming that the change of the cooling load as a

result of the control set-point changes in a predictionperiod is small, the e�ect of cooling load on COP isneglected. The COP of chillers can be modelled as Eq.(34) since the e�ect of condenser temperature changecan be neglected when simulating the e�ects of controlsetting by trials within a prediction period.

COP � COPref �1� f�Tw, in ÿ Tw, ref �� �34�Where the parameter f can be obtained by the data ofsystem operation, which is constant approximately fora chiller. The reference COPref is obtained from themeasured cooling load and the chiller power consump-tion as shown in Eq. (35). Where, Tw,ref is the

measured supply chilled water temperature at asampling instant used as a reference temperature. Thesame ®lter, which is shown in Eq. (21), is used to ®l-trate e�ects of the measurement noises on the esti-mated parameter and the measured chilled watertemperature.

COPkref �

Qkchil

W kchil

�35�

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3.3. System performance prediction and optimisation

The responses of the system, i.e. the zone air tem-perature, zone air humidity, zone air pollutant concen-trations, ventilation rate and the entire system powerconsumption, etc., to the changes of the control set-tings in a prediction period are predicted by themodels. In order to evaluate the overall performanceof the entire system, a cost function is constructed.

3.3.1. Cost functionThe overall cost function (J ) consists of ®ve el-

ements, which account for thermal comfort, energyuse, indoor air quality, maximum allowed relativehumidity and minimum allowed ventilation ¯ow asshown in Eq. (36). Since the system is of a dynamicnature, the cost is integrated over the entire predictionperiod. The integrated cost over the prediction periodis to be minimised by properly modifying the controlsettings.

J ��Dtpred

0

�atcJtc � aiaqJiaq � arhJrh � adftJdft

� aengJeng� dt �36�

Jtc represents the cost concerning thermal comfort asshown as Eq. (37). Where, PMVi is the PMV indexvalue of zone i which is calculated by using Fanger'scomfort Eq. [19].

Jtc �XNz

i�1�PMVi �2 �37�

Jiaq represents the cost concerning indoor air quality asshown in Eq. (38). To well maintain the indoor airquality, not only the CO2 concentration is considered,but also the VOCs concentration is considered, inorder to compromise the pollutants generated by occu-pants and pollutants generated by building materials,furnishing, etc. Where, Cc and Cv are CO2 concen-tration and VOCs concentration of the return air re-spectively. Cc,thld and Cv,thld are their threshold valuesrespectively, which are the relevant limits according tothe ASHRAE standard 62-1989R [20]. The cost-weighting factors E represents the weighting of CO2

concentration in the overall IAQ penalty.

Jiaq � E�c tan h

�Cc, thld

Cc

�ÿ 1

�� �1ÿ E�

�c tan h

�Cv, thld

Cv

�ÿ 1

� �38�

Jrh represents the cost concerning the maximumallowed relative humidity in the occupied space asshown in Eq. (39). A too high relative humidity is

harmful to the health of the occupants since too higherrelative humidity will enhance the growth of certainbacteria, even in the cases when the value of the PMVindex of a zone is acceptable to occupants.

Jrh �XNz

i�1

�c tan h

�RHmax

RHi

�ÿ 1

��39�

Jdft represents the cost concerning the total ventilationrate as shown in Eq. (40). A penalty is given if theventilation rate in a zone is below certain limit toavoid the problems such as poor mixing of supply airand zone air, inadequate ambient air circulation,dumping, etc.

Jdft �XNz

i�1

�c tan h

�msup , i

mmin , i

�ÿ 1

��40�

Jeng represents the cost concerning energy use, all ofthe power consumption is accounted as the energypenalty as shown in Eq. (41).

Jeng �Wfan �Wpump �Wchiller �41�atc, aiaq, arh, adft and aeng in the cost function are theweighting factors of the ®ve costs. Each cost representsthe quantitative penalty when an index moves awayfrom the relevant expectation up to certain thresholdor close to an unacceptable range. Since the values ofthe costs are of very di�erent orders, the order ofamplitude of the factors should be determined ®rstaccording to the actual range of each cost. It meansthat the selected factors should allow each cost to havesigni®cant contribution in cost function when an indexmoves away signi®cantly from its expectation or closeto an unacceptable range.

Minimisation of cost function results in the optimalcontrol of the entire air-conditioning system.

3.3.2. Optimisation using genetic algorithmThe genetic algorithm is employed as the optimis-

ation method to search the optimal values of thevariables (set-points) that minimise the overall costwithin the prediction period. Carroll's Genetic Al-gorithm driver [21] is modi®ed and used as the opti-miser. This driver initialises a random sample ofindividuals with di�erent variables to be optimisedusing the genetic algorithm approach, i.e. evolutionvia survival of the minimum value of cost function.The selection scheme used is tournament selectionwith a shu�ing technique for choosing randompairs for mating. The routine includes binary codingfor the individuals, jump mutation, creep mutation,and the option for single-point or uniform cross-over. Niching (sharing) and an option for the num-ber of children per pair of parents have been

S. Wang, X. Jin / Building and Environment 35 (2000) 471±487 479

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added. In the version 1.6.4 used in the control strat-

egy, an option for the use of a micro-GA has been

added.

The GA optimiser starts with a number of random

set-point trails (parents) which are within their allowed

ranges given by the `Constrains and AI Rules' pre-pro-

cessor. Each set-point trail (values of the three control

variables: outdoor ventilation air¯ow rate, supply air

temperature and chilled water temperature) is given to

the model-based predictor to predict the responses of

the system during a prediction period. Then the cost

estimator computes the `overall cost' according to the

predicted response of the system (i.e. compute the ®t-

ness of parents). The GA optimiser generates the next

generation (a group of set-points trails) according to

the ®tness of parents and its rules. Through gener-

ations of computation, GA optimiser ®nds the ®ttest

(i.e. optimal) set-point trail, which minimises the over-

all cost over the entire prediction period. The par-

ameters of the GA driver are important for

convergence speed. They are selected according to Car-

roll's recommendation and determined by simulation

test.

To obtain physically meaningful optimal control

settings, it is necessary to impose constraints on the

control variables to be optimised during GA search-

ing. A lower limit is imposed on the outdoor venti-

lation rate, which is set the on-line DVC strategy to

satisfy the requirement of ASHRAE Standard 62-

1989R [22] and updated at each sampling step. The

optimiser searches the optimal AHU supply air AHU

temperature and chilled water temperature settings

within the limits between relevant lower and upper

limits respectively.

Besides the use of these constrains, a number of arti-

®cial intelligence rules are employed to determine the

variable (control setting) ranges for the GA optimiser,

which consider the system capacity, changing speeds of

set-points and some impossible situations of the sys-

tem.

The models and online parameter estimation strat-

egies are simple and require very small memory space.

The information required from the local controllers

can be easily available in the integrated modern DDC

workstations. The program size and the searching

speed of the GA strategy are the key factors a�ecting

the practical application of the strategy in commercial

DDC workstations. Concerning the program size and

execution speed, the strategy could be used in rela-

tively powerful DDC workstations currently available

in the market.

4. Tests and evaluation of on-line optimal controlstrategy

4.1. System simulation and test conditions

4.1.1. Dynamic simulation of HVAC system and controlsystem

TRNSYS (A Transient System Simulation Program)[23] is used as the platform for the dynamic simulationof the air-conditioning system including the buildingzones and the control system [24].

One VAV terminal and one CAV terminal in eachzone are simulated. The total capacities of the VAVand CAV of each zone are simulated by multiplyingthe simulated ¯ow rates with suitable factors. A fanmodel simulates the energy and hydraulic perform-ances of the supply and return fans. The pressure-¯owbalance of the system under di�erent fan pitch anglesand VAV damper positions is simulated using amodel, which simulates the pressure-¯ow character-istics of the coils, supply ducts, return duct, air dam-pers and VAV terminals. The pressure-¯ow balance ofthe chilled water loop is simulated by modelling thehydraulic performances of the pump, pipes and valves.

The energy and dynamic performances of the coilsare simulated by a model developed based on themodel proposed in IEA Annex 17. The thermal capaci-tance of a duct is considered when simulating the heatexchange with the local environment and the time lagis considered when simulating the moisture and airpollutants transfer in the duct, which depends on theair velocity inside of the duct. The energy performanceof the chiller and pump, and the dynamics of sensorsand actuation devices are simulated.

The realistic DDC models simulate the dynamic re-sponse of the local PID DDC control loops and super-visory control algorithms. The control loops simulatedinclude the AHU and VAV temperature control loops,the outdoor air control loop, the ex®ltration ¯ow con-trol loop and VAV static pressure control loop. Thealgorithm of the ex®ltration ¯ow controller controlsthe di�erence between the supply and return ¯ow ratesto maintain a positive pressure in the space.

A supervisory controller resets the VAV static press-ure set-point. It minimises the VAV static pressure set-point in order to minimise the VAV supply fan energyconsumption [25]. The strategy makes use of all theVAV damper positions represented by relevant VAVdamper position control demands as the indicator ofrelative load of the VAV terminals associated with oneAHU. It adjusts the static pressure set-point allowingthat the VAV dampers with the highest relative loadamong all the VAV terminals are controlled to be veryclose to the fully open position.

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4.1.2. Test conditions

To evaluate the model-based optimal supervisory

control strategy using the GA optimisation method

(Strategy A), two control strategies including Strategy

A were tested on the system described earlier. The sec-

ond control strategy (Strategy B) is a conventional

control strategy. The AHU temperature set-point, out-

door air ventilation rate set-point and chilled water

set-point are set to be constant. In the tests using

Strategy A, the weighting factors of the cost function

are given in Table 1. The sampling interval of the

supervisory controller was 60 s, the prediction period

was 600 s. The simulation time step of the supervisory

controller was 60 s. The simulation time step of the

system simulation was 1 s. For Strategy B, the AHU

temperature set-point was 138C and outdoor air venti-

lation rate set-point was 0.8 m3/s. The daily operation

hour of the HVAC system is between 07:45 and

20:00 h.

The weather data of four days are selected to test

and evaluate performances of the optimal control

strategy using GA-based optimisation and the conven-

tional control strategy. These four test days are one

sunny day in summer, one cloudy day in summer, one

sunny day in spring and one sunny day in winter. The

data of outdoor air temperature of the selected test

days are shown in Fig. 4. The humidity of outdoor air

during daytime is between 0.0186 and 0.023 kg/kg,

0.0197 and 0.0226 kg/kg, 0.0102 and 0.0134 kg/kg, and

between 0.0087 and 0.0094 kg/kg in the selected sunny

summer, cloudy summer, sunny spring and sunny win-

ter test days respectively.

The occupancy, lighting and equipment loads in

each zone, the solar gain of each zone, the outdoor air

temperature, humidity and pollutants concentration

are prepared and provided as data ®les for simulation.

The PMV index is the function of the indoor air

temperature, velocity, relative humidity, mean radiant

Fig. 4. Outdoor air temperature of four test days.

Table 1

Constant parameters of optimization controller

acom aiaq aeng (Ec) ahum adft

Weighting factors of cost function

Setting I 0.8 0.04 0.0005 (0.5) 0.005 0.01

Setting II 0.5 0.3 0.0003 (0.5) 0.005 0.01

Other constant parameters Sampling interval, Dtsamp (Second) Prediction period, Dtpred (Second) Simulation time step, Dtsim (Second)

60 600 60

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temperature of surrounding surfaces of a zone, themean values of the metabolic rate and clothing level ofthe occupants. In the absence of detailed velocity dis-tributions, the velocity in a zone is assumed to bespatially uniform and computed by dividing the supplyair volumetric ¯ow rate to a zone by the ¯oor area.The occupant activity level used is 1.2 met and theclothing insulation value is 0.8. The CO2 generationrate is 5.0 � 10ÿ6 m3/s per occupant and the VOCsgeneration rate in the space is 1.0 mg/m2 h (324 mg/sin the entire ¯oor). The outdoor air CO2 and VOCsconcentrations are 360 ppm and 100 mg/m3 respect-ively, and are assumed to be constant.

Three evaluation exercises were conducted. ExerciseA is to test the GA optimiser, the tuning and stabilityof the strategy. Exercise B aims at evaluating the per-formance of the optimal strategy. The e�ects ofweighting factor on the performance of the strategy isstudied in Exercise C by comparing the system per-formances under the control of the optimal strategyusing two di�erent sets of weighting factors in the costfunction.

4.2. Test results

4.2.1. Exercise A Ð control performanceIn the tests, the population size was selected as 10,

the crossover probability was selected as 0.5 and thejump mutation probability was selected as 0.02, and it

is found that the optimal solution of each samplinginstant was converged through about 60±90 gener-ations.

The parameters of optimisation processor, i.e. theparameters of the GA optimiser, set-point changelimits and constrains, etc., need to be properly selectedto ensure the control stability. Fig. 5 shows the set-points of AHU supply air temperature, chilled watertemperature and outdoor air ventilation rate in thesunny spring test day. The set-points are reset onlywhen the predicted cost saving within a predictionperiod resulted from updating the set-points by theproposed new set of set-points is more than 1%. TheAHU temperature and chilled water temperature areraised when the cooling load is lower in order to saveenergy and to maintain ventilation rate at a reasonablelevel. When cooling load is higher, they are reduced sothat su�cient cooling can be provided to the zonesand maintain the supply air¯ow at a reasonably lowlevel.

The outdoor air ventilation rate was set at a highlevel in the morning and noon of the test spring day.In this period, the outdoor air enthalpy is low andclose to that of the return air. Increasing outdoor airintake results in reducing or increasing the coolingload slightly but the IAQ will be improved signi®-cantly. The outdoor air ventilation rate was set at alow level in the afternoon since the outdoor airenthalpy was high and the energy consumption would

Fig. 5. Set-points under control of Strategy A in sunny spring day.

S. Wang, X. Jin / Building and Environment 35 (2000) 471±487482

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be increased signi®cantly if the outdoor air ¯ow ratewas set at high level. The control of the outdoor air-¯ow rate established a compromise between the indoorair quality and energy consumption. The choice ofcoe�cients of the cost function determines the signi®-cance of the di�erent factors when the optimal control-ler decides the optimal settings. The parameters shouldbe chosen properly according to the user's require-ments and the actual system.

4.2.2. Exercise B Ð evaluation of optimal strategyThe overall energy consumption, indoor air quality

parameters and overall costs (the values of cost func-tion) of the system in four test days in this exercise aresummarised in Table 2. The overall cost is the inte-gration of the cost function. All the cost terms in thetable except the energy cost term are integrated overthe period between 08:00 and 20:00 h in each test day.The energy cost term is integrated over the entire oper-ation period.

The overall `cost' of the system under the control ofStrategy A was 11.2%, 37.5%, 56.9% and 40.6% lessthan that under the control of Strategy B in four testdays respectively. This indicates that overall perform-ance of the system is improved signi®cantly in mildand cold seasons when the optimal control strategy isused. In hot season, the improvement is not signi®-cant.

In both sunny and cloudy summer test days, thetotal energy consumption under the control of StrategyA is 2.6% less than that under control of Strategy B.The energy saving is not signi®cant. The indoor air

quality is slightly reduced than that under the controlof Strategy B as indicated by the CO2 and VOCshown in Figs. 6 and 7 and Table 2. Since the outdoorair intake results in signi®cant cooling coil load in hotseason, Strategy A controlled the outdoor air ¯ow rateat low level, which was close to the constant outdoorair¯ow setting. The saving of Strategy A mainlyresulted from a slightly lower outdoor air¯ow settingwhen the occupant number in the space is small.

The AHU supply air temperature was set at a higherlevel to avoid insu�cient ventilation and overcoolingat the late time of the day when the internal and exter-nal loads were low. As a result, the thermal comfortand ventilation in two summer test days wereimproved noticeably. The relative humidity in thespace was increased slightly.

In the sunny spring test day, the total energy con-sumption under the control of Strategy A was 2.3%less than that under control of Strategy B. The indoorair quality was improved signi®cantly as illustrated bythe CO2 and VOC pro®les in Fig. 8. The average CO2

concentration was reduced from 891±748 ppm. Thisshows that the increase of outdoor air intake did nota�ect the energy consumption signi®cantly since theoutdoor air enthalpy was close to that of the returnair, but it improved the indoor air quality signi®cantly.Strategy A also improved the thermal comfort signi®-cantly (Fig. 9), since overcooling in the early morningand late afternoon was avoided, which appeared whenthe system was controlled by Strategy B.

In the sunny winter test day, the total energyconsumption under the control of Strategy A was

Table 2

Cost and energy consumption with Setting I weighting factors in four test days

Test condition Sunny summer Cloudy summer Sunny spring Sunny winter

Supervisory control strategies Strategy A Strategy B Strategy A Strategy B Strategy A Strategy B Strategy A Strategy B

Cost

Cost of thermal comfort 3025.7 3678.6 1903.5 4280.8 3332.6 9512.7 8730.0 14759.8

Cost of IAQ 350.6 325.2 348.7 325.8 143.5 325.3 73.1 325.4

Cost of energy 1893.1 1943.1 1568.6 1610.3 1133.1 1144.7 507.3 680.5

Cost of relative humidity 153.5 113.5 173.2 118.2 153.7 130.1 140.2 153.0

Cost of ventilation e�ciency 37.4 90.4 49.4 137.1 131.3 242.2 349.7 574.1

Total cost 5460.3 6150.8 4043.4 6472.2 4894.2 11355.0 9800.3 16492.8

Indoor environment

Average PPD (%) 5.07 5.16 5.04 5.18 5.13 5.75 5.67 8.87

Average relative humidity (%) 54.6 50.3 55.1 50.7 54.6 51.8 53.6 54.4

Average CO2 concentration (ppm) 918.3 891.9 914.4 891.2 747.7 890.7 545.6 892.8

Average VOC concentration (ppm) 1.85 1.72 1.82 1.73 1.20 1.73 0.87 1.73

Energy consumption (MJ)

Chiller 1860.0 2211.0 1625.0 1949.0 1087.0 1304.0 170.3 701.4

Pump 203.9 260.4 189.1 236.1 163.2 177.9 83.4 146.6

Fan 1722.3 1413.8 1323.1 1035.4 1016 838.1 760.8 512.9

Total 3786.2 3885.2 3137.2 3220.5 2266.2 2320.0 1014.5 1360.9

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14.9% less than that under the control of StrategyB. The energy consumption of chiller and pumpwas reduced, the fan energy consumption wasincreased. Strategy A utilised `free cooling' in theearly morning and latter afternoon to reduce thechiller load. To avoid insu�cient ventilation at low

cooling load, the AHU supply air temperature was

set at a higher level and this resulted in the higher

fan energy consumption (i.e. 32.6% higher than

that under the control of Strategy B). The penalty

due to insu�cient ventilation under the control of

Fig. 6. Average concentrations of CO2 and VOC in sunny summer day.

Fig. 7. Average concentrations of CO2 and VOC in cloudy summer day.

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strategy B was 39.1% higher than that under thecontrol of Strategy A.

As shown in Fig. 5, the set-point of chilled watertemperature was raised to save chiller energy consump-tion when the cooling load was low in the early morn-ing, noon and later afternoon in the sunny spring day

test. When the cooling load increased, it was reducedto allow the AHU to cool the air to its set-point andto reduce the pump energy consumption. The energyconsumption of the pump was 8.3% less than thatunder control of Strategy B. Even more signi®cante�ects on pump energy consumption were observed in

Fig. 8. Average concentrations of CO2 and VOC in sunny spring day.

Fig. 9. Average PPD in sunny spring day.

S. Wang, X. Jin / Building and Environment 35 (2000) 471±487 485

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other three test days. There were 21.7, 20.0 and 43.1%in sunny summer day, cloudy summer day and sunnywinter day, respectively.

4.2.3. Exercise C Ð e�ects of weighting factorsStudying the correlation of the overall cost func-

tion and the ®ve original target terms controlled(thermal comfort, energy, IAQ, etc), the suitablefactors can be obtained by ®ne-tuning the factors.The ®ne-tuning is done using the trial and errormethod taking into account the expected weightingsof ®ve terms (expectation on the controlled terms)according to di�erent decision-makers.

When a user concerns more on the indoor airquality and less on the thermal comfort, the weight-ing factor of the indoor air quality term should belarger and the weighting factor of the thermal com-fort term should be smaller. Through tuning bytrial and error, the suitable factors were quanti®edand shown as Setting II in Table 1. The totalenergy consumption and total costs in four testdays are given in Table 3.

The overall `cost' under control of Strategy Awere 8.1, 15.7, 53.6 and 37.2% less than that underthe control of Strategy B in four test days respect-ively. The total energy consumption under the con-trol of Strategy A were 1.1, 0.2, 0.9 and 39.8% lessthan that under the control of Strategy B in fourtest days respectively. The indoor air quality wasimproved signi®cantly. In the sunny summer andcloudy summer test days, average CO2 was reducedslightly, e.g. from 892±860 ppm and from 891±853

ppm respectively. In the sunny spring and sunny win-ter test days, the average CO2 was reduced signi®-cantly, e.g. from 891±621 ppm and from 893±440ppm.

Comparing the individual cost terms of the systemcontrolled by the strategy with two di�erent sets ofweighting factors, it can be observed that the use ofsetting II improved the indoor air quality signi®cantly.The average CO2 was reduced by 58, 61, 127 and 106ppm in four test days respectively.

5. Conclusions

The supervisory control strategy based on predictingthe system performance using dynamic models canoptimise the on-line control at the system level. Testsshow that the genetic algorithm is a convenient tool insearching the optimal settings to minimise the overallsystem cost for on-line control application of air-con-ditioning systems. The incremental models with `self-tuning' ensure the accuracy of the models and allowthe models to be used conveniently on di�erent sys-tems without troubles in identifying the parameters.The incremental models with `self-tuning' allow thesimple models to be used in wide working range withnecessary accuracy.

The selection of cost function and coe�cient(weighting factors) of the cost function determines theweighting for the controller to compromise the con-cerns on di�erent issues, such as environment andenergy issues. The users can select or tune these

Table 3

Cost and energy consumption with Setting II weighting factors in four test days

Test condition Sunny summer Cloudy summer Sunny spring Sunny winter

Supervisory control strategies Strategy A Strategy B Strategy A Strategy B Strategy A Strategy B Strategy A Strategy B

Cost

Cost of thermal comfort 1986.1 2230.1 1999.3 2675.4 2242.0 5945.4 6662.6 9224.9

Cost of IAQ 2229.6 2439.6 2209.6 2443.5 1176.5 2439.8 648.3 2440.5

Cost of energy 1153 1166 960 966 690 696 246 408

Cost of relative humidity 141.0 113.5 126.5 118.2 148.8 130.1 145.1 153.0

Cost of ventilation e�ciency 37.4 90.4 49.5 137.1 131.3 242.2 340.9 574.1

Total cost 5547.6 6039.6 5344.9 6340.2 4388.6 9453.5 8042.9 12800.5

Indoor environment

Average PPD (%) 5.08 5.16 5.09 5.18 5.16 5.75 6.11 8.87

Average relative humidity (%) 53.6 50.3 51.2 50.7 53.8 51.8 52.2 54.4

Average CO2 concentration (ppm) 860.2 891.9 853.0 891.2 621.2 890.7 440.1 892.8

Average VOC concentration (ppm) 1.65 1.72 1.63 1.73 1.17 1.73 0.21 1.73

Energy consumption (MJ)

Chiller 1883.0 2211.0 1652.0 1949.0 1260.0 1304.0 153.4 701.4

Pump 212.8 260.4 201.8 236.1 157.7 177.9 95.6 146.6

Fan 1747.6 1413.8 1359.0 1035.4 881.8 838.1 570.1 512.9

Total 3842.4 3885.2 3212.8 3220.5 2299.5 2320.0 819.1 1360.9

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weighting factors according to their concerns on di�er-ent issues and according to the experiences on the op-eration of particular air-conditioning systems.

The results show that the optimal strategy is capableof optimising the system overall performance accord-ing to the weighting factors chosen. A good choice ofthe cost functions of individual items requires moretests. Further study on the integration of the strategyand models to the building management systems andthe real air-conditioning systems needs to be conductedbefore practically applying the strategy on buildingsystems.

Acknowledgements

The research work presented in the paper is ®nan-cially supported by the university research grant.

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