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Applied Thermal Engineering 29 (2009) 91–104 www.elsevier.com/locate/apthermeng

A model-based optimal ventilation control strategy of multi-zone VAV air-conditioning systems Xinhua Xu, Shengwei Wang *, Zhongwei Sun, Fu Xiao Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong Received 20 November 2007; accepted 4 February 2008 Available online 23 February 2008

Abstract This paper presents a model-based optimal ventilation control strategy for multi-zone VAV air-conditioning systems aiming at optimizing the total fresh air flow rate by compromising the thermal comfort, indoor air quality and total energy consumption. In this strategy, one scheme is used to correct the total fresh air flow rate dynamically by utilizing the unvitiated fresh air from the over-ventilation zones based on the detected occupancy of each zone and the related measurements. At the meantime, another scheme is developed to optimize the temperature set point for the temperature control of critical zones with the aim at reducing the variation of the required fresh air fractions among all the zones and further reducing the total fresh air intake from outdoors for energy saving when the first scheme is implemented. This scheme is based on a constructed cost function relating thermal comfort, indoor air quality and total energy consumption together while the cost function is calculated based on the prediction of system responses using dynamic simplified models. Genetic algorithm is used for optimizing the temperature set point of critical zones in the optimization process. This strategy was evaluated in a simulated building and air-conditioning environment under various weather conditions. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Model-based control; Multi-zone ventilation; Optimal temperature reset; Critical zone ventilation; Demand-controlled ventilation

1. Introduction Demand-controlled ventilation (DCV) is often used for fresh air ventilation control in commercial or public buildings to ensure acceptable indoor air quality (IAQ) while consuming the least energy [19,12]. In DCV strategies, carbon dioxide concentration (CO2) is often used as a direct parameter for ventilation control since carbon dioxide is a reliable surrogate for bioeffluents from occupancy and not a contaminant of concern in buildings [3]. However, many studies [25,3] pointed out that the CO2-based DCV control strategy cannot adequately consider the ventilation demand in a space in many situations since CO2 concentration provides no information on the adequacy of ventilation rate relative to sources of other contaminants in the room, such as those generated by building materials. *

Corresponding author. Tel.: +852 27730345. E-mail address: [email protected] (S. Wang).

1359-4311/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2008.02.017

Alternatively, CO2 concentration is also often used as an in ‘‘indirect” parameter for ventilation control (i.e. occupancy-based DCV control) where CO2 concentration is used for occupancy detection for further determining the fresh air flow rate set point [3,26,4]. The minimum fresh air rate can be determined only by the actual occupancy for different situations [4,5]. The latest standard [6] prescribes that the minimum requirement for the outdoor air ventilation rate should be determined by not only the actual occupancy, but also the occupied area, which account for people-related sources and area-related sources, respectively. The number of occupants can be identified using a steady-state method [4] or a dynamic method [28]. The above occupancy-based DCV strategies may work well in single zone air-conditioning systems. However, for multi-zone VAV (i.e. variable air volume) air-conditioning systems, the situation may be different. In a multi-zone system severed by a single air-handling unit, the required

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X. Xu et al. / Applied Thermal Engineering 29 (2009) 91–104

Nomenclature A cp C COP D e Eac f G J m M N P PMV Q Rb Rp sCO2 S t T U UAa,h UAw v V W X Y ˆ Y Z

net floor area (m2) air specific heat (kJ/kg °C) CO2 concentration (106 m3/m3) coefficient of performance moisture load (kg/s) error air change effectiveness fitness function moisture content (kg/kg) cost function air or water mass flow rate (kg/s) air mass (kg) simulation steps in one prediction period number of occupants predicted mean vote heat flow (kW) target fresh air requirement per unit area (m3/s/ m 2) target fresh air requirement per person (m3/s/ per) average CO2 generation rate of an occupant (106 m3/s/per) total CO2 generation rate of a space (106 m3/s) time (s) temperature (°C) PID control output mass transfer coefficient at the air side (kg/s) heat transfer coefficient at the water side (kW/ °C) air volumetric flow rate (m3/s) air volume (m3) power input (W) uncorrected fresh air fraction corrected fresh air fraction of critical zone or model output corrected model output fresh air fraction of critical zone

Greek symbols a coefficient or weighting factor

outdoor air fractions (the ratio of the required outdoor airflow rate to the required supply air flow rate) of each zone to satisfy the coincident ventilation requirement and the thermal load requirement may differ greatly from zone to zone since the zones may have different occupancy and thermal loads. When the detected total occupancy is used to determine the minimum fresh air intake rate for ventilation control, the identical fresh air fraction in the air stream results in over-ventilation in some zones while under-ventilation in other zones. For the fresh air control of the multi-zone VAV air-conditioning system, Nassif et al. [23] presented a supply

b c x k D

model parameter model parameter model parameter forgetting factor interval

Superscripts I number of zones j current simulation instant j+1 next simulation instant k current sampling step k  1 previous sampling step pred prediction Subscripts a, w air and water cz critical zone est estimated fr fresh air h enthalpy i the ith zone iaq indoor air quality max maximum meas measured min minimum out outlet or outdoor pow power consumption pred prediction R return air or room rtn return s supply sen sensible set set point sim simulation smp sampling tc thermal comfort thld threshold tot total zone, i the ith zone

CO2-based demand-controlled ventilation control strategy to reduce system energy use while maintaining the acceptable indoor air quality in each zone. This strategy may result in indoor air quality problems when the occupancy is very low while the non-people-generated pollutants may dominate. Xu and Wang [33] proposed an adaptive demand-controlled ventilation strategy for multi-zone airconditioning systems. The strategy identifies the critical zones online, and fully considers the outdoor air demand of critical zones and the unvitiated outdoor air in the re-circulated air from the other zones. However, the over-ventilation issue may still be serious in some zones when the

X. Xu et al. / Applied Thermal Engineering 29 (2009) 91–104

required fresh air fraction of critical zone differs significantly from the total fresh air fraction. This strategy further uses an empirical formula to reset the air temperature of critical zones for reducing the unbalance among the required fresh air fractions of all the zones. It is a good solution to correct the total fresh air flow rate for saving energy while keeping acceptable indoor air quality. However, the temperature set point of critical zones by the formula is not optimal. The algorithm of the temperature reset of critical zones may need further improvement by considering energy and environment issues simultaneously. Optimal control is widely of concern in HVAC fields [29,31,35,16]. The critical issues of control optimization problems (optimizing control set points) are to predict the system response, and to employ appropriate optimization algorithm to search for the optimal set point(s) according to the system responses. For the prediction of the system response, there are mainly three approaches. The first one is that detailed physical models are used to simulate the responses of the building and HVAC system to the changes of the control variables [18,21]. The second approach is to develop black-box models or neural network models for response prediction in optimal control applications [11,1]. The third one is to develop dynamic simplified models and identify model parameters for response prediction [29]. It is the most favorable approach. In this approach, this model should be reasonably simple, and self-tuning techniques can be used to reduce the errors progressively by using the actually online measurements [7]. Based on dynamic simplified models with the parameters identified online [29], developed a supervisory control

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strategy for optimizing the supply air temperature set point of an air-handling unit, the supply chilled water temperature set point and the outdoor air ventilation rate set point simultaneously for practical control. However, this article did not take into account the unbalanced fresh air requirements of different zones in multi-zone air-conditioning systems. This paper presents a model-based optimal ventilation control strategy for multi-zone VAV air-conditioning systems aiming at reducing the energy consumption and achieving acceptable thermal comfort and indoor air quality in individual zones. This strategy includes two schemes. One is the dynamic multi-zone ventilation equation scheme. The other is the dynamic temperature set point reset scheme of critical zones. The first scheme is to correct the total fresh air flow rate set point by considering the unvitiated fresh air from the over-ventilation zones. The second scheme is to optimize the temperature set point of critical zones for zone temperature control based on the system response predicted using dynamic simplified models. This scheme aims at reducing the unbalance among the required fresh air fractions of individual zones. This strategy was evaluated in a simulated building and air-conditioning environment under various weather conditions by comparing with other DCV ventilation strategies. 2. Overview of the model-based optimal ventilation control strategy The model-based optimal ventilation control strategy (i.e. optimal strategy thereafter) consists of a dynamic multi-zone ventilation equation scheme and a dynamic

VAV supply fan CO 2

VAV

F1

VAV

VAV

VAV

T1 F2

Temperature controller Return air controller Recirculated air

Motor of damper

Pressure controller

Set point

P1

F8

Set point Measurement F3 CO 2

VAV

VAV

VAV

CO 2

From other zones

Fresh air controller Fresh Air Set point

From enthalpy controller

DCV-based fresh air set-point

Y=

X

Total Occupancy Estimator

Z

Critical Zone Detector

X 1+ X − Z

Zone Occupancy Estimator

Dynamic Multi-zone Ventilation Equation Scheme

Fig. 1. Illustration of the dynamic multi-zone ventilation equation scheme and instrumentation.

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Temperature Reset Scheme GA Optimizer Setpoint trails

Genetic Algorithm

Optimal setpoint & Cost

Range of setpoint

Constrains

Supervisor Setpoint of individual zones

Model-based predictor

Cost function estimator

Parameter estimators Parameter identification of the coil model and fan model

Identification of source terms

Identification of critical zones

Real process of the multi-zone air conditioning system Fig. 2. Illustration of the dynamic temperature set point reset scheme of critical zones.

temperature set point reset scheme of critical zones. This strategy is different from the previous studies [29,33] in that the temperature set point of critical zones is optimized dynamically and automatically, which is adaptive to the ever-changing weather conditions and the indoor condition (mainly occupancy) of each zone. The dynamic multi-zone ventilation equation scheme is shown schematically in Fig. 1. This scheme is to optimize the total fresh air flow rate directly from outdoors by considering the fresh air requirement of the critical zone in multizone VAV air-conditioning systems. In the VAV air-conditioning system serving multiple zones, some zones must be over-ventilated, and some zones are under-ventilated since the fresh air requirements (Fresh air fraction) of each zone are different. This scheme aims at counting the unvitiated fresh air from the over-ventilation zones for reducing the total fresh air flow rate directly from outdoors in hot seasons when resetting the fresh air flow rate from outdoors for energy saving. This scheme is presented in detail in Section 3. However, when the required fresh air fractions of zones differ greatly, the capability of the dynamic multi-zone ventilation equation scheme reducing total fresh air flow rate for energy saving is very limited while maintaining the acceptable indoor air quality in individual zones. If the air temperature set point of the critical zone is reset slightly (e.g. lower in cooling condition) to delivery more air to the critical zone, the required fresh air fraction of the critical zone decreases allowing the required fresh air fractions of all the zone tending to be uniform. Eventually, the demanded total outdoor air intake will decrease when the dynamic multi-zone ventilation equation scheme is implemented.

Obviously, the temperature set point reset of critical zones will affect the zonal thermal comfort more or less. The dynamic temperature set point reset scheme is to optimize the temperature set point of critical zones by compromising the indoor thermal comfort, air quality and the total energy consumption. This scheme is based on model prediction and uses genetic algorithm for optimizing the temperature set point of critical zones as shown in Fig. 2. The detail of this scheme is presented in Section 4. 3. Dynamic multi-zone ventilation equation scheme The dynamic multi-zone ventilation equation scheme and instrumentation of the VAV air-conditioning system are illustrated schematically in Fig. 1. In this scheme, the occupancy of each zone and the total occupancy need to be determined for calculating the required fresh air flow rate, and the critical zone to be identified using the measured supply air flow rates of individual zones together with the calculated coincident fresh air flow rates. Based on the identified occupancies and critical zones as well as other measurements, the demanded fresh air flow rate directly from outdoors can be estimated as presented subsequently. Dynamic occupancy detection [28] is used in this study for the detection of zonal occupancies and the total occuk pancy. The total occupancy  in the  total space (P ) and the occupancy in ith zone P kzone; i at the current sampling instant are detected as Eqs. (1) and (2), respectively based on dynamic CO2 mass balance. To increase the stability and reliability of the detected occupancy, filters are used

X. Xu et al. / Applied Thermal Engineering 29 (2009) 91–104

to decrease the effects of sensors’ noise and dynamic derivative term [28].   k  Eac vkfr þ vk1 C R  C kfr C k  C k1 fr k R ð1Þ þV R P tot ¼ sCO2 Dt 2sCO2    Eac vks; zone; i þ vk1 C kzone; i  C ks s; zone; i k P zone; i ¼ 2sCO2 þ V zone; i

C kzone; i

k1 C zone; i

 sCO2 Dt

ð2Þ

where P is the number of occupants, Eac is the air change effectiveness, vfr is the fresh air volumetric flow rate, CR is the average CO2 concentration of all the space, Cfr is the CO2 concentration of fresh air, V is the air volume in the conditioned space/zone, sCO2 is the average CO2 generation rate of an occupant, Czone is the CO2 concentration in the conditioned zone, Cs is the CO2 concentration of the supply air, subscripts s and zone, i indicate supply and the ith zone, respectively, superscripts k and k  1 represent the current and previous sampling instants, respectively. The critical zone is the zone with the greatest required fresh air fraction of the supply air although the critical zone may have the maximum fresh air flow rate requirement sometimes. The critical zone may also change due to the changes of the fresh air requirements and the cooling requirements of different zones. The fresh airflow rate requirement of each zone shall be determined by the fresh airflow rate related to occupancy and the fresh air flow rate related to the occupied area as Eq. (3). With the online measurement of the supply airflow rate of each zone, the greatest required fresh air fraction in the supply air stream is determined as Eq. (4). vfr; zone; i ¼ P zone; i RP þ Azone; i Rb   vfr; zone; i Z ¼ max vs; zone; i

ð3Þ ð4Þ

where vfr, zone, i is the fresh air requirement of the ith zone, vs, zone, i is the online measurement of supply air to the ith zone, RP and Rb are the target fresh air requirements per person and per unit area, respectively as prescribed in the standards [5,6], A is the net floor area, Z is the fresh air fraction of the critical zone. When the air-conditioning system delivers the fresh air flow rate, which is determined by the detected total occupancy as shown in Eq. (5) (i.e. the uncorrected fresh air flow rate), some zones will be over-ventilated while the others under-ventilated. Using the measurement of the total supply air flow rate, the uncorrected fresh air fraction (X) is calculated as Eq. (6). In the over-ventilation zones, the fresh air cannot be used completely (i.e. unvitiated fresh air). This part fresh air will return and join in the total supply air stream. Therefore, the re-circulated unvitiated fresh air should be counted when calculating the introduced outdoor air flow rate. The online corrected fresh air fraction (Y) from outdoors directly is calculated as Eq. (7) [3].

95

The actually corrected fresh air flow rate from outdoors directly is calculated as Eqs. (8) or (9). vfr; uncorrected ¼ P tot RP þ ARb vfr; uncorrected X ¼ vs; tot X Y ¼ 1þX Z vfr; corrected ¼ Y  vs; tot vfr; corrected ¼

ð5Þ ð6Þ ð7Þ ð8Þ

P tot RP þRb A vs; tot þRb A 1 þ P totvRs;Ptot  max

n

P zone; i RP þRb Azone; i vs; zone; i

o  vs; tot ð9Þ

where vfr, uncorrected is the uncorrected fresh air flow rate, vs, tot is the total supply airflow rate, and vfr, corrected is the actually corrected total fresh air flow rate. The corrected fresh air flow rate from outdoors is calculated using the online measurements of total supply air flow rate and the supply air flow rate to each zone, and the online ‘‘measurements” of total occupancy and occupancy in each zone. 4. Dynamic temperature set point reset scheme of critical zones The dynamic temperature set point reset scheme of critical zones (i.e. temperature reset scheme thereafter) is to the reduce the unbalance of the required fresh air fractions between the critical zones and other zones aiming at reducing the total energy consumption while maintaining acceptable thermal comfort and indoor air quality in all the zones especially in critical zones. This scheme is illustrated schematically in Fig. 2, which is parallel to the real process of the multi-zone VAV air-conditioning system for online optimizing the temperature set point of critical zones for practical applications. This scheme mainly consists of parameter estimators and genetic algorithm (GA) optimizer. These estimators are developed to identify the parameters of the cooling coil and fans for their performance predictions, and to identify the source terms (i.e. sensible cooling load, moisture load and CO2 pollutant load) in each zone for the state prediction of each zone. The parameter identification is based on the online measurements of the real process. In the GA optimizer, a model-based predictor is developed to predict the total energy consumption, thermal comfort and indoor air quality of each zone based on the online identified models and the current states of the real process as well as the temperature set point trails of critical zones. The cost function is calculated based on the predicted performance by compromising total energy consumption, thermal comfort and indoor air quality. Genetic algorithm is employed to optimize the temperature set point of critical zones within the searching range. A supervisor determines if the optimal set point is used in

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the zone temperature controller for practical control. Model development is presented in Section 4.1. System performance prediction and temperature optimization of critical zones are presented in Sections 4.2 and 4.3, respectively. 4.1. Model development for performance prediction For system performance prediction, the parameters of the coil is needed to be identified for thermal performance prediction of the coil in the prediction period, and the parameters of fans to be identified for fan power consumption prediction based on predicted air flow rates. The sensible cooling load, moisture load and pollutant load (i.e. source terms) are also needed to be identified online for the state prediction of each zone at the end of each prediction interval. 4.1.1. Incremental coil model and its parameter identification In the model-based predictor, the cooling coil model is needed to predict the required chilled water flow rate and the air moisture at the coil outlet since the inlet air conditions is given, the outlet air temperature is set, and the inlet water temperature is given. The philosophy of developing the incremental coil model is to assume that the heat transfer coefficients at the water side and the air side are related only with the water flow rate and air flow rate, respectively, and the relations are invariable within a small working range. The relations can be identified using the previous measurements. The detailed modeling approach was presented in the article [29]. The heat transfer coefficient functions at both sides are illustrated in Eqs. (10) and (11) and the parameter identification method is briefed as follows: c UAw ¼ bw ðmw Þ w c UAa;h ¼ ba ðma Þ a

ð10Þ ð11Þ

where UAa,h and UAw are the heat transfer coefficients at the air side and at the water side, respectively, m is mass flow rate, b and c are model parameters to be identified, subscripts a, h, w indicate air, enthalpy and water, respectively. To identify the parameters of b and c, both coefficients of UAa,h and UAw need to be calculated based on the inlet and outlet air states of the coil. The model parameters are considered to be slowly-varying, and be constant within a limited working range. These parameters are estimated using recursive least square (RLS) estimation technique with exponential forgetting using measurements. Using both coefficients calculated at the current and former sampling instants, RLS technique is used to estimate and update the parameters of the coil model. With the known parameters, the water flow rate and outlet air moisture content can also be computed at the prediction period. 4.1.2. Incremental fan model and its parameter identification The power input of fans can be modeled to be approximately proportional to their flow rate cubed as Eq. (12)

when the change of flow rate is in a small range. Since the power input and flow rate are measured, the parameter can be learnt and estimated directly as Eq. (13) and updated at each sampling instant. A first-order filter is used to filter the effects of the measurement noises on the parameter estimation. With the parameter, the power input of fans can be estimated as Eq. (12) based on the air flow rates. W ¼ xv3

 3 xk ¼ W k = vk

ð12Þ ð13Þ

where W is the power input, x is the parameter to be estimated. This parameter is assumed to be constant in a prediction period. 4.1.3. Incremental source terms of all the zones In the optimization process, building sensible cooling load, latent load (i.e. moisture load), and pollutant load are needed to know in advance to predict the air state of the indoor space for system performance prediction. These loads can not be measured directly. However, they can be estimated based on measurements. For each zone, the energy balance, moisture balance and pollutant balance can be expressed as Eqs. (14)–(16), respectively. In the study, CO2 concentration is used to indicate indoor air quality (IAQ) of each zone although VOCs may also be used for the index of indoor air quality. Sensible heat load (Qsen, i), moisture load (Di) and pollutant load (Si) are called source terms since they are the driving forces in these equations. In a prediction period, these three source terms can be considered to be constant, and can be computed during a sampling step as Eqs. (17)–(19). dT i ¼ ms; i cp ðT s  T i Þ þ Qsen; i dt dGi ¼ ms; i ðGs  Gi Þ þ Di Mi dt dC i ¼ vs; i ðC s  C i Þ þ S i Vi dt   T k  T ik1 Qksen; i ¼ M i cp i  mks; i cp T ks  T ki Dtsmp k   G  Gk1 i  mks; i Gks  Gki Dki ¼ M i i Dtsmp   C k  C k1 i  vks; i C ks  C ki S ki ¼ V i i Dtsmp

M i cp

ð14Þ ð15Þ ð16Þ ð17Þ ð18Þ ð19Þ

where M is the air mass of one space, T is temperature, G is the moisture content, C is the CO2 concentration, D and S are the moisture and CO2 generation rates, respectively, cp is air specific heat, Dtsmp is the sampling interval. In the optimization process of the temperature set point of critical zones in one prediction period, this set point reset will result in slightly change of the sensible cooling loads in critical zones due to the heat transfer through building envelopes and the internal mass. Therefore, the originally estimated sensible cooling load of the critical zone is needed

X. Xu et al. / Applied Thermal Engineering 29 (2009) 91–104

to be corrected, and then is used in the prediction period for system performance prediction. This correction is made approximately as Eq. (20) according to the sampling indoor air temperature and outdoor air temperature as well as the temperature set point of the critical zone. In the prediction period, the moisture load and pollutant load of each zone are assumed be the same as estimated in the sampling step. The sensible cooling loads of non-critical zones are also assumed to be the same as estimated in the sampling step. k Qpred sen; i ¼ ð1  aÞQsen; i þ

aQksen; i  T kout



T ki

T kout  T set; i



ð20Þ

where a is a coefficient accounting for the heat flow through building envelopes and internal mass, the subscript set and out indicate set point and outdoor, respectively, the superscript pred indicates prediction. 4.2. System performance prediction System performance prediction includes the prediction of the indoor air states (i.e. temperature, moisture content and pollutant) of all the zones, the supply air flow rate of each zone, the total supply air flow rate, the outlet air state of the cooling coil, the energy consumption of the cooling coil, the power consumption of fans in one prediction period. To accurately predict the dynamic process responses at the end of one prediction period (Dtpred) and within this prediction period, the prediction period is simulated by dividing this period into N simulation steps of the time step Dtsim as Eq. (21). For the performance prediction of the coil, Section 4.1.1 has given the description. During a small simulation time, supply air flow rate and conditions are assumed to be constant. Because sensible heat load, moisture load, and pollutant are slowly-varying variables, they are assumed to be constant during a prediction period. Therefore, Eq. (14)–(16) can be expressed approximately by replacing the derivative terms with finite difference terms as Eqs. (22)–(24), respectively. Dtsim ¼ Dtpred =N " j #  Qpred ms; i  j sen; i jþ1 j j Ts  Ti þ Dtsim Ti ¼ Ti þ Mi M i cp " j #   m D i s; i ¼ Gji þ Gjs  Gji þ Dtsim Gjþ1 i Mi Mi " j #  Si vs; i  j jþ1 j j Cs  Ci þ Ci ¼ Ci þ Dtsim Vi Vi

ð21Þ ð22Þ

Assuming the VAV system can deliver the demanded air flow rates to each zone, the total air flow rate of the VAV system can be expressed as Eq. (26). The return air flow rate is assumed to be equal to the total supply air flow rate. The return air temperature, moisture and pollutant are assumed to be constant using the values at the current sampling instant although they are changing in the prediction period. The changes of the total supply air and fresh air flow rates account for the change of the cooling energy consumption of the cooling coil. mjs; i ¼ ms; min; i þ U jPID; i ðms; max; i  ms; min; i Þ mjs ¼

I X

mjs; i

ð24Þ

where the subscripts j and j + 1 represent the current and the next simulation time steps, respectively, subscripts sim indicates simulation. Neglecting the delay of the VAV local supply air flow control loop responding to the change of zonal flow rate demand, the VAV supply air flow rate to each zone at the current simulation instant can be expressed as Eq. (25) by the prediction of the VAV flow rate set point.

ð25Þ ð26Þ

i¼1

where m is the air mass flow rate, subscripts max, min indicate maximum and minimum, respectively, U jPID; i is the prediction of the space temperature controller at the current simulation instant (j). This PID control output can be calculated based on the difference between the zonal air temperature and its set point of the ith zone, and the initial values of integral term and derivative term at each sampling instant. These initial values can be fetched from the relevant storage of the zonal temperature controllers. For more details of the PID algorithm, one may refer to the article [29]. These models for the prediction of the state variables (i.e. Ti, Di, Ci) are needed to be tuned further for increasing accuracy since there may be derivations between the predictions and the real processes. The tuning model as Eq. (27) is employed to correct the model predictions. At a sampling instant (tk1), the required measurement data are collected to estimate the source terms as Eqs. (17)– (19). These source terms are then used by these models as Eqs. (22)–(24) to estimate the state variables at the next sampling instant (tk) by the simulation of a few time steps. At the next sampling instant, these state variables are available and the model prediction error ðekmeas Þ can be measured. To reduce the effects of the measurement uncertainty and model uncertainty, a filter is used to stabilize the error estimation ðekest Þ as Eq. (28) for correcting the model output at the future next sampling instant (tk+1). Y^ ¼ Y þ e

ð23Þ

97

ekþ1 est

¼

kekest

ð27Þ þ ð1 

kÞekmeas

ð28Þ

where Y is the output of the model (i.e. state variables Ti, ˆ is the output of the model after correction, e is Di, Ci), Y the correction factor representing the estimated error between model prediction and real process. eest is the model error estimation, emeas is the measured model error, k is a forgetting factor. 4.3. Optimization of temperature set points of critical zones With these models proposed previously, the responses of the building and air-conditioning systems to the changes of

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the controls (i.e. total fresh air flow rate and zonal temperature set points) can be predicted in a prediction period for the optimization of the temperature set point of critical zones. In the optimization process, three elements, i.e. IAQ (represented using CO2 concentration) and the thermal comfort of each zone, and total energy consumption are significantly of concern. The total cost function (J) for the optimization is constructed as Eq. (29). Jtc is the cost function concerning the thermal comfort of all the zones as Eq. (30). Jiaq represents the cost function concerning the IAQ of all the zones as Eq. (31). It is worthwhile to mention that the thermal comfort and IAQ of all the zones are involved in the cost functions in that the building system (including all the zones) and the air conditioning system are interrelated together and affect each other although only the temperature set point of the critical zone is optimized. Jpow is the cost function of total energy consumption as Eq. (32). J ðT cz; set Þ ¼ atc J tc þ aiaq J iaq þ apow J pow Z t¼Dtpred X I J tc ¼ ðPMVi Þ2 dt 0

J iaq ¼

ð30Þ

i¼1

Z

I X

t¼Dtpred 0

J pow ¼

ð29Þ

Z

ðtan pC i =ð4C thld Þ  1Þdt

ð31Þ

i¼1 t¼Dtpred



 W fan; s þ W fan; rtn þ Qcooling =COP dt

ð32Þ

0

where J is cost function, a is the weighting factor, PMVi is the index of PMV (i.e. predicted mean vote) of each zone and can be calculated by using Fanger’s comfort equations [13], Cthld is the threshold CO2 concentration (950 ppm was used), Qcooling is the cooling energy consumption of the coil, COP is the coefficient of performance including the pump and the chiller (assumed to be constant as 2.5), subscripts cz, and rtn indicate critical zone and return, respectively. Searching for the optimal value of the temperature set point of the critical zone is a nonlinear optimization process. There exist many methods for such optimization problems such as sequential quadratic programming [15] and conjugate gradient method [24] and genetic algorithm (GA) [22], etc. GA is a good optimization method since it can quickly find a sufficiently good solution with random initialization. This algorithm was used to search for global optimal solutions in HVAC fields [30,9,34,10]. In this study, GA is also utilized to search for the optimal value of the temperature set point of the critical zone by minimizing the objective function as Eq. (29). The fitness function (f) in the genetic algorithm is represented as Eq. (33) f ðT cz;set Þ ¼

1 J ðT cz;set Þ

is near the cooler temperature border suggested by the standard [2]. Random initialization of this parameter produces the initial population to start a GA run. Each set point trail (i.e. the temperature set points of the critical zone) is given to the model-based predictor to predict the responses of the system during one prediction period as shown in Fig. 2. Then the cost function estimator computes the ‘‘overall cost” (also the fitness) according to the predicted responses of the system. According to the fitness of parents and its rules for crossover and mutation, the GA optimizer generates the next generation population, and then the system responses are predicted, and the fitness is re-evaluated. This process is repeated. The criterion to stop the GA optimizer is based on the comparison of the best fitness values of two consecutive runs. The GA estimator stops when the relative difference between the two maximum fitness values reaches a threshold value. A GA run is also terminated if the number of the current generation is equal to a predefined maximum number. The parameters of the GA driver are important for convergence speed. They are selected according to Carroll’s recommendation [8] and also determined by simulation tests.

5. Test facility The multi-zone VAV air-conditioning system is also illustrated in Fig. 1. The system serves half of a floor of a high-rise commercial building. Served floor space is divided into eight zones using partitions as Fig. 3. Zone 8 is used as a meeting room and the other zones are used as office. The conditioned air is delivered to indoor space through VAV boxes. Return air is drawn back through ceiling plenum. The design air flow rate of the VAV system is 7.2 kg/s. This system involves two fans of variable pitch angle, a cooling coil and interlocked dampers, etc. In this study, the real processes of the VAV air-conditioning system and building system are represented using detailed dynamic simulation. In simulation, all the VAV boxes serving the concerned floor space is represented by eight VAV boxes with each serving one zone. The temperature controller controls the outlet temperature of the cooling coil. The pressure controller maintains the supply air static pressure at its set point by modulating the fan pitch North Zone 1

Zone 2

Zone 3

Zone 4

Office

Office

Office

Office

145 m2

175 m2

175 m2

145 m2

Zone 5

Zone 7

Zone 8

Zone 6

Office

Office

Meeting Room

Office

110 m2

153 m2

153 m2

110 m2

East

West

ð33Þ

In the genetic algorithm, only one parameter (i.e. Tcz,set ) constitutes the chromosome of an individual. The search scope of this parameter is between 21 °C and 24 °C. 24 °C is the default set point of all the zones while 21 °C

Interior Fig. 3. Layout of the air-conditioned floor of multiple zones.

X. Xu et al. / Applied Thermal Engineering 29 (2009) 91–104

angle of the supply fan. The return air controller controls the flow rate difference to maintain a positive pressure in the building. The outdoor air controller controls the outdoor airflow rate by regulating the fresh air damper. The fresh air damper, return air damper, and re-circulated air damper are interlocked. Pressure independent VAV boxes are used to control zone temperatures. All the above controllers employ digital PID control. This system also includes an enthalpy control and DCV-based ventilation rate set point supervisory control at the high level. The enthalpy control strategy determines if more fresh air and how much fresh air are introduced by comparing the air status of outdoor air and return air to achieve best energy saving. The fresh air controller finally chooses the larger one of the set points from the enthalpy control strategy and the DCV strategy. In this study, the model-based optimal ventilation control strategy for DCV control was implemented. Most HVAC processes are nonlinear. In this study, dynamic models were used to simulate the cooling coil of the nonlinear nature [27]. The resistance characteristic of the fresh air damper is nonlinear and was simulated using the Legg’s exponential correlation [20]. The flow characteristic of the cooling coil valve is equal percentage with dead bands [32]. Dynamic sensor models were used to simulate the temperature, humidity, pressure, flow and CO2 sensors using time constant method. An actuator model was used to simulate the realistic characteristics of the actuators. The actuator is assumed to accelerate very quickly and then turn at constant speed [14]. The detailed description on the models of air-conditioning system and digital controllers can be found in the article [27].

99

The outdoor air CO2 concentration was 360 ppm. The generation rates of CO2, latent and sensible loads of one person are selected to be 5  106 m3/s, 1.17  105 kg/s and 0.065 kW, respectively. The occupancy profiles of each zone and the total occupancy profile are presented in Fig. 4. The air-conditioning system worked from 7:50 am to 19:00 pm. In out tests, we found the CO2 concentration in the meeting room is much higher than the prescribed level (i.e. about 700 ppm above the fresh air CO2 concentration) when the latest standard [6] was used. Therefore, in this study, the following rule was used to compute the fresh air requirement of each zone. The fresh air requirement is computed according to the number of occupants, i.e. 10 l/s per person for the office rooms and the meeting room [5] while the minimum fresh air requirement is taken according to the air-conditioning area, i.e. 0.3 l/s per square meter for these rooms [6]. This rule considers the minimum fresh air rate for occupant-generated pollutants and the minimum fresh air rate for diluting non-occupant-generated pollutants simultaneously. In our test, the sampling interval for this strategy was 60 s. The prediction period was 300 s while the simulation time step of the optimal control strategy was 60 s. The weighting factors of the cost functions used are given in Table 1. Many tests were carried out to test the performance of the optimal strategy in different weather conditions. Only the tests in typical sunny summer day and cloudy summer day were presented in the study. Fig. 5 shows the outdoor air dry-bulb temperature and humidity in both test days. The set point of the outdoor air flow rate was governed by DCV control in both days.

6. Test and result analysis

6.1. Test conditions The test facility was built on TRNSYS platform [17]. Many disturbances affecting building cooling load and indoor air quality are needed to be prepared as input files for TRNNSYS. The internal disturbances are occupancy, lighting and equipment loads in each zone while the external disturbances are mainly the solar gains of each zone transmitted through the windows, sol–air temperature of each external wall, the outdoor air temperature, humidity and CO2 concentration at different weather conditions.

160

70

140 Zone 8

Total occupancy

60

120

50

100

40

80

30

60

Zone 2, 3, 7 Zone 1, 4

20

40

10

20 Zone 5, 6

0 7

8

Number of total occupants

Number of actual occupants in each zone

80

The optimal strategy was tested in the above test facility with the test conditions in Section 6.1. In this strategy, many models are required for system performance prediction, and the performance of these models directly affects the performance of this optimal strategy. The main models of concern were evaluated in Section 6.2. This optimal strategy was evaluated in Section 6.3. The choice of the weighting factors relating with the indoor air quality, thermal comfort and energy consumption, and their effects on the strategy’s performance are presented in Section 6.4.

0

9 10 11 12 13 14 15 16 17 18 19 20 21

Time (h)

Fig. 4. Occupancy profiles of individual zones and the total occupancy profile.

Table 1 Control settings of the cost functions of the optimizer Weighting factors of cost functions

atc

aiaq

apow

Setting Setting Setting Setting Setting

2.00 2.00 2.00 0.00 2.00

0.35 0.50 0.00 0.35 0.50

0.01 0.01 0.01 0.01 0.00

I II II IV V

100

X. Xu et al. / Applied Thermal Engineering 29 (2009) 91–104 35.0

0.035

30.0

0.031 Cloudy summer

25.0

Humidity in the cloudy summer day

0.027

Humidity in the sunny summer day

20.0

0.023

15.0

0.019

10.0

0

2

4

6

8

10

12

14

16

18

20

22

Humidity (kg/kg)

Outdoor air dry-bulb temperature(ºC)

Sunny summer

0.015 24

Time (h)

Fig. 5. Temperature and humidity profiles of test days.

6.2. Evaluation of the model performance

6.3. Evaluation of the optimal strategy

In this study, many models are required for system performance prediction, and the performance of these models directly affects the performance of the optimal strategy. The main models of concern are the model for occupancy detection in Section 3, the cooling coil model in Section 4.1.1, the models of source terms in Section 4.1.3, and the models for estimating the zonal air state of each zone in Section 4.2. The evaluations show these models have good performance. For the conciseness of this article, only the performance evaluation of the cooling coil model is presented. Fig. 6 presents the ‘‘measured” and predicted heat transfer coefficients (i.e. UA values) of the cooling coil at the water side and the air side, respectively from 9:00 am to 7:00 pm when the weighting factors of Setting I were used. The coefficients from 8:00 am to 9:00 am were not pre-

24.0 "Measured" UA of water side (kW/ ºC) Predicted UA of water side (kW/ ºC) "Measured" UA of air side (kg/s) Predicted UA of air side (kg/s)

UA value

20.0 16.0 Water side

12.0 8.0 Air side

4.0 0.0 9

10

11

12

13

14

15

16

sented since the measurements at this period were required for the initialization of RLS algorithm. The ‘‘measured” heat transfer coefficients were calculated based on the measurements. The predicted heat transfer coefficients were calculated using Eqs. (10) and (11) while the parameters in both equations were identified in advance. The predicted coefficients of the coil at both sides agreed well with the coincident ‘‘measured” coefficients. In addition, the heat transfer coefficient at the water side is much larger than that at the air side since water is much easier to conduct heat than air. The heat transfer coefficient at the water side was much high from about 10:30 am to 12:00 am since much water flow rate was required for cooling when the meeting room was occupied densely.

17

18

19

Time (h)

Fig. 6. Heat transfer coefficients of the cooling coil at the water side and the air side.

The performance of the model-based optimal ventilation control strategy (i.e. optimal strategy) was evaluated by comparing with other two strategies. The first strategy (i.e. conventional DCV strategy thereafter) uses the detected total occupancy for estimating the total fresh air flow rate. The second strategy (i.e. multi-zone DCV strategy thereafter) only uses the dynamic ventilation equation scheme for determining the total fresh air flow rate. The costs related with the thermal comfort, indoor air quality, and total energy consumption, and the total cost in the sunny summer test day are presented in Table 2 when different control settings of the weighting factors were used. These costs were integrated over the entire operation period. The environmental and energy performance of the optimal strategy using different control settings in the sunny summer test day are presented in Table 3. The environmental and energy performance of the other two DCV ventilation strategies are also presented in this table as the benchmark. In this section, only the performance of the optimal strategy using the control setting of Setting I is analyzed subsequently in detail (For other control settings, the explanations will be addressed in Section 6.4). Table 2 shows that the optimal strategy considered these three terms (i.e. thermal comfort, IAQ and power consumption) basically evenly since the weight factors are 2.00, 0.35 and 0.01 as shown in Table 1. Using the optimal strategy, the temperature set point of critical zones can be reset. Fig. 7 presents the temperature set points of critical zones, and Fig. 8 presents the identified critical zones for reference. In most of the

Table 2 Summary of the costs of the optimal strategy with different control settings in the sunny summer test day Cost

Cost of thermal comfort Cost of IAQ Cost of power consumption Total cost

Control settings Setting I

Setting II

Setting III

Setting IV

Setting V

37,279 84,229 2,103,897 66,116

37,402 82,567 2,117,451 54,695

37,322 81,404 2,117,232 95,816

36,944 90,234 2,082,715 10,755

38,055 84,007 2,140,582 34,106

X. Xu et al. / Applied Thermal Engineering 29 (2009) 91–104

101

Table 3 Summary of the environmental and energy performance of different DCV strategies in the sunny summer test day Environmental and energy performance

Conventional DCV strategy

Multi-zone DCV strategy

Optimal strategy with different control settings Setting I

Setting II

Setting III

Setting IV

Setting V

Environmental performance Average PPD of Zone 8 (%) Maximum PPD of Zone 8 (%) Average CO2 concentration (ppm) Maximum CO2 concentration (ppm)

6.92 13.52 834 1227

8.86 16.37 700 1009

8.01 14.67 716 1083

8.08 14.69 714 1074

8.09 14.69 719 1101

8.22 14.74 710 989

7.86 14.64 709 1003

Energy performance Fan (kW h) Saving (%) Cooling energy consumption (M J) Saving (%) Overall power consumption (kW h) Saving (%)

224.73 0.20 3321.87 18.96 593.83 12.64

224.28 – 4099.07 – 679.73 –

227.04 1.23 33810.193 7.55 648.12 4.65

227.31 1.35 3810.19 7.05 650.66 4.28

227.36 1.37 3774.01 7.93 646.69 4.86

227.99 1.65 3814 6.95 651.81 4.11

226.17 0.84 3941.2 3.85 664.08 2.30

8.00

24.50

Zone 7

Zone 8

Zone 7

24.00 23.50 23.00 22.50 22.00

6.00 5.00 4.00 3.00 2.00 1.00

21.50 21.00

Fresh air flow rate set point Measured fresh air flow rate Total supply air flow rate

7.00

Air flow rate (kg/s)

Temperature setpoint (ºC)

25.00

0.00 9

8

10

11

12

13

14

15

16

17

18

19

8

9

10

11

12

Fig. 7. Temperature set points of critical zones using the optimal strategy (Setting I).

9

Air flow rate (kg/s)

Critical zone

7

Zone 7

6 5 Zone 4

3 2 Zone 1

1 0

15

16

17

18

19

8.00 Fresh air flow rate set point Measured fresh air flow rate Total supply air flow rate

7.00

4

14

Fig. 9. Total supply air and fresh air flow rates using the optimal strategy (Setting I).

Zone 8

8

13

Time (h)

Time (h)

6.00 5.00 4.00 3.00 2.00 1.00

8

9

10

11

12

13

14

15

16

17

18

19

Time (h)

0.00 8

9

10

11

12

13

14

15

16

17

18

19

Time (h)

Fig. 8. Identified critical zones.

office hours, the critical zone was Zone 7. From 9:10 am to 12:00 am, the critical zone was Zone 8 (the meeting room). With the identified critical zone, the optimal strategy optimized the temperature set point as shown in Fig. 7 while the temperature set point of the other zones kept at the default value (24 °C). When the optimal set point of the critical zone was used for the practical control, the total fresh air flow rate reduced greatly as shown in Fig. 9 when comparing with that using the multi-zone DCV strategy as shown in Fig. 10. From 10:30 am to 12:00 am, the total fresh air flow rate using the optimal strategy is about two third of that using the multi-zone DCV strategy.

Fig. 10. Total supply air and fresh air flow rates using the multi-zone DCV strategy.

Due to the reduction of fresh air flow rate, the cooling energy consumption also decreased. The cooling energy saving is 7.55% comparing with the benchmark using the multi-zone DCV strategy as shown in Table 3. The saving of the total power consumption is 4.65% while the fan power consumption increased slightly due to the slight increase of the total supply air flow rate. It is noted that the cooling energy consumption and the total power consumption using the conventional DCV strategy are less than that using the multi-zone DCV strategy and the optimal strategy. However, the indoor air quality was

1200 1100 1000 900 800 700 600 500 400 300 200

(ppm)

deteriorated seriously since the maximum CO2 concentration could be up to 1227 ppm. When the optimal strategy was implemented, the thermal comfort of Zone 8 increased slightly comparing with that using the multi-zone DCV strategy as shown in Table 3 (For other zones, the average PPD using these three strategies was almost the same, and is not presented for analysis). The average PPD decreased from 8.86 to 8.01, and the maximum PPD also decreased. When comparing with that using the conventional DCV strategy, the average and maximum PPD of Zone 8 using the optimal strategy increased slightly, but still in acceptable range. The maximum CO2 concentration is 1083 ppm, higher than the maximum value of 1009 ppm using the multi-zone DCV strategy. However, it is still acceptable since the prescribed level is 700 ppm above the CO2 concentration of the outdoor air (360 ppm in this study). The total average CO2 concentration increased from 700 ppm to 716 ppm. The CO2 concentration of each zone using the optimal strategy and the multi-zone DCV strategy are presented in Figs. 11 and 12 for comparison. The CO2 concentration of each zone using the conventional DCV strategy was presented in the previous study [33]. The environmental and energy performance of the optimal strategy using different control settings in the cloudy summer day are also presented in Table 4.

CO2 concentration of each zone

X. Xu et al. / Applied Thermal Engineering 29 (2009) 91–104

Zone 8 Zone 7

Zone 1-6

8

9

10

11

12

13

14

15

16

17

18

19

20

Time (h)

Fig. 11. CO2 concentration of each zone using the optimal strategy (Setting I).

CO2 concentration of each zone (ppm)

102

1200 1100 1000 900 800 700 600 500 400 300 200

Zone 8

Zone 7

Zone 1-6

8

9

10

11

12

13

14

15

16

17

18

19

20

Time (h)

6.4. Evaluation of the effects of weighting factors

Fig. 12. CO2 concentration of each zone using the multi-zone DCV strategy (Setting I).

Different settings of these weighting factors have significant effects on the thermal comfort, indoor air quality and the total energy consumption. Investigating the correlation of the total cost function and these three cost functions related with thermal comfort, IAQ and energy consumption, the suitable factors can be obtained by fine-tuning these factors according to different decision-makers. The fine-tuning is done using the trial and error method taking into account the expected weightings of these three terms. As presented above, the control settings of Setting I allowed these three cost function terms (i.e. thermal comfort, IAQ and power consumption) had similar contribu-

tion to the total cost function. The control parameters of Setting II considered the IAQ slightly more. Table 3 shows the IAQ improved slightly (i.e. average and maximum CO2 concentrations) in the sunny summer test day when comparing with that using the control settings of Setting I. In this case, slightly more fresh air was introduced. The total energy saving was 4.28%, 0.37% less than the saving using the control settings of Setting I. Some tests were also conducted when any two out of these three terms were considered while the third term was omitted. The control settings of Setting III omitted the cost function related with IAQ. Therefore, the average

Table 4 Summary of the environmental and energy performance of different DCV strategies in the cloudy summer test day Environmental and energy performance

Conventional DCV strategy

Multi-zone DCV strategy

Optimal strategy with different control settings Setting I

Setting II

Setting III

Setting IV

Setting V

Environmental performance Average PPD of Zone 8 (%) Maximum PPD of Zone 8 (%) Average CO2 concentration (ppm) Maximum CO2 concentration (ppm)

7.29 13.2 835 1286

9.00 18.33 703 1070

8.79 16.37 711 1022

9.03 16.41 703 936

8.57 16.33 716 1098

9.29 16.44 704 932

8.57 16.32 705 1005

Energy performance Fan (kW h) Saving (%) Cooling energy consumption (M J) Saving (%) Overall power consumption (kW h) Saving (%)

165.77 0.03 2711.89 17.36 467.09 11.94

165.82 – 3281.56 – 530.44 –

167.09 0.77 3077.34 6.22 509.02 4.04

167.59 1.07 3086.12 5.96 510.49 3.76

166.96 0.69 3056.04 6.87 506.52 4.51

167.88 1.24 3053.78 6.94 507.19 4.38

166.95 0.68 3124.09 4.80 514.07 3.09

X. Xu et al. / Applied Thermal Engineering 29 (2009) 91–104

and maximum CO2 concentrations increased obviously as shown in Table 3 when comparing those using Setting I because less fresh air flow rate was introduced. The savings of the cooling energy consumption and the total power consumption also increased. The savings are 7.93% and 4.86%, 0.38% and 0.21% more than the counterparts of the optimal strategy using Setting I. Setting IV only considered the cost functions related to the IAQ and power consumption while neglecting the cost function related with the thermal comfort. When it was used for the optimal strategy for the temperature set point optimization, the indoor thermal comfort was deteriorated when comparing with that using Setting I while the IAQ was improved as shown in Table 3. The average and maximum PPD of Zone 8 are 8.22 and 14.74. The cooling energy saving and the total power consumption saving are 6.95% and 4.11%, respectively. When the cost function of the total power consumption is neglected (i.e. the control settings of Setting V), the thermal comfort and IAQ had obvious improvement as shown in Table 3. This is due to that more fresh air was introduced since energy is not the main issue of concern. The energy saving potential using Setting V is 2.3%, the least among those using the control settings from Setting I to Setting V. The energy and environmental performance of the optimal strategy using all these control settings in the cloudy summer test day is presented in Table 4. This table also shows the similar trends of the thermal comfort, IAQ and energy saving with those in the sunny summer test day when different control settings were used. 7. Conclusion The model-based optimal ventilation control strategy is based on the system response prediction using dynamic simplified models for optimizing the indoor temperature control of critical zones to ease the unbalance of fresh air requirements among different zones. Tests show that the total cost function was constructed properly by relating thermal comfort, indoor air quality and energy consumption together, and genetic algorithm is a convenient tool for optimizing the temperature set point for online control applications by minimizing the total cost with the aim at optimally estimating the total ventilation rate in multi-zone air-conditioning systems. The evaluation of this optimal ventilation strategy shows that this strategy is capable of optimizing the system overall performance according to the chosen weighting factors. The optimal strategy was evaluated by comparing with other DCV ventilation strategies. The results show this optimal strategy can achieve significant energy saving by comparing with the multi-zone DCV strategy, and can maintain acceptable thermal comfort and indoor air quality by comparing with the conventional DCV strategy although slightly more energy is consumed. This optimal ventilation strategy was also evaluated by using different weighting factors (coefficients). The results

103

show that different coefficients in the cost function have significant impacts on the performance of the optimal strategy since these coefficients determine the weightings for the optimizer to compromise the concern on different issues, such as energy and environment. The users can select or tune these weighting factors according to their concerns on different issues and according to the experiences on the operation of particular air-conditioning systems. A good choice of these weighting factors in the cost function requires more tests. Acknowledgement The research work presented in this paper is financially supported by a Grant (5293/07E) of the Research Grants Council (RGC) of the Hong Kong SAR. References [1] A. Abbassi, L. Bahar, Application of neural network for the modeling and control of evaporative condenser cooling load, Appl. Thermal Eng. 25 (17–18) (2005) 3176–3186. [2] ASHRAE. Addendum 55a. ANSI/ASHRAE Standard 55-1992, 1994. [3] ASHRAE. ASHRAE Standard 62-1989R. Ventilation for Acceptable Indoor Quality (Public Review Draft), Atlanta, 1996. [4] ASHRAE. ASHRAE Standard 62-1999. Ventilation for Acceptable Indoor Quality, Atlanta, 1999. [5] ASHRAE. ASHRAE Standard 62-2001. Ventilation for Acceptable Indoor Quality, Atlanta, 2001. [6] ASHRAE. ASHRAE Standard 62.1-2004. Ventilation for Acceptable Indoor Quality, Atlanta, 2004. [7] K.J. Astrom, B. Wittenmark, Adaptive Control, Addison-Wesley Publishing Company, New York, 1989. [8] D.L. Carroll, FORTRAN Genetic algorithm (GA) driver. Version 1.7a. , , 2001. [9] Y.C. Chang, Genetic algorithm based optimal chiller loading for energy conservation, Appl. Therm. Eng. 25 (17–18) (2005) 2800–2815. [10] L.S. Chan, V. Hanby, T.T. Chow, Optimization of distribution piping network in district cooling system using genetic algorithm with local search, Energy Convers. Manage. 48 (10) (2007) 2622–2629. [11] T.Y. Chen, Application of adaptive predictive control to a floor heating system with a large thermal lag, Energy Build. 34 (2002) 43–51. [12] D. Elovitz, Minimum outside air control methods for VAV systems, ASHRAE Trans. 101 (2) (1995) 613–618. [13] P.O. Fanger, Thermal Comfort, McGraw-Hill, New York, 1970. [14] P. Haves, A.L. Dexter, Simulation of local loop controls, in: Proc. Building 1989, IBPSA, Vancouver, 1989. [15] J. House, T. Smith, Optimal control of a thermal system, ASHRAE Trans. 97 (2) (1991) 991–1001. [16] X. Jin, Z. Du, X. Xiao, Energy evaluation of optimal control strategies for central VWV chiller systems, Appl. Therm. Eng. 27 (5– 6) (2007) 934–941. [17] S. Klein, et al., TRNSYS, a Transient Simulation Program. Solar Energy Laboratory: University of Wisconsin, USA, Version 16.1, 2006. [18] R. Kohonen, S.W. Wang, H. Peitsman, et al., Development of emulation method. IEA Annex 17, Final Report, Helsinki, Finland, 1993. [19] T. Kusuda, Control of ventilation to conserve energy while maintaining acceptable indoor air quality, ASHRAE Trans. 82 (1) (1976) 1169–1181. [20] RC. Legg, Characteristics of single and multi-blade dampers for duct air systems, Build. Ser. Eng. Res. Technol. 7 (4) (1986) 129–135.

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