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Prediction-based online optimal control of outdoor air of multi-zone VAV air conditioning systems
Energy and Buildings 37 (2005) 939–944 www.elsevier.com/locate/enbuild
Prediction-based online optimal control of outdoor air of multi-zone VAV air conditioning systems Xinqiao Jin *, Haigang Ren, Xiaokun Xiao Department of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200030, China Received 5 August 2004; received in revised form 21 October 2004; accepted 26 November 2004
Abstract An optimal strategy for outdoor air control is developed using a system approach based on prediction to minimize energy consumption. ARMA model is used to predict the energy performance which is expressed by an energy-increment equation. The energy-increment equation is formed to involve the real-time variations of AHU load and energy use of reheaters of VAV terminals. To minimize the Energy-increment equation by genetic algorithm, the optimal settings of outdoor air ratio of AHU and reheating could be obtained. The strategy is tested and evaluated in a simulated environment under various outdoor and indoor conditions. # 2005 Elsevier B.V. All rights reserved. Keywords: VAV air conditioning systems; Outdoor air control; Energy-Increment equation
1. Introduction The optimal control of outdoor air in VAV (variable air volume) air-conditioning systems aims at providing accepted indoor air quality with least energy input under dynamic outdoor conditions and indoor loads. In a multi-zone building, there are differences among zones in orient, lighting, occupancy etc., so there are differences in cooling load and outdoor air requirement. For the zones served by one AHU (air handling unit), supply air flows of VAV terminals have the same outdoor air ratio, and outdoor air flow ventilated to each zone depends on the supply air flow rate of its served VAV terminal. However, supply air flow rate of VAV terminal in each zone is controlled to satisfy zone temperature setpoint and varied with zone load. So it is difficult to set the outdoor air ratio of AHU: the lower setting may lead to some of zones in under ventilation and higher one may lead to some of zones in over ventilation. The former will result in poor indoor air quality and the latter will result in more energy used. Even if the total outdoor air flow of AHU intake is set to equal to the total requirement of zones for * Corresponding author. Tel.: +86 21 62933351; fax: +86 21 62932601. E-mail address: [email protected] (X. Jin). 0378-7788/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2004.11.011
satisfy ASHRAE Stand 62-1999 [1], the problem that some of zones in under/over ventilation still presents because of varying of supply air flows of VAV terminals [2]. There are three ways to solve the problem of outdoor air control and distribution in multi-zone building and VAV systems: (I) Using the highest outdoor air ratio of requirements of zones as the setpoint of the control of AHU outdoor air intake. (II) Raising setpoint of AHU outlet air temperature. (III) Reheating supply air in some of VAV terminals. The first way will result in that all of zones are ventilated by more outdoor air than their minimum requirement except the zone which has the highest outdoor air ratio requirement. It implies that more outdoor air has to be conditioned and more energy has to be used in summer and winter. Raising AHU outlet air temperature will increase the supply air flow rates of all zones. It could not change the outdoor air percentage of supply air bringing to zones, and it will have the same result of the first way. Meanwhile, increasing the total supply air flow rate will also result in increasing fan energy consumption. Reheating is usually used to adjust supply air temperature in comfortable HVAC systems. It is considered to increase energy consumption of systems in cooling mode, because it increases energy use not only in reheating but also in cooling load. In fact, reheating in one
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X. Jin et al. / Energy and Buildings 37 (2005) 939–944
Nomenclature d e G H i M R T V y Z
air humidity (kg/kg) error mass flow rate (kg/s) enthalpy (kJ/kg) zone number mass flow rate of requirement (kg/s) resistance of electric reheater temperature (8C) input voltage of electric reheater (V) outdoor air ratio of AHU outdoor air ratio requirement of zone
Subscript oa outdoor air sa supply air of zone set setpoint sup total supply air of AHU Superscript j time period Top-script ^ prediction
VAV terminal to increase the supply air flow rate of its served zone will result in more mass of outdoor air brought into the zone than it used to be without reheating in the case of the same outdoor air ratio of AHU. It implies that reheating could be used to adjust the outdoor air distributing in zones. Mumma and co-workers [3,4] concluded their research works that the outdoor air control by use of reheating can maintain acceptable indoor air quality in multizone building with less outdoor air intake. There are two problems in outdoor air control with VAV terminals reheating. The first problem is how to determine the suitable setting of outdoor air ratio of AHU. The higher setpoint may result in more outdoor air intake; the lower one may result in more energy used by reheaters of VAV terminals, it should be optimized. The second is how to eliminate the effect of heat capacitance of reheaters on the online control of reheaters. The response of supply air flow rate is delayed by heat capacitance, a feed back control of reheater to adjust supply air flow rate of VAV terminal results in poor control performance [5], it should be improved. This paper presents an on-line outdoor air control strategy of multi-zone VAV air-conditioning systems using system approach, which is suitable to be used in BAS (building automation system) with integrated digital control stations for VAV terminals and AHUs. An energy consumption function is formed which concerns the energy consumption of systems including reheater and chiller (i.e. AHU loads). A genetic algorithm is used to search the optimal setting of
outdoor air ratio of AHU by minimizing the energy consumption function. A feed-forward control is used for control of reheaters based on the prediction, which ARMA (autoregressive moving average) model is used for predicting the supply air flows and outdoor air requirements of zones with the method of occupancy detection based on measurement of indoor and outdoor CO2 concentrations. The strategy is tested and evaluated under various conditions online on a centralised VAV air-conditioning system simulated using detailed HVAC dynamic models. This paper presents the control strategy, ARMA-based prediction model, GA-based optimization approach and evaluation of the control strategy.
2. Air-conditioning and control systems description The building is one floor office located in Shanghai. It has a total floor area of 1166 m2 and is divided into eight zones. A VAV terminal with electric reheater is equipped in each zone. A schematic of the air conditioning and control systems is shown in Fig. 1. The air-conditioning systems consist of one AHU, which supplying handled air to VAV terminals, supply and return fans, ducts, dampers, VAV terminals and chilled water valve of AHU coil. The conditions within the system are regulated by local controllers. The air temperature in each zone is controlled by a pressure-independent VAV controller. One PID controller controls the VAV damper position to maintain the supply air flow rate at its setpoint. This air flow rate setpoint is reset by a PID temperature controller to maintain a desired space temperature. The electric reheater is controlled by moderating its input voltage to maintain supply air temperature of each VAV terminal. AHU outlet air temperature is controlled by moderating the opening of the valve and therefore adjusting the chilled water flow rate through the AHU coil. Two variable speed fans are used as the VAV supply fan and return fan. The supply fan is controlled by a PID controller to maintain the supply air static pressure at its setpoint, and the return fan is controlled by the ex-filtration flow controller, which controls the difference between the total supply and return air flow rates at certain setpoint to maintain a positive pressure moderating the speed. The outdoor air ratio is controlled by the outdoor air controller by moderating the positions of the mixing damper, outdoor air damper and exhaust damper. The control and sensor signals are depicted as dash line in Fig. 1.
3. Optimal control strategy To ensure all zones to maintain acceptable indoor air quality, the setting of outdoor air ratio of AHU intake may be the highest one of the requirements of zones. However, it may bring more outdoor air into building which resulting in
X. Jin et al. / Energy and Buildings 37 (2005) 939–944
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Fig. 1. Schematic of VAV air conditioning and control systems.
more energy using for AHU load in summer and winter. Lowering the setting of outdoor air ratio can reduce the energy consumption but resulting in insufficiency of outdoor air flow in some zones. Rising the supply air flows to those zones by reheating can supply sufficient outdoor air flows but resulting in additional energy using. So, there could be an optimal problem to minimize the energy use by optimizing the settings of outdoor air ratio and voltages of reheaters. The optimal control strategy is set up and illustrated in Fig. 2.
3.1. Data processing The measurements of sensors at and before current time step are sampled and stored in ‘Data processing’ module. They are processed to obtain the data needed by other two modules which includes: (I) requirement of outdoor air mass flow of each zone, Moa[i]; (II) supply air mass flow of each zone without the effect of reheating, G0 sa ½i; (III) enthalpy of AHU supply air (total supply air) and outdoor air, Hsup and Hoa. The requirement of outdoor air mass flow of each zone is estimated according to ASHRAE Standard using indoor and
outdoor air CO2 concentrations and occupied area [6]. G0 sa ½i can be obtained by Eq. (1) described below: G0 sa ½i ¼ Gsa ½i
H set ½i H sa ½i H set ½i H sup
(1)
Where, the subscript ‘set’ represents the condition at setpoint. Hsup and Hsa can be calculated by temperature and humidity. 3.2. Online prediction The principle of ARMA model is to predict the value of a time-varying variable at current time (x j) using the previous time series data of the variable, which including the average (m), the measurements series (x j1, x j2, . . ., x jm), the prediction errors series (e j1, e j2, . . ., e jn) and a random error (e j). It can be expressed as Eq. (2): x j m ¼ f1 ðx j1 mÞ þ f2 ðx j2 mÞ þ þ fm ðx jm mÞ þ e j u1 e j1 u2 e j2 un e jn
(2)
where m and n are order numbers of the processes for autoregressive and moving average components, respectively; f and u are parameters. Before prediction, the time period of prediction should be selected. Time period of 15 min is used and then one-day time is divided into 96 time periods. To predict the
Fig. 2. Logic of optimal control strategy.
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requirements of outdoor air mass flow and supply air mass flows, they should be stabilized using Eqs. (3) and (4), respectively: j j1 j96 j97 aj ½i ¼ ðMoa ½i Moa ½iÞ ðMoa ½i Moa ½iÞ
(3)
bj ½i ¼ ðG0sa j½i 2G0sa j 1½i þ G0sa j 2½iÞ ðG0sa j 96½i 2G0sa j 97½i þ G0sa j 98½iÞ
(4)
and then ARMA(1,1) model is selected [7] and set up as shown in Eqs. (5) and (6): aˆ jþ1 ½i ¼ ð1 f1 ½iÞm1 ½i þ f1 ½iaj ½i u1 ½ie1 j ½i
(5)
ˆ jþ1
(6)
b
½i ¼ ð1 f2 ½iÞm2 ½i þ f2 ½ibj ½i u2 ½ie2 j ½i
where, the subscripts 1 and 2 represent to predict Moa[i] and G0 sa ½i, respectively. The parameter vectors F = (f[1], f[2] . . . f[8]) and Q = (u[1], u[2] . . . u[8]) in Eqs. (5) and (6) are estimated by the last 20 values of the time series and updated every periods. The average values of Moa[i] and G0 sa ½i in next time period can be predicted by Eq. (3) and Eq. (4), respectively. ˆ jþ1 ½i ¼ aˆ jþ1 ½i þ M j ½i þ M j95 ½i M j96 ½i M oa oa oa oa ˆ 0 jþ1 ½i G sa
(7)
ˆ jþ1
j j1 ¼ b ½i þ 2G0 sa ½i G0 sa ½i j95 j96 þ G0 sa ½i 2G0 sa ½i j97 þ G0 sa ½i
(8)
The aim of the optimal strategy is to minimize the energy consumption of systems, which includes energy used to remove AHU cooling load, energy used by reheating and energy used by fans. In the strategy presented in this paper, the difference of energy consumption of systems between with using and without using of reheating is concerned instead of energy consumption. The objective function, which called Energy-increment equation (Eq. (9)) in this paper, is made for optimization under the assumptions below: (I) the difference of energy used by fans is neglected because the addition of total supply air flow is less; (II) the energy used to remove AHU load is calculated using AHU load divided by COP, and COP is considered as a constant. 0 Zˆ cr y ˆ Gsup ðHoa Hset Þ COP ! ˆ0 X 1 Z ½i 1 1þ COP y 0 i 2 Z ½i > y
Gˆ 0 sa ½iðHset Hsa Þ ˆ0
where Z ½i ¼
ˆ oa ½i M ˆ 0 sa ½i G
ˆ0
V½i 8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ˆ oa ½i > M < Gˆ0 sa ½iÞðHset Hsup ÞR½i; Z 0 ½i > y ð (10) ¼ y > : 0; Z 0 ½i < y The optimal control can be achieved by controlling the dampers of AHU and the reheaters according to the optimal setpoints of outdoor air ratio and input voltages, respectively.
4. Tests and evaluation of on-line optimal control strategy 4.1. System simulation and test conditions
3.3. Optimization
DE ¼
Genetic algorithm is employed as optimization method to compute the optimal value of variable (setpoint of outdoor air ratio) that minimizing Energy-Increment equation. D.L. Carroll’s FORTRAN Genetic Algorithm Driver [8] is modified and incorporated into the optimization module. After obtaining the optimal value of y, the optimal setpoints of input voltage of reheaters can be computed by Eq. (10).
(9) ˆ0
and Z cr ¼ maxðZ ½iÞ. The variables
above with symbol ‘^’ represent that they are predicted values from prediction module.
A Transient Thermal System Simulation Program TRNSYS [9] is used as the platform for the dynamic simulation of the air-conditioning systems including building zones and control system [10]. VAV terminal in each zone is simulated. The total capacities of the VAV of each zone are simulated by multiplying the simulated flow rates with factors. A fan model simulates the energy and hydraulic performances of supply and return fans. The hydraulic resistance of coil, supply duct, return duct and VAV terminals are simulated. The energy and dynamic performances of coil are simulated. The ducts are considered as they exchange heat to air outside of ducts with heat capacities and they transfer moisture with the lag which is according the air velocity of inside ducts. The static pressure balance of the system under different fan speeds and VAV damper positions is simulated. The dynamics of sensors and actuation devices are simulated. Realistic DDC models simulate the dynamic response of the local PID DDC control loops. The control loops simulated include the AHU and VAV temperature control loops, the supply air and outdoor air control loops, the exfiltration flow control. The algorithm of the exfiltration flow controller attempts to maintain positive pressure in space and outdoor air intake. To analyse this optimal supervisory control strategy presented in this paper (Called Strategy Reheat), another supervisory control strategy (Called Strategy MaxY) is used to compare the performances in the systems described above. Strategy MaxY is to reset the setpoint of outdoor air ratio online using the maximum one of requirements of
X. Jin et al. / Energy and Buildings 37 (2005) 939–944
outdoor air ratio of zones and there is no use of reheating in VAV terminals. The occupancy, lighting and equipment loads in each zone, the solar gain of each zone transmitting through windows, temperature of each exterior zone, the outdoor air temperature, humidity and pollutants concentration are provided by data files during simulation as test conditions. The transmission solar gain and equivalent ‘sol-air’ temperature are computed by a pre-processor prior to simulation according to building construction data, the solar radiation and outdoor air temperature recorded in the selected days. The data of outdoor air temperature and humidity of selected days are selected from Shanghai weather data records. The chilling systems i.e. chillers, pumps and pipes, etc. are not included in the simulation. The energy used to cool AHU load is computed by the value of COP. COP is selected to be 2.5 and it is considered to be constant. The occupant activity level used is 1.2 met and the CO2 generation rate is 5.0 106 m3/s per occupant. The outdoor air CO2 concentration is selected to be 360 ppm and it is considered to be constant. The value of COP is selected to be 2.5 and it is considered to be constant. The AHU temperature setpoint is 13 8C. The HVAC system works from 7:45 a.m. to 20:00 p.m. each day.
943
Fig. 4. Relative error of prediction of outdoor air flow.
air flow brought into zone (Goa) and requirement of outdoor air flow of zone (Moa). j½i ¼
Goa ½i M oa ½i
(11)
4.2.2. Tests of system performances To evaluate the control performance of the optimal strategy, a criterion index j is introduced and defined as Eq. (11) which implicates the comparison between outdoor
The minimum (jmin) and the maximum (jmax) among j[i] of zones are used to appraise the condition of satisfying the requirement and condition of over ventilation of outdoor air under the control of strategy, respectively. The results of jmin and jmax of one-day test under controls of Strategy Reheat and Strategy MaxY are shown in Figs. 5 and 6, respectively. It is found that the values of jmin of both of strategies are almost near to 1.0, which means that both of strategies can control the outdoor air flows to satisfy the requirements of zones. However, the values of jmax of Strategy MaxY are greater than that of Strategy Reheat, which means that more outdoor air are intaken into AHU and more energy should be used to cooling AHU load under control of Strategy MaxY when enthalpy of outdoor air is greater than that of return air. The total energy consumption of the test day, including energy used to cool AHU load, energy used by fan and energy used by reheaters, is shown in Fig. 7. It is found that the energy used to cool AHU load under control of Strategy Reheat is approximately 13.8% less than that under control of Strategy MaxY. Although more energy used by fan under
Fig. 3. Relative error of prediction of supply air flow.
Fig. 5. Value of jmin under control of two strategies.
4.2. Test results 4.2.1. Tests of prediction To validate the prediction method, tests for predicting supply air flows and the requirements of outdoor air flow of zones had been done and the results of relative error of one of zones are shown in Figs. 3 and 4, respectively. It can be concluded that the error of prediction could be accepted because almost all of the relative errors are within 5%.
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air flows prediction based on ARMA model, and genetic algorithm optimization approach. An Energy-Increment equation is made to generalize the energy performance of systems. The setpoint of outdoor air ratio of AHU can be optimized and the setpoints of input voltage of reheaters can be pre-reset to eliminate effect of heat capacitance of reheaters on the online control of reheaters according to the optimal setpoint of outdoor air ratio of AHU. This optimal strategy has been tested and the results show that it is better than Strategy MaxY, and it is capable of optimizing the energy performance of systems and maintaining acceptable indoor air quality. Fig. 6. Value of jmax under control of two strategies.
References
Fig. 7. Energy consumption under the controls of Strategy Reheat and Strategy Reheat.
control of Strategy Reheat as well as additional energy used by reheaters because of reheating, the total energy consumption under control of Strategy Reheat is approximately 7.8% less than that under control of Strategy MaxY.
5. Conclusions The optimal control strategy using genetic algorithm is presented that supply air flows and requirements of outdoor
[1] ASHRAE, 1999. ANSI/ASHRAE Standard 62-1999, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., Atlantic. [2] M.D. Stophen, Differential CO2 based demand control ventilation: (maximum energy savings & optimized IAQ) history, theory and myths, Energy Engineering 96 (5) (1999) 58–68. [3] S.A. Mumma, R.J. Bolin, Real-time, on-line optimization of VAV system control to minimize the energy consumption rate to satisfy ASHRAE 62-1989 for All occupied Zones, ASHRAE Transaction 98 (1991) 431–443. [4] Y.P. Ke, S.A. Mumma, D. Stanke, Simulation results and analysis of eight ventilation control strategies in VAV systems, ASHRAE Transactions 104 (1997) 1221–1233. [5] X.Q. Jin, H.G. Ren, X.F. Li, Study on outdoor air ventilation and distribution control of multi-zone VAV air-conditioning systems, HV&AC 31 (6) (2001) 1–4. [6] S.W. Wang, X.Q. Jin, CO2-based occupancy detection for on-line outdoor air flow control, Indoor Built Environment 7 (3) (1998) 165– 181. [7] X.Q. Jin, H.G. Ren, X.F. Li, Online prediction of outdoor air for VAV air conditioning systems, Journal of Shanghai Jiaotong University 36 (11) (2002) 1640–1644. [8] D.L. Carroll, FORTRAN Genetic Algorithm Driver, University of Illinois, USA, 1997. [9] Klein, S.A., 1990. TRNSYS, A Transient Simulation Program, version 13.1, Solar energy laboratory, University of Wisconsin, USA. [10] X.Q. Jin, J. Xia, S.W. Wang, Simulation of multi-zone VAV system and local DDC controllers, Journal of Refrigeration 1 (1999) 31–35.
Prediction-based online optimal control of outdoor air of multi-zone VAV air conditioning systems Xinqiao Jin *, Haigang Ren, Xiaokun Xiao Department of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200030, China Received 5 August 2004; received in revised form 21 October 2004; accepted 26 November 2004
Abstract An optimal strategy for outdoor air control is developed using a system approach based on prediction to minimize energy consumption. ARMA model is used to predict the energy performance which is expressed by an energy-increment equation. The energy-increment equation is formed to involve the real-time variations of AHU load and energy use of reheaters of VAV terminals. To minimize the Energy-increment equation by genetic algorithm, the optimal settings of outdoor air ratio of AHU and reheating could be obtained. The strategy is tested and evaluated in a simulated environment under various outdoor and indoor conditions. # 2005 Elsevier B.V. All rights reserved. Keywords: VAV air conditioning systems; Outdoor air control; Energy-Increment equation
1. Introduction The optimal control of outdoor air in VAV (variable air volume) air-conditioning systems aims at providing accepted indoor air quality with least energy input under dynamic outdoor conditions and indoor loads. In a multi-zone building, there are differences among zones in orient, lighting, occupancy etc., so there are differences in cooling load and outdoor air requirement. For the zones served by one AHU (air handling unit), supply air flows of VAV terminals have the same outdoor air ratio, and outdoor air flow ventilated to each zone depends on the supply air flow rate of its served VAV terminal. However, supply air flow rate of VAV terminal in each zone is controlled to satisfy zone temperature setpoint and varied with zone load. So it is difficult to set the outdoor air ratio of AHU: the lower setting may lead to some of zones in under ventilation and higher one may lead to some of zones in over ventilation. The former will result in poor indoor air quality and the latter will result in more energy used. Even if the total outdoor air flow of AHU intake is set to equal to the total requirement of zones for * Corresponding author. Tel.: +86 21 62933351; fax: +86 21 62932601. E-mail address: [email protected] (X. Jin). 0378-7788/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2004.11.011
satisfy ASHRAE Stand 62-1999 [1], the problem that some of zones in under/over ventilation still presents because of varying of supply air flows of VAV terminals [2]. There are three ways to solve the problem of outdoor air control and distribution in multi-zone building and VAV systems: (I) Using the highest outdoor air ratio of requirements of zones as the setpoint of the control of AHU outdoor air intake. (II) Raising setpoint of AHU outlet air temperature. (III) Reheating supply air in some of VAV terminals. The first way will result in that all of zones are ventilated by more outdoor air than their minimum requirement except the zone which has the highest outdoor air ratio requirement. It implies that more outdoor air has to be conditioned and more energy has to be used in summer and winter. Raising AHU outlet air temperature will increase the supply air flow rates of all zones. It could not change the outdoor air percentage of supply air bringing to zones, and it will have the same result of the first way. Meanwhile, increasing the total supply air flow rate will also result in increasing fan energy consumption. Reheating is usually used to adjust supply air temperature in comfortable HVAC systems. It is considered to increase energy consumption of systems in cooling mode, because it increases energy use not only in reheating but also in cooling load. In fact, reheating in one
940
X. Jin et al. / Energy and Buildings 37 (2005) 939–944
Nomenclature d e G H i M R T V y Z
air humidity (kg/kg) error mass flow rate (kg/s) enthalpy (kJ/kg) zone number mass flow rate of requirement (kg/s) resistance of electric reheater temperature (8C) input voltage of electric reheater (V) outdoor air ratio of AHU outdoor air ratio requirement of zone
Subscript oa outdoor air sa supply air of zone set setpoint sup total supply air of AHU Superscript j time period Top-script ^ prediction
VAV terminal to increase the supply air flow rate of its served zone will result in more mass of outdoor air brought into the zone than it used to be without reheating in the case of the same outdoor air ratio of AHU. It implies that reheating could be used to adjust the outdoor air distributing in zones. Mumma and co-workers [3,4] concluded their research works that the outdoor air control by use of reheating can maintain acceptable indoor air quality in multizone building with less outdoor air intake. There are two problems in outdoor air control with VAV terminals reheating. The first problem is how to determine the suitable setting of outdoor air ratio of AHU. The higher setpoint may result in more outdoor air intake; the lower one may result in more energy used by reheaters of VAV terminals, it should be optimized. The second is how to eliminate the effect of heat capacitance of reheaters on the online control of reheaters. The response of supply air flow rate is delayed by heat capacitance, a feed back control of reheater to adjust supply air flow rate of VAV terminal results in poor control performance [5], it should be improved. This paper presents an on-line outdoor air control strategy of multi-zone VAV air-conditioning systems using system approach, which is suitable to be used in BAS (building automation system) with integrated digital control stations for VAV terminals and AHUs. An energy consumption function is formed which concerns the energy consumption of systems including reheater and chiller (i.e. AHU loads). A genetic algorithm is used to search the optimal setting of
outdoor air ratio of AHU by minimizing the energy consumption function. A feed-forward control is used for control of reheaters based on the prediction, which ARMA (autoregressive moving average) model is used for predicting the supply air flows and outdoor air requirements of zones with the method of occupancy detection based on measurement of indoor and outdoor CO2 concentrations. The strategy is tested and evaluated under various conditions online on a centralised VAV air-conditioning system simulated using detailed HVAC dynamic models. This paper presents the control strategy, ARMA-based prediction model, GA-based optimization approach and evaluation of the control strategy.
2. Air-conditioning and control systems description The building is one floor office located in Shanghai. It has a total floor area of 1166 m2 and is divided into eight zones. A VAV terminal with electric reheater is equipped in each zone. A schematic of the air conditioning and control systems is shown in Fig. 1. The air-conditioning systems consist of one AHU, which supplying handled air to VAV terminals, supply and return fans, ducts, dampers, VAV terminals and chilled water valve of AHU coil. The conditions within the system are regulated by local controllers. The air temperature in each zone is controlled by a pressure-independent VAV controller. One PID controller controls the VAV damper position to maintain the supply air flow rate at its setpoint. This air flow rate setpoint is reset by a PID temperature controller to maintain a desired space temperature. The electric reheater is controlled by moderating its input voltage to maintain supply air temperature of each VAV terminal. AHU outlet air temperature is controlled by moderating the opening of the valve and therefore adjusting the chilled water flow rate through the AHU coil. Two variable speed fans are used as the VAV supply fan and return fan. The supply fan is controlled by a PID controller to maintain the supply air static pressure at its setpoint, and the return fan is controlled by the ex-filtration flow controller, which controls the difference between the total supply and return air flow rates at certain setpoint to maintain a positive pressure moderating the speed. The outdoor air ratio is controlled by the outdoor air controller by moderating the positions of the mixing damper, outdoor air damper and exhaust damper. The control and sensor signals are depicted as dash line in Fig. 1.
3. Optimal control strategy To ensure all zones to maintain acceptable indoor air quality, the setting of outdoor air ratio of AHU intake may be the highest one of the requirements of zones. However, it may bring more outdoor air into building which resulting in
X. Jin et al. / Energy and Buildings 37 (2005) 939–944
941
Fig. 1. Schematic of VAV air conditioning and control systems.
more energy using for AHU load in summer and winter. Lowering the setting of outdoor air ratio can reduce the energy consumption but resulting in insufficiency of outdoor air flow in some zones. Rising the supply air flows to those zones by reheating can supply sufficient outdoor air flows but resulting in additional energy using. So, there could be an optimal problem to minimize the energy use by optimizing the settings of outdoor air ratio and voltages of reheaters. The optimal control strategy is set up and illustrated in Fig. 2.
3.1. Data processing The measurements of sensors at and before current time step are sampled and stored in ‘Data processing’ module. They are processed to obtain the data needed by other two modules which includes: (I) requirement of outdoor air mass flow of each zone, Moa[i]; (II) supply air mass flow of each zone without the effect of reheating, G0 sa ½i; (III) enthalpy of AHU supply air (total supply air) and outdoor air, Hsup and Hoa. The requirement of outdoor air mass flow of each zone is estimated according to ASHRAE Standard using indoor and
outdoor air CO2 concentrations and occupied area [6]. G0 sa ½i can be obtained by Eq. (1) described below: G0 sa ½i ¼ Gsa ½i
H set ½i H sa ½i H set ½i H sup
(1)
Where, the subscript ‘set’ represents the condition at setpoint. Hsup and Hsa can be calculated by temperature and humidity. 3.2. Online prediction The principle of ARMA model is to predict the value of a time-varying variable at current time (x j) using the previous time series data of the variable, which including the average (m), the measurements series (x j1, x j2, . . ., x jm), the prediction errors series (e j1, e j2, . . ., e jn) and a random error (e j). It can be expressed as Eq. (2): x j m ¼ f1 ðx j1 mÞ þ f2 ðx j2 mÞ þ þ fm ðx jm mÞ þ e j u1 e j1 u2 e j2 un e jn
(2)
where m and n are order numbers of the processes for autoregressive and moving average components, respectively; f and u are parameters. Before prediction, the time period of prediction should be selected. Time period of 15 min is used and then one-day time is divided into 96 time periods. To predict the
Fig. 2. Logic of optimal control strategy.
942
X. Jin et al. / Energy and Buildings 37 (2005) 939–944
requirements of outdoor air mass flow and supply air mass flows, they should be stabilized using Eqs. (3) and (4), respectively: j j1 j96 j97 aj ½i ¼ ðMoa ½i Moa ½iÞ ðMoa ½i Moa ½iÞ
(3)
bj ½i ¼ ðG0sa j½i 2G0sa j 1½i þ G0sa j 2½iÞ ðG0sa j 96½i 2G0sa j 97½i þ G0sa j 98½iÞ
(4)
and then ARMA(1,1) model is selected [7] and set up as shown in Eqs. (5) and (6): aˆ jþ1 ½i ¼ ð1 f1 ½iÞm1 ½i þ f1 ½iaj ½i u1 ½ie1 j ½i
(5)
ˆ jþ1
(6)
b
½i ¼ ð1 f2 ½iÞm2 ½i þ f2 ½ibj ½i u2 ½ie2 j ½i
where, the subscripts 1 and 2 represent to predict Moa[i] and G0 sa ½i, respectively. The parameter vectors F = (f[1], f[2] . . . f[8]) and Q = (u[1], u[2] . . . u[8]) in Eqs. (5) and (6) are estimated by the last 20 values of the time series and updated every periods. The average values of Moa[i] and G0 sa ½i in next time period can be predicted by Eq. (3) and Eq. (4), respectively. ˆ jþ1 ½i ¼ aˆ jþ1 ½i þ M j ½i þ M j95 ½i M j96 ½i M oa oa oa oa ˆ 0 jþ1 ½i G sa
(7)
ˆ jþ1
j j1 ¼ b ½i þ 2G0 sa ½i G0 sa ½i j95 j96 þ G0 sa ½i 2G0 sa ½i j97 þ G0 sa ½i
(8)
The aim of the optimal strategy is to minimize the energy consumption of systems, which includes energy used to remove AHU cooling load, energy used by reheating and energy used by fans. In the strategy presented in this paper, the difference of energy consumption of systems between with using and without using of reheating is concerned instead of energy consumption. The objective function, which called Energy-increment equation (Eq. (9)) in this paper, is made for optimization under the assumptions below: (I) the difference of energy used by fans is neglected because the addition of total supply air flow is less; (II) the energy used to remove AHU load is calculated using AHU load divided by COP, and COP is considered as a constant. 0 Zˆ cr y ˆ Gsup ðHoa Hset Þ COP ! ˆ0 X 1 Z ½i 1 1þ COP y 0 i 2 Z ½i > y
Gˆ 0 sa ½iðHset Hsa Þ ˆ0
where Z ½i ¼
ˆ oa ½i M ˆ 0 sa ½i G
ˆ0
V½i 8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ˆ oa ½i > M < Gˆ0 sa ½iÞðHset Hsup ÞR½i; Z 0 ½i > y ð (10) ¼ y > : 0; Z 0 ½i < y The optimal control can be achieved by controlling the dampers of AHU and the reheaters according to the optimal setpoints of outdoor air ratio and input voltages, respectively.
4. Tests and evaluation of on-line optimal control strategy 4.1. System simulation and test conditions
3.3. Optimization
DE ¼
Genetic algorithm is employed as optimization method to compute the optimal value of variable (setpoint of outdoor air ratio) that minimizing Energy-Increment equation. D.L. Carroll’s FORTRAN Genetic Algorithm Driver [8] is modified and incorporated into the optimization module. After obtaining the optimal value of y, the optimal setpoints of input voltage of reheaters can be computed by Eq. (10).
(9) ˆ0
and Z cr ¼ maxðZ ½iÞ. The variables
above with symbol ‘^’ represent that they are predicted values from prediction module.
A Transient Thermal System Simulation Program TRNSYS [9] is used as the platform for the dynamic simulation of the air-conditioning systems including building zones and control system [10]. VAV terminal in each zone is simulated. The total capacities of the VAV of each zone are simulated by multiplying the simulated flow rates with factors. A fan model simulates the energy and hydraulic performances of supply and return fans. The hydraulic resistance of coil, supply duct, return duct and VAV terminals are simulated. The energy and dynamic performances of coil are simulated. The ducts are considered as they exchange heat to air outside of ducts with heat capacities and they transfer moisture with the lag which is according the air velocity of inside ducts. The static pressure balance of the system under different fan speeds and VAV damper positions is simulated. The dynamics of sensors and actuation devices are simulated. Realistic DDC models simulate the dynamic response of the local PID DDC control loops. The control loops simulated include the AHU and VAV temperature control loops, the supply air and outdoor air control loops, the exfiltration flow control. The algorithm of the exfiltration flow controller attempts to maintain positive pressure in space and outdoor air intake. To analyse this optimal supervisory control strategy presented in this paper (Called Strategy Reheat), another supervisory control strategy (Called Strategy MaxY) is used to compare the performances in the systems described above. Strategy MaxY is to reset the setpoint of outdoor air ratio online using the maximum one of requirements of
X. Jin et al. / Energy and Buildings 37 (2005) 939–944
outdoor air ratio of zones and there is no use of reheating in VAV terminals. The occupancy, lighting and equipment loads in each zone, the solar gain of each zone transmitting through windows, temperature of each exterior zone, the outdoor air temperature, humidity and pollutants concentration are provided by data files during simulation as test conditions. The transmission solar gain and equivalent ‘sol-air’ temperature are computed by a pre-processor prior to simulation according to building construction data, the solar radiation and outdoor air temperature recorded in the selected days. The data of outdoor air temperature and humidity of selected days are selected from Shanghai weather data records. The chilling systems i.e. chillers, pumps and pipes, etc. are not included in the simulation. The energy used to cool AHU load is computed by the value of COP. COP is selected to be 2.5 and it is considered to be constant. The occupant activity level used is 1.2 met and the CO2 generation rate is 5.0 106 m3/s per occupant. The outdoor air CO2 concentration is selected to be 360 ppm and it is considered to be constant. The value of COP is selected to be 2.5 and it is considered to be constant. The AHU temperature setpoint is 13 8C. The HVAC system works from 7:45 a.m. to 20:00 p.m. each day.
943
Fig. 4. Relative error of prediction of outdoor air flow.
air flow brought into zone (Goa) and requirement of outdoor air flow of zone (Moa). j½i ¼
Goa ½i M oa ½i
(11)
4.2.2. Tests of system performances To evaluate the control performance of the optimal strategy, a criterion index j is introduced and defined as Eq. (11) which implicates the comparison between outdoor
The minimum (jmin) and the maximum (jmax) among j[i] of zones are used to appraise the condition of satisfying the requirement and condition of over ventilation of outdoor air under the control of strategy, respectively. The results of jmin and jmax of one-day test under controls of Strategy Reheat and Strategy MaxY are shown in Figs. 5 and 6, respectively. It is found that the values of jmin of both of strategies are almost near to 1.0, which means that both of strategies can control the outdoor air flows to satisfy the requirements of zones. However, the values of jmax of Strategy MaxY are greater than that of Strategy Reheat, which means that more outdoor air are intaken into AHU and more energy should be used to cooling AHU load under control of Strategy MaxY when enthalpy of outdoor air is greater than that of return air. The total energy consumption of the test day, including energy used to cool AHU load, energy used by fan and energy used by reheaters, is shown in Fig. 7. It is found that the energy used to cool AHU load under control of Strategy Reheat is approximately 13.8% less than that under control of Strategy MaxY. Although more energy used by fan under
Fig. 3. Relative error of prediction of supply air flow.
Fig. 5. Value of jmin under control of two strategies.
4.2. Test results 4.2.1. Tests of prediction To validate the prediction method, tests for predicting supply air flows and the requirements of outdoor air flow of zones had been done and the results of relative error of one of zones are shown in Figs. 3 and 4, respectively. It can be concluded that the error of prediction could be accepted because almost all of the relative errors are within 5%.
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X. Jin et al. / Energy and Buildings 37 (2005) 939–944
air flows prediction based on ARMA model, and genetic algorithm optimization approach. An Energy-Increment equation is made to generalize the energy performance of systems. The setpoint of outdoor air ratio of AHU can be optimized and the setpoints of input voltage of reheaters can be pre-reset to eliminate effect of heat capacitance of reheaters on the online control of reheaters according to the optimal setpoint of outdoor air ratio of AHU. This optimal strategy has been tested and the results show that it is better than Strategy MaxY, and it is capable of optimizing the energy performance of systems and maintaining acceptable indoor air quality. Fig. 6. Value of jmax under control of two strategies.
References
Fig. 7. Energy consumption under the controls of Strategy Reheat and Strategy Reheat.
control of Strategy Reheat as well as additional energy used by reheaters because of reheating, the total energy consumption under control of Strategy Reheat is approximately 7.8% less than that under control of Strategy MaxY.
5. Conclusions The optimal control strategy using genetic algorithm is presented that supply air flows and requirements of outdoor
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