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Adaptive HVAC zone modeling for sustainable buildings
Energy and Buildings 42 (2010) 412–421
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Adaptive HVAC zone modeling for sustainable buildings Glenn Platt a, Jiaming Li b,*, Ronxin Li b, Geoff Poulton b, Geoff James a, Josh Wall a a b
CSIRO Energy Technology, Australia CSIRO ICT Centre, Australia
A R T I C L E I N F O
A B S T R A C T
Article history: Received 16 April 2009 Received in revised form 28 September 2009 Accepted 4 October 2009
Control of energy flows within a building is critical to achieving optimal performance of heating, ventilation and air-conditioning (HVAC) systems. To design optimal HVAC control strategies, a dynamic model of the HVAC system – particularly the building zones that it services – is essential. As analysis of building energy consumption is facilitated by the accurate prediction of indoor environmental conditions, techniques that dynamically model HVAC zones are crucial, and as such, is an active area of research. This paper focuses on real-time HVAC zone model fitting and prediction techniques based on physical principles, as well as the use of genetic algorithms for optimization. The proposed approach is validated by comparing real-time HVAC zone model fitting and prediction against the corresponding experimental measurements. In addition, comparison with prediction results using an algorithm based on feedback-delayed Kalman filters has demonstrated the superiority of the proposed approach in terms of prediction accuracy. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Genetic algorithms HVAC control HVAC zone modeling Kalman filtering
1. Introduction Heating, ventilation and air-conditioning (HVAC) systems play a dominant role in regulating the indoor climate, providing people with a comfortable and safe work environment. In most buildings the performance of the HVAC system can influence energy consumption as well as indoor air quality. The amount of energy used by HVAC systems is a significant concern that impacts on issues from national policy to personal desires of cost and comfort, and as such, HVAC modeling is a very active research topic [1,2]. A HVAC system comprises a variety of continuous and discrete control components interacting with the building via sensors and actuators. Control of the energy flows in the building and its environment is the key to achieving optimum performance from an HVAC system. Such control is secured through monitoring and altering the cooling/heating sources to maintain the desired thermal and air quality conditions in a space, while external and internal conditions change over time. The building with its technical equipment and its environment consists of several coupled processes which, in general, cannot be influenced independently. This complicates the design of high-quality control algorithms and requires model-based design methodologies for
Abbreviations: AHU, air-handling unit; BMCS, building management & control system; OA, outside air; RA, return air; SA, supply air; CHWV, chilled water valve; HWV, hot water valve; SP, set-point; OAF, outside air fan; SAF, supply air fan; RAF, return air fan. * Corresponding author. Tel.: +61 2 9372 4707; fax: +61 2 9372 4161. E-mail address: [email protected] (J. Li). 0378-7788/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2009.10.009
optimum performance. For the energy-efficient design of buildings and their associated control systems, it is necessary to obtain approximate dynamic mathematical models for system components. These models are used for a wide range of tasks including operating strategy planning, cost analysis and comfort evaluation. The dynamic model can be especially useful for control strategies that require knowledge of the dynamic characteristics of HVAC systems. The system component that we will focus on in this paper is the zone. A HVAC zone is a group of adjacent offices and/or spaces serviced by a common air-handling unit (AHU) or air-terminal device. Since the external and internal environment of the zone always changes, any model of the zone has to emulate the dynamic thermal processes within the zone as well as the interaction with the environment. Modeling such a time-variant system is a challenging task. Traditionally, zone models are mainly based on static or shortterm modeling of the HVAC zone. Four approaches have been reported in recent literature. The first uses lumped capacitance in an analogue electric circuit to represent thermal elements of a building [1,3,4]. A second approach is a building thermal model based on energy-and-mass balance [5], where every component of the HVAC system is represented by energy-and-mass balance equations. The third approach is based on machine learning, in which artificial neural networks [6] or support vector machines [7] model non-linear processes, such as utility loads or an individual building’s energy consumption. A fourth approach is evident more recently, as researchers have started exploring the response of HVAC systems to dynamic
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Nomenclature Two Twi To Tz Tsp Fsp Tsa Fsa fa Ca
ra Vz Uw Aw Gw Ro Io Ia Ra Iz Cz
outlet water temperature (8C) inlet water temperature (8C) external (outside) temperature (8C) zone temperature (8C) supply air temperature set-point (8C) supply air fan speed set-point (% of maximum speed) supply air temperature (8C) supply air fan speed (% of maximum speed) supply air flow rate (m3/s) specific heat of air (kJ/(kg 8C)) density of the air (kg/m3) volume of the zone (m3) thermal conductivity of the wall (W/mK) heat transfer area of the wall, i.e. area of each wall (m2) wall thickness (m) resistor of outside wall representing its function of transferring heat between outside and inside current of outside air representing its heat flow current of supply air representing its heat flow resistor of supply air representing the air convection current of zone air representing its heat flow overall thermal capacity (kJ/C) of the zone
environments [8–12]. These models, however, tend to be rather cumbersome, and do not adequately adapt to the dynamics of the zone environment in real time. In addition, many existing models do not take into account long-term dynamic properties of the building, due to changes accumulated over a long time period. We investigate a real-time model fitting and prediction algorithm using only few parameters, that is well suited to short-term predictions and also adapts to long-term dynamics. In Australia, the electricity market cycle is half-hourly [13], and our proposed algorithm is very suitable for applications on this time scale. The algorithm is applied to a dynamic zone model of a HVAC system, intended to allow the implementation of control strategies to reduce energy consumption and improve the quality of the indoor environment. The paper has two major contributions. One is the formation of a mathematical model of the zone based on physical principles and circuit theory—the model we propose is the first one that combines energy/mass balance and basic circuit theory. The second contribution is the real-time model fitting and prediction algorithm for a time-variant zone, taking advantage of genetic algorithms (GA). The model and algorithm are then validated using measurements of a real HVAC system. Throughout the paper the HVAC zone is represented as a sixfaced box. The zone model is firstly deduced from an energy-andmass balance and then represented using electric circuit theory. Electric circuit elements are used to represent functions of the building elements, e.g., a wall is modelled as a resistor to represent its function of transferring heat between outside and inside, and an entire zone is modelled as a capacitor to represent its heat storage function. This kind of zone model is very simple and generic, applicable to a zone with any internal structure and material. Following development of the zone model structure, a methodology of soft real-time zone model fitting and prediction is given, e.g., zone model fitting and prediction every 5 or 30 min. Since the zone
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model is fitted in soft real-time (every 5 min) it can easily cope with the changes of the zone’s dynamics and give accurate internal temperature prediction. Lastly, we present results using an alternative technique, the Kalman filter, to perform the model fitting. The Kalman filter [14] is an efficient recursive filter that predicts the state of a dynamic system from a series of incomplete and noisy measurements. The Kalman filter is traditionally viewed as a prediction-correction filtering algorithm and is a classic method used for dynamic systems. Recently, various parameter estimation techniques based on extended Kalman filters have been applied to thermal modeling and model refinement (e.g. [15,16]). A series of experimental results using a modified Kalman filter with delayed feedback is presented for comparison with our own technique. The results show that our model is capable of giving more accurate prediction for the indoor temperature of a dynamic zone compared to the Kalman filter technique. This paper is organized as follows. Section 2 introduces the HVAC system. Section 3 presents a mathematical zone model based on physical principles. Section 4 introduces soft real-time zone model fitting and prediction based on genetic algorithms. Section 5 gives a series of experimental results to quantify the performance of model fitting and prediction. For comparison purposes, a feedback-delayed Kalman filtering method is presented in Section 6. Finally, a conclusion is drawn in Section 7. 2. HVAC system description Many HVAC systems use a central plant to provide hot water (e.g., with temperature of 32 8C) for heating purposes or cold water (e.g., with temperature of 6 8C) for cooling purposes. Fig. 1 is a schematic diagram of a typical HVAC system with multiple zones for cooling purpose. The water path is presented by black arrows, which shows that cold water with temperature Two flows from the central plant along the pipework and into the cooling coils. The chilled water valves (CHWV) are used to control the volume of water flowing through the coils. A cooling coil exchanges heat energy between air from the mixing box and water from the central plant, with the output water flowing back to the central plant with a slightly higher temperature Twi. The air path is represented by grey arrows. The outside air can be drawn in by an outside air fan (OAF) and outside air damper into the mixing box. A mix of outside air and return air then flows through the air filter and passes over the cooling coil. A supply air fan (SAF) then forces the air through an insulated supply duct into the zone area as supply air (SA) for the zone. The supply air gains part of its heat from the zone to replace the heat that is leaking through the walls, roof, etc. The supply air then passes through the
Fig. 1. Schematic diagram of a typical HVAC system for cooling purpose.
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room and into the return air inlets. Some return air is exhausted through an exhaust air damper. The remaining return air passes through the re-circulation air damper into the mixing box and mixes with the outside air. The outside air dampers and exhaust air dampers control the amount of air flow amount from the outside air (OA) and return air (RA) streams respectively.
Min. Control Point), with a Tz of 21.7 8C is defined as the Intermediate Control Point. Lastly, a Tz of 27 8C is defined as the fan speed maximum control point (Fan Speed Max. Control Point). In a typical HVAC system, control variables related to temperature can often oscillate around their set-point, with fan speed related variables usually maintained very close to their set-point. Air flow rate fa is largely proportional to supply air fan speed Fsa.
2.1. Air-handling unit 3. HVAC zone modeling The air-handling unit (AHU) is a device used to condition and circulate air as part of a HVAC system. Usually, the AHU is a large metal box containing fans, heating and/or cooling coils, filter racks or chambers, sound attenuators, and dampers. Building indoor temperature is maintained at set-point (SP) values by the AHU, which usually connects to ductwork that distributes conditioned air to the zone. Fig. 2 shows a typical operation schematic for each AHU. The AHU draws air from the zone with temperature Tz(t), which determines supply air temperature set-points (expected supply air temperature, Tsp) and supply air fan speed set-points (expected supply air fan speed, Fsp). The AHU forces the air from the mixing box through cooling/heating coils with flow rate fa, which is largely proportional to the fan speed Fsa, resulting in supply air with temperature Tsa, and then discharges the cooled/heated air back into the zone. A certain amount of fresh air may be introduced from the outside air inlet so that fresh air in the zone may be gradually introduced. Fig. 3 shows an example of proportional control relationship between the supply air temperature set-point (Tsp) and supply air fan speed set-point (Fsp) versus zone temperature (Tz) for a particular HVAC system, in which the supply air temperature setpoint varies between 18 8C and 32 8C, with the supply air fan speed set-point varying between 40% and 100%. The supply air temperature set-point (Tsp) is the expected supply air temperature, which is a function of zone temperature, and has inflexion points at the zone temperatures of 19 8C and 21.7 8C. The supply air fan speed set-point (Fsp) is the expected supply air fan speed, which is also a function of zone temperature, and has inflexion points at the zone temperatures of 21.7 8C and 27 8C. A Tz, equal to 19 8C in this instance, is defined as the supply air minimum control point (SA
In this section, we focus on an HVAC zone modeling technique based on physical principles. The assumption for the model is that the supply air flowing into the zone is evenly distributed throughout the whole zone; adjacent zones have the same temperature; and we ignore the thermal storage of all walls. Firstly, the model is deduced from an energy-and-mass balance. Then the model is explained using basic electrical circuit theory. Each zone can be modeled as a box with 6 faces as shown in Fig. 4, in which face ACGE is the wall connecting outside with temperature To; EFHG is the ground floor with temperature TG; ABDC is ceiling with temperature TC; CDHG, BDHF and ABFE are the walls connecting with adjacent zones that have the same temperature TA. The overall heat flow in the zone comes from air convection and wall conduction, as expressed in the following equation: Cz
dT z f r C a ðT sa T z Þ þ U w Aw ðT o T z Þ ¼ a a Gw dt
(1)
where Cz = CaraVz is the overall thermal capacity (kJ/C) of the zone; Ca is the specific heat of air (kJ/(kg 8C)); ra is the density of the air (kg/m3); Vz is volume of the zone; fa is the air flow rate (m3/s); Tsa is supply air temperature (8C); Tz is the zone temperature (8C); To is external temperature (8C); the thermal conductivity of the wall is denoted by Uw (W/mK); Aw is heat transfer area (m2), i.e. area of each wall; and Gw is wall thickness (m). Gw To simplify this, letting Ro ¼ Uw Aw be a resistor representing the thermal properties of the wall, Eq. (1) becomes: Cz
dT z f r C a ðT sa T z Þ þ ðT o T z Þ ¼ a a Ro dt
(2)
Eq. (2) can be explained using RC circuit theory as follows. Heat flow generated from a temperature difference, is analogous to electrical current generated from a voltage difference. Therefore, temperature can be modeled as voltage and heat flow can be modeled as current, i.e., Ia ¼
dH ¼ f a ra C a ðT sa T z Þ: dt
Fig. 5 is a simple analogue electric circuit used to represent functions of the building elements, in which the outside wall is Fig. 2. Operation schematic for a typical AHU system.
Fig. 3. Supply air temperature and fan speed set-points vs. zone temperature.
Fig. 4. Zone thermal interfaces.
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where D1 = faraCa, fa is the air flow rate, which is proportional to the fan speed Fsa; supply air temperature Tsa usually oscillates around its set-point Tsp, which is a function of zone temperature as shown in Fig. 3; ra is the density of the air with value 1.204 (kg/m3) at 20 8C; Ca is specific heat of air with value 1.005 (kJ/kg 8C). Parameter D2 is added to take into account factors such as leakage of the zone, measurement error, dynamics of the zone, etc. 4. Dynamic zone model fitting using a genetic algorithm
Fig. 5. Simple RC model of an HVAC zone’s thermal performance.
modeled as a resistor (Ro) to represent its function of transferring heat between outside and inside. The zone is modeled as a capacitor (Cz) to represent its function of both ‘charging’ through heat input from supply air and ‘discharging’ through heat. In the figure, the zone’s average temperature is Tz. It has two sources, one is supply air source with node voltage (temperature) Tsa; another is outside air source with node voltage (temperature) To. The current (heat flow) is Ia ¼ dH ¼ f a ra C a ðT sa T z Þ, where dt (Tsa Tz) is voltage (temperature) difference in the zone, Ra ¼ 1= f a ra C a is the variable zone air resistance. The wall has resistance Ro. The voltage (temperature difference) across Ro is (To Tz). Therefore current (heat flow) flowing through Ro is Io = (To Tz)/Ro. The voltage (temperature) difference on capacitor Cz is DTz, and thus the current (heat flow) flowing through the capacitor will be Iz ¼ C z
dT z dt
(3)
We know Iz = Ia + Io, which is represented by Eq. (2). Until now we have deduced the zone model from both energy/ mass balance and basic circuit theory point of view. The zone is a dynamic environment that changes over time. The dynamics of this environment are partly attributable to events such as people walking in or out, doors and windows being opened or closed. To realize adaptability to the dynamic environment and simplify the analysis, the zone model shown in Fig. 5 can be represented as a time-variant system, represented by a time-variant RC circuit (variant RoCz, or variant Ro). Suppose the air supplied into the zone is evenly distributed across the whole zone; outside air with temperature To transfers the air into the zone through the outside wall, i.e., ACGE in Fig. 4; the ceiling, ground and corridor in adjacent zones have the same temperature as the zone under study, i.e., Tz = TA in Fig. 4. Such a model ignores the thermal storage of all walls. The discrete expression of (2) is C z ðT z ðnÞ T z ðn 1ÞÞ ¼ f a ra C a ðT sa ðn 1Þ T z ðnÞÞ Dt ðT o ðn 1Þ T z ðnÞÞ þ Ro T z ðnÞ ¼
(4)
f a ra C a DtT sa ðn 1Þ þ ðDt=Ro ÞT o ðn 1Þ þ C z T z ðn 1Þ C z þ f a ra C a Dt þ ðDt=Ro Þ
To take into account factors such as the leakage of the zone and measurement error, a parameter D2 can be added to the above equation. Therefore the zone temperature can be expressed as Eq. (5):
T z ðnÞ ¼
Having derived a basic model for the zone, our aim is to find optimal parameters for the zone model that best fit with the measured data. We obtain the solutions using a genetic algorithm of a kind that has previously achieved successful model fitting [2], multi-agent coordination [17–22] and been used in similar applications related to electricity markets [23]. 4.1. Genetic algorithm A genetic algorithm (GA) [8,9,24] is a search method inspired by natural selection and survival of the fittest in the biological world. A GA is a type of ‘‘evolutionary algorithm’’. By using a GA approach, excellent results can be achieved through the evolution of the system. A colony of rule sets can be evolved for a number of generations, improving the performance of the colony. Techniques of fitness determination, selection, cross-over, reproduction, and mutation are applied to the rules and their chromosomal representation. Essentially, the parameters we are seeking for the zone model are ‘‘evolved’’ over successive generations. The first generation of parameters (initial population) can be either random or predetermined values. At each subsequent generation of parameters, every individual of the population must be evaluated to be able to distinguish between good and bad individuals. This is done by mapping the objective function to a ‘‘fitness function’’, which is a non-negative well-behaved measure of relative fitness of the parameters. The better the fitness of a given rule, the more likely it is to be selected. After the two parent rules are selected, each is represented by a ‘‘chromosomal’’ string and then combined to determine the chromosomes of the two resulting rules (offspring). These chromosomes are subjected to potential mutation, and are then converted back to their equivalent rule representation. The selected parents are then replaced in the colony by the offspring. This mechanism of natural selection is expected to eventually result in a population with a higher performance. 4.2. Genetic algorithm design for our system 4.2.1. Fitness function of optimization The simulated prediction of the zone temperature with the model expressed as Eq. (5) is used to compare with the measured zone temperature. The optimized parameters are D1, D2 and Ro of the model that give the best fit with the operational data. The objective function, O, of such an optimization employs mean square fitting errors defined in Eq. (6). Eq. (7) represents the fitness function f, which is the reciprocal of the objective function. OðD1 ; D2 ; Ro Þ ¼
N 1X 2 0 ðT ðiÞ T z ðiÞÞ N i¼1 z
where Tz and T 0z are the fitted and measured zone temperature respectively, and N is the number of the sample data. f ¼ f ðD1 ; D2 ; Ro Þ ¼
D1 DtT sa ðn 1Þ þ ðDt=Ro ÞT o ðn 1Þ þ C z T z ðn 1Þ þ D2 C z þ D1 Dt þ ðDt=Ro Þ (5)
(6)
1 OðD1 ; D2 ; Ro Þ
(7)
A genetic algorithm (GA) is employed to search for the optimal values as illustrated in Section 4.2.2.
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Table 1 Parameters for zone modeling. Name
Definition
Parameter availability
D1 D2 Ro
Time varying coefficient in Eq. (5) Time varying coefficient in Eq. (5) Time varying resistor of the wall connecting outside in Eq. (5) Average zone temperature Outside temperature Supply air temperature
Learning parameter Learning parameter Learning parameter
Tz To Tsa
Fig. 6. AHU GA operation.
4.2.2. Optimization As shown in Fig. 2, the supply air temperature set-points (expected supply air temperature, Tsp) and supply air fan speed setpoints (expected supply fan speed Fsp) are predetermined inputs based on the current zone temperature (Tz(t)) specified in the building management and control system (BMCS) logic. The BMCS controls supply air fan speed Fsa based on set-points to allow mixed air to pass over the cooling/heating coil with air flow rate fa, resulting in supply air with temperature Tsa. Supply air with temperature Tsa flows through the insulated supply duct into the
Fig. 7. Flow chart of GA learner for fitting the zone model parameters.
Measured parameter Measured parameter Measured parameter
zone area with flow rate fa and then exchanges heat with the zone. The next step zone temperature Tz(t + 1) is a function of the zone model, supply air temperature and supply air flow rate. The AHU GA operation is shown in Fig. 6. Fig. 6 are supply air temperature set-points, fan speed setpoints, current zone temperature and current external temperature. The output is the next step zone temperature. As expressed in Eq. (5), the zone model is determined by several parameters. Some of them are known; some are measured; some can be calculated; and some are unknown parameters that need to be learnt by the genetic algorithm. Table 1 summarizes the parameters for zone modeling, where the set of learning parameters must each be learnt by the GA. Fig. 7 shows schematically the flow chart of the GA learner developed for fitting the zone model parameters. In the genetic algorithm, the three parameters (D1, D2, Ro) constitute the chromosome of an individual. Initializing the three parameters produces an initial population to start the first generation GA process. Termination of a GA process is decided if the number of the current generation is equal to a predefined maximum generation number. At least two generations are necessary when running the GA optimization.
Fig. 8. Real-time zone model fitting and prediction using GA learner: (a) flow chart of ½ hour zone model fitting and prediction; (b) time series of model fitting and prediction.
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4.2.3. Real-time zone model fitting and prediction using GA As we have described above, the HVAC zone is a dynamic environment. To cope with its dynamics, a real-time zone model fitting using GA learner is developed. Fig. 8(a) shows schematically the flow chart of ½ hour zone model fitting and prediction based on the GA learner introduced above. Fig. 8(b) shows the time series of model fitting and prediction. In the figure T 0z represents the measured zone temperature and Tz represents the calculated (fitted and predicted) zone temperatures. Suppose current time is tn. Training data collected in past time period, Vi ¼ t n t nN , is used for model fitting using the genetic algorithm, and generates the best parameters for the zone model, which is called the fitted model. The fitted model is then used to predict the future zone temperature, e.g., temperature during time period V j ¼ t nþM t n . The training data used in the process includes measured supply air temperature Tsa, external temperature To and supply air fan speed Fsa. The process is repeated for every tk time interval. The details of the process are as follows. 1. The measured zone temperature over a past time period is represented as
ture Tz(n + 1); using predicted zone temperature Tz(n + 1) to get next step predicted zone temperature Tz(n + 2); and so on. T z ðnÞ ) T z ðn þ 1Þ ) T z ðn þ 2Þ ) ) T z ðn þ MÞ 5. Experimental results 5.1. Training data A number of measurements have been conducted to gather historical data for the purposes of thermal model fitting within the CSIRO Energy Centre Level 3 (East) office wing, in which three AHUs service three adjacent HVAC zones consisting of 18 offices and associated corridors. Each office or space has a dry bulb temperature sensor to detect the internal temperature. The zone temperature is the average value across all offices and/or spaces in the zone. Fig. 9 shows the CSIRO energy centre building. Fig. 10 gives a floor plan of the AHUs and their associated offices/spaces, where different zones are represented as different grey color shades. AHU-08 solely services office 331, with AHU-09 and AHU-
½T 0z ðn NÞ; T 0z ðn N þ 1Þ; . . . ; T 0z ðn 2Þ; T 0z ðn 1Þ; T 0z ðnÞ where N is the number of sample data points in the past time period. 2. The fitted zone temperature based on Eq. (5) is represented as ½T z ðn NÞ; T z ðn N þ 1Þ; . . . ; T z ðn 2Þ; T z ðn 1Þ; T z ðnÞ 3. The predicted zone temperature based on Eq. (5) is represented as ½T z ðnÞ; T z ðn þ 1Þ; T z ðn þ 2Þ; . . . ; T z ðn þ M 1Þ; T z ðn þ MÞ 4. In each generation of GA, each population of learning parameters gives the calculated zone temperature one by one using Eq. (5), i.e., using measured zone temperature T 0z ðn NÞ to calculate zone temperature Tz(n N + 1); using fitted (calculated) zone temperature Tz(n N + 1) to get another zone temperature Tz(n N + 2) and so on.
Fig. 10. CSIRO Energy Centre Level 3 (East).
T 0z ðn NÞ ) T z ðn N þ 1Þ ) ) T z ðn 1Þ ) T z ðnÞ 5. Compare the measured zone temperatures with the fitted ones to calculate fitness value for each population as Eq. (7). 6. ‘‘Parent’’ rules are selected based on a fitness value. After the two parent rules are selected, each is represented by a ‘‘chromosomal’’ string and are then combined to form two new chromosomes. These chromosomes are subjected to potential mutation, and are then converted back to their equivalent rule representation. The selected parents are then replaced in the colony by the offspring. 7. Repeat the process steps 4–6 for the number of required generations and obtain the best population, i.e., the best learning parameters. 8. Based on the best learned parameters for the past time period, do the prediction for the future time one by one, i.e., using current zone temperature Tz(n) to get predicted zone tempera-
Fig. 9. The CSIRO Energy Centre, Newcastle NSW, Australia.
417
Fig. 11. Collected data for the AHU between 3rd and 4th of April 2007.
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Fig. 12. External temperature.
10 servicing the northern and southern zones respectively. In addition AHU-09 also services the corridor. The data we used in this work was collected between the 3rd and 4th of April 2007, as shown in Fig. 11. Each day, the AHU runs between 7:00 am and 5:00 pm, with a constant supply air setpoint of 18 8C. The data sample rate was 5 min. Our experiments were carried out using Matlab on a laptop with 2 GB RAM and an Intel Core 2 Duo T7600 CPU running at 2.33 GHz. 5.2. Real-time zone modeling and temperature prediction An HVAC zone is a dynamic environment with people walking in and out, doors opening and closing, etc. To cope with such an environment, a dynamic model is necessary. To achieve this we have developed a soft real-time model fitting and prediction algorithm. Every V time interval, the past Vi period data is used for zone model fitting with the GA, then the fitted zone model is used to predict future Vj period zone temperature as described in Section 4.2.3. 5.2.1. Supply air and external air prediction As shown in Fig. 6, the future zone states are a function of the zone model, external temperature and supply air. The predicted supply and external air properties are essential to model and predict zone temperature. In our experiments, external temperature in some future period of time is assumed to be the same as current external temperature. This assumption is reasonable for short-term prediction. Fig. 12 shows the external temperature Tˆo for ½ hour prediction, i.e., next ½ hour external temperature is very close to the current one. The supply air properties include temperature and flow rate that are proportional to fan speed. Both expected supply air fan speed and temperature can be calculated through the supply air set-point function as shown in Fig. 3. Suppose we have current zone temperature Tz, then based on the function shown in Fig. 3 we will know our expected supply air fan speed Fsp and temperature Tsp. If we assume the BMCS is able to obtain the expected supply air perfectly, Fsp and Tsp can be used as predicted supply air fan speed Fˆsa and temperature Tˆsa , i.e., Fˆsa ¼ F sp and Fˆsa ¼ F sp . Applying Tˆo , Fˆsa and Tˆsa to the zone model, the next step zone temperature will be predicted Tˆz , which will be used to get next step Fsp and Tsp, then Fˆsa and Tˆsa afterwards, and so on. Fig. 13 shows the predicted supply air fan speed and temperature based on the set-point function and compared with the measured one. As we have mentioned before, the real supply air temperature Tsa generally oscillates around its
Fig. 13. Supply air fan speed (a) and temperature (b).
set-point Tsp, and supply air fan speed Fsa is maintained very close to its set-point Fsp. 5.2.2. Model fitting and zone temperature prediction 5.2.2.1. Using predicted external temperature. In our experiments, external temperature in some future time, e.g., ½ h, 1 h or 2 h, is assumed to be the same as the current one and used for model fitting and zone temperature prediction. Experiment results are shown in Table 2 and Fig. 14. Table 2 gives fitting and prediction accuracy measurement using the mean square error (MSE). Fig. 14 shows the zone model fitting and zone temperature prediction results for different time strategies. The past ½ hour’s data is used to fit the model, and then predict the next ½ hour zone temperature, and this process repeats every ½ hour as shown in Fig. 14(a). Table 2 Parameters for zone modeling. Time strategy
Fitting error (8C)
Prediction error (8C)
½ hour fitting, prediction and ½ hour repetition 1 hour fitting, prediction and 1 hour repetition 1 hour fitting, 2 hour prediction and 2 hour repetition
0.0008
0.0034
0.0013
0.0099
0.0031
0.0287
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Fig. 15. Zone model fitting and temperature prediction with precise external temperature; (a) ½ hour fitting, ½ hour prediction and ½ hour repetition; (b) 1 hour fitting, 2 hour prediction and 2 hour repetition.
Fig. 14. Zone model fitting and temperature prediction for different fitting and prediction strategies; (a) ½ hour fitting, ½ hour prediction and ½ hour repetition; (b) 1 hour fitting, 1 hour prediction and 1 hour repetition; (c) 1 hour fitting, 2 hour prediction and 2 hour repetition.
From the experimental results, we can see that the model fitting is very good for different fitting times, and the prediction accuracy is strongly dependant on the prediction period. The shorter the prediction time, the more accurate the prediction for the indoor temperature that is achieved. This difference is due to the dynamics of zone environment and external temperature variation. 5.2.2.2. Using precise external temperature. In order to see the effect of inaccurate external temperature predictions on the zone model prediction accuracy, experiments were run using the real external temperature. The results are shown in Fig. 15 for short time prediction (e.g., ½ hour) and long time prediction (e.g., 2 h). By comparing corresponding results in Figs. 14 and 15, we can see that for ½ hour prediction the zone temperature prediction error caused by inaccurate external temperature predictions is much smaller than for the 2 hour predictions.
5.2.2.3. Model fitting and zone temperature prediction for variable supply air set-point data. Supply air set-point function as illustrated in Fig. 3 has constant value at the two ends and variable value in the middle. The experiments above work on constant supply air temperature set-point, e.g. 18 8C, where it was found our proposed model fitting and prediction algorithm works very well. To investigate the algorithm’s adaptability to variable supply air temperature set-points, further experiments were conducted. The data for these experiments was collected between the 11th and 13th of March 2008 as shown in Fig. 16. Each day, the AHU runs between 4:00 am and 5:00 pm, with the supply air set-point varied between 18 8C and 20 8C. Data sample rate is 5 min. Fig. 17 shows the results of different fitting and prediction strategies for such variable set-point data. From the figure, we can see that our algorithm can properly adapt to variable supply air set-points. 6. A Kalman filtering method with delayed feedback To evaluate the performance of our modeling technique, we compare it with a Kalman-filter-based modeling technique. The standard Kalman filter is a recursive filter that estimates the state of a dynamic and often noisy system from a series of incomplete measurements, which are sometimes further degraded by measurement noise. The main mechanism in a Kalman filter is feedback control: the filter iteratively estimates the process state and obtains feedback in the form of measurements. Thus, each iteration comprises two distinct phases prediction and correction.
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Fig. 16. Variable supply air data for the AHU between 11th and 13th of March 2008.
In the prediction phase, the next state of the system is predicted based upon predetermined process equations. This reflects the a priori understanding of the process. The corresponding estimated error covariance matrix is also computed in this phase. Both these estimates are updated when a measurement becomes available at the next time step. The amount of the correction in this update phase is heavily dependent on a factor called the Kalman gain, which is calculated from a model of how the process is measured/ observed, the covariance of the measurement noise, and the estimated error covariance. Unfortunately, the standard Kalman filter is not directly applicable to our zone modeling problem. Our requirement is for a single phase of continuously sliding-forward prediction that lasts a relatively long period, without any injection of feedback measurements at any time during that period. In our application, measurements are only available at the end of each period. Therefore, a key ingredient in the Kalman approach is not accessible. On the other hand, feedback-based correction is definitely necessary. This is because for a dynamic process our a priori knowledge is highly unlikely to be accurate all the time. Therefore, in the complete absence of measurement-based updates, the prediction error is likely to be unacceptable. A possible approach to addressing the dilemma is to take advantage of historical trends in the corrections or updates. Our experiments are based upon such an attempt, albeit a relatively straightforward one. Our system is described by the state vector Tz xn ¼ F sa Although the temperature in the HVAC zone can be rather accurately determined, the measured fan speed is subject to significant noise due to mechanical inaccuracy and latency. In our experiments, the measurement noise is assumed to be 10 times as high as the process noise. The Kalman procedure we employ can be
Fig. 17. Zone model fitting and temperature prediction for different fitting and prediction strategies; (a) ½ hour fitting, ½ hour prediction and ½ hour repetition; (b) 1 hour fitting, 1 hour prediction and 1 hour repetition; (c) 1 hour fitting, 2 hour prediction and 2 hour repetition.
described in two phases in a forward-sliding time window, as follows: 1. For the initial N time intervals, the standard Kalman algorithm is used. The update amount in each iteration is recorded for future use; 2. Starting from the nth interval, and through to the (n + M)th interval, the corrections are no longer based on instant feedback, but instead based on the correction applied at the previous corresponding time instant; 3. The above two phases are repeated as the time window slides forward.
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volatility of wholesale electricity prices and assist constrained networks during summer and winter demand peaks. The proposed method is quite suitable for near-term predictions as required by Australia’s half-hour electricity market cycle. As follow-up work, we are focussing on heat exchanger modeling in order to model the whole HVAC system and provide HVAC power usage predictions. With such predictions, we can properly control energy flows in the entire building and thus holistically optimize HVAC performance, as well as managing its power consumption strategically for the purpose of demand management. References
Fig. 18. Feedback-delayed Kalman prediction of the zone temperature for future time windows of ½ hour (a), 1 h (b) and 2 h (c).
Table 3 Feedback-delayed Kalman prediction of the zone temperature. Time strategy
Prediction Error
½ hour prediction 1 hour prediction 2 hour prediction
0.0043 0.0133 0.0635
Several experiments have been conducted using the constant supply air set-point data as used in Section 5.2.2.1. The results using feedback-delayed Kalman zone temperature prediction for future time windows of ½ h (a), 1 h (b) and 2 h (c) are presented in Fig. 18. Note that in this figure the first N data points are based upon instant feedback as per the standard Kalman filter. The subsequent results are computed using the feedback-delayed algorithm. Error analysis of the feedback-delayed Kalman prediction of the zone temperature is tabulated in Table 3. The rows represent predictions over time windows of ½ h, 1 h, 2 h and 3 h. As in Table 2, the prediction errors are quantified by the MSE. By comparing Tables 2 and 3, we can clearly see that our realtime HVAC zone modeling and temperature prediction algorithm achieves more accurate prediction of zone temperatures compared to the feedback-delayed Kalman filter method. 7. Conclusions This paper has introduced a soft real-time HVAC zone modeling and temperature prediction algorithm using a simple time varying zone model with only a few parameters. The algorithm through real-time learning can adequately adapt to the dynamics of the HVAC zone environment in an efficient manner, dealing with both short-term unexpected changes and relatively long-term accumulated changes. Modeling and prediction results from this work have shown to be promising. The shorter the prediction time, the more accurate the prediction of indoor temperature that can be achieved. Based on this work, we can model and predict zone status, which is a necessary step for managing and controlling HVAC systems as distributed energy resources [20] to reduce the
[1] G. Hudson, C.P. Underwood, A simple building modeling procedure for MATLAB/ SIMULINK, in: Proceedings of the International Building Performance and Simulation Conference, Kyoto, 1999. [2] K. Tor, F. Ritter, Using a genetic algorithm to optimize the fit of cognitive models, in: Proceedings of the International Conference on Cognitive Modeling, 2004, pp. 308–313. [3] .G.J. Levermore, Building Energy Management Systems, E & FN Spon, London, 1992 [4] G.J. Levermore, Simple model for an optimiser, Building Services Engineering Research & Technology 9 (3) (1988) 109–116. [5] B. Tashtoush, M. Molhim, M. Rousan, Dynamic model of an HVAC system for control analysis, Energy 30 (2005) 1729–1745. [6] S. Karatasou, M. Santamouris, V. Geros, Modeling and predicting building’s energy use with artificial neural networks: methods and results, Journal of Energy and Buildings 38 (2006) 949–958. [7] B. Dong, C. Cao, S. Lee, Applying support vector machines to predict building energy consumption in tropical region, Journal of Energy and Buildings 37 (2005) 545–553. [8] S.W. Wang, X.H. Xu, Simplified building model for transient thermal performance estimation using GA-based parameter identification, International Journal of Thermal Science 45 (4) (2006) 419–432. [9] S.W. Wang, X.H. Xu, Parameter estimation of internal thermal mass of building dynamic models using genetic algorithm, Energy Conversion and Management 47 (13–14) (2006) 1927–1941. [10] S.W. Wang, Dynamic simulation of building VAV air-conditioning system and evaluation of EMCS on-line control strategies, Building and Environment 34 (6) (1999) 681–705. [11] C.-S. Park, G. Augenbroe, T. Messadi, M. Thitisawat, N. Sadegh, Calibration of a lumped simulation model for double-skin fac¸ade systems, Energy and Buildings 36 (2004) 1117–1130. [12] N. Djuric, V. Novakovic, F. Frydenlund, Heating system performance estimation using optimization tool and BEMS data, Energy and Buildings 40 (2008) 1367– 1376. [13] National Electricity Market Management Company (NEMMCO), Australia, 2007. http://www.nemmco.com.au/, accessed December 2008. [14] G. Welch, G. Bishop, An Introduction to the Kalman Filter, Technique Report Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3175, 2006. [15] F. Ashley, Emery, Estimating parameters and refining thermal models by using the extended Kalman filter approach, Journal Heat Transfer 126 (5) (2004) 809–817. [16] Saeid Habibi, Parameter estimation using a combined variable structure and Kalman filtering approach, Journal of Dynamic Systems, Measurement, and Control 130 (September (5)) (2008) 051004 (14 pages). [17] I.F. MacGill, Optimising decentralised power system operation using dual evolutionary programming, Ph.D. Thesis, UNSW, Australia, 1998. [18] Y. Guo, J. Li, G. James, Evolutionary optimisation of distributed energy resources, in: The 18th Australian Joint Conference on Artificial Intelligence (AI’05), Sydney, Australia, December 5–9, (2005), pp. 1086–1091. [19] J. Li, G. Poulton, G. James, Agent-based distributed energy management, in: 20th Australian Joint Conference on Artificial Intelligence (AI’07), Gold Coast, Queensland, Australia, December 2–6, (2007), pp. 569–578. [20] R. Li, J. Li, G. Poulton, G. James, Agent-based optimisation systems for electrical load management, in: Proc. First International Workshop on Optimisation in Multi-Agent Systems (OPTMAS), Estoril, Portugal, (2008), pp. 60–69, in pewaa May. [21] J. Li, G. Poulton, G. James, Y. Guo, Multiple energy resource agent coordination based on electricity price, Journal of Distributed Energy Resources 5 (April–June (2)) (2009) 103–120. [22] J. Li, G. James, G. Poulton, Set-points based optimal multi-agent coordination for controlling distributed energy loads, in: 3rd IEEE International Conference on Self-Adaptive and Self-Organizing Systems, San Francisco, California, September 14–18, 2009. [23] F.R. Tully, R.J. Kaye, Unit commitment in competitive electricity markets using genetic algorithms, Trans. of the Institute of Electrical Engineers of Japan 117-B (6) (1997) 815–821. [24] J.P. Rennard, Introduction to genetic algorithms, PhD thesis, 2000.
Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Adaptive HVAC zone modeling for sustainable buildings Glenn Platt a, Jiaming Li b,*, Ronxin Li b, Geoff Poulton b, Geoff James a, Josh Wall a a b
CSIRO Energy Technology, Australia CSIRO ICT Centre, Australia
A R T I C L E I N F O
A B S T R A C T
Article history: Received 16 April 2009 Received in revised form 28 September 2009 Accepted 4 October 2009
Control of energy flows within a building is critical to achieving optimal performance of heating, ventilation and air-conditioning (HVAC) systems. To design optimal HVAC control strategies, a dynamic model of the HVAC system – particularly the building zones that it services – is essential. As analysis of building energy consumption is facilitated by the accurate prediction of indoor environmental conditions, techniques that dynamically model HVAC zones are crucial, and as such, is an active area of research. This paper focuses on real-time HVAC zone model fitting and prediction techniques based on physical principles, as well as the use of genetic algorithms for optimization. The proposed approach is validated by comparing real-time HVAC zone model fitting and prediction against the corresponding experimental measurements. In addition, comparison with prediction results using an algorithm based on feedback-delayed Kalman filters has demonstrated the superiority of the proposed approach in terms of prediction accuracy. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Genetic algorithms HVAC control HVAC zone modeling Kalman filtering
1. Introduction Heating, ventilation and air-conditioning (HVAC) systems play a dominant role in regulating the indoor climate, providing people with a comfortable and safe work environment. In most buildings the performance of the HVAC system can influence energy consumption as well as indoor air quality. The amount of energy used by HVAC systems is a significant concern that impacts on issues from national policy to personal desires of cost and comfort, and as such, HVAC modeling is a very active research topic [1,2]. A HVAC system comprises a variety of continuous and discrete control components interacting with the building via sensors and actuators. Control of the energy flows in the building and its environment is the key to achieving optimum performance from an HVAC system. Such control is secured through monitoring and altering the cooling/heating sources to maintain the desired thermal and air quality conditions in a space, while external and internal conditions change over time. The building with its technical equipment and its environment consists of several coupled processes which, in general, cannot be influenced independently. This complicates the design of high-quality control algorithms and requires model-based design methodologies for
Abbreviations: AHU, air-handling unit; BMCS, building management & control system; OA, outside air; RA, return air; SA, supply air; CHWV, chilled water valve; HWV, hot water valve; SP, set-point; OAF, outside air fan; SAF, supply air fan; RAF, return air fan. * Corresponding author. Tel.: +61 2 9372 4707; fax: +61 2 9372 4161. E-mail address: [email protected] (J. Li). 0378-7788/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2009.10.009
optimum performance. For the energy-efficient design of buildings and their associated control systems, it is necessary to obtain approximate dynamic mathematical models for system components. These models are used for a wide range of tasks including operating strategy planning, cost analysis and comfort evaluation. The dynamic model can be especially useful for control strategies that require knowledge of the dynamic characteristics of HVAC systems. The system component that we will focus on in this paper is the zone. A HVAC zone is a group of adjacent offices and/or spaces serviced by a common air-handling unit (AHU) or air-terminal device. Since the external and internal environment of the zone always changes, any model of the zone has to emulate the dynamic thermal processes within the zone as well as the interaction with the environment. Modeling such a time-variant system is a challenging task. Traditionally, zone models are mainly based on static or shortterm modeling of the HVAC zone. Four approaches have been reported in recent literature. The first uses lumped capacitance in an analogue electric circuit to represent thermal elements of a building [1,3,4]. A second approach is a building thermal model based on energy-and-mass balance [5], where every component of the HVAC system is represented by energy-and-mass balance equations. The third approach is based on machine learning, in which artificial neural networks [6] or support vector machines [7] model non-linear processes, such as utility loads or an individual building’s energy consumption. A fourth approach is evident more recently, as researchers have started exploring the response of HVAC systems to dynamic
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Nomenclature Two Twi To Tz Tsp Fsp Tsa Fsa fa Ca
ra Vz Uw Aw Gw Ro Io Ia Ra Iz Cz
outlet water temperature (8C) inlet water temperature (8C) external (outside) temperature (8C) zone temperature (8C) supply air temperature set-point (8C) supply air fan speed set-point (% of maximum speed) supply air temperature (8C) supply air fan speed (% of maximum speed) supply air flow rate (m3/s) specific heat of air (kJ/(kg 8C)) density of the air (kg/m3) volume of the zone (m3) thermal conductivity of the wall (W/mK) heat transfer area of the wall, i.e. area of each wall (m2) wall thickness (m) resistor of outside wall representing its function of transferring heat between outside and inside current of outside air representing its heat flow current of supply air representing its heat flow resistor of supply air representing the air convection current of zone air representing its heat flow overall thermal capacity (kJ/C) of the zone
environments [8–12]. These models, however, tend to be rather cumbersome, and do not adequately adapt to the dynamics of the zone environment in real time. In addition, many existing models do not take into account long-term dynamic properties of the building, due to changes accumulated over a long time period. We investigate a real-time model fitting and prediction algorithm using only few parameters, that is well suited to short-term predictions and also adapts to long-term dynamics. In Australia, the electricity market cycle is half-hourly [13], and our proposed algorithm is very suitable for applications on this time scale. The algorithm is applied to a dynamic zone model of a HVAC system, intended to allow the implementation of control strategies to reduce energy consumption and improve the quality of the indoor environment. The paper has two major contributions. One is the formation of a mathematical model of the zone based on physical principles and circuit theory—the model we propose is the first one that combines energy/mass balance and basic circuit theory. The second contribution is the real-time model fitting and prediction algorithm for a time-variant zone, taking advantage of genetic algorithms (GA). The model and algorithm are then validated using measurements of a real HVAC system. Throughout the paper the HVAC zone is represented as a sixfaced box. The zone model is firstly deduced from an energy-andmass balance and then represented using electric circuit theory. Electric circuit elements are used to represent functions of the building elements, e.g., a wall is modelled as a resistor to represent its function of transferring heat between outside and inside, and an entire zone is modelled as a capacitor to represent its heat storage function. This kind of zone model is very simple and generic, applicable to a zone with any internal structure and material. Following development of the zone model structure, a methodology of soft real-time zone model fitting and prediction is given, e.g., zone model fitting and prediction every 5 or 30 min. Since the zone
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model is fitted in soft real-time (every 5 min) it can easily cope with the changes of the zone’s dynamics and give accurate internal temperature prediction. Lastly, we present results using an alternative technique, the Kalman filter, to perform the model fitting. The Kalman filter [14] is an efficient recursive filter that predicts the state of a dynamic system from a series of incomplete and noisy measurements. The Kalman filter is traditionally viewed as a prediction-correction filtering algorithm and is a classic method used for dynamic systems. Recently, various parameter estimation techniques based on extended Kalman filters have been applied to thermal modeling and model refinement (e.g. [15,16]). A series of experimental results using a modified Kalman filter with delayed feedback is presented for comparison with our own technique. The results show that our model is capable of giving more accurate prediction for the indoor temperature of a dynamic zone compared to the Kalman filter technique. This paper is organized as follows. Section 2 introduces the HVAC system. Section 3 presents a mathematical zone model based on physical principles. Section 4 introduces soft real-time zone model fitting and prediction based on genetic algorithms. Section 5 gives a series of experimental results to quantify the performance of model fitting and prediction. For comparison purposes, a feedback-delayed Kalman filtering method is presented in Section 6. Finally, a conclusion is drawn in Section 7. 2. HVAC system description Many HVAC systems use a central plant to provide hot water (e.g., with temperature of 32 8C) for heating purposes or cold water (e.g., with temperature of 6 8C) for cooling purposes. Fig. 1 is a schematic diagram of a typical HVAC system with multiple zones for cooling purpose. The water path is presented by black arrows, which shows that cold water with temperature Two flows from the central plant along the pipework and into the cooling coils. The chilled water valves (CHWV) are used to control the volume of water flowing through the coils. A cooling coil exchanges heat energy between air from the mixing box and water from the central plant, with the output water flowing back to the central plant with a slightly higher temperature Twi. The air path is represented by grey arrows. The outside air can be drawn in by an outside air fan (OAF) and outside air damper into the mixing box. A mix of outside air and return air then flows through the air filter and passes over the cooling coil. A supply air fan (SAF) then forces the air through an insulated supply duct into the zone area as supply air (SA) for the zone. The supply air gains part of its heat from the zone to replace the heat that is leaking through the walls, roof, etc. The supply air then passes through the
Fig. 1. Schematic diagram of a typical HVAC system for cooling purpose.
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room and into the return air inlets. Some return air is exhausted through an exhaust air damper. The remaining return air passes through the re-circulation air damper into the mixing box and mixes with the outside air. The outside air dampers and exhaust air dampers control the amount of air flow amount from the outside air (OA) and return air (RA) streams respectively.
Min. Control Point), with a Tz of 21.7 8C is defined as the Intermediate Control Point. Lastly, a Tz of 27 8C is defined as the fan speed maximum control point (Fan Speed Max. Control Point). In a typical HVAC system, control variables related to temperature can often oscillate around their set-point, with fan speed related variables usually maintained very close to their set-point. Air flow rate fa is largely proportional to supply air fan speed Fsa.
2.1. Air-handling unit 3. HVAC zone modeling The air-handling unit (AHU) is a device used to condition and circulate air as part of a HVAC system. Usually, the AHU is a large metal box containing fans, heating and/or cooling coils, filter racks or chambers, sound attenuators, and dampers. Building indoor temperature is maintained at set-point (SP) values by the AHU, which usually connects to ductwork that distributes conditioned air to the zone. Fig. 2 shows a typical operation schematic for each AHU. The AHU draws air from the zone with temperature Tz(t), which determines supply air temperature set-points (expected supply air temperature, Tsp) and supply air fan speed set-points (expected supply air fan speed, Fsp). The AHU forces the air from the mixing box through cooling/heating coils with flow rate fa, which is largely proportional to the fan speed Fsa, resulting in supply air with temperature Tsa, and then discharges the cooled/heated air back into the zone. A certain amount of fresh air may be introduced from the outside air inlet so that fresh air in the zone may be gradually introduced. Fig. 3 shows an example of proportional control relationship between the supply air temperature set-point (Tsp) and supply air fan speed set-point (Fsp) versus zone temperature (Tz) for a particular HVAC system, in which the supply air temperature setpoint varies between 18 8C and 32 8C, with the supply air fan speed set-point varying between 40% and 100%. The supply air temperature set-point (Tsp) is the expected supply air temperature, which is a function of zone temperature, and has inflexion points at the zone temperatures of 19 8C and 21.7 8C. The supply air fan speed set-point (Fsp) is the expected supply air fan speed, which is also a function of zone temperature, and has inflexion points at the zone temperatures of 21.7 8C and 27 8C. A Tz, equal to 19 8C in this instance, is defined as the supply air minimum control point (SA
In this section, we focus on an HVAC zone modeling technique based on physical principles. The assumption for the model is that the supply air flowing into the zone is evenly distributed throughout the whole zone; adjacent zones have the same temperature; and we ignore the thermal storage of all walls. Firstly, the model is deduced from an energy-and-mass balance. Then the model is explained using basic electrical circuit theory. Each zone can be modeled as a box with 6 faces as shown in Fig. 4, in which face ACGE is the wall connecting outside with temperature To; EFHG is the ground floor with temperature TG; ABDC is ceiling with temperature TC; CDHG, BDHF and ABFE are the walls connecting with adjacent zones that have the same temperature TA. The overall heat flow in the zone comes from air convection and wall conduction, as expressed in the following equation: Cz
dT z f r C a ðT sa T z Þ þ U w Aw ðT o T z Þ ¼ a a Gw dt
(1)
where Cz = CaraVz is the overall thermal capacity (kJ/C) of the zone; Ca is the specific heat of air (kJ/(kg 8C)); ra is the density of the air (kg/m3); Vz is volume of the zone; fa is the air flow rate (m3/s); Tsa is supply air temperature (8C); Tz is the zone temperature (8C); To is external temperature (8C); the thermal conductivity of the wall is denoted by Uw (W/mK); Aw is heat transfer area (m2), i.e. area of each wall; and Gw is wall thickness (m). Gw To simplify this, letting Ro ¼ Uw Aw be a resistor representing the thermal properties of the wall, Eq. (1) becomes: Cz
dT z f r C a ðT sa T z Þ þ ðT o T z Þ ¼ a a Ro dt
(2)
Eq. (2) can be explained using RC circuit theory as follows. Heat flow generated from a temperature difference, is analogous to electrical current generated from a voltage difference. Therefore, temperature can be modeled as voltage and heat flow can be modeled as current, i.e., Ia ¼
dH ¼ f a ra C a ðT sa T z Þ: dt
Fig. 5 is a simple analogue electric circuit used to represent functions of the building elements, in which the outside wall is Fig. 2. Operation schematic for a typical AHU system.
Fig. 3. Supply air temperature and fan speed set-points vs. zone temperature.
Fig. 4. Zone thermal interfaces.
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where D1 = faraCa, fa is the air flow rate, which is proportional to the fan speed Fsa; supply air temperature Tsa usually oscillates around its set-point Tsp, which is a function of zone temperature as shown in Fig. 3; ra is the density of the air with value 1.204 (kg/m3) at 20 8C; Ca is specific heat of air with value 1.005 (kJ/kg 8C). Parameter D2 is added to take into account factors such as leakage of the zone, measurement error, dynamics of the zone, etc. 4. Dynamic zone model fitting using a genetic algorithm
Fig. 5. Simple RC model of an HVAC zone’s thermal performance.
modeled as a resistor (Ro) to represent its function of transferring heat between outside and inside. The zone is modeled as a capacitor (Cz) to represent its function of both ‘charging’ through heat input from supply air and ‘discharging’ through heat. In the figure, the zone’s average temperature is Tz. It has two sources, one is supply air source with node voltage (temperature) Tsa; another is outside air source with node voltage (temperature) To. The current (heat flow) is Ia ¼ dH ¼ f a ra C a ðT sa T z Þ, where dt (Tsa Tz) is voltage (temperature) difference in the zone, Ra ¼ 1= f a ra C a is the variable zone air resistance. The wall has resistance Ro. The voltage (temperature difference) across Ro is (To Tz). Therefore current (heat flow) flowing through Ro is Io = (To Tz)/Ro. The voltage (temperature) difference on capacitor Cz is DTz, and thus the current (heat flow) flowing through the capacitor will be Iz ¼ C z
dT z dt
(3)
We know Iz = Ia + Io, which is represented by Eq. (2). Until now we have deduced the zone model from both energy/ mass balance and basic circuit theory point of view. The zone is a dynamic environment that changes over time. The dynamics of this environment are partly attributable to events such as people walking in or out, doors and windows being opened or closed. To realize adaptability to the dynamic environment and simplify the analysis, the zone model shown in Fig. 5 can be represented as a time-variant system, represented by a time-variant RC circuit (variant RoCz, or variant Ro). Suppose the air supplied into the zone is evenly distributed across the whole zone; outside air with temperature To transfers the air into the zone through the outside wall, i.e., ACGE in Fig. 4; the ceiling, ground and corridor in adjacent zones have the same temperature as the zone under study, i.e., Tz = TA in Fig. 4. Such a model ignores the thermal storage of all walls. The discrete expression of (2) is C z ðT z ðnÞ T z ðn 1ÞÞ ¼ f a ra C a ðT sa ðn 1Þ T z ðnÞÞ Dt ðT o ðn 1Þ T z ðnÞÞ þ Ro T z ðnÞ ¼
(4)
f a ra C a DtT sa ðn 1Þ þ ðDt=Ro ÞT o ðn 1Þ þ C z T z ðn 1Þ C z þ f a ra C a Dt þ ðDt=Ro Þ
To take into account factors such as the leakage of the zone and measurement error, a parameter D2 can be added to the above equation. Therefore the zone temperature can be expressed as Eq. (5):
T z ðnÞ ¼
Having derived a basic model for the zone, our aim is to find optimal parameters for the zone model that best fit with the measured data. We obtain the solutions using a genetic algorithm of a kind that has previously achieved successful model fitting [2], multi-agent coordination [17–22] and been used in similar applications related to electricity markets [23]. 4.1. Genetic algorithm A genetic algorithm (GA) [8,9,24] is a search method inspired by natural selection and survival of the fittest in the biological world. A GA is a type of ‘‘evolutionary algorithm’’. By using a GA approach, excellent results can be achieved through the evolution of the system. A colony of rule sets can be evolved for a number of generations, improving the performance of the colony. Techniques of fitness determination, selection, cross-over, reproduction, and mutation are applied to the rules and their chromosomal representation. Essentially, the parameters we are seeking for the zone model are ‘‘evolved’’ over successive generations. The first generation of parameters (initial population) can be either random or predetermined values. At each subsequent generation of parameters, every individual of the population must be evaluated to be able to distinguish between good and bad individuals. This is done by mapping the objective function to a ‘‘fitness function’’, which is a non-negative well-behaved measure of relative fitness of the parameters. The better the fitness of a given rule, the more likely it is to be selected. After the two parent rules are selected, each is represented by a ‘‘chromosomal’’ string and then combined to determine the chromosomes of the two resulting rules (offspring). These chromosomes are subjected to potential mutation, and are then converted back to their equivalent rule representation. The selected parents are then replaced in the colony by the offspring. This mechanism of natural selection is expected to eventually result in a population with a higher performance. 4.2. Genetic algorithm design for our system 4.2.1. Fitness function of optimization The simulated prediction of the zone temperature with the model expressed as Eq. (5) is used to compare with the measured zone temperature. The optimized parameters are D1, D2 and Ro of the model that give the best fit with the operational data. The objective function, O, of such an optimization employs mean square fitting errors defined in Eq. (6). Eq. (7) represents the fitness function f, which is the reciprocal of the objective function. OðD1 ; D2 ; Ro Þ ¼
N 1X 2 0 ðT ðiÞ T z ðiÞÞ N i¼1 z
where Tz and T 0z are the fitted and measured zone temperature respectively, and N is the number of the sample data. f ¼ f ðD1 ; D2 ; Ro Þ ¼
D1 DtT sa ðn 1Þ þ ðDt=Ro ÞT o ðn 1Þ þ C z T z ðn 1Þ þ D2 C z þ D1 Dt þ ðDt=Ro Þ (5)
(6)
1 OðD1 ; D2 ; Ro Þ
(7)
A genetic algorithm (GA) is employed to search for the optimal values as illustrated in Section 4.2.2.
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Table 1 Parameters for zone modeling. Name
Definition
Parameter availability
D1 D2 Ro
Time varying coefficient in Eq. (5) Time varying coefficient in Eq. (5) Time varying resistor of the wall connecting outside in Eq. (5) Average zone temperature Outside temperature Supply air temperature
Learning parameter Learning parameter Learning parameter
Tz To Tsa
Fig. 6. AHU GA operation.
4.2.2. Optimization As shown in Fig. 2, the supply air temperature set-points (expected supply air temperature, Tsp) and supply air fan speed setpoints (expected supply fan speed Fsp) are predetermined inputs based on the current zone temperature (Tz(t)) specified in the building management and control system (BMCS) logic. The BMCS controls supply air fan speed Fsa based on set-points to allow mixed air to pass over the cooling/heating coil with air flow rate fa, resulting in supply air with temperature Tsa. Supply air with temperature Tsa flows through the insulated supply duct into the
Fig. 7. Flow chart of GA learner for fitting the zone model parameters.
Measured parameter Measured parameter Measured parameter
zone area with flow rate fa and then exchanges heat with the zone. The next step zone temperature Tz(t + 1) is a function of the zone model, supply air temperature and supply air flow rate. The AHU GA operation is shown in Fig. 6. Fig. 6 are supply air temperature set-points, fan speed setpoints, current zone temperature and current external temperature. The output is the next step zone temperature. As expressed in Eq. (5), the zone model is determined by several parameters. Some of them are known; some are measured; some can be calculated; and some are unknown parameters that need to be learnt by the genetic algorithm. Table 1 summarizes the parameters for zone modeling, where the set of learning parameters must each be learnt by the GA. Fig. 7 shows schematically the flow chart of the GA learner developed for fitting the zone model parameters. In the genetic algorithm, the three parameters (D1, D2, Ro) constitute the chromosome of an individual. Initializing the three parameters produces an initial population to start the first generation GA process. Termination of a GA process is decided if the number of the current generation is equal to a predefined maximum generation number. At least two generations are necessary when running the GA optimization.
Fig. 8. Real-time zone model fitting and prediction using GA learner: (a) flow chart of ½ hour zone model fitting and prediction; (b) time series of model fitting and prediction.
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4.2.3. Real-time zone model fitting and prediction using GA As we have described above, the HVAC zone is a dynamic environment. To cope with its dynamics, a real-time zone model fitting using GA learner is developed. Fig. 8(a) shows schematically the flow chart of ½ hour zone model fitting and prediction based on the GA learner introduced above. Fig. 8(b) shows the time series of model fitting and prediction. In the figure T 0z represents the measured zone temperature and Tz represents the calculated (fitted and predicted) zone temperatures. Suppose current time is tn. Training data collected in past time period, Vi ¼ t n t nN , is used for model fitting using the genetic algorithm, and generates the best parameters for the zone model, which is called the fitted model. The fitted model is then used to predict the future zone temperature, e.g., temperature during time period V j ¼ t nþM t n . The training data used in the process includes measured supply air temperature Tsa, external temperature To and supply air fan speed Fsa. The process is repeated for every tk time interval. The details of the process are as follows. 1. The measured zone temperature over a past time period is represented as
ture Tz(n + 1); using predicted zone temperature Tz(n + 1) to get next step predicted zone temperature Tz(n + 2); and so on. T z ðnÞ ) T z ðn þ 1Þ ) T z ðn þ 2Þ ) ) T z ðn þ MÞ 5. Experimental results 5.1. Training data A number of measurements have been conducted to gather historical data for the purposes of thermal model fitting within the CSIRO Energy Centre Level 3 (East) office wing, in which three AHUs service three adjacent HVAC zones consisting of 18 offices and associated corridors. Each office or space has a dry bulb temperature sensor to detect the internal temperature. The zone temperature is the average value across all offices and/or spaces in the zone. Fig. 9 shows the CSIRO energy centre building. Fig. 10 gives a floor plan of the AHUs and their associated offices/spaces, where different zones are represented as different grey color shades. AHU-08 solely services office 331, with AHU-09 and AHU-
½T 0z ðn NÞ; T 0z ðn N þ 1Þ; . . . ; T 0z ðn 2Þ; T 0z ðn 1Þ; T 0z ðnÞ where N is the number of sample data points in the past time period. 2. The fitted zone temperature based on Eq. (5) is represented as ½T z ðn NÞ; T z ðn N þ 1Þ; . . . ; T z ðn 2Þ; T z ðn 1Þ; T z ðnÞ 3. The predicted zone temperature based on Eq. (5) is represented as ½T z ðnÞ; T z ðn þ 1Þ; T z ðn þ 2Þ; . . . ; T z ðn þ M 1Þ; T z ðn þ MÞ 4. In each generation of GA, each population of learning parameters gives the calculated zone temperature one by one using Eq. (5), i.e., using measured zone temperature T 0z ðn NÞ to calculate zone temperature Tz(n N + 1); using fitted (calculated) zone temperature Tz(n N + 1) to get another zone temperature Tz(n N + 2) and so on.
Fig. 10. CSIRO Energy Centre Level 3 (East).
T 0z ðn NÞ ) T z ðn N þ 1Þ ) ) T z ðn 1Þ ) T z ðnÞ 5. Compare the measured zone temperatures with the fitted ones to calculate fitness value for each population as Eq. (7). 6. ‘‘Parent’’ rules are selected based on a fitness value. After the two parent rules are selected, each is represented by a ‘‘chromosomal’’ string and are then combined to form two new chromosomes. These chromosomes are subjected to potential mutation, and are then converted back to their equivalent rule representation. The selected parents are then replaced in the colony by the offspring. 7. Repeat the process steps 4–6 for the number of required generations and obtain the best population, i.e., the best learning parameters. 8. Based on the best learned parameters for the past time period, do the prediction for the future time one by one, i.e., using current zone temperature Tz(n) to get predicted zone tempera-
Fig. 9. The CSIRO Energy Centre, Newcastle NSW, Australia.
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Fig. 11. Collected data for the AHU between 3rd and 4th of April 2007.
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Fig. 12. External temperature.
10 servicing the northern and southern zones respectively. In addition AHU-09 also services the corridor. The data we used in this work was collected between the 3rd and 4th of April 2007, as shown in Fig. 11. Each day, the AHU runs between 7:00 am and 5:00 pm, with a constant supply air setpoint of 18 8C. The data sample rate was 5 min. Our experiments were carried out using Matlab on a laptop with 2 GB RAM and an Intel Core 2 Duo T7600 CPU running at 2.33 GHz. 5.2. Real-time zone modeling and temperature prediction An HVAC zone is a dynamic environment with people walking in and out, doors opening and closing, etc. To cope with such an environment, a dynamic model is necessary. To achieve this we have developed a soft real-time model fitting and prediction algorithm. Every V time interval, the past Vi period data is used for zone model fitting with the GA, then the fitted zone model is used to predict future Vj period zone temperature as described in Section 4.2.3. 5.2.1. Supply air and external air prediction As shown in Fig. 6, the future zone states are a function of the zone model, external temperature and supply air. The predicted supply and external air properties are essential to model and predict zone temperature. In our experiments, external temperature in some future period of time is assumed to be the same as current external temperature. This assumption is reasonable for short-term prediction. Fig. 12 shows the external temperature Tˆo for ½ hour prediction, i.e., next ½ hour external temperature is very close to the current one. The supply air properties include temperature and flow rate that are proportional to fan speed. Both expected supply air fan speed and temperature can be calculated through the supply air set-point function as shown in Fig. 3. Suppose we have current zone temperature Tz, then based on the function shown in Fig. 3 we will know our expected supply air fan speed Fsp and temperature Tsp. If we assume the BMCS is able to obtain the expected supply air perfectly, Fsp and Tsp can be used as predicted supply air fan speed Fˆsa and temperature Tˆsa , i.e., Fˆsa ¼ F sp and Fˆsa ¼ F sp . Applying Tˆo , Fˆsa and Tˆsa to the zone model, the next step zone temperature will be predicted Tˆz , which will be used to get next step Fsp and Tsp, then Fˆsa and Tˆsa afterwards, and so on. Fig. 13 shows the predicted supply air fan speed and temperature based on the set-point function and compared with the measured one. As we have mentioned before, the real supply air temperature Tsa generally oscillates around its
Fig. 13. Supply air fan speed (a) and temperature (b).
set-point Tsp, and supply air fan speed Fsa is maintained very close to its set-point Fsp. 5.2.2. Model fitting and zone temperature prediction 5.2.2.1. Using predicted external temperature. In our experiments, external temperature in some future time, e.g., ½ h, 1 h or 2 h, is assumed to be the same as the current one and used for model fitting and zone temperature prediction. Experiment results are shown in Table 2 and Fig. 14. Table 2 gives fitting and prediction accuracy measurement using the mean square error (MSE). Fig. 14 shows the zone model fitting and zone temperature prediction results for different time strategies. The past ½ hour’s data is used to fit the model, and then predict the next ½ hour zone temperature, and this process repeats every ½ hour as shown in Fig. 14(a). Table 2 Parameters for zone modeling. Time strategy
Fitting error (8C)
Prediction error (8C)
½ hour fitting, prediction and ½ hour repetition 1 hour fitting, prediction and 1 hour repetition 1 hour fitting, 2 hour prediction and 2 hour repetition
0.0008
0.0034
0.0013
0.0099
0.0031
0.0287
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Fig. 15. Zone model fitting and temperature prediction with precise external temperature; (a) ½ hour fitting, ½ hour prediction and ½ hour repetition; (b) 1 hour fitting, 2 hour prediction and 2 hour repetition.
Fig. 14. Zone model fitting and temperature prediction for different fitting and prediction strategies; (a) ½ hour fitting, ½ hour prediction and ½ hour repetition; (b) 1 hour fitting, 1 hour prediction and 1 hour repetition; (c) 1 hour fitting, 2 hour prediction and 2 hour repetition.
From the experimental results, we can see that the model fitting is very good for different fitting times, and the prediction accuracy is strongly dependant on the prediction period. The shorter the prediction time, the more accurate the prediction for the indoor temperature that is achieved. This difference is due to the dynamics of zone environment and external temperature variation. 5.2.2.2. Using precise external temperature. In order to see the effect of inaccurate external temperature predictions on the zone model prediction accuracy, experiments were run using the real external temperature. The results are shown in Fig. 15 for short time prediction (e.g., ½ hour) and long time prediction (e.g., 2 h). By comparing corresponding results in Figs. 14 and 15, we can see that for ½ hour prediction the zone temperature prediction error caused by inaccurate external temperature predictions is much smaller than for the 2 hour predictions.
5.2.2.3. Model fitting and zone temperature prediction for variable supply air set-point data. Supply air set-point function as illustrated in Fig. 3 has constant value at the two ends and variable value in the middle. The experiments above work on constant supply air temperature set-point, e.g. 18 8C, where it was found our proposed model fitting and prediction algorithm works very well. To investigate the algorithm’s adaptability to variable supply air temperature set-points, further experiments were conducted. The data for these experiments was collected between the 11th and 13th of March 2008 as shown in Fig. 16. Each day, the AHU runs between 4:00 am and 5:00 pm, with the supply air set-point varied between 18 8C and 20 8C. Data sample rate is 5 min. Fig. 17 shows the results of different fitting and prediction strategies for such variable set-point data. From the figure, we can see that our algorithm can properly adapt to variable supply air set-points. 6. A Kalman filtering method with delayed feedback To evaluate the performance of our modeling technique, we compare it with a Kalman-filter-based modeling technique. The standard Kalman filter is a recursive filter that estimates the state of a dynamic and often noisy system from a series of incomplete measurements, which are sometimes further degraded by measurement noise. The main mechanism in a Kalman filter is feedback control: the filter iteratively estimates the process state and obtains feedback in the form of measurements. Thus, each iteration comprises two distinct phases prediction and correction.
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Fig. 16. Variable supply air data for the AHU between 11th and 13th of March 2008.
In the prediction phase, the next state of the system is predicted based upon predetermined process equations. This reflects the a priori understanding of the process. The corresponding estimated error covariance matrix is also computed in this phase. Both these estimates are updated when a measurement becomes available at the next time step. The amount of the correction in this update phase is heavily dependent on a factor called the Kalman gain, which is calculated from a model of how the process is measured/ observed, the covariance of the measurement noise, and the estimated error covariance. Unfortunately, the standard Kalman filter is not directly applicable to our zone modeling problem. Our requirement is for a single phase of continuously sliding-forward prediction that lasts a relatively long period, without any injection of feedback measurements at any time during that period. In our application, measurements are only available at the end of each period. Therefore, a key ingredient in the Kalman approach is not accessible. On the other hand, feedback-based correction is definitely necessary. This is because for a dynamic process our a priori knowledge is highly unlikely to be accurate all the time. Therefore, in the complete absence of measurement-based updates, the prediction error is likely to be unacceptable. A possible approach to addressing the dilemma is to take advantage of historical trends in the corrections or updates. Our experiments are based upon such an attempt, albeit a relatively straightforward one. Our system is described by the state vector Tz xn ¼ F sa Although the temperature in the HVAC zone can be rather accurately determined, the measured fan speed is subject to significant noise due to mechanical inaccuracy and latency. In our experiments, the measurement noise is assumed to be 10 times as high as the process noise. The Kalman procedure we employ can be
Fig. 17. Zone model fitting and temperature prediction for different fitting and prediction strategies; (a) ½ hour fitting, ½ hour prediction and ½ hour repetition; (b) 1 hour fitting, 1 hour prediction and 1 hour repetition; (c) 1 hour fitting, 2 hour prediction and 2 hour repetition.
described in two phases in a forward-sliding time window, as follows: 1. For the initial N time intervals, the standard Kalman algorithm is used. The update amount in each iteration is recorded for future use; 2. Starting from the nth interval, and through to the (n + M)th interval, the corrections are no longer based on instant feedback, but instead based on the correction applied at the previous corresponding time instant; 3. The above two phases are repeated as the time window slides forward.
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volatility of wholesale electricity prices and assist constrained networks during summer and winter demand peaks. The proposed method is quite suitable for near-term predictions as required by Australia’s half-hour electricity market cycle. As follow-up work, we are focussing on heat exchanger modeling in order to model the whole HVAC system and provide HVAC power usage predictions. With such predictions, we can properly control energy flows in the entire building and thus holistically optimize HVAC performance, as well as managing its power consumption strategically for the purpose of demand management. References
Fig. 18. Feedback-delayed Kalman prediction of the zone temperature for future time windows of ½ hour (a), 1 h (b) and 2 h (c).
Table 3 Feedback-delayed Kalman prediction of the zone temperature. Time strategy
Prediction Error
½ hour prediction 1 hour prediction 2 hour prediction
0.0043 0.0133 0.0635
Several experiments have been conducted using the constant supply air set-point data as used in Section 5.2.2.1. The results using feedback-delayed Kalman zone temperature prediction for future time windows of ½ h (a), 1 h (b) and 2 h (c) are presented in Fig. 18. Note that in this figure the first N data points are based upon instant feedback as per the standard Kalman filter. The subsequent results are computed using the feedback-delayed algorithm. Error analysis of the feedback-delayed Kalman prediction of the zone temperature is tabulated in Table 3. The rows represent predictions over time windows of ½ h, 1 h, 2 h and 3 h. As in Table 2, the prediction errors are quantified by the MSE. By comparing Tables 2 and 3, we can clearly see that our realtime HVAC zone modeling and temperature prediction algorithm achieves more accurate prediction of zone temperatures compared to the feedback-delayed Kalman filter method. 7. Conclusions This paper has introduced a soft real-time HVAC zone modeling and temperature prediction algorithm using a simple time varying zone model with only a few parameters. The algorithm through real-time learning can adequately adapt to the dynamics of the HVAC zone environment in an efficient manner, dealing with both short-term unexpected changes and relatively long-term accumulated changes. Modeling and prediction results from this work have shown to be promising. The shorter the prediction time, the more accurate the prediction of indoor temperature that can be achieved. Based on this work, we can model and predict zone status, which is a necessary step for managing and controlling HVAC systems as distributed energy resources [20] to reduce the
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