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HVAC system optimization with CO2 concentration control using genetic algorithms
Energy and Buildings 41 (2009) 571–577
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
HVAC system optimization with CO2 concentration control using genetic algorithms Velimir Congradac *, Filip Kulic Faculty of Technical Sciences, Trg D. Obradovic´a 6, 2100 Novi Sad, Serbia
A R T I C L E I N F O
A B S T R A C T
Article history: Received 9 November 2008 Received in revised form 1 December 2008 Accepted 1 December 2008
This study describes the use of genetic algorithms (GAs) for operating standard HVAC systems (HVAC— heating, ventilation and air conditioning) in order to optimize performance, primarily with regard to power saving. Genetic algorithms were introduced as an instrument for solving optimization problems. Analytic optimization procedures are widely used in other fields of engineering, but they are difficult to operate within HVAC systems, because the range of the research is usually too broad, the problems are not linear but rather discontinuous, and they mostly have complex limitations. This is why for this type of system genetic algorithms are used, since they have the qualities of robustness and efficiency that are crucial for finding the optimal solution. A simulation is conducted in order to demonstrate how much power can be saved by using the suggested method of CO2 concentration control in a standard HVAC system. In addition to Matlab Simulink, the suggested method is verified with Energy software. ß 2008 Elsevier B.V. All rights reserved.
Keywords: Genetic algorithm HVAC systems Optimization Control
1. Introduction For the past few years, HVAC systems have been extremely popular in business office buildings where their prime role is to provide convenient working conditions. Convenient working conditions include desirable air temperature, the required amount of oxygen and carbon dioxide, regular circulation of the air in the offices, etc. For satisfying such requirements, it is necessary to implement an efficient and high-quality operating mode for the HVAC system that would not only answer all the demands mentioned, but would take energy efficiency into account as well. This means it is necessary to fulfill all these tasks using as little energy as possible. There are a great number of different methodologies that describe the design of controllers for the exact purpose of operating HVAC systems. One of the possibilities is the use of genetic algorithms, due to their very favorable characteristics and the wide range of problems they cover [23]. Genetic algorithms are very good at finding the optimal solution among the appropriate scope of solutions they search [24]. Genetic algorithms are search algorithms based upon the principles of Darwin’s theory of natural selection. The basic
* Corresponding author. E-mail address: [email protected] (V. Congradac). 0378-7788/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2008.12.004
operations that genetic algorithms utilize are reproduction, hybridization, mutation and selection. Reproduction ensures the continuation of the best individuals, that is to say, the individuals with the highest fitness, from the present to the next generation. Hybridization combines the genes of two parental individuals and produces a completely unique individual. Mutation changes the structure of genes of each individual separately. Using the previous operations, new individuals are being derived upon whom a selection will be conducted with the aim of choosing the best individuals, i.e. the individuals with the best features that will directly be passed into the next generation. The quality of each individual is presented through its fitness function used by the operation of selection. The theory of genetic algorithms and their application to HVAC optimization is presented by Lu et al. [1], Atthajariyakul and Leephakpreeda [2], Huang and Lam [3], Asiedu et al. [4], Chow et al. [5]. 2. Genetic algorithms Genetic algorithms are powerful general purpose stochastic optimization methods which have been inspired by the Darwinian evolution of a population subject to reproduction, crossover the mutations in a selective environment where the fitness survive. GA combines the artificial survival of the fitness with genetic operators abstracted from nature to form a very robust mechanism
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Nomenclature Ade Adr Avp Cbs Cde Cdr Cvp Cwc Fa Fw Fws Pwc Tae Tao Tar Tai Twi Two Tws
command damper external—pneumatic signal command damper return—pneumatic signal command valve position—pneumatic signal command blower speed command damper external command damper return command valve position command water chiller flow rate of air flow rate of water flow rate of water bypassing exchanger power (input) water chiller temperature of air external temperature of air output temperature of air return temperature of air input temperature of water input temperature of water output temperature of water supply
that is suitable for a variety of optimization problems. In mathematical terms the goal of genetic algorithm is to minimize an objection function F(Sk), where Sk is the search candidate (optimal solution), which is kth individual in the population S (where the population is set of possible solutions). The individuals of the population are expressed in a binary string form and the GA then manipulates these strings by using genetic operators (reproduction, crossover, mutation) to obtain improved solutions (where the fittest individual survive), until the optimal solution is obtained [21,22]. It is one of advantages of a GA that is uses stochastic operators instead of deterministic rules to search for a solution. Furthermore, a GA consider many points in the search space simultaneously, not a single point, thus it has a reduced chance of converging to local minimum, in which other algorithms may end up. Genetic algorithms can be used to tune controller parameters or for directly generation of control action. It is necessary to use fitness function that reflect the controller’s ability to reach the set point from a number initial condition cases. 3. Description of HVAC systems and principle of work In Fig. 1, the HVAC system discussed in this paper is symbolically presented. It consists of several functional components described. The system consists of supply tubes through which the outside and the return air are delivered, a mixing box for mixing of these two airs, a cooling coil, a chiller, a three-way valve, a blower, outside and return air dampers, and a one-speed pump which supplies a permanent flow of water through the chiller. The valve and the dampers contain pneumatic propelling elements that, according to the operating signals, bring them to the required position. Previously, electric operating signals are converted into pneumatic signals. Also, there is an air filter in the system which is used for purifying the air from particulates. Depending on the position of the openings of the dampers, operated by the commanding signal Cdr, suitable amounts of outside and return air are let through. The outside air is fresh air that comes into a building from its surroundings and the return air is the air that has already been in the room inside of the building.
The decision as to how much outside and return air will be inserted into the mixing box, i.e. the positions of the dampers, is made according to the temperatures of both airs mentioned, and the concentration of CO2 in the outside and return air. The dampers are mechanically connected, thus, a single signal is used for operating them, the previously mentioned Cdr. When these two airs pass into the mixing box, in this way being mixed into one new air, they pass over the cooling coil, through which cold water flows from the chiller. Since this is the case of cooling, the air that goes over the cooling coil loses its thermal energy and its temperature decreases. Thermal energy from the air is transferred to the cold water that goes through the cooling coil and its temperature increases. This water is recirculated into the chiller where it is subsequently cooled. The degree of air-cooling is adjusted by using the three-way valve. This valve is operated by the commanding signal Cvp. If it is necessary to intensify the air-cooling, the valve will open to allow a greater amount of cold water to pass through the cooling coil and a smaller amount of cold water will bypass the cooling coil. This means that the chiller will use more energy to cool the water that is coming from the cooling coil. In other words, Cvp will rise to a higher value than in the case where the temperature of the air that comes into the zone is closer to the required value, i.e. when it is necessary to allow less water through the cooling coil and thus cool the air with much less intensity. In the latter case, less water goes through the cooling coil and more through the bypass, consequently the chiller uses less energy to cool the water that recirculates into it. This simply happens because the temperature of the water that passes through the cooling coil does not rise much and then there is no need for greater cooling of that water when it comes back into the chiller. The Cvp signal is of a lower value in this case. The blower is used for providing the supply of the appropriate amount of air into the rooms. It always works at a constant speed that is set in response to the Cbs signal. 4. Model of HVAC systems On the modeling of HVAC systems, steady-state models have been largely presented such as in Knabe and Le [6], Hensen [7], Chow et al. [8], Bourdouxhe and Andre´ [9], Lam et al. [10], Cui et al. [11]. On the other hand, unsteady-state mathematical models have been presented by Novak et al. [12] and Barbosa and Mendes [13]. The mathematical model of the HVAC system used in this paper, with its functional scheme given in Fig. 1, is completely realized in Matlab’s tool ‘Simulink’ (Anderson et al. [14]). Fig. 2 shows a Simulink model of an HVAC system with all its functional components mentioned in the description of the system as a whole. There, all connections established between the individual blocks, entrances and exits of the blocks, as well as entrances and exits of the very model, can be observed. The Matlab tool, ‘gatool’, represents a graphic interface that enables a simpler and faster utilization of genetic algorithms, as well as easier setting of parameters. This tool uses as its input a function whose behaviour it tries to optimize. As the criterion of optimization it takes the output signals from the model (CO2 and Cvp) into account, and as a result of a genetic algorithm, the value of the operating signal (Cdr) that operates the dampers is derived Eq. (1): I¼
X
Cv2p þ K
X
ðCO2 CO2
desired Þ
2
(1)
The genetic algorithm strives to achieve the optimal value of the Cdr such that the lowest value of the Cvp (the lowest energetic use) can be accomplished and at the same time provide that the concentration of CO2 is as close to the required value as it can be.
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Table 1 Values of initial parameters of model.
Fig. 1. HVAC system.
5. Simulation results using Matlab Simulink The simulation was conducted in such manner that all the input parameters into the simulink model were redefined and returned into that model, while only for the input of Cdr such values are used that would entirely open the outer air damper (case 1), or values were used that were derived through a previous calculation by means of a genetic algorithm (cases 2, 3 and 4). For that reason, for the purpose of the simulation, the following values are set at the initiation of the model: (Table 1). The operating signal of the blower rotation speed and the operating signal of the chiller are set to constant values. In order to
Title
Description
Temperatere of air external Temperature of air return Concentration of CO2 (external air) Concentration of CO2 (return air)
36 8C 24 8C 300 ppm 300–1000 ppm
perceive the difference in operating and energy saving, several simulations are conducted, using different parameters. First of all, there is an illustration of how the system behaves when the outer air damper is completely opened, that is, when the return air damper is completely closed. This means that here the genetic algorithm is not used as an ‘intelligent operating’ algorithm. Therefore, only the outer air is allowed to pass (at a temperature of 368 C and a CO2 concentration of 300 ppm), so in this case, there is no energy saving since the chiller cools the maximal amount of water continuously, which is necessary in order to achieve the required air temperature. In the next three cases, however, genetic algorithms are used as algorithms for intelligent operating, and as their results they give the values of the Cdr signal. This signal operates the position of outer and return dampers, that is, it brings these into the appropriate positions so that the required power saving can be achieved, in addition to satisfying the defined criterion of optimization. The result is air produced by mixing of the two previously mentioned airs Eq. (2), with a lower temperature than outside air, which means that it is necessary to use less energy to bring the temperature of the air being cooled to the required value. CO2i ¼ CO2r jC dr j þ CO2e jC dr þ 1j
(2)
The Cvp signal value is presented in Fig. 3. While observing this signal, the energetic efficiency attained by using the genetic algorithms for operating can be noted indirectly, as opposed to the case without their use. The Cvp1 signal (the blue signal) in this picture is the operating signal obtained without the use of genetic algorithms. The Cvp2 (the
Fig. 2. Simulink model of HVAC system.
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Fig. 3. Comparative draft of operating signals Cvp1, Cvp2, Cvp3 i Cvp4.
Fig. 4. Comparative draft of flow signals Fw1, Fw2, Fw3 i Fw4.
red signal) is the operating signal obtained by means of genetic algorithms, in the case where the desired carbon dioxide concentration value was set to 800 ppm. The lower value of this signal in comparison with the Cvp1 indicates a less opened valve, that is, a lessened flow of cold water through the valve, which directly indicates the lowered energetic needs of the chiller which uses energy for cooling the water. Hence, the conclusion is that by using Cvp2, a higher energetic efficiency could be achieved than by using the Cvp1 signal. Similarly, the Cvp3 (the green signal) in Fig. 3 is a signal obtained using a genetic algorithm as well, but here the desired concentration value was set to 600 ppm. In this case, it can be noted that a power saving is still present, if instead of the Cvp1 signal, Cvp3 is used, but the savings is reduced relative to the case when Cvp2 is used. The last, yellow signal in the picture is the Cvp4 which is obtained by using genetic algorithms, with the desired carbon dioxide concentration value set to 400 ppm. In this case, power saving is still present, since the Cvp4 signal value is lower than the Cvp1 signal value, which was obtained without the use of genetic algorithms for operating. This energy saving is, however, the least in comparison with the previous cases and the Cvp2 i Cvp3 signals, which is also logical, keeping in mind the chosen carbon dioxide concentration value. All in all, the main conclusion from examining the signals presented in Fig. 3 is that by using genetic algorithms an optimized valve operating brings about some energy saving. Fig. 4 shows a draft of the signals for cold water flow through the cooling coil that was conducted by applying the previously described Cvp1, Cvp2, Cvp3 i Cvp4 signals to the three-way valve. The blue signal in Fig. 4 (Fw1) indicates the flow without the use of genetic algorithms. The red signal (Fw2) indicates flow with the use of genetic algorithms, as the Cvp2 signal from Fig. 3 is used as the signal that operates the opening of the valve. The green signal in Fig. 4 (Fw3) also indicates the flow through the cooling coil, but with the Cvp3 signal as the operating signal. And finally, the yellow signal in this figure indicates the flow through the cooling coil (Fw4) with the Cvp4 signal. It is obvious that Fw1 has a higher value in comparison with the Fw2, Fw3 i Fw4 flow rates, separately, which means that without the use of a genetic algorithm, there is an increased flow of cold water through the cooling coil. This directly implies that in the case of the Fw1 signal much more energy is needed for cooling the water in the chiller than in the cases of the Fw2, Fw3 or Fw4 signals, providing additional support for the conclusion that application of genetic algorithms to the operation of HVAC systems accomplishes greater power savings than in the cases when these are not used.
Based on the given results, it shows that there is more saving in case of the use of the Cvp2 signal (CO2desired = 800 ppm), than in the case of the Cvp3 signal (CO2desired = 600 ppm) or the Cvp4 signal (CO2desired = 400 ppm). The reason for this lies in the fact that the desired concentration of carbon dioxide when using the Cvp4 signal is closer to the value of the outside air (300 ppm), so that, more outside air must to be taken in, and consequently more energy for cooling the water in the chiller is required. 6. Result verification using EnergyPlus software EnergyPlus, which is widely accepted as a tool for simulation, enables checking new solutions on real building models in a very simple way. In a similar way, a multi-zone airflow model was confirmed by Huang et al. [15], building heat balance by Strand et al. [16] and other simulations by Fisher et al. [17], Brent and Ellis [18], Strand and Baumgartner [19], Zhou et al. [20]. Based on previously mentioned models, a detailed model of a business building in Belgrade (Fig. 5) was analyzed using the EnergyPlus software to confirm levels of energy savings using genetic algorithms at different CO2 levels. The previous section presented values of three-way valve signals, which have indirectly demonstrated affects on energy costs. The genetic algorithm gives values of the external air damper position (the dampers are mechanically connected, the greater opening of one results in closing of the other).
Fig. 5. Office building in Belgrade.
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Table 2 Damper position for external air [%].
Fig. 6. Damper position for external air.
The model created in EnergyPlus simulates a summer working day between 8 a.m. and 5 p.m. The temperature of the water of chiller is 7 8C with constant flow of water using a single-speed pump. The parameters of the position of dampers were entered according to standards (which are used in reality, but without genetic algorithm), i.e. the position when the dampers of the external air are maximally opened (100% outside air with a CO2 concentration of 300 ppm). Then, in different simulations, values of dampers that result from application of genetic algorithms for 400, 600 and 800 ppm as desired concentration of CO2 were entered. Parameters were entered every 10 min, but here, they are presented every 30 min for clarity. EnergyPlus enables adjustment of time intervals in the report of results. Fig. 6 shows the values of the openness of the dampers for external air (expressed in percentage, Table 2), in the case without genetic algorithm and the other three cases when the genetic algorithm was used for different values for the desired carbon dioxide concentration. This figure indirectly shows the openness of return air because dampers are mechanically connected. For example, if the damper for passing external air is opened 60%, the damper for return air will be opened 40%. Fig. 6 shows that carbon dioxide concentration in a room is higher and consequently the openness of the dampers for the external air is less, which is of course logical. Less openness of the dampers for the external air means that return air which was cooled down is used more. This air is cooler than external air so we need less energy for cooling because its temperature is closer to the desired temperature value inside the zones. Fig. 7 shows the following temperatures (Fig. 7 is a case when the carbon dioxide concentration is 800 ppm): External temperature. The temperature of the air that was in the zones (return air).
Time
CO2 400 ppm
CO2 600 ppm
CO2 800 ppm
8:00:00 8:30:00 9:00:00 9:30:00 10:00:00 10:30:00 11:00:00 11:30:00 12:00:00 12:30:00 13:00:00 13:30:00 14:00:00 14:30:00 15:00:00 15:30:00 16:00:00 16:30:00 17:00:00
63 64 91 0 0 90 0 86 100 91 85 92 0 0 87 87 64 38 100
1 61 27 62 63 55 63 54 51 51 58 39 69 61 56 72 100 8 75
18 13 15 34 17 51 37 34 1 100 28 20 14 20 28 46 100 1 26
Average openness
59.89
54
31.73
The temperature when external temperature and the temperature of the air that was in the zones are mixed (exit from mixing box). In Figs. 7 and 8 one can see that the air mixes according to rule, i.e. the temperature which leaves mixing box and goes through the cooling coil is closer to the temperature of the outside air with more open dampers. This is most obvious at 12:30 when the dampers for external air are 100% opened. Then the temperature of the mixed air is completely the same as the temperature of the outside air.
Fig. 8. Values of damper positions obtained using the genetic algorithm where the desired value of CO2 is 800 ppm.
Fig. 7. Temperatures of external, return and mixed air.
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In the last chapter when the savings were counted, a daily flow of coolant through the cooling coil was examined and it was expressed in monetary units. The percentage of the savings is the same as found in EnergyPlus. EnergyPlus can both simulate the costs of all components of the system and it can show the savings of energy of chiller. 7. Conclusion
Fig. 9. Chiller consumption.
Finally, we come to the energy costs of chiller. From the very beginning, the aim was to save energy of HVAC system using genetic algorithm. Fig. 9 shows the energy costs of chiller. As expected, in prototypical case where the optimization algorithm is not used, the costs are the greatest. In the case where the genetic algorithm is used costs decrease, again as expected. Table 3 shows the chiller energy consumption during one working day with minimal, maximal, average and summary consumption for different carbon dioxide concentration. In comparison to the costs when the genetic algorithm is not used, we have the following savings (in a period between 8 a.m. and 5 p.m.) (Table 4).
Table 3 Chiller consumption [kWh]. Time
CO2 300 ppm
CO2 400 ppm
CO2 600 ppm
CO2 800 ppm
8:00:00 8:30:00 9:00:00 9:30:00 10:00:00 10:30:00 11:00:00 11:30:00 12:00:00 12:30:00 13:00:00 13:30:00 14:00:00 14:30:00 15:00:00 15:30:00 16:00:00 16:30:00 17:00:00 Minimal consumption Maximal consumption Average consumption Summary consumption
17430.99 18986.44 21025.96 22561.42 24084.49 24934.5 25781.41 29835.89 35924.84 31311.15 27796.32 28015.91 28044.8 26726.03 25249.38 24274.78 23246.62 22040.9 20772.99 17.430 35.924 25.160 478.044
18.030 19.050 20.786 19.197 19.295 23.657 19.285 23.843 24.637 24.697 24.888 25.892 19.331 18.700 24.793 25.599 23.998 21.675 25.772 18.030 25.892 22.270 423.135
18.166 18.126 18.640 20.367 21.453 21.526 22.476 23.916 25.935 24.217 23.149 22.097 24.115 22.882 21.679 21.754 22.378 18.119 19.261 18.119 25.935 21.592 410.261
17.602 17.815 18.090 19.227 19.076 20.751 20.459 21.534 19.268 28.167 20.492 20.088 19.483 19.161 18.975 19.354 21.344 17.011 17.008 17.008 28.167 19.732 374.914
Table 4 Gained savings of chiller and cooling coil. Carbon dioxide concentration [ppm]
Cost savings for chiller [%]
Reduced flow of water through cooling coil [%]
400 600 800
11 14 21
38 72 83
If we accept, for example, that 1 m3 of cold water cooled by our chiller costs 0.5 euro (s), then recalculating the total daily flow (from 08.00 a.m. to 05.00 p.m. during 1 day) in all four cases, we get a daily sum (calculated in euros) that is necessary to cover the expense for cooling the water with the chiller. In the case where the genetic algorithm is not applied, 14.25 m3 of cold water flows through the cooling coil. In that case the price of cooling is 7.12s on a daily basis. The flow of cold water through the cooling coil using the Cvp2 signal amounts to 2.52 m3, so it costs 1.29s. The flow of cold water through the cooling coil using the Cvp3 signal amounts to 5.18 m3, so the price is 2.59s. The flow of the cold water through the cooling coil using the Cvp4 signal amounts to 11.34 m3, the price of it being 5.67s. According to the displayed results, saving can be calculated in terms of money. We come to conclusion that the savings should not be disregarded. Application of values that one obtains by using the genetic algorithm in Matlab and in EnergyPlus model building gave us expected results in energy and cost savings. References [1] L. Lu, W. Cai, L. Xie, S. Li, Y.C. Soh, HVAC system optimisation—in-building section, Energy and Buildings (2005). [2] S. Atthajariyakul, T. Leephakpreeda, Neural computing thermal comfort index for HVAC systems, Energy Conversion and Management 46 (2005) 2553–2565. [3] W. Huang, H.N. Lam, Using genetic algorithms to optimize controller parameters for HVAC systems, Energy and Buildings 26 (1997) 277–282. [4] Y. Asiedu, R.W. Besant, P. Gu, HVAC duct system design using genetic algorithms, HVAC&R Research 6 (2) (2000) 149–173. [5] T.T. Chow, Q.G. Zhang, Z. Lin, C.L. Song, Global optimization of absorption chiller system by genetic algorithm and neural network, Energy and Buildings 34 (2002) 103–109. [6] G. Knabe, H. Le, Building simulation by application of a HVAC system considering the thermal and moisture behaviors of the perimeter walls, in: Proceedings of the International Conference on Building Performance Simulation (IBPSA0 01), vol. 1, Rio de Janeiro, Brazil, (2001), pp. 965–972. [7] J.L.M. Hensen, On the thermal interaction of building structure and heating and ventilating system, PhD Thesis, Eindhoven University of Technology, 1991. [8] T.T. Chow, J.A. Clarke, A. Dunn, Primitive parts: an approach to air-conditioning component modeling, Energy and Buildings 26 (1997) 165–173. [9] J.P. Bourdouxhe, P. Andre´, Simulation of a centralized cooling plant under different control strategies, in: Proceedings of the International Conference on Building Performance Simulation (IBPSA0 97), vol. 1, Prague, Czech Republic, (1997), pp. 95–102. [10] C.L. Lam, S.C.M. Hui, A.L.S. Chan, Regression analysis of high-rise fully air-conditioned office buildings, Energy and Buildings 26 (1997) 189–197. [11] J. Cui, T. Watanabe, Y. Ryu, Y. Akashi, N. Nishiyama, Numerical simulation on simultaneous control process of indoor air temperature and humidity, in: Proceedings of the International Conference on Building Performance Simulation (IBPSA0 99), vol. 2, Kyoto, Japan, (1999), p. 1012. [12] P.R. Novak, N. Mendes, G.H.C. Oliveira, Simulation and analysis of a secondary HVAC system using MATLAB/SIMULINK platform, in: Proceedings of the International Mechanical Engineering Congress, USA, 2004. [13] R.M. Barbosa, N. Mendes, Dynamic simulation of fan-coil systems, in: Proceedings of the 17th International Congress of Mechanical Engineering, COBEM’2003, Sa˜o Paulo, Brazil, November, 2003. [14] M. Anderson, M. Buehner, P. Young, D. Hittle, C. Anderson, J. Tu, D. Hodgson, An experimental system for advanced heating, ventilating and air conditioning (HVAC) control, Energy and Buildings 39 (2007) 136–147. [15] Y.J. Huang, F.C. Winkelmann, W.F. Buhl, C.O. Pedersen, D.E. Fisher, R.J. Liesen, R. Taylor, R.K. Strand, D.B. Crawley, L.K. Lawrie, Linking the COMIS multi-zone airflow model with the EnergyPlus building energy simulation program, in: Proceedings of Building Simulation’99, IBPSA, vol. II, Kyoto, Japan, September, (1999), pp. 1065–1070. [16] R. Strand, F. Winkelmann, F. Buhl, J. Huang, R. Liesen, C. Pedersen, D. Fisher, R. Taylor, D. Crawley, L. Lawrie, Enhancing and extending the capabilities of the building heat balance simulation technique for use in EnergyPlus, in: Proceedings of Building Simulation’99, IBPSA, vol. II, Kyoto, Japan, September, (1999), pp. 653–660.
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Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
HVAC system optimization with CO2 concentration control using genetic algorithms Velimir Congradac *, Filip Kulic Faculty of Technical Sciences, Trg D. Obradovic´a 6, 2100 Novi Sad, Serbia
A R T I C L E I N F O
A B S T R A C T
Article history: Received 9 November 2008 Received in revised form 1 December 2008 Accepted 1 December 2008
This study describes the use of genetic algorithms (GAs) for operating standard HVAC systems (HVAC— heating, ventilation and air conditioning) in order to optimize performance, primarily with regard to power saving. Genetic algorithms were introduced as an instrument for solving optimization problems. Analytic optimization procedures are widely used in other fields of engineering, but they are difficult to operate within HVAC systems, because the range of the research is usually too broad, the problems are not linear but rather discontinuous, and they mostly have complex limitations. This is why for this type of system genetic algorithms are used, since they have the qualities of robustness and efficiency that are crucial for finding the optimal solution. A simulation is conducted in order to demonstrate how much power can be saved by using the suggested method of CO2 concentration control in a standard HVAC system. In addition to Matlab Simulink, the suggested method is verified with Energy software. ß 2008 Elsevier B.V. All rights reserved.
Keywords: Genetic algorithm HVAC systems Optimization Control
1. Introduction For the past few years, HVAC systems have been extremely popular in business office buildings where their prime role is to provide convenient working conditions. Convenient working conditions include desirable air temperature, the required amount of oxygen and carbon dioxide, regular circulation of the air in the offices, etc. For satisfying such requirements, it is necessary to implement an efficient and high-quality operating mode for the HVAC system that would not only answer all the demands mentioned, but would take energy efficiency into account as well. This means it is necessary to fulfill all these tasks using as little energy as possible. There are a great number of different methodologies that describe the design of controllers for the exact purpose of operating HVAC systems. One of the possibilities is the use of genetic algorithms, due to their very favorable characteristics and the wide range of problems they cover [23]. Genetic algorithms are very good at finding the optimal solution among the appropriate scope of solutions they search [24]. Genetic algorithms are search algorithms based upon the principles of Darwin’s theory of natural selection. The basic
* Corresponding author. E-mail address: [email protected] (V. Congradac). 0378-7788/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2008.12.004
operations that genetic algorithms utilize are reproduction, hybridization, mutation and selection. Reproduction ensures the continuation of the best individuals, that is to say, the individuals with the highest fitness, from the present to the next generation. Hybridization combines the genes of two parental individuals and produces a completely unique individual. Mutation changes the structure of genes of each individual separately. Using the previous operations, new individuals are being derived upon whom a selection will be conducted with the aim of choosing the best individuals, i.e. the individuals with the best features that will directly be passed into the next generation. The quality of each individual is presented through its fitness function used by the operation of selection. The theory of genetic algorithms and their application to HVAC optimization is presented by Lu et al. [1], Atthajariyakul and Leephakpreeda [2], Huang and Lam [3], Asiedu et al. [4], Chow et al. [5]. 2. Genetic algorithms Genetic algorithms are powerful general purpose stochastic optimization methods which have been inspired by the Darwinian evolution of a population subject to reproduction, crossover the mutations in a selective environment where the fitness survive. GA combines the artificial survival of the fitness with genetic operators abstracted from nature to form a very robust mechanism
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Nomenclature Ade Adr Avp Cbs Cde Cdr Cvp Cwc Fa Fw Fws Pwc Tae Tao Tar Tai Twi Two Tws
command damper external—pneumatic signal command damper return—pneumatic signal command valve position—pneumatic signal command blower speed command damper external command damper return command valve position command water chiller flow rate of air flow rate of water flow rate of water bypassing exchanger power (input) water chiller temperature of air external temperature of air output temperature of air return temperature of air input temperature of water input temperature of water output temperature of water supply
that is suitable for a variety of optimization problems. In mathematical terms the goal of genetic algorithm is to minimize an objection function F(Sk), where Sk is the search candidate (optimal solution), which is kth individual in the population S (where the population is set of possible solutions). The individuals of the population are expressed in a binary string form and the GA then manipulates these strings by using genetic operators (reproduction, crossover, mutation) to obtain improved solutions (where the fittest individual survive), until the optimal solution is obtained [21,22]. It is one of advantages of a GA that is uses stochastic operators instead of deterministic rules to search for a solution. Furthermore, a GA consider many points in the search space simultaneously, not a single point, thus it has a reduced chance of converging to local minimum, in which other algorithms may end up. Genetic algorithms can be used to tune controller parameters or for directly generation of control action. It is necessary to use fitness function that reflect the controller’s ability to reach the set point from a number initial condition cases. 3. Description of HVAC systems and principle of work In Fig. 1, the HVAC system discussed in this paper is symbolically presented. It consists of several functional components described. The system consists of supply tubes through which the outside and the return air are delivered, a mixing box for mixing of these two airs, a cooling coil, a chiller, a three-way valve, a blower, outside and return air dampers, and a one-speed pump which supplies a permanent flow of water through the chiller. The valve and the dampers contain pneumatic propelling elements that, according to the operating signals, bring them to the required position. Previously, electric operating signals are converted into pneumatic signals. Also, there is an air filter in the system which is used for purifying the air from particulates. Depending on the position of the openings of the dampers, operated by the commanding signal Cdr, suitable amounts of outside and return air are let through. The outside air is fresh air that comes into a building from its surroundings and the return air is the air that has already been in the room inside of the building.
The decision as to how much outside and return air will be inserted into the mixing box, i.e. the positions of the dampers, is made according to the temperatures of both airs mentioned, and the concentration of CO2 in the outside and return air. The dampers are mechanically connected, thus, a single signal is used for operating them, the previously mentioned Cdr. When these two airs pass into the mixing box, in this way being mixed into one new air, they pass over the cooling coil, through which cold water flows from the chiller. Since this is the case of cooling, the air that goes over the cooling coil loses its thermal energy and its temperature decreases. Thermal energy from the air is transferred to the cold water that goes through the cooling coil and its temperature increases. This water is recirculated into the chiller where it is subsequently cooled. The degree of air-cooling is adjusted by using the three-way valve. This valve is operated by the commanding signal Cvp. If it is necessary to intensify the air-cooling, the valve will open to allow a greater amount of cold water to pass through the cooling coil and a smaller amount of cold water will bypass the cooling coil. This means that the chiller will use more energy to cool the water that is coming from the cooling coil. In other words, Cvp will rise to a higher value than in the case where the temperature of the air that comes into the zone is closer to the required value, i.e. when it is necessary to allow less water through the cooling coil and thus cool the air with much less intensity. In the latter case, less water goes through the cooling coil and more through the bypass, consequently the chiller uses less energy to cool the water that recirculates into it. This simply happens because the temperature of the water that passes through the cooling coil does not rise much and then there is no need for greater cooling of that water when it comes back into the chiller. The Cvp signal is of a lower value in this case. The blower is used for providing the supply of the appropriate amount of air into the rooms. It always works at a constant speed that is set in response to the Cbs signal. 4. Model of HVAC systems On the modeling of HVAC systems, steady-state models have been largely presented such as in Knabe and Le [6], Hensen [7], Chow et al. [8], Bourdouxhe and Andre´ [9], Lam et al. [10], Cui et al. [11]. On the other hand, unsteady-state mathematical models have been presented by Novak et al. [12] and Barbosa and Mendes [13]. The mathematical model of the HVAC system used in this paper, with its functional scheme given in Fig. 1, is completely realized in Matlab’s tool ‘Simulink’ (Anderson et al. [14]). Fig. 2 shows a Simulink model of an HVAC system with all its functional components mentioned in the description of the system as a whole. There, all connections established between the individual blocks, entrances and exits of the blocks, as well as entrances and exits of the very model, can be observed. The Matlab tool, ‘gatool’, represents a graphic interface that enables a simpler and faster utilization of genetic algorithms, as well as easier setting of parameters. This tool uses as its input a function whose behaviour it tries to optimize. As the criterion of optimization it takes the output signals from the model (CO2 and Cvp) into account, and as a result of a genetic algorithm, the value of the operating signal (Cdr) that operates the dampers is derived Eq. (1): I¼
X
Cv2p þ K
X
ðCO2 CO2
desired Þ
2
(1)
The genetic algorithm strives to achieve the optimal value of the Cdr such that the lowest value of the Cvp (the lowest energetic use) can be accomplished and at the same time provide that the concentration of CO2 is as close to the required value as it can be.
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Table 1 Values of initial parameters of model.
Fig. 1. HVAC system.
5. Simulation results using Matlab Simulink The simulation was conducted in such manner that all the input parameters into the simulink model were redefined and returned into that model, while only for the input of Cdr such values are used that would entirely open the outer air damper (case 1), or values were used that were derived through a previous calculation by means of a genetic algorithm (cases 2, 3 and 4). For that reason, for the purpose of the simulation, the following values are set at the initiation of the model: (Table 1). The operating signal of the blower rotation speed and the operating signal of the chiller are set to constant values. In order to
Title
Description
Temperatere of air external Temperature of air return Concentration of CO2 (external air) Concentration of CO2 (return air)
36 8C 24 8C 300 ppm 300–1000 ppm
perceive the difference in operating and energy saving, several simulations are conducted, using different parameters. First of all, there is an illustration of how the system behaves when the outer air damper is completely opened, that is, when the return air damper is completely closed. This means that here the genetic algorithm is not used as an ‘intelligent operating’ algorithm. Therefore, only the outer air is allowed to pass (at a temperature of 368 C and a CO2 concentration of 300 ppm), so in this case, there is no energy saving since the chiller cools the maximal amount of water continuously, which is necessary in order to achieve the required air temperature. In the next three cases, however, genetic algorithms are used as algorithms for intelligent operating, and as their results they give the values of the Cdr signal. This signal operates the position of outer and return dampers, that is, it brings these into the appropriate positions so that the required power saving can be achieved, in addition to satisfying the defined criterion of optimization. The result is air produced by mixing of the two previously mentioned airs Eq. (2), with a lower temperature than outside air, which means that it is necessary to use less energy to bring the temperature of the air being cooled to the required value. CO2i ¼ CO2r jC dr j þ CO2e jC dr þ 1j
(2)
The Cvp signal value is presented in Fig. 3. While observing this signal, the energetic efficiency attained by using the genetic algorithms for operating can be noted indirectly, as opposed to the case without their use. The Cvp1 signal (the blue signal) in this picture is the operating signal obtained without the use of genetic algorithms. The Cvp2 (the
Fig. 2. Simulink model of HVAC system.
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Fig. 3. Comparative draft of operating signals Cvp1, Cvp2, Cvp3 i Cvp4.
Fig. 4. Comparative draft of flow signals Fw1, Fw2, Fw3 i Fw4.
red signal) is the operating signal obtained by means of genetic algorithms, in the case where the desired carbon dioxide concentration value was set to 800 ppm. The lower value of this signal in comparison with the Cvp1 indicates a less opened valve, that is, a lessened flow of cold water through the valve, which directly indicates the lowered energetic needs of the chiller which uses energy for cooling the water. Hence, the conclusion is that by using Cvp2, a higher energetic efficiency could be achieved than by using the Cvp1 signal. Similarly, the Cvp3 (the green signal) in Fig. 3 is a signal obtained using a genetic algorithm as well, but here the desired concentration value was set to 600 ppm. In this case, it can be noted that a power saving is still present, if instead of the Cvp1 signal, Cvp3 is used, but the savings is reduced relative to the case when Cvp2 is used. The last, yellow signal in the picture is the Cvp4 which is obtained by using genetic algorithms, with the desired carbon dioxide concentration value set to 400 ppm. In this case, power saving is still present, since the Cvp4 signal value is lower than the Cvp1 signal value, which was obtained without the use of genetic algorithms for operating. This energy saving is, however, the least in comparison with the previous cases and the Cvp2 i Cvp3 signals, which is also logical, keeping in mind the chosen carbon dioxide concentration value. All in all, the main conclusion from examining the signals presented in Fig. 3 is that by using genetic algorithms an optimized valve operating brings about some energy saving. Fig. 4 shows a draft of the signals for cold water flow through the cooling coil that was conducted by applying the previously described Cvp1, Cvp2, Cvp3 i Cvp4 signals to the three-way valve. The blue signal in Fig. 4 (Fw1) indicates the flow without the use of genetic algorithms. The red signal (Fw2) indicates flow with the use of genetic algorithms, as the Cvp2 signal from Fig. 3 is used as the signal that operates the opening of the valve. The green signal in Fig. 4 (Fw3) also indicates the flow through the cooling coil, but with the Cvp3 signal as the operating signal. And finally, the yellow signal in this figure indicates the flow through the cooling coil (Fw4) with the Cvp4 signal. It is obvious that Fw1 has a higher value in comparison with the Fw2, Fw3 i Fw4 flow rates, separately, which means that without the use of a genetic algorithm, there is an increased flow of cold water through the cooling coil. This directly implies that in the case of the Fw1 signal much more energy is needed for cooling the water in the chiller than in the cases of the Fw2, Fw3 or Fw4 signals, providing additional support for the conclusion that application of genetic algorithms to the operation of HVAC systems accomplishes greater power savings than in the cases when these are not used.
Based on the given results, it shows that there is more saving in case of the use of the Cvp2 signal (CO2desired = 800 ppm), than in the case of the Cvp3 signal (CO2desired = 600 ppm) or the Cvp4 signal (CO2desired = 400 ppm). The reason for this lies in the fact that the desired concentration of carbon dioxide when using the Cvp4 signal is closer to the value of the outside air (300 ppm), so that, more outside air must to be taken in, and consequently more energy for cooling the water in the chiller is required. 6. Result verification using EnergyPlus software EnergyPlus, which is widely accepted as a tool for simulation, enables checking new solutions on real building models in a very simple way. In a similar way, a multi-zone airflow model was confirmed by Huang et al. [15], building heat balance by Strand et al. [16] and other simulations by Fisher et al. [17], Brent and Ellis [18], Strand and Baumgartner [19], Zhou et al. [20]. Based on previously mentioned models, a detailed model of a business building in Belgrade (Fig. 5) was analyzed using the EnergyPlus software to confirm levels of energy savings using genetic algorithms at different CO2 levels. The previous section presented values of three-way valve signals, which have indirectly demonstrated affects on energy costs. The genetic algorithm gives values of the external air damper position (the dampers are mechanically connected, the greater opening of one results in closing of the other).
Fig. 5. Office building in Belgrade.
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Table 2 Damper position for external air [%].
Fig. 6. Damper position for external air.
The model created in EnergyPlus simulates a summer working day between 8 a.m. and 5 p.m. The temperature of the water of chiller is 7 8C with constant flow of water using a single-speed pump. The parameters of the position of dampers were entered according to standards (which are used in reality, but without genetic algorithm), i.e. the position when the dampers of the external air are maximally opened (100% outside air with a CO2 concentration of 300 ppm). Then, in different simulations, values of dampers that result from application of genetic algorithms for 400, 600 and 800 ppm as desired concentration of CO2 were entered. Parameters were entered every 10 min, but here, they are presented every 30 min for clarity. EnergyPlus enables adjustment of time intervals in the report of results. Fig. 6 shows the values of the openness of the dampers for external air (expressed in percentage, Table 2), in the case without genetic algorithm and the other three cases when the genetic algorithm was used for different values for the desired carbon dioxide concentration. This figure indirectly shows the openness of return air because dampers are mechanically connected. For example, if the damper for passing external air is opened 60%, the damper for return air will be opened 40%. Fig. 6 shows that carbon dioxide concentration in a room is higher and consequently the openness of the dampers for the external air is less, which is of course logical. Less openness of the dampers for the external air means that return air which was cooled down is used more. This air is cooler than external air so we need less energy for cooling because its temperature is closer to the desired temperature value inside the zones. Fig. 7 shows the following temperatures (Fig. 7 is a case when the carbon dioxide concentration is 800 ppm): External temperature. The temperature of the air that was in the zones (return air).
Time
CO2 400 ppm
CO2 600 ppm
CO2 800 ppm
8:00:00 8:30:00 9:00:00 9:30:00 10:00:00 10:30:00 11:00:00 11:30:00 12:00:00 12:30:00 13:00:00 13:30:00 14:00:00 14:30:00 15:00:00 15:30:00 16:00:00 16:30:00 17:00:00
63 64 91 0 0 90 0 86 100 91 85 92 0 0 87 87 64 38 100
1 61 27 62 63 55 63 54 51 51 58 39 69 61 56 72 100 8 75
18 13 15 34 17 51 37 34 1 100 28 20 14 20 28 46 100 1 26
Average openness
59.89
54
31.73
The temperature when external temperature and the temperature of the air that was in the zones are mixed (exit from mixing box). In Figs. 7 and 8 one can see that the air mixes according to rule, i.e. the temperature which leaves mixing box and goes through the cooling coil is closer to the temperature of the outside air with more open dampers. This is most obvious at 12:30 when the dampers for external air are 100% opened. Then the temperature of the mixed air is completely the same as the temperature of the outside air.
Fig. 8. Values of damper positions obtained using the genetic algorithm where the desired value of CO2 is 800 ppm.
Fig. 7. Temperatures of external, return and mixed air.
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In the last chapter when the savings were counted, a daily flow of coolant through the cooling coil was examined and it was expressed in monetary units. The percentage of the savings is the same as found in EnergyPlus. EnergyPlus can both simulate the costs of all components of the system and it can show the savings of energy of chiller. 7. Conclusion
Fig. 9. Chiller consumption.
Finally, we come to the energy costs of chiller. From the very beginning, the aim was to save energy of HVAC system using genetic algorithm. Fig. 9 shows the energy costs of chiller. As expected, in prototypical case where the optimization algorithm is not used, the costs are the greatest. In the case where the genetic algorithm is used costs decrease, again as expected. Table 3 shows the chiller energy consumption during one working day with minimal, maximal, average and summary consumption for different carbon dioxide concentration. In comparison to the costs when the genetic algorithm is not used, we have the following savings (in a period between 8 a.m. and 5 p.m.) (Table 4).
Table 3 Chiller consumption [kWh]. Time
CO2 300 ppm
CO2 400 ppm
CO2 600 ppm
CO2 800 ppm
8:00:00 8:30:00 9:00:00 9:30:00 10:00:00 10:30:00 11:00:00 11:30:00 12:00:00 12:30:00 13:00:00 13:30:00 14:00:00 14:30:00 15:00:00 15:30:00 16:00:00 16:30:00 17:00:00 Minimal consumption Maximal consumption Average consumption Summary consumption
17430.99 18986.44 21025.96 22561.42 24084.49 24934.5 25781.41 29835.89 35924.84 31311.15 27796.32 28015.91 28044.8 26726.03 25249.38 24274.78 23246.62 22040.9 20772.99 17.430 35.924 25.160 478.044
18.030 19.050 20.786 19.197 19.295 23.657 19.285 23.843 24.637 24.697 24.888 25.892 19.331 18.700 24.793 25.599 23.998 21.675 25.772 18.030 25.892 22.270 423.135
18.166 18.126 18.640 20.367 21.453 21.526 22.476 23.916 25.935 24.217 23.149 22.097 24.115 22.882 21.679 21.754 22.378 18.119 19.261 18.119 25.935 21.592 410.261
17.602 17.815 18.090 19.227 19.076 20.751 20.459 21.534 19.268 28.167 20.492 20.088 19.483 19.161 18.975 19.354 21.344 17.011 17.008 17.008 28.167 19.732 374.914
Table 4 Gained savings of chiller and cooling coil. Carbon dioxide concentration [ppm]
Cost savings for chiller [%]
Reduced flow of water through cooling coil [%]
400 600 800
11 14 21
38 72 83
If we accept, for example, that 1 m3 of cold water cooled by our chiller costs 0.5 euro (s), then recalculating the total daily flow (from 08.00 a.m. to 05.00 p.m. during 1 day) in all four cases, we get a daily sum (calculated in euros) that is necessary to cover the expense for cooling the water with the chiller. In the case where the genetic algorithm is not applied, 14.25 m3 of cold water flows through the cooling coil. In that case the price of cooling is 7.12s on a daily basis. The flow of cold water through the cooling coil using the Cvp2 signal amounts to 2.52 m3, so it costs 1.29s. The flow of cold water through the cooling coil using the Cvp3 signal amounts to 5.18 m3, so the price is 2.59s. The flow of the cold water through the cooling coil using the Cvp4 signal amounts to 11.34 m3, the price of it being 5.67s. According to the displayed results, saving can be calculated in terms of money. We come to conclusion that the savings should not be disregarded. Application of values that one obtains by using the genetic algorithm in Matlab and in EnergyPlus model building gave us expected results in energy and cost savings. References [1] L. Lu, W. Cai, L. Xie, S. Li, Y.C. Soh, HVAC system optimisation—in-building section, Energy and Buildings (2005). [2] S. Atthajariyakul, T. Leephakpreeda, Neural computing thermal comfort index for HVAC systems, Energy Conversion and Management 46 (2005) 2553–2565. [3] W. Huang, H.N. Lam, Using genetic algorithms to optimize controller parameters for HVAC systems, Energy and Buildings 26 (1997) 277–282. [4] Y. Asiedu, R.W. Besant, P. Gu, HVAC duct system design using genetic algorithms, HVAC&R Research 6 (2) (2000) 149–173. [5] T.T. Chow, Q.G. Zhang, Z. Lin, C.L. Song, Global optimization of absorption chiller system by genetic algorithm and neural network, Energy and Buildings 34 (2002) 103–109. [6] G. Knabe, H. Le, Building simulation by application of a HVAC system considering the thermal and moisture behaviors of the perimeter walls, in: Proceedings of the International Conference on Building Performance Simulation (IBPSA0 01), vol. 1, Rio de Janeiro, Brazil, (2001), pp. 965–972. [7] J.L.M. Hensen, On the thermal interaction of building structure and heating and ventilating system, PhD Thesis, Eindhoven University of Technology, 1991. [8] T.T. Chow, J.A. Clarke, A. Dunn, Primitive parts: an approach to air-conditioning component modeling, Energy and Buildings 26 (1997) 165–173. [9] J.P. Bourdouxhe, P. Andre´, Simulation of a centralized cooling plant under different control strategies, in: Proceedings of the International Conference on Building Performance Simulation (IBPSA0 97), vol. 1, Prague, Czech Republic, (1997), pp. 95–102. [10] C.L. Lam, S.C.M. Hui, A.L.S. Chan, Regression analysis of high-rise fully air-conditioned office buildings, Energy and Buildings 26 (1997) 189–197. [11] J. Cui, T. Watanabe, Y. Ryu, Y. Akashi, N. Nishiyama, Numerical simulation on simultaneous control process of indoor air temperature and humidity, in: Proceedings of the International Conference on Building Performance Simulation (IBPSA0 99), vol. 2, Kyoto, Japan, (1999), p. 1012. [12] P.R. Novak, N. Mendes, G.H.C. Oliveira, Simulation and analysis of a secondary HVAC system using MATLAB/SIMULINK platform, in: Proceedings of the International Mechanical Engineering Congress, USA, 2004. [13] R.M. Barbosa, N. Mendes, Dynamic simulation of fan-coil systems, in: Proceedings of the 17th International Congress of Mechanical Engineering, COBEM’2003, Sa˜o Paulo, Brazil, November, 2003. [14] M. Anderson, M. Buehner, P. Young, D. Hittle, C. Anderson, J. Tu, D. Hodgson, An experimental system for advanced heating, ventilating and air conditioning (HVAC) control, Energy and Buildings 39 (2007) 136–147. [15] Y.J. Huang, F.C. Winkelmann, W.F. Buhl, C.O. Pedersen, D.E. Fisher, R.J. Liesen, R. Taylor, R.K. Strand, D.B. Crawley, L.K. Lawrie, Linking the COMIS multi-zone airflow model with the EnergyPlus building energy simulation program, in: Proceedings of Building Simulation’99, IBPSA, vol. II, Kyoto, Japan, September, (1999), pp. 1065–1070. [16] R. Strand, F. Winkelmann, F. Buhl, J. Huang, R. Liesen, C. Pedersen, D. Fisher, R. Taylor, D. Crawley, L. Lawrie, Enhancing and extending the capabilities of the building heat balance simulation technique for use in EnergyPlus, in: Proceedings of Building Simulation’99, IBPSA, vol. II, Kyoto, Japan, September, (1999), pp. 653–660.
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