2010 IEEE International Conference on Control Applications Part of 2010 IEEE Multi-Conference on Systems and Control Yokohama, Japan, September 8-10, 2010
Two-Layer Control of Multi-Chiller Systems Alessandro Beghi∗ , Luca Cecchinato† , Giovanni Cosi∗ and Mirco Rampazzo∗ ∗ Dipartimento
di Ingegneria dell’Informazione, Universit`a di Padova Via Gradenigo 6/B, I-35131 Padova, Italy. Email: {beghi, mirco.rampazzo}@dei.unipd.it,
[email protected] † Dipartimento
di Fisica Tecnica, Universit`a di Padova Via Venezia 1, I-35131 Padova, Italy. Email:
[email protected]
Abstract—In HVAC plants of medium-high cooling capacity, multiple chiller systems are often employed. The performance of the system is evaluated in terms of user comfort, energy use, and financial costs. In this paper a two-layer control structure is proposed for control and optimization of a multiple chiller system. Set points and operating modes for cooling plant equipment can be set by the supervisor to maximize overall operating efficiency. At any given time, cooling needs can be met with various combinations of modes of operation and set points. In the proposed control architecture, a cooling load estimation algorithm is employed, and the selection of the optimal set of operation modes and set point values is performed by means of a PSO algorithm. The performance of the two-layer control is evaluated by resorting to a dynamic simulation environment developed in Matlab/Simulink™, where the plant dynamics are accurately described. It is shown that the proposed technique gives superior performance with respect to standard approaches.
I. I NTRODUCTION In HVAC plants of medium-high cooling capacity, multiple chiller systems [1] are often adopted to achieve a satisfactory trade-off between reliability and cost. Multiple chillers are normally used in parallel configuration, where every chiller is independent of each other to provide standby capacity and operational flexibility, while requiring less disruption maintenance. Compared with single-chiller systems, multiplechiller systems have reduced starting in-rush current and a reduced power cost under part load conditions [2]. However, the overall energy performance of a multiple chiller systems is difficult to characterize since it depends on many factors. The capacity regulation and part load efficiency of each chiller (and therefore of the entire system) strongly depend the choice of refrigerating unit, refrigerant circuit design, type and number of compressors, and so on. For instance, multiscroll chillers equipped with twin compressors on the same circuit present high part load Energy Efficiency Ratio values (EER, defined as the ratio of cooling capacity and total power absorption, fans included), whereas screw compressors units are strongly penalized, mainly because of the reduction of screw compressor isentropic efficiency at low cooling loads. Therefore, the problem of optimizing the energy performance of multiple-chiller systems is a complex one. In the HVAC literature methods to perform such optimization on line are presented, but in these approaches the system dynamics are typically ignored [3], [4]. However, it is quite clear that an
978-1-4244-5363-4/10/$26.00 ©2010 IEEE
efficient control algorithm has to be capable of adapting its action in response to the time varying operational ambient conditions and cooling loads. To meet such requirement, in this paper a Two-Layer Control (TLC) structure for control and optimization of a multiple chiller system is proposed, that consists of a local control loop and a supervisory control loop. Proper tuning of the local-loop controller can enhance comfort, reduce energy use, and increase component life. Set points and operating modes for cooling plant equipment can be adjusted by the supervisor to maximize overall operating efficiency. At any given time cooling needs can be met with various combinations of modes of operation and set points for the chilled water temperature. In the proposed TLC structure, a cooling load estimation algorithm is adopted to obtain information on the cooling needs. Once the cooling needs have been estimated, the selection of the optimal set of operation modes and set point values is then performed by means of a Particle Swarm Optimization (PSO) algorithm. The performance of the TLC is evaluated by resorting to a dynamic simulation environment developed in Matlab/Simulink™, where the plant dynamics are accurately described. The results of the simulations indicate that the proposed algorithm gives superior performance with respect to standard approaches (Sequential strategy and Symmetric strategy), in terms of both energy performance and load profile following. The paper is organized as follows. In Section 2, the plant structure of a multi-chiller systems is presented. In Section 3, the problem of efficiently managing multi-chiller systems is detailed. In section 4 the TLC architecture is illustrated. In Section 5, performance of the proposed control algorithm is compared with that of conventional methods through extensive dynamic simulation examples. Conclusions are drawn in Section 6. II. P LANT S TRUCTURE In Fig. 1 the block structure of the system considered in the paper is reported. Three basic blocks can be pointed out:
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1) the energy production section (e.g., a packaged aircooled water chiller); 2) the hydraulic section where a common primarysecondary pumping arrangement is adopted with constant water flow rate on the secondary, thus decoupling the chiller section from the distribution one;
Secondary
Tank
Chiller n
Chiller 2
TSp Tchwr
Low Level Control
Two-Layer Control
Production section
TLin
Cooling Coils
Status on/off
PSO
Chiller 1
Tchws Load Estimation
Cooling Coils
High Level Control
Cooling Coils
Primary
TLout
m˙ c
Load section
Figure 1: plant and Two-Layer Control architecture.
3) the load section: the building thermal load and capacity are represented in the scheme by cooling coils and a water tank of suitable capacity.
•
The thermal behavior of the plant can be usefully analyzed by a lumped formulation of the conservation equations. The elements of the plant are simulated through blocks, and the heat transfer processes are considered as concentrated inside the blocks. As described in details in [5], the system dynamics are governed by the mass and energy conservation laws. The mass and energy equations are implemented as block equations for each component of the plant. Each block is modelled as a thermodynamic open system. The dynamic behavior of the plant is thus obtained by solving the fluid flow problem and the energy problem. The resulting system of non-linear equations obtained for each block is finally integrated in the Matlab/Simulink™ environment through a stiff integrator.
•
III. E FFICENT M ANAGEMENT OF M ULTIPLE C HILLER S YSTEM Significant energy savings can be achieved by optimizing the chiller operation of HVAC systems. In particular, the performance of a system increases if chiller’s EER is maximized while the load is satisfied. The cooling needs can be met with various combinations of modes of operation and chilled water temperature set points for the different chillers, that have different characteristics and capacities. Optimal chiller management (i.e., minimum energy consumption for a given load demand) is therefore achieved by choosing the best combination of chiller operational modes and set points that grants matching of the cooling needs. Specifically, in this paper the chiller operational mode is described in terms of its status (on-line or off-line) and its loading ratio for a given load demand. The supervisory control loop has to determine values for these parameters so that minimum energy consumption is achieved, whereas local control loops are used to maintain the specified set points for the chilled water temperature. The supervisor control task can be described in terms of the socalled Optimal Chiller Loading (OCL) and Optimal Chiller Sequencing (OCS) problems.
OCL Problem: the cooling load is generally expressed as a Partial Load Ratio (PLR), which is the chiller cooling load divided by its designed capacity. The OCL problem consists in finding which is the load fraction that each chiller has to satisfy while minimizing the overall energy consumption. OCS Problem: multiple chillers system are operated by staging the equipment to meet the varying load conditions. The term “sequencing” refers to activating or deactivating chiller units. Hence, the combination of available chillers that maximize the operating system efficiency has to be selected. From a practical standpoint, it is required to avoid large number of switches (chiller activation/deactivation) in order to reduce chiller startup and shutdown times and increase equipment life. The OCS problem consists in determining which of the chillers should be on-line and off-line, while minimizing the input power and satisfying the chiller operational constraints.
A. Problem Formulation In order to minimize the input electric power while satisfying the chiller operational constraints, at each supervision period, the OCL and OCS problems are solved, simultaneously, to determine for each chiller: • • •
the status: on-line or off-line; the fraction of the total cooling load to be supplied; the chilled water outlet set-point temperature.
Multiple chiller optimization is a nonlinear, constrained, combinatorial optimization with both continuous and discrete variables, and as such, it is a challenge to standard optimization methods. On a given ∆τ time interval, the problem can be formulated as follows: Find
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arg min (P LRi, statusi )
subject to:
X i
Pe,i ,
(1)
Pc,i = PˆL ,
(2)
i
P LRi − P LRiprev ≦ κi ,
i = 1, ..., n .
(3)
In (1) and (2), Pe,i and Pc,i are the i−th chiller power consumption and cooling capacity, respectively. PˆL is the estimated cooling demand on ∆τ and P LRi is the i-th chiller cooling load divided by its nominal design capacity. The constraint specified in (3) is introduced to avoid large variations of the cooling load attributed to a single chiller between two successive supervision steps (P LRi and P LRiprev , respectively), thus reducing the need of actuating the unit and, consequently, the mechanical stress. To solve the optimization problem, an evaluation of how operating in part load conditions affects the chiller energy performance is required. In the hypothesis of using air condensed chillers, the electric power consumption and the cooling power, at full load conditions, are expressed as a function of return water temperature, external air temperature, and water mass flow rate. For the i−th chiller, the part load operation influence is taken into account by multiplying the full load energy consumption by a part load factor Z [6], calculated as a function of P LR and air temperature, and by multiplying the full cooling capacity by P LR.
There are three main parameters affecting chiller performance: the water temperature set-point, the temperature differential, and the thermal gap ∆T , that can be computed as the difference between the input and output water temperatures. A low value of the water temperature differential grants a higher control bandwidth and allows to obtain a more constant water temperature. On the other hand, there is an upper bound to the number of compressor start-ups per hour, which is set by the compressor manufacturer. As a consequence, there is an upper bound to the achievable control bandwidth. Also, the value of the temperature differential cannot be decreased arbitrarily, but there is a lower limit value which depends on the plant water content [7].
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10
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u rat
re
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Pe,i = Z · Pe,f ull |i .
te Wa
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ut
em rT
(4) 6
IV. T WO -L AYER C ONTROL A RCHITECTURE
7
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Input Water Temperature[◦ C]
With reference to Fig. 1 a Two Layer Control structure for multiple chiller system operation is proposed. In the lowlevel layer, each chiller set-point is maintained using a local controller. In the high-level layer, a supervisor specifies the modes of operation and the set-points for each chiller. The set points, and thus the individual cooling loads of the units, are determined by simultaneously solving the OCL and OCS problems. A. Low Level Controller Typically, a chiller without capacity control can be regulated in two different ways, namely by controlling the chiller evaporator water outlet temperature or the chiller evaporator water inlet temperature. In both cases, a relay control law is used, where the compressor is switched on and off when the controlled temperature reaches given threshold values. The difference between the upper and lower threshold values is called water temperature differential, and its value clearly affects the width of the oscillations of the supply water temperature as well as the number of start-ups of the compressor. While both control strategies maintain constant water supply temperature in full load conditions, outlet water temperature control grants better performance during chiller part load operations since it maintains the mean water supply temperature fairly constant during on/off operations.
Figure 2: logic regulation for a chiller with four capacity partialization steps. DM is the temperature differential when controlling the chiller evaporator water outlet, DR is the temperature differential when controlling the chiller evaporator water inlet. Most machines are equipped with several steps of regulation (capacity or partialization steps). An example of the relevant water temperatures behavior for a machine with four regulation steps is shown in Fig. 2. When the chiller operates at full load condition, with input temperature at 12 °C and thermal gap equal to 5 °C, the output temperature is equal to 7 °C (Fig. 2, point 1). If the thermal load of the plant is less than the chiller capacity, then the evaporator input temperature diminishes and, consequently, so does the output one. When the input temperature is equal to 10.75 °C, the output temperature is equal to 5.75 °C (point 2) and the first partialization step is switched off. Power is reduced by a quarter and consequently, since the water throughput is constant, the thermal gap is reduced from 5 °C to 3.75 °C. The output temperature is then again 7 °C (point 3). If the cooling power provided by the chiller is still greater than the cooling demand, then the temperature falls down again towards point 5, where another partialization step is switched off, therefore reducing the thermal gap to only 2.5 °C
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(point 6). Instead, if the cooling power is less than the cooling demand, then the temperature raises, until the partialization step is switched on again (point 4) and the thermal gap ∆T becomes again 5 °C. Therefore, every partialization step draws a four-sided figure in the diagram. Output temperature “moves” over the figure sides as a function of the input temperature: when the step is activated (step On) temperatures move along the solid-line sides, when it is deactivated (step Off) temperatures move along dashed-line sides. As the load diminishes, the various steps are deactivated and the operating point moves towards the four-sided figure on the left. In the TLC architecture proposed in this paper, in the lowlevel control loop a chiller evaporator water outlet relay control law is used. The chiller capacity step is activated/deactivated when the controlled temperature reaches given threshold values. In the general case of a multi-compressor unit equipped with compressors with different capacity steps, the unit capacity steps can be obtained by combing the number of active compressors and their capacity steps. Such combinations depend on the unit refrigerant circuit design, type and number of compressors. B. High Level Controller: Supervisory The supervisor structure consists of two main components: 1) a load estimation algorithm; 2) a PSO algorithm for solving the OCL and OCS problems. At each supervision period (i.e. 10 minutes) the system cooling demand is estimated, and the estimate is used by the PSO optimization algorithm that solves, simultaneously, the OCL and OCS problems thus determining, for each chiller, the cooling load, in the form of local set-points, and the status (on/off). The computations required by the optimization process can be performed within a time length of five minutes on a personal computer, thus granting an on-line implementation. 1) Load Estimation Algorithm: In order to solve the OCL and OCS problems during each supervision period, knowledge of the total cooling demand is needed. The thermal load estimation algorithm is designed following [5], under the key assumption that information on the plant (Fig. 1) is available in terms of measurements of the inlet and supply water temperatures (Tchwr and Tchws ) and the inlet load-side water temperature (TLin ). Therefore, although there are many different thermal loads affecting the plant, it is appropriate to consider a mean-value approach as follows. The energy equation for the hydraulic circuits are obtained under the assumptions that the bypass line is adiabatic and the liquid inside it is negligible, that is, dTLin +m ˙ C cp (Tchwr − Tchws ) , (5) dτ where PL is the plant thermal load, VT ank is the volume of the water content in the load-side hydronic circuit, and m˙C is the water flow rate in the chiller section. The thermal load PL = ρcp VT ank
dynamics are slow with respect to the chillers dynamics, as a consequence, as is common in standard disturbance estimation schemes, it is assumed that PL has constant dynamics. The resulting overall state space model is the following: P˙L = 0 T˙L = in
1 m˙C m˙C PL + Tchws − Tchwr ρcp VT ank ρVT ank ρVT ank
(6)
On the basis of state space model (6), a standard Luenberger observer is designed in order to obtain the estimated load PˆL . To reduce the effects of compressors switching, that causes large transients in the estimation error in particular when the plant water content is small, PˆL is low-pass filtered. 2) PSO: In order to solve the optimization problem (1) a PSO algorithm is employed. Particle Swarm Optimization is a population-based optimization technique inspired by the motion of a bird flock, or fish schooling [8]. It is one of the most recent evolutionary optimization methods, and its most relevant feature is that there it requires the setting of a very limited number of parameters. The constrained optimization problem (1) is reduced to an unconstrained optimization problem by using a modified objective function with penalty and then it is solved by means of an ad-hoc PSO algorithm. In details, a multi-phase PSO algorithm is employed, which uses a simple PSO with many phases. Each phase is initialized with a set of best particles from the previous phase and a random set of other particles. The multiple phases are introduced in a simple PSO in order to realize the effect of multiple initializations. The number of phases are decided on the basis of the swarm size and the maximum number of iterations. The particles’ position of the first phase is randomly chosen and the algorithm proceeds until it reaches a specified number of iterations. The number of iterations for each phase is calculated by a monotonically increasing function of phases’ number. In this way, a balance between global and local exploration abilities of the swarm is guaranteed. The algorithm provides, for each chiller, the best solution evaluated in term of P LR and on/off status. The water outlet set-point temperature for the i-th chiller can be estimated as: Tspi = Tchws +
PˆL − P LRi PM ax
!
∆T ,
(7)
where ∆T is the thermal gap and PM ax is the nominal design cooling capacity. V. E XAMPLES AND R ESULTS The system shown in Fig. 1 and the TLC control described in Section IV have been implemented in the Matlab/Simulink™ environment. Extensive simulations have been performed to estimate and illustrate the time dynamics of the process and to evaluate the system energy consumption and performance. To better assess the TLC performance, two standard sequencing strategies have been implemented for comparison. For a set of n-parallel chillers with mdiscrete capacity steps system, two common strategies are the following:
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capacity control on isentropic compression efficiency. 1.4
1.4 T
air
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(b) TCAVBZ 2810, screw unit.
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Figure 3: Y and Z curves.
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Figure 4: cooling load, TLC vs MS and SS. 1) sequential strategy (MS): chillers status is represented as a sorted sequence Ch1,j , ... , Chi,j , ..., Chn,j with 1 ≤ j ≤ m; if, at a given instant t, chillers Ch1,m , ... , Chi−1,m , Chi,s are operating and load demand is not satisfied, then chiller Chi,s+1 is switched on. In this approach, the last chiller only operates at part load condition, whereas the others operate at full capacity;
7.8 7.6 7.4 7.2
2) symmetric strategy (SS): if, at given instant t, chillers Ch1,s , ..., Chi,s , Chi+1,s−1 , ..., Chn,s−1 are operating and load demand is not satisfied, then chiller Chi+1,s is switched on.
[°C]
7 6.8 6.6 6.4
TLC SS
The case study of a Milan’s directional building (Northern Italy) on a typical cooling season ranging from May to September has been analysed. The building load demand profiles have been calculated by a DesignBuilder® simulation model with 10 minutes time step [9]. The packaged, aircooled, water chillers are described in the PSO algorithm and in the plant dynamic model by using experimental data provided by the manufacturer. The considered units are TCAE4200 (201 kW nominal cooling power) and TCAE4320 (325 kW nominal cooling power), both with four scroll compressors and two refrigerant circuit, and TCAVBZ2810 (809 kW nominal cooling power) with a two screw compressor and two refrigerant circuit. In Fig. 3, Z and Y (defined as the ratio of P LR and Z) curves for two chiller models are plotted as a function of the P LR and air temperature. It is worth noticing that for the scroll unit there are four different capacity steps, whereas for the screw unit there are six different capacity steps. As shown in Fig. 3, at part load condition the system with scroll compressors behaves better than the one with screw compressors. This fact has to be associated with the effect of
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MS
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800
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Figure 5: water supply temperature, TLC vs MS and SS. An interesting feature of the two layer control algorithm is that it can be applied to mixed multi-scroll/multi-screw chillers system. Considering the different shapes of the Y-curve for the two refrigerating units, it would be hard to define a priori a strategy for optimal system management. For this reason, in practical applications such mixed systems are rarely used. However, such configuration are appealing for their flexibility, modularity and improved part load efficiency. As an example, a mixed system is simulated and TLC performances are compared to both SS and MS strategies. When MS is used, the screw units are switched on before the scroll units. The mixed multi-chillers system consists of two screw (TCAVBZ2810) and two scroll (TCAE4200 and TCAE4320) units. The total
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Table I: monthly and seasonal performances, TLC vs MS and SS strategies. Cooling energy load demand [kWh] Cooling energy MS [kWh] Cooling energy SS [kWh] Cooling energy TLC [kWh] STD errload MS [kW] STD errload SS [kW] STD errload TLC [kW] STD errwst MS[ °C] STD errwst SS [°C] STD errwst TLC [°C] EER MS EER SS EER TLC ∆%EER (TLC-MS) ∆%EER (TLC-SS)
May
June
July
August
September
seasonal
67752 85017 82004 69526 164 173 53 0.2593 0.2339 0.0904 3.4668 3.6656 3.8634 11.44 5.40
196860 218630 215990 202970 250 255 73 0.3392 0.3268 0.0982 3.3213 3.4712 3.5886 8.05 3.38
323140 357980 357640 334000 320 317 89 0.4075 0.4164 0.0907 3.1917 3.2110 3.3939 6.34 5.70
270510 303680 302470 282470 276 285 80 0.3825 0.3840 0.0939 3.2825 3.4080 3.5275 7.46 3.51
128320 150810 147870 133190 205 210 65 0.3049 0.2973 0.1043 3.4086 3.5656 3.7222 9.20 4.39
986580 1116100 1106000 1022200 249 254 73 0.3435 0.3385 0.0971 3.2897 3.4163 3.5390 7.58 3.59
cooling capacity, at 35 °C external air temperature, amounts to 2144 kW, the plant water content is 5 l/kW and supply water set-point temperature is 7 °C, the thermal gap is 5 °C, whereas the water temperature differential is fixed to 1 °C. In Tab. I, the monthly and seasonal integrated values of cooling capacity and the system performances, in terms of EER and standard deviation of the cooling load error (difference between the cooling load demand and the cooling supply, errload ) as well as the standard deviation of the water supply temperature error (difference between the water temperature set-point and the water supply temperature, errwst ) are reported for MS, SS and TLC strategies. The TLC algorithm exhibits a seasonal EER 7.58% improvement with respect to MS strategy and 3.59% with respect to SS strategy. In Fig. 4 and 5 cooling capacity and water supply temperature are plotted for the 15-th of July. With respect to MS and SS strategy it can be observed that the TLC offers better trends and slightly lower fluctuations in the supply water temperature. VI. C ONCLUSIONS In this paper Two-Layer Control for multi-chiller systems has been presented. To achieve optimal performance in terms of reducing both power consumption and operative costs, as well as granting good load tracking properties, the OCL and OCS problems are simultaneously solved, making use of information on the actual thermal load applied to the plant. Such information is gained from measurements from the plant by means of a linear observer, that is designed on the basis of a dynamic model describing the load time behavior. Once an estimate of the load is available, it is possible to optimize the system operation by minimizing the energy consumption under the constraint that the cooling demand be satisfied. The resulting nonlinear, constrained, combinatorial optimization with both continuous and discrete variables has been successfully solved by using a PSO algorithm. There are several advantages associated with this choice, such as the computational efficiency that grants implementation in realtime on commercial platforms and the possibility of easily
extending the approach by inserting extra penalty terms in the performance index. The approach can also be extended to include the management of more complex systems comprising air handling units and radiant and fan coil systems. Furthermore, information from load forecasting models for the energy and economic management of thermal storages could be easily exploited by simple modifications of the load estimation scheme and performance index. The performance of the algorithm has been evaluated by means of simulation performed with a dynamic model of the plant, so that all the actual operational conditions have been taken into consideration. The results show that it is possible to achieve substantial energy savings while granting good satisfaction of the cooling demand, if compared with standard MS and SS algorithms. Implementation of the algorithm on a commercial supervisory system is presently under development. R EFERENCES [1] M. Schwedler. Applications Engineering Manual. Multiple-ChillerSystem Design and Control. TRANE, 2001. [2] ASHRAE. ASHRAE Handbook - HVAC Systems and Equipment. American Society of Heating, Refrigerating and Air-Conditioning Engineers. Atlanta (Chapter 42), 2008. [3] Y.C. Chang. An outstanding method for saving energy-optimal chiller operation. IEEE J EC, 21(2):527–532, 2006. [4] Y.C. Chang, J.K. Lin, and M.H. Chuang. Optimal chiller loading by genetic algorithm for reducing energy consumption. Energy and Buildings, 37(2):147–155, 2005. [5] M. Albieri, A. Beghi, C. Bodo, and L. Cecchinato. Advanced control systems for single compressor chiller units. International Journal of Refrigeration, 32(5):1068 –1076, 2009. [6] E. Bettanini, A. Gastaldello, and L. Schibuola. Simplified models to simulate part load performances of air conditioning equipments. In Eighth International IBPSA Conference Eindhoven, Netherlands, August 11-14, 2003. [7] ASHRAE. ASHRAE Handbook - HVAC Applications. American Society of Heating, Refrigeration and Air Conditioning Engineers. Atlanta (Chapter 41), 2007. [8] R. Eberhart and J. Kennedy. A new optimizer using particle swarm theory. In Proc. Sixth International Symposium on Micro Machine and Human Science MHS ’95, pages 39–43, 4–6 Oct. 1995. [9] DesignBuilder 2009. http://www.designbuilder.co.uk/.
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