# The Optimization of Chiller Loading by Adaptive Neuro-Fuzzy Inference System and Genetic Algorithms

Authors: Jyun-Ting Lu; Yung-Chung Chang; Cheng-Yi Ho
Journal: Mathematical Problems in Engineering
 (2015)

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## Abstract

A central air-conditioning (AC) system includes the chiller, chiller water pump, cooling water pump,  cooling tower, and chilled water secondary pumps. Among these devices, the chiller consumes most power of the central AC system. In this paper, the     adaptive neuro-fuzzy inference system (ANFIS) and genetic algorithm (GA) were utilized for optimizing  the chiller loading. The ANFIS could construct a power consumption model of the chiller, reduce modeling period, and maintain the accuracy. GA could optimize the chiller loading for better energy efficiency. The simulating results indicated that ANFIS combined with GA could optimize the chiller loading. The power consumption was reduced by 6.32–18.96% when partial load ratio was located at the range of 0.6~0.95. The chiller power consumption model established by ANFIS could also increase the convergence speed. Therefore, the ANFIS with GA could optimize the chiller loading for reducing power consumption.


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## Body

## 1. Introduction

The air-conditioning system is highly demanded in human’s life and industrial process. However, it consumes electrical power with the ratio around 50% [1, 2]. Therefore, how to reduce the power consumption of air-conditioning system may be one of the most important issues to utilize the AC system and achieve energy. The AC system includes window, separating, and central types. Among them, the central type is suitable for office and factory and so forth.A central air-conditioning system includes the chiller, chiller water pump, cooling water pump, cooling water tower, and chilled water secondary pumps. Among these devices, the chiller consumes most power of the central air-conditioning system. The consumed energy is related to the loading of system.There were several literatures discussing how to optimize the chiller loading. Braun et al. (1989) proposed the equal loading distribution (ELD) method. This method was established under the same operating characteristics of chiller [3–5]. Due to the different operating characteristics of the chiller, Braun et al. suggested that the power consumption of the chiller was correlated with load of air conditioners, cooling water return temperature, and chiller water supply temperature. This correlation may explain the optimal chiller loading (OCL) method. Chang et al. (2005) adopted partial load ratio (PLR) method as gene coding principle of genetic algorithm (GA) to minimize power consumption of the chiller, which served as an objective function. The results showed that Lagrangian multiplier method (LGM) could converge the low load conditions and achieve high accuracy performance [6]. Bonissone et al. (2006) discussed implicit and explicit knowledge representation mechanisms for evolutionary algorithms and applied domain customized mutation operators for a well-sampled Pareto front showing all the nondominated solutions [7]. Haber and Alique (2007) applied fuzzy-logic for torque control system, embedded in an open-architecture computer numerical control (CNC) [8]. Martín et al. (2009) proposed GA applied to the networked control of a high performance drilling process for optimal tuning of a linear controller [9]. Lee and Lin (2009) applied particle swarm optimization (PSO) method for optimizing the chiller loading, design, and operating strategies of air-conditioning system [10]. Lee et al. (2011) compared the results of differential evolution algorithm with equal loading distribution, as well as LGM and PSO [11]. Gajate et al. (2012) proposed two model-based approaches for tool wear monitoring on the basis of neuro-fuzzy techniques. The comparative study demonstrates that the transductive neuro-fuzzy model provides better error-based performance indices [12]. Chen et al. (2014) utilize neural networks (NN) to establish the power consumption model of the chiller and PSO for optimal loading and saving energy [13].From the previous studies, the equal loading distribution method was often used to reduce power consumption. However, the LGM may cause system divergence. The NN method adopted try-and-error principle to find number of better neurons on a hidden layer. It may cause longer period. Hence, there is no single method suitable for all the conditions.In the study, the ANFIS combined with GA are utilized to optimize the chiller loading and reduce the power consumption and operating period.


## 2. System Architecture

The general decoupled system of a central air-conditioning system is shown in Figure1 [14]. The common piping is the division line of the central air-conditioning system. For separating the system into two parts, including the first side (chiller side) and secondary side (load side), the first side contains the chiller and chiller water pump, and the secondary side is chilled water secondary pumps and air handing unit. The secondary variable frequency pump is installed on the secondary side for controlling the flow speed to improve energy efficiency. The total load of this system can be expressed by(1)CL=m˙CpTchwr-Tchws,where CL is the cooling load (kW), m˙ is the flow rate of chiller water (kg/s), Cp is the specific heat capacity of chilled water (J/kg·K), Tchwr is the cooling water return temperature (K), and Tchws is the chilled water supply temperature (K).Figure 1
Decoupled system of a central AC system [14].


## 3. Chiller Power Consumption Model

Generally speaking, the capacity of the chiller is designed to meet the need of peak load. However, most of the chiller is operated under the condition of partial load, and this would result in larger designed capacity and power consumption. The partial load ratio of a chiller is defined in(2)PLR=coolingloadchillercapacity.The variables of the power consumption model include chilled water supply temperature, cooling water return temperature, and partial load ratio. The power consumption model could be presented in [15] (3)Pch,i=a0,i+a1,iTchwr,i-Tchws,i+a2,iTchwr,i-Tchws,i2+a3,iPLRch,i+a4,iPLRch,i2+a5,iTchwr,i-Tchws,iPLRch,i,where a0,i~a5,i is the regression coefficient, Tchwr,i is the cooling water return temperature, Tchws,i is the chilled water supply temperature, and PLRch,i is the partial load ratio. All of these parameters are for the ith chiller.The chiller power consumption model could be established by ANFIS. The program could be expressed by(4)Pch,i=fTchwr,i-Tchws,i,PLRch,i.After establishing the power consumption model, in order to satisfy OCL, the minimum power consumption of the chiller could be viewed as the objective function. The objective function could be presented by(5)Objectivefunction=Min∑inPch,i,where n = set number of operating chiller (set).The restrictive limitations could be presented in(6)CL=∑i=1nPLRch,i×chillercapacity,i,0.5LowLimit≦PLRch,i≦1UpperLimit.In order to prevent the low operating efficiency and surge of the chiller, the chiller could be set to the lowest load (PLR=0.5). Conversely, when the PLR was greater than or equal to 1, the load of the chiller would be full.


## 4. Analysis Method

### 4.1. Adaptive Neuro-Fuzzy Inference System (ANFIS)

The ANFIS was proposed by Jang [16] in 1993 and combined the NN and fuzzy methods. ANFIS has been used to solve the difficulty of traditional fuzzy system in defining fuzzy rule base using expert experience, establish the if-then rules based on hybrid learning procedure, and adjust suitable regression function to satisfy input-output relationship of fuzzy inference. Moreover, ANFIS have been applied on the NN system to determine the number of neurons in hidden layer during initialization. The proper number of neurons can be found by try-and-error.Figure2 demonstrated the ANFIS architecture with fuzzy inference of the one order Sugeno fuzzy model. In Figure 2, the nodes of each layer had the same function.Figure 2
ANFIS architecture of the one order Sugeno fuzzy model.The functions of five layers are described as follows:(1)
First layer: membership function of inputsx and y, as described by (7)μAx=11+x-ci/ai2bi,where ai, bi, and ci are the premise parameters.(2)
Second layer: multiplication of the input signals, as described by (8).It represents the firing strength of each fuzzy rule:(8)wi=μAjx·μBjy,i=1~4,j=1,2.(3)
Third layer: normalization ofith fuzzy rule’s firing strength, as described by(9)wi¯=wi∑i=14wi,i=1~4.(4)
Fourth layer: node function described by(10)wi¯fi=wi¯pix+qiy+ri,i=1~4.(5)
Fifth layer: summation of previous layer as the output, as described by(11)f=∑i=14fiwi¯,i=1~4.In Figure2, the ANFIS architecture was composed of two input variables (x,y) and one output (f). Each input had two membership functions and composed four fuzzy rules, totally.In this study, the temperature differences between cooling water return temperature (Tchwr), chilled water supply temperature (Tchws), and partial load ratio were assumed as the input variables. Power consumption was assumed as the output variable. Each input had three membership functions and composed nine fuzzy rules, totally.The software programs of Matlab, Mathematica 5, and Fuzzy Logic Toolbox were adopted to build the model for simulation. The ANFIS training flow chart was shown in Figure3. First, the operating conditions of chiller were collected, and the proper training data was selected. Then, the ANFIS parameters were set and trained through the loop. When the iteration number was achieved, the ANFIS training was completed.Figure 3
ANFIS training flow chart.


### 4.2. Genetic Algorithm (GA)

GA was proposed by Holland et al. in 1970 and based on Darwin’s doctrine of evolution, natural selection, and survival of the fittest [6]. GA mainly transforms problems into gene permutation and continuously optimizes them through selection or reproduction, crossover, and mutation. The algorithm could seek optimal solution through parallel search in wide solution domain and has been widely applied on various fields.


#### 4.2.1. Characteristics of GA

GA is different from the traditional optimization method and has the characteristics of stability and efficiency. The main features are shown as follows.(
1) Prevent Complicated Mathematical Model Deviation. For calculation, fitness function is used as the measuring standard to prevent complicated mathematical model deviation.(
2) Convergence Speed for Calculation. The parallel search method is used for calculating parameter. Instead of single-point method, multipoint method can be performed at the same time to accelerate convergence speed for calculation.(
3) Prevent Local Optimal Solution. GA includes mutation operation. Chromosomes could practice the mutation change during evolution to prevent local optimal solution in search process.


## 4.1. Adaptive Neuro-Fuzzy Inference System (ANFIS)

The ANFIS was proposed by Jang [16] in 1993 and combined the NN and fuzzy methods. ANFIS has been used to solve the difficulty of traditional fuzzy system in defining fuzzy rule base using expert experience, establish the if-then rules based on hybrid learning procedure, and adjust suitable regression function to satisfy input-output relationship of fuzzy inference. Moreover, ANFIS have been applied on the NN system to determine the number of neurons in hidden layer during initialization. The proper number of neurons can be found by try-and-error.Figure2 demonstrated the ANFIS architecture with fuzzy inference of the one order Sugeno fuzzy model. In Figure 2, the nodes of each layer had the same function.Figure 2
ANFIS architecture of the one order Sugeno fuzzy model.The functions of five layers are described as follows:(1)
First layer: membership function of inputsx and y, as described by (7)μAx=11+x-ci/ai2bi,where ai, bi, and ci are the premise parameters.(2)
Second layer: multiplication of the input signals, as described by (8).It represents the firing strength of each fuzzy rule:(8)wi=μAjx·μBjy,i=1~4,j=1,2.(3)
Third layer: normalization ofith fuzzy rule’s firing strength, as described by(9)wi¯=wi∑i=14wi,i=1~4.(4)
Fourth layer: node function described by(10)wi¯fi=wi¯pix+qiy+ri,i=1~4.(5)
Fifth layer: summation of previous layer as the output, as described by(11)f=∑i=14fiwi¯,i=1~4.In Figure2, the ANFIS architecture was composed of two input variables (x,y) and one output (f). Each input had two membership functions and composed four fuzzy rules, totally.In this study, the temperature differences between cooling water return temperature (Tchwr), chilled water supply temperature (Tchws), and partial load ratio were assumed as the input variables. Power consumption was assumed as the output variable. Each input had three membership functions and composed nine fuzzy rules, totally.The software programs of Matlab, Mathematica 5, and Fuzzy Logic Toolbox were adopted to build the model for simulation. The ANFIS training flow chart was shown in Figure3. First, the operating conditions of chiller were collected, and the proper training data was selected. Then, the ANFIS parameters were set and trained through the loop. When the iteration number was achieved, the ANFIS training was completed.Figure 3
ANFIS training flow chart.


## 4.2. Genetic Algorithm (GA)

GA was proposed by Holland et al. in 1970 and based on Darwin’s doctrine of evolution, natural selection, and survival of the fittest [6]. GA mainly transforms problems into gene permutation and continuously optimizes them through selection or reproduction, crossover, and mutation. The algorithm could seek optimal solution through parallel search in wide solution domain and has been widely applied on various fields.


### 4.2.1. Characteristics of GA

GA is different from the traditional optimization method and has the characteristics of stability and efficiency. The main features are shown as follows.(
1) Prevent Complicated Mathematical Model Deviation. For calculation, fitness function is used as the measuring standard to prevent complicated mathematical model deviation.(
2) Convergence Speed for Calculation. The parallel search method is used for calculating parameter. Instead of single-point method, multipoint method can be performed at the same time to accelerate convergence speed for calculation.(
3) Prevent Local Optimal Solution. GA includes mutation operation. Chromosomes could practice the mutation change during evolution to prevent local optimal solution in search process.


## 4.2.1. Characteristics of GA

GA is different from the traditional optimization method and has the characteristics of stability and efficiency. The main features are shown as follows.(
1) Prevent Complicated Mathematical Model Deviation. For calculation, fitness function is used as the measuring standard to prevent complicated mathematical model deviation.(
2) Convergence Speed for Calculation. The parallel search method is used for calculating parameter. Instead of single-point method, multipoint method can be performed at the same time to accelerate convergence speed for calculation.(
3) Prevent Local Optimal Solution. GA includes mutation operation. Chromosomes could practice the mutation change during evolution to prevent local optimal solution in search process.


## 5. Case Analysis and Results

In this paper, a semiconductor factory with five chillers was under investigation. The specifications of these chillers are shown in Table1. The operating conditions of these chillers, including power consumption, the temperature at chilled water supply, and cooling water return, were recorded every 5 min during entire experiments. There are totally 10580 data sets in the experiments.Table 1
Operating conditions of chiller system.
Chiller
1
2
3
4
5
Chiller water supply temperature (°C)
5
5
5
5
5
Cooling water return temperature (°C)
28
28
28
28
28
Chiller water flow rate (m3/hr)
531
501
567
521
528
Cooling water flow rate (m3/hr)
705
742
698
722
674
Cooling capacity (RT)
1,280
1,280
1,280
1,250
1,250
Voltage (V)
4,160
4,160
4,160
4,160
4,160
Input power (kW)
1,062
1,062
1,062
957
957


### 5.1. Chiller Power Consumption Model Using Regression Analysis

The linear regression (LR) analysis method is utilized to build and analyze the power consumption model of the chiller system with accurate prediction in short-term period [17]. In this study, the software of Mathematica 5 was used to establish regression analysis model. The calculated regression coefficients, R2 (coefficient of determination), and average percentage error (err%) are shown in Table 2. In Table 2, a0~a5 are curve coefficients of the chiller system in (3) by the regression analysis. Figure 4 shows the relationship between simulated power consumption and actual power consumption of chiller 1. In the actual power consumption range from 520 to 920 kW, the simulated power consumption by NN increases from 520 to 920 kW, with the averaged R2 and percentage error (err%) of 0.985 and 0.973%, respectively. For the above main modeling parameters R2 and err%, the temperature differences between cooling water return temperature (Tchwr), chilled water supply temperature (Tchws), and partial load ratio were assumed as the independent variables.Table 2
Coefficients of the chiller power consumption models from quadratic regression analysis.
Chiller
1
2
3
4
5
a
0
a
0
150.80
236.17
−108.65
386.31
222.16
a
1
12.79
−2.08
16.21
−6.19
−0.80
a
2
−0.51
−0.56
−0.56
0.18
−0.22
a
3
−620.23
−235.58
35.14
−670.01
−349.20
a
4
510.82
−369.19
−34.55
763.31
270.52
a
5
49.92
81.75
44.82
28.37
47.76
R
2
0.984181
0.983730
0.985550
0.985485
0.983580
Error (%)
1.420413
0.854415
0.849768
0.845402
0.89693Figure 4
Distribution of actual power consumption and simulated power consumption of chiller 1 by using regression analysis.


### 5.2. Chiller Power Consumption Model Using NN and ANFIS

NN method is often adopted to build power consumption model of chiller system by try-and-error principle. The ANFIS method is improved from NN method. Therefore, it is in our interest to compare the chiller power consumption model built by regression analysis, NN, and ANFIS methods in this section. The model of chiller 1 is chosen as an example. Figure5 shows the relationship between simulated power consumption by NN method and actual power consumption of chiller 1. In the actual power consumption range from 520 to 920 kW, the simulated power consumption increases from 520 to 920 kW. The solid line is the fitting curve by least square error method. This fitting method would be applied for the following sections. R2 and averaged err% between data and fitting line are 0.99988 and 0.8769, respectively.Figure 5
Distribution of actual power consumption and simulated power consumption of chiller 1 by using NN.Figure6 shows the relationship between simulated power consumption by ANFIS method and actual power consumption of chiller 1. In the actual power consumption range from 520 to 920 kW, the simulated power consumption increases from 520 to 920 kW. R2 and averaged err% between data and fitting line are 0.99988 and 0.88359, respectively.Figure 6
Distribution of actual power consumption and simulated power consumption of chiller 1 by using ANFIS.The calculatedR2 and err% of these chillers simulated by NN and ANFIS methods are shown in Tables 3 and 4, respectively. In Table 3, the range of R2 and err% is from 0.99988 to 0.9999 and from 0.79796 to 0.8769%, respectively. The averaged R2 and err% are 0.99988 and 0.834472, respectively. In Table 4, the range of R2 and err% is from 0.99988 to 0.9999 and from 0.81413 to 0.88359%, respectively. The averaged R2 and err% are 0.99988 and 0.843964, respectively.Table 3
Regression coefficients and average percentage error of chillers by NN model.
Chiller
1
2
4
5
6
R
2
R
2
0.9998
0.9998
0.9999
0.9998
0.9998
err%
0.88
0.83
0.80
0.82
0.85Table 4
Regression coefficients and average percentage error of chillers by ANFIS model.
Chiller
1
2
4
5
6
R
2
R
2
0.99988
0.99989
0.9999
0.99989
0.99988
err%
0.88
0.83
0.81
0.83
0.86From Tables2 to 4, the simulated results by NN and ANFIS methods had similar accuracy. The averaged R2 by NN and ANFIS methods are higher than that by regression analysis method. However, the averaged err% by NN and ANFIS are lower than that by regression analysis method.In order to understand further the responding time of the utilized methods, the modeling speeds of the chillers for semiconductor factory simulated by ANFIS and NN are presented in Table5. The chiller power consumption model by using NN method adopted 40 neurons on a single hidden layer. The output layer of one neuron is utilized for modeling. Based on the results, the iteration period by ANFIS in Table 5 presents more efficient modeling speed, with average of 2 min 15 sec. Therefore, the ANFIS is utilized to design the rule base through automatic learning for achieving optimal output status.Table 5
Chiller modeling speed of NN and ANFIS methods.
Chiller
1
2
4
5
6
NN modeling speed
3 min 30 sec
3 min 27 sec
3 min 37 sec
3 min 34 sec
3 min 30 sec
ANFIS modeling speed
2 min 07 sec
2 min 17 sec
2 min 17 sec
2 min 17 sec
2 min 17 sec


### 5.3. Loading Distribution Results of LR + ELD, LR + GA, NN + GA, and ANFIS + GA

LR method could build and analyse power consumption model of the chiller system with accurate prediction. This method includes several order calculation principles. Here, 2nd-order LR method is adopted for calculating multiple parameters with better accuracy [13]. The ELD method of equal load is also commonly adopted to operate chillers [3–5]. Therefore, it is in our interest to compare the simulating results by LR + ELD, LR + GA, NN + GA, and ANFIS + GA methods.Table6 shows the optimal chiller loading by LR + ELD and LR + GA methods under partial load ratio of 0.55~0.95. The results indicated that the LR + GA method had better energy savings than LR + ELD method by 0.77% to 2.25% in the partial load ratios of 0.55 to 0.95, with the average energy savings of 1.58%. The power consumption of chiller, simulated by LR + ELD and LR + GA methods, increased from 2991 to 5301.3 kW and from 2967.9 to 5240.8 kW, respectively.Table 6
Optimal chiller loading comparison by LRELD and LRGA methods.
Cooling load (RT)
Chiller
LR + ELD
LR + GA
Saving A − B (%)
PLR
Load (RT)
Total (kW) (A)
PLR
Load (RT)
Total (kW) (B)
6023 (95%)
1
0.95
1216
5301.3
0.83431
1067.92
5240.8
2
0.95
1216
0.99902
1278.75
4
0.95
1216
0.99951
1279.37
1.14%
5
0.95
1187.5
0.92864
1160.80
6
0.95
1187.5
0.98925
1236.56
5706 (90%)
1
0.9
1152
4986.5
0.76197
975.32
4894.3
2
0.9
1152
1
1280.00
4
0.9
1152
0.99951
1279.37
1.85%
5
0.9
1125
0.85924
1074.05
6
0.9
1125
0.87781
1097.26
5389 (85%)
1
0.85
1088
4679.1
0.67253
860.84
4574.4
2
0.85
1088
1
1280.00
4
0.85
1088
1
1280.00
2.24%
5
0.85
1062.5
0.80303
1003.79
6
0.85
1062.5
0.77175
964.69
5072 (80%)
1
0.8
1024
4379.2
0.58798
752.61
4280.6
2
0.8
1024
0.99902
1278.75
4
0.8
1024
0.99902
1278.75
2.25%
5
0.8
1000
0.74145
926.81
6
0.8
1000
0.66813
835.16
4755 (75%)
1
0.75
960
4086.7
0.53666
686.92
4012.1
2
0.75
960
0.99902
1278.75
4
0.75
960
1
1280.00
1.83%
5
0.75
937.5
0.66569
832.11
6
0.75
937.5
0.54203
677.54
4438 (70%)
1
0.7
896
3801.6
0.60068
768.87
3737.6
2
0.7
896
0.50098
641.25
4
0.7
896
0.99951
1279.37
1.68%
5
0.7
875
0.74633
932.91
6
0.7
875
0.65249
815.61
4121 (65%)
1
0.65
832
3523.9
0.5176
662.53
3468.9
2
0.65
832
0.5
640.00
4
0.65
832
0.99951
1279.37
1.56%
5
0.65
812.5
0.66618
832.73
6
0.65
812.5
0.56549
706.86
3804 (60%)
1
0.6
768
3253.7
0.52981
678.16
3223.2
2
0.6
768
0.50098
641.25
4
0.6
768
0.74438
952.81
0.94%
5
0.6
750
0.67302
841.28
6
0.6
750
0.55279
690.99
3487 (55%)
1
0.55
704
2991
0.52884
676.92
2967.9
2
0.55
704
0.5
640.00
4
0.55
704
0.51222
655.64
0.77%
5
0.55
687.5
0.67058
838.23
6
0.55
687.5
0.54106
676.33Table7 shows the optimal chiller loading by LR + ELD and NN + GA methods under partial load ratio of 0.55~0.95. The results indicated that the NN + GA method had better energy savings than LR + ELD method by 2.63% to 16.95% in the partial load ratios of 0.55 to 0.95, with the average energy savings of 12.14%. The power consumption of chiller simulated by LR + ELD and NN + GA methods increased from 2991 to 5301.3 kW and from 29127.3 to 4405.2 kW, respectively.Table 7
Optimal chiller loading comparison by LRELD and NNGA methods.
Cooling load (RT)
Chiller
LR + ELD
NN + GA
Saving A − B (%)
PLR
Load (RT)
Total (kW)  (A)
PLR
Load (RT)
Total (kW)  (B)
6023 (95%)
1
0.95
1216
5301.3
0.99658
1275.62
4405.2
2
0.95
1216
1
1280.00
4
0.95
1216
1
1280.00
16.90%
5
0.95
1187.5
1
1250.00
6
0.95
1187.5
0.75024
937.80
5706 (90%)
1
0.9
1152
4986.5
0.99316
1271.24
4141.4
2
0.9
1152
1
1280.00
4
0.9
1152
1
1280.00
16.95%
5
0.9
1125
1
1250.00
6
0.9
1125
0.5
625.00
5389 (85%)
1
0.85
1088
4679.1
0.74536
954.06
3937.3
2
0.85
1088
1
1280.00
4
0.85
1088
1
1280.00
15.85%
5
0.85
1062.5
1
1250.00
6
0.85
1062.5
0.5
625.00
5072 (80%)
1
0.8
1024
4379.2
0.5
640.00
3696
2
0.8
1024
1
1280.00
4
0.8
1024
1
1280.00
15.60%
5
0.8
1000
0.99804
1247.55
6
0.8
1000
0.5
625.00
4755 (75%)
1
0.75
960
4086.7
0.50489
646.26
3547.7
2
0.75
960
1
1280.00
4
0.75
960
1
1280.00
13.19%
5
0.75
937.5
0.67791
847.39
6
0.75
937.5
0.56109
701.36
4438 (70%)
1
0.7
896
3801.6
0.5
640.00
3344
2
0.7
896
1
1280.00
4
0.7
896
0.99071
1268.11
12.04%
5
0.7
875
0.5
625.00
6
0.7
875
0.5
625.00
4121 (65%)
1
0.65
832
3523.9
0.5
640.00
3177.9
2
0.65
832
1
1280.00
4
0.65
832
0.61193
783.27
9.82%
5
0.65
812.5
0.5826
728.25
6
0.65
812.5
0.55279
690.99
3804 (60%)
1
0.6
768
3253.7
0.5
640.00
3048
2
0.6
768
0.9956
1274.37
4
0.6
768
0.5
640.00
6.32%
5
0.6
750
0.5
625.00
6
0.6
750
0.5
625.00
3487 (55%)
1
0.55
704
2991
0.5
640.00
2912.3
2
0.55
704
0.69208
885.86
4
0.55
704
0.55572
711.32
2.63%
5
0.55
687.5
0.5
625.00
6
0.55
687.5
0.5
625.00Table8 shows the optimal chiller loading by LR + ELD and ANFIS + GA methods under partial load ratio of 0.55~0.95. The results indicated that the ANFIS + GA method had better energy savings than LR + ELD method by 0.36% to 186.96% in the partial load ratios of 0.55 to 0.95, with the average energy savings of 12.84%. The power consumption of chiller, simulated by LR + ELD and ANFIS + GA methods, increased from 2991 to 5301.3 kW and from 2980.2 to 4296.3 kW, respectively. Table 9 presents the operating conditions of chiller system by using ANFIS + GA method.Table 8
Optimal chiller loading comparison by LRELD and ANFIS + GA methods.
Cooling load (RT)
Chiller
LR + ELD
ANFIS + GA
Saving A − B (%)
PLR
Load (RT)
Total (kW)  (A)
PLR
Load (RT)
Total (kW)  (B)
6023 (95%)
1
0.95
1216
5301.3
0.87537
1120.47
4296.3
2
0.95
1216
0.87732
1122.97
4
0.95
1216
1
1280
18.96%
5
0.95
1187.5
1
1250
6
0.95
1187.5
1
1250
5706 (90%)
1
0.9
1152
4986.5
0.56549
723.8272
4052.9
2
0.9
1152
0.93939
1202.42
4
0.9
1152
1
1280
18.72%
5
0.9
1125
1
1250
6
0.9
1125
1
1250
5389 (85%)
1
0.85
1088
4679.1
0.5
640
3831.3
2
0.85
1088
0.75806
9703.32
4
0.85
1088
1
1280
18.12%
5
0.85
1062.5
0.99902
1248.78
6
0.85
1062.5
1
1250
5072 (80%)
1
0.8
1024
4379.2
0.51075
653.76
3625.8
2
0.8
1024
0.5
640
4
0.8
1024
1
1280
17.20%
5
0.8
1000
0.99902
1248.78
6
0.8
1000
1
1250
4755 (75%)
1
0.75
960
4086.7
0.5
640
3478.3
2
0.75
960
0.5
640
4
0.75
960
1
1280
14.89%
5
0.75
937.5
0.88416
1105.2
6
0.75
937.5
0.87195
1089.94
4438 (70%)
1
0.7
896
3801.6
0.5
640
3284.3
2
0.7
896
0.5
640
4
0.7
896
1
1280
11.66%
5
0.7
875
0.93744
1171.8
6
0.7
875
0.565
706.25
4121 (65%)
1
0.65
832
3523.9
0.55034
704.44
3195.8
2
0.65
832
0.5
640
4
0.65
832
0.63099
807.67
9.31%
5
0.65
812.5
1
1250
6
0.65
812.5
0.57527
719.09
3804 (60%)
1
0.6
768
3253.7
0.5
640
3048.2
2
0.6
768
0.5
640
4
0.6
768
0.59677
763.87
6.32%
5
0.6
750
0.88172
1093.6
6
0.6
750
0.52639
666.55
3487 (55%)
1
0.55
704
2991
0.5
640
2980.2
2
0.55
704
0.5
640
4
0.55
704
0.61975
793.28
0.36%
5
0.55
687.5
0.56207
702.59
6
0.55
687.5
0.56891
711.14Table 9
Optimal loading conditions of chiller system operated by ANFIS + GA method.
ANFIS
Type
Training
Generate FIS
Gird partition
MF type
psigmf
MF type
Linear
Train FIS optim. methood
Hybrid
Epochs
100
GA
Popsize
300
Maxgen
400
Crossover rate
0.5
Mutation rate
0.05From Tables6 to 8, the chiller operated by ANFIS + GA method would have better energy savings of 18.96% among these three methods. This may be due to the better combination capability of GA method for the chiller under partial load ratios to achieve better energy savings.In order to further understand the relationships of energy usages and savings with these methods, the power consumptions and energy savings of these methods with respect to the partial load ratios are shown in Figure7. In Figure 7, in the partial load ratio range of 0.55 to 0.95, the power consumption increased from 2980.2 to 4296.3 kW, from 2912.3 to 4405.2 kW, from 2967.9 to 5240.8 kW, and from 2991 to 5301.3 kW for ANFIS + GA, NN + GA, LR + GA, and LR + ELD methods, respectively. The chiller simulated by ANFIS + GA method consumed the least power. Compared with LR + ELD, in the partial load ratio range of 0.55 to 0.95, the energy savings increased from 0.36 to 18.96%, from 2.63 to 16.90%, and from 0.77 to 1.14% for the simulating methods of ANFIS + GA, NN + GA, and LR + GA, respectively. Among them, the chiller simulated by ANFIS + GA had better energy savings of 12.84%. This may be due to the better inference capability and solving ability of ANFIS method for nonlinear problems and more flexible combinations and better energy saving effect of GA method.Figure 7
Power consumption between LR + ELD, LR + GA, NN + GA, and ANFIS + GA methods.


## 5.1. Chiller Power Consumption Model Using Regression Analysis

The linear regression (LR) analysis method is utilized to build and analyze the power consumption model of the chiller system with accurate prediction in short-term period [17]. In this study, the software of Mathematica 5 was used to establish regression analysis model. The calculated regression coefficients, R2 (coefficient of determination), and average percentage error (err%) are shown in Table 2. In Table 2, a0~a5 are curve coefficients of the chiller system in (3) by the regression analysis. Figure 4 shows the relationship between simulated power consumption and actual power consumption of chiller 1. In the actual power consumption range from 520 to 920 kW, the simulated power consumption by NN increases from 520 to 920 kW, with the averaged R2 and percentage error (err%) of 0.985 and 0.973%, respectively. For the above main modeling parameters R2 and err%, the temperature differences between cooling water return temperature (Tchwr), chilled water supply temperature (Tchws), and partial load ratio were assumed as the independent variables.Table 2
Coefficients of the chiller power consumption models from quadratic regression analysis.
Chiller
1
2
3
4
5
a
0
a
0
150.80
236.17
−108.65
386.31
222.16
a
1
12.79
−2.08
16.21
−6.19
−0.80
a
2
−0.51
−0.56
−0.56
0.18
−0.22
a
3
−620.23
−235.58
35.14
−670.01
−349.20
a
4
510.82
−369.19
−34.55
763.31
270.52
a
5
49.92
81.75
44.82
28.37
47.76
R
2
0.984181
0.983730
0.985550
0.985485
0.983580
Error (%)
1.420413
0.854415
0.849768
0.845402
0.89693Figure 4
Distribution of actual power consumption and simulated power consumption of chiller 1 by using regression analysis.


## 5.2. Chiller Power Consumption Model Using NN and ANFIS

NN method is often adopted to build power consumption model of chiller system by try-and-error principle. The ANFIS method is improved from NN method. Therefore, it is in our interest to compare the chiller power consumption model built by regression analysis, NN, and ANFIS methods in this section. The model of chiller 1 is chosen as an example. Figure5 shows the relationship between simulated power consumption by NN method and actual power consumption of chiller 1. In the actual power consumption range from 520 to 920 kW, the simulated power consumption increases from 520 to 920 kW. The solid line is the fitting curve by least square error method. This fitting method would be applied for the following sections. R2 and averaged err% between data and fitting line are 0.99988 and 0.8769, respectively.Figure 5
Distribution of actual power consumption and simulated power consumption of chiller 1 by using NN.Figure6 shows the relationship between simulated power consumption by ANFIS method and actual power consumption of chiller 1. In the actual power consumption range from 520 to 920 kW, the simulated power consumption increases from 520 to 920 kW. R2 and averaged err% between data and fitting line are 0.99988 and 0.88359, respectively.Figure 6
Distribution of actual power consumption and simulated power consumption of chiller 1 by using ANFIS.The calculatedR2 and err% of these chillers simulated by NN and ANFIS methods are shown in Tables 3 and 4, respectively. In Table 3, the range of R2 and err% is from 0.99988 to 0.9999 and from 0.79796 to 0.8769%, respectively. The averaged R2 and err% are 0.99988 and 0.834472, respectively. In Table 4, the range of R2 and err% is from 0.99988 to 0.9999 and from 0.81413 to 0.88359%, respectively. The averaged R2 and err% are 0.99988 and 0.843964, respectively.Table 3
Regression coefficients and average percentage error of chillers by NN model.
Chiller
1
2
4
5
6
R
2
R
2
0.9998
0.9998
0.9999
0.9998
0.9998
err%
0.88
0.83
0.80
0.82
0.85Table 4
Regression coefficients and average percentage error of chillers by ANFIS model.
Chiller
1
2
4
5
6
R
2
R
2
0.99988
0.99989
0.9999
0.99989
0.99988
err%
0.88
0.83
0.81
0.83
0.86From Tables2 to 4, the simulated results by NN and ANFIS methods had similar accuracy. The averaged R2 by NN and ANFIS methods are higher than that by regression analysis method. However, the averaged err% by NN and ANFIS are lower than that by regression analysis method.In order to understand further the responding time of the utilized methods, the modeling speeds of the chillers for semiconductor factory simulated by ANFIS and NN are presented in Table5. The chiller power consumption model by using NN method adopted 40 neurons on a single hidden layer. The output layer of one neuron is utilized for modeling. Based on the results, the iteration period by ANFIS in Table 5 presents more efficient modeling speed, with average of 2 min 15 sec. Therefore, the ANFIS is utilized to design the rule base through automatic learning for achieving optimal output status.Table 5
Chiller modeling speed of NN and ANFIS methods.
Chiller
1
2
4
5
6
NN modeling speed
3 min 30 sec
3 min 27 sec
3 min 37 sec
3 min 34 sec
3 min 30 sec
ANFIS modeling speed
2 min 07 sec
2 min 17 sec
2 min 17 sec
2 min 17 sec
2 min 17 sec


## 5.3. Loading Distribution Results of LR + ELD, LR + GA, NN + GA, and ANFIS + GA

LR method could build and analyse power consumption model of the chiller system with accurate prediction. This method includes several order calculation principles. Here, 2nd-order LR method is adopted for calculating multiple parameters with better accuracy [13]. The ELD method of equal load is also commonly adopted to operate chillers [3–5]. Therefore, it is in our interest to compare the simulating results by LR + ELD, LR + GA, NN + GA, and ANFIS + GA methods.Table6 shows the optimal chiller loading by LR + ELD and LR + GA methods under partial load ratio of 0.55~0.95. The results indicated that the LR + GA method had better energy savings than LR + ELD method by 0.77% to 2.25% in the partial load ratios of 0.55 to 0.95, with the average energy savings of 1.58%. The power consumption of chiller, simulated by LR + ELD and LR + GA methods, increased from 2991 to 5301.3 kW and from 2967.9 to 5240.8 kW, respectively.Table 6
Optimal chiller loading comparison by LRELD and LRGA methods.
Cooling load (RT)
Chiller
LR + ELD
LR + GA
Saving A − B (%)
PLR
Load (RT)
Total (kW) (A)
PLR
Load (RT)
Total (kW) (B)
6023 (95%)
1
0.95
1216
5301.3
0.83431
1067.92
5240.8
2
0.95
1216
0.99902
1278.75
4
0.95
1216
0.99951
1279.37
1.14%
5
0.95
1187.5
0.92864
1160.80
6
0.95
1187.5
0.98925
1236.56
5706 (90%)
1
0.9
1152
4986.5
0.76197
975.32
4894.3
2
0.9
1152
1
1280.00
4
0.9
1152
0.99951
1279.37
1.85%
5
0.9
1125
0.85924
1074.05
6
0.9
1125
0.87781
1097.26
5389 (85%)
1
0.85
1088
4679.1
0.67253
860.84
4574.4
2
0.85
1088
1
1280.00
4
0.85
1088
1
1280.00
2.24%
5
0.85
1062.5
0.80303
1003.79
6
0.85
1062.5
0.77175
964.69
5072 (80%)
1
0.8
1024
4379.2
0.58798
752.61
4280.6
2
0.8
1024
0.99902
1278.75
4
0.8
1024
0.99902
1278.75
2.25%
5
0.8
1000
0.74145
926.81
6
0.8
1000
0.66813
835.16
4755 (75%)
1
0.75
960
4086.7
0.53666
686.92
4012.1
2
0.75
960
0.99902
1278.75
4
0.75
960
1
1280.00
1.83%
5
0.75
937.5
0.66569
832.11
6
0.75
937.5
0.54203
677.54
4438 (70%)
1
0.7
896
3801.6
0.60068
768.87
3737.6
2
0.7
896
0.50098
641.25
4
0.7
896
0.99951
1279.37
1.68%
5
0.7
875
0.74633
932.91
6
0.7
875
0.65249
815.61
4121 (65%)
1
0.65
832
3523.9
0.5176
662.53
3468.9
2
0.65
832
0.5
640.00
4
0.65
832
0.99951
1279.37
1.56%
5
0.65
812.5
0.66618
832.73
6
0.65
812.5
0.56549
706.86
3804 (60%)
1
0.6
768
3253.7
0.52981
678.16
3223.2
2
0.6
768
0.50098
641.25
4
0.6
768
0.74438
952.81
0.94%
5
0.6
750
0.67302
841.28
6
0.6
750
0.55279
690.99
3487 (55%)
1
0.55
704
2991
0.52884
676.92
2967.9
2
0.55
704
0.5
640.00
4
0.55
704
0.51222
655.64
0.77%
5
0.55
687.5
0.67058
838.23
6
0.55
687.5
0.54106
676.33Table7 shows the optimal chiller loading by LR + ELD and NN + GA methods under partial load ratio of 0.55~0.95. The results indicated that the NN + GA method had better energy savings than LR + ELD method by 2.63% to 16.95% in the partial load ratios of 0.55 to 0.95, with the average energy savings of 12.14%. The power consumption of chiller simulated by LR + ELD and NN + GA methods increased from 2991 to 5301.3 kW and from 29127.3 to 4405.2 kW, respectively.Table 7
Optimal chiller loading comparison by LRELD and NNGA methods.
Cooling load (RT)
Chiller
LR + ELD
NN + GA
Saving A − B (%)
PLR
Load (RT)
Total (kW)  (A)
PLR
Load (RT)
Total (kW)  (B)
6023 (95%)
1
0.95
1216
5301.3
0.99658
1275.62
4405.2
2
0.95
1216
1
1280.00
4
0.95
1216
1
1280.00
16.90%
5
0.95
1187.5
1
1250.00
6
0.95
1187.5
0.75024
937.80
5706 (90%)
1
0.9
1152
4986.5
0.99316
1271.24
4141.4
2
0.9
1152
1
1280.00
4
0.9
1152
1
1280.00
16.95%
5
0.9
1125
1
1250.00
6
0.9
1125
0.5
625.00
5389 (85%)
1
0.85
1088
4679.1
0.74536
954.06
3937.3
2
0.85
1088
1
1280.00
4
0.85
1088
1
1280.00
15.85%
5
0.85
1062.5
1
1250.00
6
0.85
1062.5
0.5
625.00
5072 (80%)
1
0.8
1024
4379.2
0.5
640.00
3696
2
0.8
1024
1
1280.00
4
0.8
1024
1
1280.00
15.60%
5
0.8
1000
0.99804
1247.55
6
0.8
1000
0.5
625.00
4755 (75%)
1
0.75
960
4086.7
0.50489
646.26
3547.7
2
0.75
960
1
1280.00
4
0.75
960
1
1280.00
13.19%
5
0.75
937.5
0.67791
847.39
6
0.75
937.5
0.56109
701.36
4438 (70%)
1
0.7
896
3801.6
0.5
640.00
3344
2
0.7
896
1
1280.00
4
0.7
896
0.99071
1268.11
12.04%
5
0.7
875
0.5
625.00
6
0.7
875
0.5
625.00
4121 (65%)
1
0.65
832
3523.9
0.5
640.00
3177.9
2
0.65
832
1
1280.00
4
0.65
832
0.61193
783.27
9.82%
5
0.65
812.5
0.5826
728.25
6
0.65
812.5
0.55279
690.99
3804 (60%)
1
0.6
768
3253.7
0.5
640.00
3048
2
0.6
768
0.9956
1274.37
4
0.6
768
0.5
640.00
6.32%
5
0.6
750
0.5
625.00
6
0.6
750
0.5
625.00
3487 (55%)
1
0.55
704
2991
0.5
640.00
2912.3
2
0.55
704
0.69208
885.86
4
0.55
704
0.55572
711.32
2.63%
5
0.55
687.5
0.5
625.00
6
0.55
687.5
0.5
625.00Table8 shows the optimal chiller loading by LR + ELD and ANFIS + GA methods under partial load ratio of 0.55~0.95. The results indicated that the ANFIS + GA method had better energy savings than LR + ELD method by 0.36% to 186.96% in the partial load ratios of 0.55 to 0.95, with the average energy savings of 12.84%. The power consumption of chiller, simulated by LR + ELD and ANFIS + GA methods, increased from 2991 to 5301.3 kW and from 2980.2 to 4296.3 kW, respectively. Table 9 presents the operating conditions of chiller system by using ANFIS + GA method.Table 8
Optimal chiller loading comparison by LRELD and ANFIS + GA methods.
Cooling load (RT)
Chiller
LR + ELD
ANFIS + GA
Saving A − B (%)
PLR
Load (RT)
Total (kW)  (A)
PLR
Load (RT)
Total (kW)  (B)
6023 (95%)
1
0.95
1216
5301.3
0.87537
1120.47
4296.3
2
0.95
1216
0.87732
1122.97
4
0.95
1216
1
1280
18.96%
5
0.95
1187.5
1
1250
6
0.95
1187.5
1
1250
5706 (90%)
1
0.9
1152
4986.5
0.56549
723.8272
4052.9
2
0.9
1152
0.93939
1202.42
4
0.9
1152
1
1280
18.72%
5
0.9
1125
1
1250
6
0.9
1125
1
1250
5389 (85%)
1
0.85
1088
4679.1
0.5
640
3831.3
2
0.85
1088
0.75806
9703.32
4
0.85
1088
1
1280
18.12%
5
0.85
1062.5
0.99902
1248.78
6
0.85
1062.5
1
1250
5072 (80%)
1
0.8
1024
4379.2
0.51075
653.76
3625.8
2
0.8
1024
0.5
640
4
0.8
1024
1
1280
17.20%
5
0.8
1000
0.99902
1248.78
6
0.8
1000
1
1250
4755 (75%)
1
0.75
960
4086.7
0.5
640
3478.3
2
0.75
960
0.5
640
4
0.75
960
1
1280
14.89%
5
0.75
937.5
0.88416
1105.2
6
0.75
937.5
0.87195
1089.94
4438 (70%)
1
0.7
896
3801.6
0.5
640
3284.3
2
0.7
896
0.5
640
4
0.7
896
1
1280
11.66%
5
0.7
875
0.93744
1171.8
6
0.7
875
0.565
706.25
4121 (65%)
1
0.65
832
3523.9
0.55034
704.44
3195.8
2
0.65
832
0.5
640
4
0.65
832
0.63099
807.67
9.31%
5
0.65
812.5
1
1250
6
0.65
812.5
0.57527
719.09
3804 (60%)
1
0.6
768
3253.7
0.5
640
3048.2
2
0.6
768
0.5
640
4
0.6
768
0.59677
763.87
6.32%
5
0.6
750
0.88172
1093.6
6
0.6
750
0.52639
666.55
3487 (55%)
1
0.55
704
2991
0.5
640
2980.2
2
0.55
704
0.5
640
4
0.55
704
0.61975
793.28
0.36%
5
0.55
687.5
0.56207
702.59
6
0.55
687.5
0.56891
711.14Table 9
Optimal loading conditions of chiller system operated by ANFIS + GA method.
ANFIS
Type
Training
Generate FIS
Gird partition
MF type
psigmf
MF type
Linear
Train FIS optim. methood
Hybrid
Epochs
100
GA
Popsize
300
Maxgen
400
Crossover rate
0.5
Mutation rate
0.05From Tables6 to 8, the chiller operated by ANFIS + GA method would have better energy savings of 18.96% among these three methods. This may be due to the better combination capability of GA method for the chiller under partial load ratios to achieve better energy savings.In order to further understand the relationships of energy usages and savings with these methods, the power consumptions and energy savings of these methods with respect to the partial load ratios are shown in Figure7. In Figure 7, in the partial load ratio range of 0.55 to 0.95, the power consumption increased from 2980.2 to 4296.3 kW, from 2912.3 to 4405.2 kW, from 2967.9 to 5240.8 kW, and from 2991 to 5301.3 kW for ANFIS + GA, NN + GA, LR + GA, and LR + ELD methods, respectively. The chiller simulated by ANFIS + GA method consumed the least power. Compared with LR + ELD, in the partial load ratio range of 0.55 to 0.95, the energy savings increased from 0.36 to 18.96%, from 2.63 to 16.90%, and from 0.77 to 1.14% for the simulating methods of ANFIS + GA, NN + GA, and LR + GA, respectively. Among them, the chiller simulated by ANFIS + GA had better energy savings of 12.84%. This may be due to the better inference capability and solving ability of ANFIS method for nonlinear problems and more flexible combinations and better energy saving effect of GA method.Figure 7
Power consumption between LR + ELD, LR + GA, NN + GA, and ANFIS + GA methods.


## 6. Conclusion

A central air-conditioning (AC) system includes the chiller‚ chiller water pump‚ cooling water pump‚ cooling tower, and chilled water secondary pumps. Among these devices, the chiller consumes most power of the central AC system. In this paper, the adaptive neuro-fuzzy inference system (ANFIS) and genetic algorithm (GA) were utilized for optimizing the chiller loading. The ANFIS could construct a power consumption model of the chiller, reduce modeling period, and maintain the accuracy. GA could optimize the chiller loading for better energy efficiency. The simulating results indicated that ANFIS combined with GA could optimize the chiller loading. The power consumption was reduced by 6.32%–18.96% when partial load ratio was located at the range of 0.6~0.95. The chiller power consumption model established by ANFIS could also increase the convergence speed. Therefore, the ANFIS with GA could optimize the chiller loading for reducing power consumption.The chiller power consumption model established by ANFIS could also increase the convergence speed with average processing period of 2 min 15 sec. Compared with LR + ELD, ANFIS + GA, NN + GA, and LR + GA methods, the chiller simulated by ANFIS + GA method had better energy savings of 12.84%. This may be due to the better inference capability and solving ability of ANFIS method for nonlinear problems and more flexible combinations and better energy saving effect of GA method. Therefore, the ANFIS with GA could optimize the chiller loading for reducing power consumption.



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*Source: 306401-2015-07-01.xml*