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 air-conditioning system is highly demanded in human’s life and industrial process. However, it consumes electrical power with the ratio around 50% [
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 [
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.
The general decoupled system of a central air-conditioning system is shown in Figure
Decoupled system of a central AC system [
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
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 [
The chiller power consumption model could be established by ANFIS. The program could be expressed by
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
The restrictive limitations could be presented in
In order to prevent the low operating efficiency and surge of the chiller, the chiller could be set to the lowest load (
The ANFIS was proposed by Jang [
Figure
ANFIS architecture of the one order Sugeno fuzzy model.
The functions of five layers are described as follows: First layer: membership function of inputs Second layer: multiplication of the input signals, as described by ( It represents the firing strength of each fuzzy rule: Third layer: normalization of Fourth layer: node function described by Fifth layer: summation of previous layer as the output, as described by
In Figure
In this study, the temperature differences between cooling water return temperature (
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 Figure
ANFIS training flow chart.
GA was proposed by Holland et al. in 1970 and based on Darwin’s doctrine of evolution, natural selection, and survival of the fittest [
GA is different from the traditional optimization method and has the characteristics of stability and efficiency. The main features are shown as follows.
In this paper, a semiconductor factory with five chillers was under investigation. The specifications of these chillers are shown in Table
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 |
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 [
Coefficients of the chiller power consumption models from quadratic regression analysis.
Chiller | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
|
150.80 | 236.17 | −108.65 | 386.31 | 222.16 |
|
12.79 | −2.08 | 16.21 | −6.19 | −0.80 |
|
−0.51 | −0.56 | −0.56 | 0.18 | −0.22 |
|
−620.23 | −235.58 | 35.14 | −670.01 | −349.20 |
|
510.82 | −369.19 | −34.55 | 763.31 | 270.52 |
|
49.92 | 81.75 | 44.82 | 28.37 | 47.76 |
|
0.984181 | 0.983730 | 0.985550 | 0.985485 | 0.983580 |
Error (%) | 1.420413 | 0.854415 | 0.849768 | 0.845402 | 0.89693 |
Distribution of actual power consumption and simulated power consumption of chiller 1 by using regression analysis.
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. Figure
Distribution of actual power consumption and simulated power consumption of chiller 1 by using NN.
Figure
Distribution of actual power consumption and simulated power consumption of chiller 1 by using ANFIS.
The calculated
Regression coefficients and average percentage error of chillers by NN model.
Chiller | 1 | 2 | 4 | 5 | 6 |
---|---|---|---|---|---|
|
0.9998 | 0.9998 | 0.9999 | 0.9998 | 0.9998 |
err% | 0.88 | 0.83 | 0.80 | 0.82 | 0.85 |
Regression coefficients and average percentage error of chillers by ANFIS model.
Chiller | 1 | 2 | 4 | 5 | 6 |
---|---|---|---|---|---|
|
0.99988 | 0.99989 | 0.9999 | 0.99989 | 0.99988 |
err% | 0.88 | 0.83 | 0.81 | 0.83 | 0.86 |
From Tables
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 Table
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 |
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 [
Table
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 | 676.33 |
Table
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 | 625.00 |
Table
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 | 711.14 |
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 | 0.05 |
From Tables
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 Figure
Power consumption between LR + ELD, LR + GA, NN + GA, and ANFIS + GA methods.
A central air-conditioning (AC) system includes the chiller
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.
The authors declare no conflict of interests.