Applying Two-Stage Differential Evolution for Energy Saving in Optimal Chiller Loading
Abstract
:1. Introduction
2. Introduction to Multi-chiller System
3. Two-Stage Differential Evolution Algorithm
3.1. Differential Evolution Algorithm
3.1.1. Mutation Operator
3.1.2. Crossover Operator
3.1.3. Selection Operator
3.2. Modified Binary Differential Evolution (MBDE) Algorithm
3.2.1. Mutation Operator
3.2.2. Crossover Operator
3.2.3. Selection Operator
3.3. Two-Stage Differential Evolution Algorithm
4. Results, Analyses and Discussions
4.1. Case Study 1
4.2. Case Study 2
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Chiller | Rated RT | |||
---|---|---|---|---|
1 | 399.345 | −122.12 | 206.30 | 1280 |
2 | 287.116 | 80.04 | 700.48 | 1280 |
3 | −120.505 | 1525.99 | −502.14 | 1280 |
4 | −19.121 | 898.76 | −98.15 | 1280 |
5 | −95.029 | 1202.39 | −352.16 | 1280 |
6 | 191.75 | 224.86 | 524.04 | 1280 |
CL | Algorithm | MIN (kW) | Average (kW) | Max (kW) | SD |
---|---|---|---|---|---|
6868 (90%) | Two-stage DE | 4738.575 | 4733.575 | 4738.575 | 3.919x10−6 |
DCSA | 4738.575 | 4738.575 | 4738.575 | 5.313 × 10−7 | |
6477 (85%) | Two-stage DE | 4421.649 | 4421.649 | 4421.650 | 6.355 × 10−5 |
DCSA | 4421.649 | 4421.650 | 4421.650 | 2.301 × 10−4 | |
6096 (80%) | Two-stage DE | 4143.706 | 4143.709 | 4143.714 | 3.211 × 10−4 |
DCSA | 4143.706 | 4143.710 | 4143.709 | 4.299 × 10−4 | |
5717 (75%) | Two-stage DE | 3838.208 | 3838.217 | 3838.225 | 6.702 × 10−4 |
DCSA | 3840.055 | 3840.458 | 3843.766 | 9.428 × 10−1 | |
5334 (70%) | Two-stage DE | 3507.270 | 3507.278 | 3507.302 | 1.356 × 10−3 |
DCSA | 3507.270 | 3507.715 | 3511.760 | 1.036 |
CL | Chiller No. | SA [20] | Power (kW) | PSO [6] | Power (kW) | DCSA [8] | Power (kW) | Two Stage DE | Power (kW) |
---|---|---|---|---|---|---|---|---|---|
i | PLRi | of | PLRi | of | PLRi | of | PLRi | of | |
6898 (90%) | 1 | 0.7789 | 4777.03 | 0.8026 | 4739.53 | 0.812726 | 4738.575 | 0.81273 | 4738.5750 |
2 | 0.7587 | 0.7799 | 0.749619 | 0.749554 | |||||
3 | 0.9791 | 0.9996 | 1.000000 | 1.000000 | |||||
4 | 0.9781 | 0.9998 | 1.000000 | 1.000000 | |||||
5 | 0.9820 | 0.9999 | 1.000000 | 1.000000 | |||||
6 | 0.9265 | 0.8183 | 0.838559 | 0.838621 | |||||
6477 (85%) | 1 | 0.8051 | 4453.67 | 0.7606 | 4423.04 | 0.727731 | 4421.649 | 0.720409 | 4421.6486 |
2 | 0.6056 | 0.6555 | 0.656132 | 0.634290 | |||||
3 | 0.9689 | 1.0000 | 1.000000 | 1.000000 | |||||
4 | 0.9941 | 1.0000 | 1.000000 | 1.000000 | |||||
5 | 0.9866 | 1.0000 | 1.000000 | 1.000000 | |||||
6 | 0.7432 | 0.6835 | 0.716524 | 0.746387 | |||||
6096 (80%) | 1 | 0.5635 | 4178.73 | 0.6591 | 4147.69 | 0.642735 | 4143.706 | 0.642368 | 4143.7064 |
2 | 0.5743 | 0.5798 | 0.562645 | 0.562711 | |||||
3 | 0.9675 | 0.9991 | 1.000000 | 0.999999 | |||||
4 | 0.9798 | 0.9979 | 1.000000 | 0.999999 | |||||
5 | 0.9845 | 0.9921 | 1.000000 | 0.999999 | |||||
6 | 0.7338 | 0.5710 | 0.594490 | 0.594798 | |||||
5717 (75%) | 1 | 0.6140 | 3925.51 | 0.7713 | 3921.07 | 0.843697 | 3840.055 | 0.843243 | 3838.2079 |
2 | 0.4429 | 0.7177 | 0.783794 | 0.783222 | |||||
3 | 0.9891 | 0.3000 | 0.000001 | 0.000000 | |||||
4 | 0.8867 | 0.9991 | 1.000000 | 0.999999 | |||||
5 | 0.9841 | 1.0000 | 1.000000 | 0.999999 | |||||
6 | 0.587S | 0.7187 | 0.883049 | 0.882499 | |||||
5334 (70%) | 1 | 0.6265 | 3675.34 | 0.6418 | 3642.55 | 0.749969 | 3507.270 | 0.758176 | 3507.269 |
2 | 0.7403 | 0.6621 | 0.682477 | 0.689668 | |||||
3 | 0.3093 | 0.3301 | 0.000012 | 0.000000 | |||||
4 | 0.9546 | 0.9906 | 1.000000 | 1.000000 | |||||
5 | 0.9511 | 0.9990 | 1.000000 | 1.000000 | |||||
6 | 0.6250 | 0.5806 | 0.776363 | 0.760606 |
Chiller | Rated RT | ||||
---|---|---|---|---|---|
1 | 104.09 | 166.57 | −430.13 | 512.53 | 450 |
2 | −67.15 | 1177.79 | −2174.53 | 1456.53 | 450 |
3 | 384.71 | −779.13 | 1151.42 | −63.2 | 1000 |
4 | 541.63 | 413.48 | −3626.5 | 4021.41 | 1000 |
CL | Algorithm | MIN (kW) | Average (kW) | Max (kW) | SD |
---|---|---|---|---|---|
2610 (90%) | Two-Stage DE | 1857.297 | 1858.031 | 1859.626 | 1.317 × 10−1 |
DCSA | 1857.299 | 1857.315 | 1857.401 | 2.329 × 10−2 | |
2320 (80%) | Two-Stage DE | 1458.334 | 1458.344 | 1458.931 | 2.130 × 10−2 |
DCSA | 1455.665 | 1455.810 | 1458.478 | 5.303 × 10−1 | |
2030 (70%) | Two-Stage DE | 1178.138 | 1178.928 | 1182.952 | 0.2006 |
DCSA | 1178.137 | 1181.067 | 1199.495 | 4.803 | |
1740 (60%) | Two-Stage DE | 942.050 | 976.182 | 1001.170 | 4.9418 |
DCSA | 942.183 | 972.076 | 1008.493 | 25.721 | |
1450 (50%) | Two-Stage DE | 752.963 | 759.612 | 792.907 | 1.851 |
DCSA | 753.004 | 765.340 | 824.347 | 17.429 | |
1160 (40%) | Two-Stage DE | 583.938 | 630.990 | 661.460 | 3.985 |
DCSA | 583.923 | 644.933 | 726.016 | 44.015 |
CL | Chiller No. | GA [4] | Power (kW) | DE [7] | Power (kW) | PSO [6] | Power (kW) | DCSA [8] | Power (kW) | Two Stage DE | Power (kW) |
---|---|---|---|---|---|---|---|---|---|---|---|
i | PLRi | of | PLRi | of | PLRi | of | PLRi | of | PLRi | of | |
2610 (90%) | 1 | 0.990000 | 1862.18 | 0.99000 | 1857.30 | 0.990000 | 1857.30 | 0.990988 | 1857.299 | 0.990491 | 1857.297 |
2 | 0.950000 | 0.91000 | 0.910000 | 0.905473 | 0.905503 | ||||||
3 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | ||||||
4 | 0.740000 | 0.760000 | 0.760000 | 0.756593 | 0.756791 | ||||||
2320 (85%) | 1 | 0.860000 | 1457.23 | 0.830000 | 1455.66 | 0.830000 | 1455.66 | 0.828756 | 1455.665 | 0.822981 | 1455.733 |
2 | 0.810000 | 0.810000 | 0.810000 | 0.805457 | 0.801856 | ||||||
3 | 0.880000 | 0.900000 | 0.900000 | 0.896722 | 0.885369 | ||||||
4 | 0.6900D0 | 0.690000 | 0.690000 | 0.687883 | 0.685549 | ||||||
2030 (70%) | 1 | 0.660000 | 1183.80 | 0.730000 | 1178.14 | 0.730000 | 1178.14 | 0.773478 | 1178.137 | 0.725289 | 1178.138 |
2 | 0.760000 | 0.740000 | 0.740000 | 0.739801 | 0.739752 | ||||||
3 | 0.760000 | 0.720000 | 0.720000 | 0.721146 | 0.722185 | ||||||
4 | 0.640000 | 0.650000 | 0.650000 | 0.627878 | 0.648549 | ||||||
1740 (60%) | 1 | 0.600000 | 1001.62 | 0.600000 | 998.53 | 0.600000 | 998.53 | 0.767678 | 942.183 | 0.745135 | 942.059 |
2 | 0.700000 | 0.660000 | 0.660000 | 0.004531 | 0.000000 | ||||||
3 | 0.510000 | 0.560000 | 0.560000 | 0.746317 | 0.748647 | ||||||
4 | 0.590000 | 0.610000 | 0.610000 | 0.646189 | 0.656017 | ||||||
1450 (50%) | 1 | 0.600000 | 907.72 | 0.610000 | 820.07 | 0.610000 | 820.07 | 0.515832 | 753.004 | 0.599201 | 752.963 |
2 | 0.360000 | 0.000000 | 0.000000 | 0.000001 | 0.000000 | ||||||
4 | 0.440000 | 0.570000 | 0.570000 | 0.610547 | 0.S71431 | ||||||
4 | 0.580000 | 0.610000 | 0.610000 | 0,607328 | 0.656017 | ||||||
1160 (40%) | 1 | 0.330000 | 856.30 | 0.000000 | 651.07 | 0.000000 | 651.07 | 0,000000 | 583.923 | 0.000000 | 583.938 |
2 | 0.320000 | 0.000000 | 0.000000 | 0.000014 | 0.000012 | ||||||
3 | 0.320000 | 0.560000 | 0.560000 | 0.570369 | 0.556082 | ||||||
4 | 0.540000 | 0.600000 | 0.600000 | 0.589625 | 0.603912 |
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Lin, C.-M.; Wu, C.-Y.; Tseng, K.-Y.; Ku, C.-C.; Lin, S.-F. Applying Two-Stage Differential Evolution for Energy Saving in Optimal Chiller Loading. Energies 2019, 12, 622. https://doi.org/10.3390/en12040622
Lin C-M, Wu C-Y, Tseng K-Y, Ku C-C, Lin S-F. Applying Two-Stage Differential Evolution for Energy Saving in Optimal Chiller Loading. Energies. 2019; 12(4):622. https://doi.org/10.3390/en12040622
Chicago/Turabian StyleLin, Chang-Ming, Chun-Yin Wu, Ko-Ying Tseng, Chih-Chiang Ku, and Sheng-Fuu Lin. 2019. "Applying Two-Stage Differential Evolution for Energy Saving in Optimal Chiller Loading" Energies 12, no. 4: 622. https://doi.org/10.3390/en12040622
APA StyleLin, C.-M., Wu, C.-Y., Tseng, K.-Y., Ku, C.-C., & Lin, S.-F. (2019). Applying Two-Stage Differential Evolution for Energy Saving in Optimal Chiller Loading. Energies, 12(4), 622. https://doi.org/10.3390/en12040622