CHP-Based Economic Emission Dispatch of Microgrid Using Harris Hawks Optimization
Abstract
:1. Introduction
- The HHO algorithm was implemented to analyze its effectiveness in solving the DG placement and the load dispatch problem for an MG.
- Selection of optimal size and location of DGs for a 14-bus RDS.
- Load dispatch was conducted under two different scenarios (i.e., with and without renewable energy for minimization of cost and minimization of emission.
- TOPSIS was implemented to obtain the best-compromised solution (BCS).
2. Problem Formulation
2.1. Optimal Placement of DG
2.2. Economic Dispatch
2.2.1. Modeling of Conventional Thermal Generators
2.2.2. Modeling of Wind Power Plant
2.2.3. Modeling of Fuel-Cell Unit
2.3. Emission Dispatch
2.4. Formulation of Multiobjective CHPEED Problem
2.5. Constraints
2.6. TOPSIS
3. Harris Hawks Optimization
- A prey for the Harris hawk is a rabbit having great escaping energy; therefore, several hawks cooperatively attack to prey simultaneously from different directions.
- This attack can be completed quickly, but sometimes considering the escape ability and behavior of the prey, it takes a few short-length, quick dives nearby the prey.
- The different phase of chasing a prey depends on the prey’s escaping pattern with other dynamic conditions.
- The switching strategy occurs when the best hawk (leader) stops and becomes lost on the hunt, and one of the other group members will pursue the chase.
- The Harris hawk can switch between these phases to confuse the prey, which leads to their exhaustion, and increases its vulnerability.
- Furthermore, by confusing the escaping prey, it cannot recover its defensive abilities and, in the end, it cannot escape from the team and encounter one of the hawks, which is often the most powerful and experienced, easily grabs the tired prey, and shares it with another group member.
3.1. Exploration Stage
3.2. Transition from Exploration to Exploitation
3.3. Exploitation Stage
3.3.1. Soft Besiege
3.3.2. Hard Besiege
3.3.3. Soft Besiege with Progressive Rapid Dives
3.3.4. Hard Besiege with Progressive Rapid Dives
4. Simulation Results
4.1. Description of Test Cases
- (i)
- A two-diesel generator (Dg) with the sizes of 200 kW and 100 kW was selected and placed on buses 7 and 13, respectively. Similarly, the two microturbines (MTs) were selected with the sizes of 80 kW and 30 kW and placed on buses 3 and 14, respectively. A Dg with the size of 500 kW was selected as a virtual generator to cover the peak demand of 495 kW.
- (ii)
- To analyze the impact of renewable energy integration(REI), the Dg of capacity 100 kW at bus 13 was replaced by a fuel cell (FC), the MT of 30 kW of bus 14 was replaced by a wind turbine with a capacity of 40 kW, and rest was the same as above.
4.2. Discussion
4.2.1. Best Cost Solution
4.2.2. Best Emission Solution
4.2.3. Best Compromise Solution
4.2.4. Heat Output
5. Conclusions
- HHO is simple to implement and found to be impactful for the solution of both SCHPEED and MCHPEED complex constrained optimization problems.
- With REI, fuel cost is reduced by 6.53 USD/h (18%) and emission is reduced by 1.519 g/kWh(3.4%) for SCHPEED, whereas fuel cost is reduced by USD 179.759 (14.95%) and emission is reduced by 59.60 g/kW (5.58%) for MCHPEED.
- Heat output is found to be sensitive to changes in load demand
- Operational cost, emission, and heat output are minimized with REI.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
FC | Fuel cell | RDS | Radial distribution system |
DG | distributed generators | CHP | Combined heat and power |
MG | microgrid | EED | Economic emission dispatch |
WPP | Wind power plant | SCHPEED | CHP under EED for static (fixed) load |
MT | Micro Turbine | MCHPEED | CHP under EED for Multiple (dynamic) load |
REI | Renewable Energy Integration | BCS | Best compromise solution |
penalty cost due to underestimation of wind | Probability distribution function | ||
reserve cost due to overestimation of wind | Minimum and maximum voltage | ||
shape factor | cost of thermal units, wind power plant, and fuel cell, respectively | ||
scale factor | Cut-in velocity, cut-out velocity, and rated velocity in m/s, respectively | ||
Total heat output | Heat-to-power ratio of ith DG unit | ||
Total heat demand. | Cost and emission function | ||
Price penalty factor | Weighting factor |
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Bus No. | Start Bus | End Bus | R | X | Real | Reactive |
---|---|---|---|---|---|---|
1 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 1 | 2 | 0.0133 | 0.042 | 20 | 6 |
3 | 2 | 3 | 0.0194 | 0.059 | 85 | 27 |
4 | 3 | 4 | 0.0312 | 0.16 | 40 | 1 |
5 | 2 | 5 | 0.023 | 0.12 | 20 | 6 |
6 | 5 | 6 | 0.023 | 0.12 | 20 | 6 |
7 | 6 | 7 | 0.0193 | 0.059 | 76 | 16 |
8 | 6 | 8 | 0.032 | 0.084 | 10 | 30 |
9 | 7 | 9 | 0.034 | 0.17 | 61 | 16 |
10 | 2 | 10 | 0.016 | 0.042 | 12 | 75 |
11 | 10 | 11 | 0.193 | 0.059 | 10 | 90 |
12 | 11 | 12 | 0.067 | 0.17 | 16 | 61 |
13 | 12 | 13 | 0.04 | 0.1 | 90 | 59 |
14 | 11 | 14 | 0.05 | 0.15 | 35 | 61 |
Parameters | Without DGs | With 4 DGs |
---|---|---|
Power Loss (kW) | 0.1995 | 0.1297 |
Loss Reduction (%) | - | 34.99 |
DGs Size (kW) /Location | - | 90.3178/3, 187.9/7, 114.9414/13, 44.8314/14 |
Total DG Size (kW) | - | 437.9906 |
(pu) | 0.9992 | 0.9995 |
(pu) | 0.9998 | 0.9999 |
Type | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Dg | 500 | 0.00 | 500 | 10.193 | 105.18 | 62.56 | 26.55 | −16.1836 | 7.0508 | 10,314 |
Dg | 200 | 40 | 200 | 2.035 | 60.28 | 44.0 | 14.4296 | −64.1535 | 130.4094 | 11,041 |
MT | 80 | 16 | 80 | 0.5768 | 57.783 | −133.0915 | 3.0358 | −57.3403 | 311.5728 | 11,373 |
Dg | 100 | 20 | 100 | 1.1825 | 65.34 | 44.0 | 19.38 | −176.6946 | 821.6573 | 10,581 |
MT | 30 | 6.0 | 30 | 0.338 | 89.1476 | −547.619 | 1.0346 | −60.384 | 943.1898 | 12,186 |
FC | 100 | 0 | 100 | 0 | 0.07 | 0 | 0 | 0 | 0 | 0 |
WPP | 40 | 0 | 40 | 0 | 0.22 | 0 | 0 | 0 | 0 | 0 |
Scenarios | Methods | Fuel Cost (USD/h) | Emission (g/kWh) | Heat (kWh) | Loss (kW) | |||||
---|---|---|---|---|---|---|---|---|---|---|
Best Cost | HHO | 0.00 | 157.09 | 80.00 | 73.1552 | 30.00 | 35.8483 | 45.4856 | 347.5639 | 2.2452 |
DE [32] | 0.00 | 166.30 | 80.00 | 64.30 | 30.00 | 35.8974 | 45.8467 | 348.048 | --- | |
PSO [32] | 0.00 | 166.68 | 80.00 | 63.89 | 30.00 | 35.897 | 45.870 | 348.000 | --- | |
Best Emission | HHO | 0.00 | 168.8009 | 57.1848 | 96.0540 | 21.0526 | 36.9396 | 44.8121 | 329.3694 | 5.0922 |
DE [32] | 0.00 | 166.50 | 58.30 | 96.10 | 21.50 | 36.851 | 44.820 | 329.790 | --- | |
PSO [32] | 0.00 | 166.20 | 58.64 | 96.07 | 21.66 | 36.840 | 44.820 | 330.070 | --- | |
BCS | HHO | 0.00 | 146.4312 | 80.00 | 89.92 | 24.7656 | 35.9695 | 45.0773 | 344.0685 | 3.1168 |
DE [32] | 0.00 | 150.54 | 80.00 | 90.92 | 20.55 | 36.0720 | 45.020 | 341.7225 | --- | |
PSO [32] | 0.00 | 150.20 | 80.00 | 89.86 | 21.95 | 36.0600 | 45.030 | 342.7200 | ---- |
Scenario | Total Cost (USD/h) | Fuel Cost (USD/h) | Wind Cost (USD/h) | Emission (g/kWh) | Heat (kWh) | Loss (kW) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
Best Cost | 0.00 | 174.8425 | 95.6318 | 33.2694 | 39.8741 | 29.3180 | 27.5252 | 1.7928 | 48.1604 | 171.1845 | 5.6179 |
Best Emission | 0.00 | 200.00 | 50.1720 | 100.00 | 0.4670 | 34.4114 | 34.2040 | 0.2074 | 43.2924 | 244.9725 | 12.6390 |
BCS | 0.00 | 155.0687 | 92.0436 | 88.6900 | 9.1448 | 30.3835 | 29.9638 | 0.4197 | 44.3393 | 198.7907 | 6.9470 |
Scenario | MCHPEED | MCHPEED with REI | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Total Cost (USD) | Emission (g/kW) | Heat (kW) | Loss (kW) | Total Cost (USD) | Fuel Cost (USD) | Wind Cost (USD) | Emission (g/kW) | Heat (kW) | Loss (kW) | |
Min.Cost | 1203.0999 | 1089.9256 | 15,587.8723 | 203.5641 | 1023.3403 | 1003.2465 | 20.0938 | 1085.8532 | 15,528.2799 | 167.1917 |
Min. Emis | 1250.0066 | 1068.1567 | 15,918.5405 | 309.1087 | 1384.1995 | 1361.902 | 22.2975 | 1008.5490 | 17,674.5642 | 555.1573 |
BCS | 1211.5507 | 1077.6050 | 15,588.9110 | 212.6814 | 1094.9539 | 1070.9602 | 23.9937 | 1050.8518 | 15,579.2478 | 253.8731 |
S. No. | SCHPEED | SCHPEED with REI | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Fuel Cost (USD/h) | Emission (g/kWh) | TOPSIS | Total Cost (USD/h) | Emission (g/kWh) | TOPSIS | |||||
1 | 35.9695 | 45.0773 | 0.002 | 0.0079 | 0.796 | 30.3835 | 44.3393 | 0.0111 | 0.0415 | 0.7886 |
2 | 36.0148 | 45.0389 | 0.002 | 0.0077 | 0.7941 | 30.5396 | 44.2242 | 0.0117 | 0.041 | 0.7784 |
3 | 35.8766 | 45.1944 | 0.0026 | 0.0083 | 0.7613 | 30.0147 | 45.1952 | 0.014 | 0.0407 | 0.7433 |
4 | 36.1974 | 44.96 | 0.0028 | 0.0067 | 0.7039 | 30.2459 | 45.2667 | 0.0153 | 0.0388 | 0.7172 |
5 | 35.8483 | 45.4856 | 0.0046 | 0.0083 | 0.6436 | 30.3843 | 45.336 | 0.0163 | 0.0376 | 0.698 |
6 | 36.4597 | 44.8753 | 0.0046 | 0.0056 | 0.5464 | 31.5101 | 43.9487 | 0.0182 | 0.0368 | 0.6697 |
7 | 36.6261 | 44.8394 | 0.0059 | 0.0051 | 0.4633 | 31.4086 | 44.444 | 0.0185 | 0.0349 | 0.6531 |
8 | 36.7405 | 44.8232 | 0.0068 | 0.0048 | 0.4177 | 31.8543 | 44.1804 | 0.0213 | 0.0339 | 0.6146 |
9 | 36.8258 | 44.8157 | 0.0074 | 0.0047 | 0.3901 | 29.6449 | 47.2935 | 0.0272 | 0.0388 | 0.5877 |
10 | 36.9396 | 44.8121 | 0.0083 | 0.0047 | 0.3614 | 29.318 | 48.1604 | 0.0329 | 0.041 | 0.5542 |
S. No. | MCHPEED | MCHPEED with REI | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Fuel Cost (USD) | Emission (g/kW) | TOPSIS | Total Cost (USD) | Emission (g/kW) | TOPSIS | |||||
1 | 1211.551 | 1077.605 | 0.0342 | 0.1084 | 0.7602 | 1094.954 | 1050.852 | 0.1551 | 0.5313 | 0.7741 |
2 | 1216.566 | 1072.838 | 0.0381 | 0.1015 | 0.7268 | 1137.664 | 1039.921 | 0.2188 | 0.4576 | 0.6765 |
3 | 1216.921 | 1074.578 | 0.0406 | 0.0988 | 0.709 | 1175.755 | 1033.977 | 0.2841 | 0.3924 | 0.58 |
4 | 1203.1 | 1089.926 | 0.0561 | 0.1241 | 0.6888 | 1199.708 | 1030.557 | 0.3263 | 0.3522 | 0.5191 |
5 | 1221.714 | 1073.912 | 0.0509 | 0.0891 | 0.6365 | 1228.073 | 1028.583 | 0.3772 | 0.3045 | 0.4467 |
6 | 1222.0187 | 1082.3297 | 0.044 | 0.0578 | 0.5677 | 1260.982 | 1023.543 | 0.4362 | 0.2537 | 0.3677 |
7 | 1223.182 | 1087.8793 | 0.0522 | 0.0542 | 0.5093 | 1280.761 | 1022.409 | 0.4721 | 0.2236 | 0.3214 |
8 | 1227.4204 | 1086.4162 | 0.056 | 0.0471 | 0.4568 | 1306.819 | 1015.037 | 0.519 | 0.1947 | 0.2728 |
9 | 1230.0698 | 1089.8465 | 0.0635 | 0.0421 | 0.3983 | 1347.69 | 1013.701 | 0.5934 | 0.1521 | 0.204 |
10 | 1250.007 | 1068.157 | 0.1173 | 0.057 | 0.3272 | 1384.2 | 1008.549 | 0.6598 | 0.1465 | 0.183 |
Hr. | Load (kW) | Heat (kW) | |||||
---|---|---|---|---|---|---|---|
1 | 0.1742 | 43.8226 | 18.95 | 28.9484 | 13.7722 | 105 | 107.6286 |
2 | 0.0439 | 100.2222 | 20.8996 | 57.2967 | 15.1846 | 190 | 181.4153 |
3 | 7.9917 | 106.5203 | 41.9026 | 82.8549 | 15.4974 | 250 | 257.7412 |
4 | 34.6496 | 86.6041 | 79.7197 | 95.8914 | 16.1365 | 310 | 375.0671 |
5 | 79.0714 | 122.3964 | 76.6417 | 98.9171 | 25.9711 | 400 | 532.2534 |
6 | 111.5772 | 186.8943 | 79.5952 | 91.3479 | 24.9627 | 490 | 666.1347 |
7 | 146.7594 | 199.9927 | 78.8478 | 99.8593 | 29.8921 | 550 | 780.8991 |
8 | 256.9116 | 199.6686 | 77.2061 | 99.9982 | 29.1331 | 650 | 1061.2783 |
9 | 300.363 | 199.9386 | 79.9998 | 99.7264 | 28.9461 | 690 | 1177.0124 |
10 | 364.7395 | 199.1256 | 78.1749 | 99.9798 | 28.6631 | 740 | 1339.5097 |
11 | 377.7434 | 200 | 79.9864 | 98.3194 | 27.7766 | 750 | 1373.6715 |
12 | 353.816 | 197.5439 | 79.9687 | 100 | 27.3565 | 730 | 1310.6095 |
13 | 292.299 | 196.903 | 78.4594 | 99.9998 | 30 | 680 | 1153.3381 |
14 | 232.1257 | 199.7308 | 80 | 99.892 | 28.6524 | 630 | 1000.5748 |
15 | 183.5236 | 198.0663 | 78.5526 | 97.0593 | 29.4762 | 580 | 870.8251 |
16 | 173.3918 | 175.3966 | 64.5036 | 99.9331 | 27.4251 | 535 | 805.1119 |
17 | 137.2064 | 147.8064 | 78.3677 | 79.0651 | 21.3752 | 460 | 682.8948 |
18 | 99.7382 | 139.1221 | 67.8092 | 85.6515 | 20.4403 | 410 | 567.8843 |
19 | 59.8613 | 75.3932 | 79.433 | 89.8884 | 17.4494 | 320 | 427.6205 |
20 | 1.3002 | 129.0986 | 56.3055 | 76.8063 | 11.8101 | 270 | 269.2425 |
21 | 6.216 | 92.0592 | 22.5511 | 77.3491 | 11.2522 | 205 | 202.8413 |
22 | 2.9803 | 72.9563 | 33.5925 | 52.3411 | 10.0549 | 170 | 172.7066 |
23 | 0 | 58.0973 | 31.3545 | 53.8645 | 8.5012 | 150 | 148.3782 |
24 | 4.6627 | 41.2238 | 27.9014 | 23.5275 | 12.9832 | 110 | 124.272 |
Hr. | Load (kW) | Heat (kW) | |||||
---|---|---|---|---|---|---|---|
1 | 0.4602 | 55.8001 | 0.0026 | 38.1092 | 12.2087 | 105 | 77.6358 |
2 | 0.0014 | 67.2099 | 32.6849 | 76.9633 | 16.9728 | 190 | 116.7346 |
3 | 16.6051 | 76.3607 | 49.985 | 97.6993 | 13.7738 | 250 | 183.5804 |
4 | 43.8702 | 95.4026 | 65.24 | 86.5622 | 21.4451 | 310 | 260.8134 |
5 | 2.0257 | 193.1514 | 84.1992 | 99.9095 | 31.4198 | 400 | 244.4528 |
6 | 137.9878 | 156.3819 | 94.3015 | 81.5604 | 23.9735 | 490 | 550.0218 |
7 | 172.6773 | 181.9743 | 83.4654 | 84.7427 | 33.0027 | 550 | 663.1865 |
8 | 248.3451 | 198.6839 | 88.2413 | 97.6099 | 29.5584 | 650 | 882.3438 |
9 | 339.0121 | 193.143 | 90.55 | 73.6115 | 23.326 | 690 | 1092.496 |
10 | 389.558 | 193.4966 | 93.7557 | 85.5281 | 17.9975 | 740 | 1232.578 |
11 | 372.8658 | 192.9266 | 95.0478 | 96.2457 | 27.3994 | 750 | 1197.57 |
12 | 365.0877 | 198.1613 | 72.7586 | 87.811 | 37.2745 | 730 | 1175.156 |
13 | 288.2583 | 183.1858 | 95.2879 | 96.5362 | 34.9216 | 680 | 971.5743 |
14 | 238.2183 | 198.1671 | 83.9061 | 83.2904 | 37.8205 | 630 | 844.4403 |
15 | 198.0663 | 199.9986 | 68.8349 | 84.5582 | 35.8806 | 580 | 743.4311 |
16 | 161.1864 | 184.6829 | 70.2232 | 89.7806 | 34.1974 | 535 | 639.7981 |
17 | 98.8017 | 154.436 | 88.2272 | 92.8929 | 28.9415 | 460 | 456.3623 |
18 | 33.2158 | 174.0753 | 76.4767 | 99.9994 | 33.2225 | 410 | 309.1514 |
19 | 16.428 | 103.6468 | 67.9597 | 97.0659 | 39.9701 | 320 | 205.216 |
20 | 15.2292 | 136.6882 | 29.9529 | 62.3144 | 30.3556 | 270 | 201.9077 |
21 | 0 | 59.1014 | 39.9741 | 90.1443 | 20.5677 | 205 | 120.4767 |
22 | 9.5316 | 78.936 | 2.6982 | 64.9587 | 17.4007 | 170 | 141.4918 |
23 | 1.3006 | 47.4008 | 42.5158 | 51.3921 | 8.6482 | 150 | 83.3885 |
24 | 0.2675 | 60.3013 | 12.1609 | 36.1635 | 2.3829 | 110 | 79.3222 |
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Tiwari, V.; Dubey, H.M.; Pandit, M.; Salkuti, S.R. CHP-Based Economic Emission Dispatch of Microgrid Using Harris Hawks Optimization. Fluids 2022, 7, 248. https://doi.org/10.3390/fluids7070248
Tiwari V, Dubey HM, Pandit M, Salkuti SR. CHP-Based Economic Emission Dispatch of Microgrid Using Harris Hawks Optimization. Fluids. 2022; 7(7):248. https://doi.org/10.3390/fluids7070248
Chicago/Turabian StyleTiwari, Vimal, Hari Mohan Dubey, Manjaree Pandit, and Surender Reddy Salkuti. 2022. "CHP-Based Economic Emission Dispatch of Microgrid Using Harris Hawks Optimization" Fluids 7, no. 7: 248. https://doi.org/10.3390/fluids7070248