Scenario-Based Network Reconfiguration and Renewable Energy Resources Integration in Large-Scale Distribution Systems Considering Parameters Uncertainty
Abstract
:1. Introduction
- (1).
- Optimal allocation of WTs and PVs is performed while considering their uncertainties, including wind speed and solar irradiance, respectively.
- (2).
- Load uncertainty is considered in this study to step on the real-life benefits of DGs penetration during load alterations.
- (3).
- A bilevel multi-objective optimization approach is formulated to optimally size renewable WT/PV DGs along with network optimization from the planning and operational perspectives. Further, the optimal solution is chosen from the pareto solutions via a decision-making algorithm called ‘Technique for Order of Preference by Similarity to Ideal Solution’ (TOPSIS).
- (4).
- Case studies are conducted on real distribution networks, including the 59-node distribution network in Cairo and the 83-node distribution network of the Taiwan power company. Furthermore, the proposed optimization approach is tested on the 415-and 880-node large distribution networks, which are ensembled from the 83- node real distribution network.
2. Materials and Methods
2.1. Power Flow Equations
2.2. Distribution Network Reconfiguration
2.3. DG modeling
2.3.1. Wind Turbine DG
2.3.2. Solar Photovoltaic DG
2.4. Scenarios Reduction
2.5. TOPSIS
- Phase 1:
- A matrix , where and denote the number of alternatives and the criteria, respectively. A vector of preset weights is established for each criterion in which the sum of its weights equals one. After that, a matrix () called the ‘normalized matrix’ is established, where , and its elements are obtained using the following equation:
- Phase 2:
- A new matrix () is calculated, whose dimensions are , and its elements are calculated as follows:
- Phase 3:
- At this phase, the best and the worst alternatives are denoted by the vectors: and , respectively. The elements of and are denoted by and , respectively.
- Phase 4:
- For each alternative, the least-squares distances between the th alternative and and are expressed in Equations (12) and (13), respectively.
- Phase 5:
- At this phase, the similarity index for the th alternative () expressed in Equation (12) is calculated to sort the alternatives.
- Phase 6:
- Display the best alternative having the highest value.
2.6. System Performance Indices
2.6.1. Load Balancing Index (LBI)
2.6.2. Aggregate Voltage Deviation Index (AVDI)
2.6.3. Fast Voltage Stability Index (FVSI)
3. Problem Formulation
3.1. Objective Function
3.2. Constraints
Algorithm 1 The proposed bilevel multi-objective optimization for HC maximization |
|
4. Results and Discussion
5. Conclusions and Future Works
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Input Data and Indices | |
Aggregated voltage deviation index | |
Aggregated voltage deviation index at the sth scenario | |
Overall aggregated voltage deviation index for all scenarios | |
The set of nodes | |
The set of lines | |
Aggregated fast voltage stability index | |
Aggregated FVSI for all distribution system lines at the sth scenario | |
FVSI of the bth line at the sth scenario | |
Overall aggregated fast voltage stability index for all scenarios | |
Solar irradiance | |
Standard solar irradiance | |
Solar irradiance at the sth scenario | |
Magnitude of the branch current flowing in the bth branch at the sth scenario | |
Loading level at the sth scenario | |
Load balancing index | |
LBI at the sth scenario for the bth line | |
Aggregated LBI for all lines at the sth scenario | |
Overall LBI for all scenarios | |
Total number of scenarios | |
Probabilistic hosting capacity | |
Apparent power injected to the kth node | |
Load’s apparent power connected to the kth node | |
Probability of the sth scenario | |
Probabilistic total active loss for all the studied scenarios | |
Total power loss at the normal loading conditions | |
Active power delivered by the substation at the sth scenario | |
Specific irradiance threshold | |
Impedance of the bth line | |
Total power loss reduction | |
Maximum capacity of the installed PV | |
Maximum capacity of the installed WT | |
Nodal voltage at the kth node | |
Magnitude of the kth node at the sth scenario | |
Lower nodal voltage limit | |
Upper nodal voltage limit | |
WT rated speed | |
WT cut-in speed | |
WT cut-out speed | |
Wind speed at the sth scenario | |
Reactive component of the bth line impedance | |
Impedance of the bth line at the sth scenario | |
Decision variables of the upper-level optimization | |
Actual penetration of a PV DG at the sth scenario | |
Actual penetration of a WT DG at the sth scenario | |
Size of the installed WT at the node | |
Size of the installed PV unit at the node | |
Decision variables of the graphically based DNR (lower-level optimization) | |
Binary vector indicates the best open/close status of the distribution network tie-lines | |
Temporary binary vector indicates open/close status of the network tie-lines |
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s | (%) | (m/s) | s | (%) | (m/s) | ||||
---|---|---|---|---|---|---|---|---|---|
1 | 33.09869 | 0 | 0 | 0.02363 | 16 | 54.70679 | 6.9 | 0 | 0.03664 |
2 | 33.82429 | 8.1 | 0 | 0.02432 | 17 | 54.97036 | 0 | 0 | 0.03916 |
3 | 34.79878 | 4.6 | 0 | 0.03139 | 18 | 55.89388 | 11.5 | 455 | 0.02603 |
4 | 34.85638 | 11.5 | 0 | 0.02454 | 19 | 55.97981 | 0 | 263 | 0.02180 |
5 | 42.43202 | 3.5 | 0 | 0.04030 | 20 | 58.78500 | 10.4 | 856 | 0.01712 |
6 | 43.78283 | 10.4 | 0 | 0.05023 | 21 | 59.61178 | 4.6 | 529 | 0.02957 |
7 | 44.43556 | 5.8 | 448 | 0.01507 | 22 | 60.01654 | 11.5 | 1 | 0.02546 |
8 | 45.37022 | 8.1 | 0 | 0.09349 | 23 | 65.52149 | 4.6 | 842 | 0.01507 |
9 | 46.58196 | 9.2 | 900 | 0.04692 | 24 | 69.68230 | 4.6 | 0 | 0.02386 |
10 | 46.80610 | 12.7 | 0 | 0.03744 | 25 | 70.07522 | 9.2 | 0 | 0.03219 |
11 | 47.00383 | 0 | 0 | 0.04441 | 26 | 72.52334 | 0 | 0 | 0.01393 |
12 | 47.66340 | 13.8 | 520 | 0.02420 | 27 | 76.89657 | 10.4 | 935 | 0.03984 |
13 | 48.58249 | 16.1 | 0 | 0.02877 | 28 | 78.68899 | 6.9 | 0 | 0.05479 |
14 | 49.39537 | 3.5 | 0 | 0.06975 | 29 | 86.35351 | 13.8 | 363 | 0.01062 |
15 | 49.46533 | 13.8 | 814 | 0.04384 | 30 | 93.01955 | 10.4 | 478 | 0.01564 |
Distribution Network | Feeders | Nodes Count | Lines Count | Tie-Lines Count | Load (MVA) |
---|---|---|---|---|---|
16-node | 3 | 13 | 16 | 3 | 28.7 + 17.3 |
59-node | 8 | 59 | 64 | 6 | 50.348 + 21.448 |
69-node | 1 | 69 | 73 | 5 | 3.80219 + 2.6946 |
83-node | 11 | 83 | 96 | 13 | 28.4 + 20.7 |
415-node | 55 | 415 | 480 | 65 | 141.8 + 103.5 |
880-node | 7 | 873 | 900 | 27 | 124.9 + 74.4 i |
Parameter | Value | Parameter | Value |
---|---|---|---|
(m/s) | 3 | (W/) [29] | 150 |
(m/s) | 26 | (MW) | [0,50] |
(m/s) | 15 | (A) | 300 |
(MW) | [0,50] | (p.u.) | 0.95 |
(W/) [29] | 1000 | (p.u.) | 1.05 |
System | WT Nodes | PV Nodes |
---|---|---|
16-node | 4,5,16 | 8,9,12 |
59-node | 13,24,31,52,55,56 | 2,7,22,29,43,50 |
69-node | 7,8,16,17,18,37,40,54 | 11,12,21,38,39,48,50,53 |
83-node | 14,17,18,45,51,52,53,54,58,81 | 6,12,13,19,28,31,34,71,75,79 |
415-node | 24,27,28,62,63,64,68,91,118,121, 122,156,157,158,162,185,212,215,216,243, 249,250,251,252,256,279,305,306,309,310, 326,337,343,344,345,346,350,373,399,400, 403,404,420,431,437,438,439,440,444,467 | 16,22,23,29,38,41,44,55,61,81,85,89,110, 116,117,123,132,135,138,149,155,175,179, 183,204,210,211,217,226,229,232,269,273, 277,298,304,311,320,323,363,367,371,392, 398,405,414,417,457,461,465 |
880-node | 13,18,43,53,54,59,89,90,101,122,137,140, 144,146,151,171,174,196,214,219,244,254, 255,260,290,291,302,323,338,341,345,350, 351,362,383,389,393,398,399,410,416,420, 440,455,458,464,465,470,498,500,501,512, 533,548,551,555,558,560,561,593,599,603, 606,608,609,620,626,630,633,650,665,668, 670,672,673,705,720,723,727,730,732,733, 765,771,775,778,780,781,792,798,802,805, 822,837,840,842,848,852,855,872 | 11,19,20,33,40,52,70,80,85,87,94,95,111, 112,138,139,152,153,172,173,185,186,212, 220,221,234,241,253,271,281,286,288,295, 296,312,313,339,340,348,355,356,372,373, 387,388,396,403,414,415,423,429,430,456, 457,463,481,491,496,505,506,522,523,549, 550,565,566,582,583,597,598,613,624,625, 639,640,666,667,677,678,694,695,721,722, 737,738,754,755,769,770,785,796,797,811, 812,838,839,846,847,861,862 |
System | Index | Initial | NSGA-II | MOPSO |
---|---|---|---|---|
16-node | (%) | - | 17.9159 | 13.6892 |
(%) | 0 | 79.5223 | 79.9342 | |
1.1432 | 0.7997 | 0.7858 | ||
0.1111 | 0.0750 | 0.0834 | ||
0.0539 | 0.0485 | 0.0452 | ||
min (p.u.) | 0.9715 | 0.9778 | 0.9778 | |
max (p.u.) | 1 | 1.0039 | 1.0056 | |
Time (h) | - | 3.3254 | 5.7375 | |
59-node | (%) | - | 18.087 | 14.05 |
(%) | 0 | 83.3078 | 81.8076 | |
3.6844 | 2.4137 | 2.9178 | ||
0.1407 | 0.0844 | 0.0847 | ||
0.0666 | 0.0549 | 0.0523 | ||
min (p.u.) | 0.9874 | 0.9944 | 0.9931 | |
max (p.u.) | 1 | 1.0004 | 1.0029 | |
Time (h) | - | 5.3130 | 6.2609 | |
69-node | (%) | - | 17.0725 | 18.6119 |
(%) | 0 | 89.1300 | 87.9905 | |
1.2040 | 0.5814 | 0.6098 | ||
0.9485 | 0.3513 | 0.3198 | ||
0.4003 | 0.2609 | 0.2681 | ||
min (p.u.) | 0.9161 | 0.9554 | 0.9536 | |
max (p.u.) | 1 | 1.0036 | 1.0140 | |
Time (h) | - | 1.5584 | 0.9694 | |
83-node | (%) | - | 17.9875 | 17.6474 |
(%) | 0 | 80.7985 | 80.3160 | |
4.3873 | 3.0877 | 3.0516 | ||
1.3348 | 1.0697 | 1.1120 | ||
0.6173 | 0.5900 | 0.6005 | ||
min (p.u.) | 0.9339 | 0.9601 | 0.9589 | |
max (p.u.) | 1 | 1 | 1 | |
Time (h) | - | 9.1571 | 8.8585 | |
415-node | (%) | - | 17.7173 | 17.5299 |
(%) | 0 | 74.5320 | 79.2044 | |
21.9362 | 19.3506 | 16.4757 | ||
6.6732 | 6.0285 | 5.3153 | ||
3.0863 | 3.0565 | 2.9472 | ||
min (p.u.) | 0.9339 | 0.9511 | 0.9566 | |
max (p.u.) | 1 | 1.0066 | 1.0040 | |
Time (h) | - | 74.2285 | 74.3252 | |
880-node | (%) | - | 18.0692 | 18.0224 |
(%) | 0 | 93.5010 | 93.4466 | |
4.1141 | 1.2709 | 1.3006 | ||
6.0015 | 1.7829 | 1.7772 | ||
0.2474 | 0.1490 | 0.1439 | ||
min (p.u.) | 0.9593 | 0.9935 | 0.9936 | |
max (p.u.) | 1 | 1 | 1.0004 | |
Time (h) | - | 105.7501 | 104.7001 |
WT Node | WT Size | WT Node | WT Size | PV Node | PV Size | PV Node | PV Size |
---|---|---|---|---|---|---|---|
16-node distribution network | |||||||
4 | 2 | 5 | 1 | 8 | 2.8 | 9 | 3 |
16 | 5.9 | - | - | 12 | 1.8 | - | - |
59-node distribution network | |||||||
13 | 1.7 | 52 | 2.1 | 2 | 2.4 | 29 | 1.4 |
24 | 5.5 | 55 | 2.8 | 7 | 2.8 | 43 | 2.2 |
31 | 1.7 | 56 | 2.3 | 22 | 2.3 | 50 | 1.7 |
69-node distribution network | |||||||
7 | 0.1 | 18 | 0.1 | 11 | 0 | 39 | 0.2 |
8 | 0.2 | 37 | 0.2 | 12 | 0.2 | 48 | 0.2 |
16 | 0.1 | 40 | 0.1 | 21 | 0.2 | 50 | 0 |
17 | 0.1 | 54 | 0.1 | 38 | 0.2 | 53 | 0.2 |
83-node distribution network | |||||||
14 | 0.8 | 52 | 0.4 | 6 | 0.8 | 31 | 0.7 |
17 | 0.7 | 53 | 0.7 | 12 | 0.5 | 34 | 1 |
18 | 1 | 54 | 0.7 | 13 | 0.7 | 71 | 1.1 |
45 | 1.1 | 58 | 0.9 | 19 | 0.2 | 75 | 0.5 |
51 | 0.9 | 81 | 1.8 | 28 | 0.7 | 79 | 1 |
415-node distribution network | |||||||
24 | 0 | 279 | 3 | 16 | 0 | 210 | 0.2 |
27 | 0 | 305 | 2 | 22 | 0 | 211 | 0 |
28 | 0.9 | 306 | 0 | 23 | 0.3 | 217 | 1.8 |
62 | 0 | 309 | 3.3 | 29 | 0 | 226 | 2 |
63 | 2.2 | 310 | 2 | 38 | 0 | 229 | 0 |
64 | 0.5 | 326 | 0 | 41 | 3.3 | 232 | 1.1 |
68 | 0 | 337 | 0 | 44 | 2 | 269 | 0 |
91 | 0 | 343 | 1.5 | 55 | 0 | 273 | 0 |
118 | 3.5 | 344 | 0 | 61 | 2.2 | 277 | 0.8 |
121 | 2.8 | 345 | 3.3 | 81 | 0 | 298 | 0 |
122 | 2.8 | 346 | 3.5 | 85 | 1.7 | 304 | 0 |
156 | 0.9 | 350 | 0 | 89 | 0 | 311 | 1.5 |
157 | 0 | 373 | 0 | 110 | 2.8 | 320 | 2.9 |
158 | 2 | 399 | 0 | 116 | 0 | 323 | 0 |
162 | 1.9 | 400 | 0 | 117 | 0 | 363 | 0 |
185 | 0 | 403 | 0 | 123 | 0 | 367 | 0 |
212 | 0 | 404 | 1.7 | 132 | 0 | 371 | 0 |
215 | 0 | 420 | 3.6 | 135 | 0 | 392 | 0 |
216 | 0 | 431 | 0 | 138 | 0 | 398 | 0.4 |
243 | 0 | 437 | 0 | 149 | 0 | 405 | 1.2 |
249 | 0 | 438 | 0 | 155 | 0 | 414 | 1.7 |
250 | 0 | 439 | 0 | 175 | 0 | 417 | 0 |
251 | 0 | 440 | 0 | 179 | 0 | 457 | 1.9 |
252 | 0 | 444 | 0 | 183 | 2.1 | 461 | 2.5 |
256 | 0 | 467 | 2.8 | 204 | 0 | 465 | 3.3 |
WT Node | WT Size | WT Node | WT Size | PV Node | PV Size | PV Node | PV Size |
---|---|---|---|---|---|---|---|
16-node distribution network | |||||||
4 | 1 | 5 | 1 | 8 | 4.2 | 9 | 4.3 |
16 | 1 | - | - | 12 | 4.7 | - | - |
59-node distribution network | |||||||
13 | 1 | 52 | 1 | 2 | 2.1 | 29 | 1 |
24 | 1 | 55 | 1 | 7 | 4.4 | 43 | 0 |
31 | 1 | 56 | 1 | 22 | 2.9 | 50 | 12.2 |
69-node distribution network | |||||||
7 | 0 | 18 | 0.1 | 11 | 0 | 39 | 0.3 |
8 | 0.3 | 37 | 0 | 12 | 0.3 | 48 | 0 |
16 | 0.4 | 40 | 0 | 21 | 0.3 | 50 | 0 |
17 | 0 | 54 | 0.5 | 38 | 0 | 53 | 0 |
83-node distribution network | |||||||
14 | 1 | 52 | 0.9 | 6 | 0.7 | 31 | 0.6 |
17 | 0.7 | 53 | 0.8 | 12 | 1.4 | 34 | 0 |
18 | 0.5 | 54 | 0.9 | 13 | 0.3 | 71 | 0.7 |
45 | 0.6 | 58 | 1 | 19 | 1.7 | 75 | 0.5 |
51 | 1 | 81 | 1 | 28 | 0.8 | 79 | 1.2 |
415-node distribution network | |||||||
24 | 0 | 279 | 3 | 16 | 0 | 210 | 0.8 |
27 | 0 | 305 | 2 | 22 | 0 | 211 | 0 |
28 | 0.9 | 306 | 0 | 23 | 0 | 217 | 2.6 |
62 | 0 | 309 | 3.3 | 29 | 0.4 | 226 | 0.7 |
63 | 2.2 | 310 | 2 | 38 | 0 | 229 | 0 |
64 | 0.5 | 326 | 0 | 41 | 0 | 232 | 2.5 |
68 | 0 | 337 | 0 | 44 | 0.3 | 269 | 2.5 |
91 | 0 | 343 | 1.5 | 55 | 1.7 | 273 | 0 |
118 | 3.5 | 344 | 0 | 61 | 0 | 277 | 0 |
121 | 2.8 | 345 | 3.3 | 81 | 0 | 298 | 0 |
122 | 2.8 | 346 | 3.5 | 85 | 0.5 | 304 | 2.6 |
156 | 0.9 | 350 | 0 | 89 | 1.6 | 311 | 0 |
157 | 0 | 373 | 0 | 110 | 2.3 | 320 | 1.9 |
158 | 2 | 399 | 0 | 116 | 0.1 | 323 | 0.1 |
162 | 1.9 | 400 | 0 | 117 | 2.3 | 363 | 2.4 |
185 | 0 | 403 | 0 | 123 | 0 | 367 | 0 |
212 | 0 | 404 | 1.7 | 132 | 1.6 | 371 | 0.4 |
215 | 0 | 420 | 3.6 | 135 | 0 | 392 | 0 |
216 | 0 | 431 | 0 | 138 | 2.6 | 398 | 0 |
243 | 0 | 437 | 0 | 149 | 2.6 | 405 | 0 |
249 | 0 | 438 | 0 | 155 | 0 | 414 | 1.2 |
250 | 0 | 439 | 0 | 175 | 0.9 | 417 | 0.5 |
251 | 0 | 440 | 0 | 179 | 2.3 | 457 | 0 |
252 | 0 | 444 | 0 | 183 | 1.1 | 461 | 2 |
256 | 0 | 467 | 2.8 | 204 | 1.5 | 465 | 0 |
Configuration (Tie-Lines) | ||
---|---|---|
NSGA-II | MOPSO | |
1 | 7,8,16 | 7,8,16 |
5 | ||
13 | 3,7,8 | |
17 | 7,8,16 | |
29 | 4,7,8 |
Configuration (Tie-Lines) | ||
---|---|---|
NSGA-II | MOPSO | |
1 | 7,18,46,60,63,64 | 7,19,46,60,63,64 |
5 | 7,17,47,60,63,64 | 7,18,46,60,63,64 |
13 | 7,17,37,47,60,63 | |
17 | 7,17,38,48,60,63 | |
29 | 7,18,38,46,60,63 | 7,18,38,46,60,63 |
Configuration (Tie-Lines) | ||
---|---|---|
NSGA-II | MOPSO | |
1 | 14,47,50,69,70 | 14,46,50,69,70 |
5 | 14,44,50,69,70 | 14,18,45,50,69 |
13 | 13,44,50,69,70 | 14,20,46,50,69 |
17 | 14,45,50,69,70 | 13,20,45,50,69 |
29 | 13,46,50,69,70 | 12,13,47,50,69 |
Configuration (Tie-Lines) | ||
---|---|---|
NSGA-II | MOPSO | |
1 | 6,12,33,38,41,54,60,71,82,85,88,89,91 | 6,33,41,54,60,71,82,85,87,88,89,91,92 |
5 | 6,33,38,41,54,60,71,82,85,87,88,89,91 | 6,33,41,52,60,71,82,85,87,88,89,91,92 |
13 | 6,33,41,53,60,71,78,85,87,88,89,91,92 | 6,33,41,52,53,71,85,87,88,89,90,91,92 |
17 | 6,32,41,53,60,71,81,85,87,88,89,91,92 | 6,33,41,53,63,71,85,87,88,89,90,91,92 |
29 | 6,32,41,54,60,71,82,85,87,88,89,91,92 | 6,33,38,41,53,61,71,81,85,87,88,89,91 |
Configuration (Tie-Lines) | ||
---|---|---|
NSGA-II | MOPSO | |
1 | 6,54,142,143,154,164,220,255,302,320,330, | 6,33,38,41,54,61,71,82,89,116,121,124, |
336,338,417,418,419,420,421,422,423,424, | 144,154,165,172,199,204,207,219,226, | |
425,426,427,428,430,432,433,434,436,437, | 237,248,255,282,287,290,310,320,331, | |
438,439,442,443,444,445,446,447,448,449, | 338,344,365,370,373,385,392,403,414, | |
450,451,452,453,456,458,459,460,462,463, | 417,419,420,421,423,428,430,432,433, | |
464,465,466,469,470,471,472,473,474,475, | 434,436,443,445,446,447,449,454,456, | |
476,477,478,479 | 458,459,460,462,469,000,000,000 | |
5 | 6,54,141,143,154,164,220,255,301,302,320, | 6,33,38,41,54,61,71,82,89,116,121,124, |
330,336,338,417,418,419,420,421,422,423, | 144,154,165,172,199,204,207,219,226, | |
424,425,426,427,428,430,432,433,434,436, | 237,248,255,261,282,287,290,310,317, | |
437,438,439,442,443,444,445,446,447,448, | 331,338,344,365,370,373,385,392,403, | |
449,450,451,452,453,456,458,459,460,462, | 414,417,419,420,421,423,428,430,432, | |
463,464,465,469,470,471,472,473,474,475, | 433,434,436,443,445,446,447,449,454, | |
476,477,478,479 | 456,459,460,462,469,000,000,000 | |
13 | 52,54,140,143,151,164,172,220,255,301, | 6,33,38,41,53,61,71,82,89,116,121,124, |
302,320,330,338,417,418,419,420,421,422, | 144,154,165,172,199,204,207,219,226, | |
423,424,425,426,428,430,432,433,434,436, | 237,248,255,261,282,287,290,310,317, | |
437,438,439,443,444,445,446,447,448,449, | 331,338,344,365,370,373,384,392,403, | |
450,451,452,453,456,458,459,460,462,463, | 414,417,419,420,421,423,428,430,432, | |
464,465,467,469,470,471,472,473,474,475, | 433,434,436,443,445,446,447,449,454, | |
476,477,478,479 | 456,459,460,462,469,000,000,000 | |
17 | 52,54,141,143,151,164,172,220,255,287, | 6,33,38,41,53,61,71,82,89,116,121,124, |
301,302,320,330,338,417,418,419,420,421, | 144,154,165,172,199,204,207,219,226, | |
422,423,424,425,426,428,430,432,433,434, | 237,248,255,261,262,282,287,290,310, | |
436,437,438,439,443,444,445,446,447,448, | 319,331,338,344,365,370,373,385,392, | |
449,450,451,452,453,456,458,459,460,462, | 403,414,417,419,420,421,423,428,430, | |
464,465,467,469,470,471,472,473,474, | 432,433,434,436,443,445,446,447,449, | |
475,476,477,478,479 | 454,456,460,462,469,000,000,000 | |
29 | 6,12,33,38,41,54,61,71,82,89,95,116,121, | 6,33,38,41,54,61,71,82,89,116,121,124, |
124,137,144,152,165,172,178,199,204, | 137,144,154,165,172,199,204,207,219, | |
207,220,227,237,248,255,261,282,287, | 226,237,248,255,261,282,287,290,310, | |
290,310,320,331,338,344,365,370,373, | 317,331,338,344,365,370,373,385,392, | |
386,393,403,414,417,420,421,423,430, | 403,414,417,419,420,421,423,430,432, | |
433,434,436,443,446,447,449,454,456, | 433,434,436,443,445,446,447,449,454, | |
459,460,462,469,472,000,000 | 456,459,460,462,469,000,000,000 |
Number of Scenarios | NSGA-II | MOPSO | ||
---|---|---|---|---|
HC (%) | HC (%) | |||
10 | 17.1015 | 83.5396 | 12.23 | 72.037 |
20 | 18.8370 | 84.5515 | 12.02 | 80.411 |
30 | 18.0870 | 83.3078 | 14.05 | 81.807 |
40 | 18.5500 | 84.5329 | 11.13 | 78.225 |
50 | 17.0012 | 84.3349 | 11.37 | 80.124 |
Average | 17.9153 | 84.0533 | 12.16 | 78.5208 |
Standard deviation | 0.8336 | 0.5867 | 1.1491 | 3.8428 |
Optimizer | Year | HC (%) | Average Time | |
---|---|---|---|---|
NSGA-II | 2002 | 18.0870 | 83.3078 | 5.3130 |
MOPSO | 2002 | 14.0500 | 81.8070 | 6.2609 |
MOFPA | 2014 | 12.3543 | 81.1698 | 4.0531 |
MOMVO | 2017 | 12.3953 | 72.8587 | 2.6988 |
Index | Initial | [15] | [41] | [44] | Proposed |
---|---|---|---|---|---|
HC (%) | 0 | N/A | 60.71 | N/A | 17.9875 |
Power loss (kW) | 532.0 | 469.9 | N/A | 471.1 | 104.718 |
Min voltage (p.u.) | 0.929 | 0.953 | 0.951 | 0.952 | 0.9589 |
DGs uncertainty consideration | No | N/A | No | N/A | Yes |
Load uncertainty consideration | No | N/A | Yes | N/A | Yes |
Index | Initial | [15] | [15] | [45] | Proposed |
---|---|---|---|---|---|
HC (%) | 0 | N/A | N/A | 58.68 | 17.7173 |
Power loss (kW) | 2660.0 | 2350.7 | 2359.9 | 1534.3 | 677.4488 |
Min voltage (p.u.) | 0.929 | N/A | N/A | 0.951 | 0.9511 |
DGs uncertainty consideration | No | N/A | N/A | No | Yes |
Load uncertainty consideration | No | N/A | N/A | Yes | Yes |
Index | Initial | [16] | [17] | Proposed |
---|---|---|---|---|
HC (%) | 0 | N/A | N/A | 18.0692 |
Power loss (kW) | 1496.4 | 461.0 | 461.4 | 98.065 |
Min voltage (p.u.) | 0.956 | 0.992 | 0.982 | 0.9511 |
DGs uncertainty consideration | No | N/A | N/A | Yes |
Load uncertainty consideration | No | N/A | N/A | Yes |
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Ali, Z.M.; Diaaeldin, I.M.; H. E. Abdel Aleem, S.; El-Rafei, A.; Abdelaziz, A.Y.; Jurado, F. Scenario-Based Network Reconfiguration and Renewable Energy Resources Integration in Large-Scale Distribution Systems Considering Parameters Uncertainty. Mathematics 2021, 9, 26. https://doi.org/10.3390/math9010026
Ali ZM, Diaaeldin IM, H. E. Abdel Aleem S, El-Rafei A, Abdelaziz AY, Jurado F. Scenario-Based Network Reconfiguration and Renewable Energy Resources Integration in Large-Scale Distribution Systems Considering Parameters Uncertainty. Mathematics. 2021; 9(1):26. https://doi.org/10.3390/math9010026
Chicago/Turabian StyleAli, Ziad M., Ibrahim Mohamed Diaaeldin, Shady H. E. Abdel Aleem, Ahmed El-Rafei, Almoataz Y. Abdelaziz, and Francisco Jurado. 2021. "Scenario-Based Network Reconfiguration and Renewable Energy Resources Integration in Large-Scale Distribution Systems Considering Parameters Uncertainty" Mathematics 9, no. 1: 26. https://doi.org/10.3390/math9010026
APA StyleAli, Z. M., Diaaeldin, I. M., H. E. Abdel Aleem, S., El-Rafei, A., Abdelaziz, A. Y., & Jurado, F. (2021). Scenario-Based Network Reconfiguration and Renewable Energy Resources Integration in Large-Scale Distribution Systems Considering Parameters Uncertainty. Mathematics, 9(1), 26. https://doi.org/10.3390/math9010026