A Novel Graphically-Based Network Reconfiguration for Power Loss Minimization in Large Distribution Systems
Abstract
:1. Introduction
2. Problem Statement
2.1. Power Flow Equations
2.2. Proposed Graphical Distribution Network Reconfiguration
- (a)
- Set .
- (b)
- Start from the tie-line in represented by and connected from the node to the node. A set is formed, including sectionalized lines connected by their ends to the line nodes, as shown in Figure 2, in which these sectionalized lines are proposed to be tie-lines where and do not include main feeder lines.
- (c)
- A weighted voltage deviation () index is calculated for each candidate sectionalized line in the set and its corresponding tie-line . The index for the sectionalized line in is formulated as follows:
- (d)
- Tie-lines and their corresponding sectionalized lines are then sorted according to their value, where the highest value takes the highest priority. Let represent the number of possible trials to reconfigure the distribution network. Further, a matrix is formed, with rows and columns . Its first and second columns include the tie-lines and their corresponding sectionalized lines, respectively, after the sorting procedure is done.
- (e)
- Set .
- (f)
- Set and .
- (g)
- Calculate the objective function. Thus,
- -
- Assume that the mathematical problem is minimization. If the objective function is better than the initial objective function value, then update and repeat the reconfiguration process, starting from Step 2.
- -
- If the objective function value is greater than the initial objective function value or the power flow did not converge, and , then set and repeat sub-step f.
- -
- If , then jump to Step 5.
Illustrative Example on the Proposed DNR
3. Problem Formulation
3.1. Objective Function
3.2. Constraints
4. Results and Discussion
DNR Only
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
ALO | Ant-lion optimization algorithm |
DC-HSS | Discrete-continuous hyper-spherical search algorithm |
DNR | Distribution network reconfiguration |
FNSGA | Fast nondominated sorting genetic algorithm |
GA | Genetic algorithm |
GPU | Graphics processing unit |
MICP | Mixed-integer cone programming |
MILP | Mixed-integer linear programming |
MINLP | Mixed-integer nonlinear programming |
MISOCP | Mixed-integer second-order cone programming |
Nomenclature
Iteration number. | |
, | The set of lines (edges) and nodes (vertices), respectively. |
Line-node incidence matrix. | |
, | The number of lines and nodes, respectively. |
The number of possible trials to reconfigure the distribution network. | |
, | The injected active and reactive powers at the node. |
, | The active and reactive powers of the connected loads onto node . |
, | The feeder resistance and reactance between nodes and . |
The magnitude of the node voltage. | |
Weighted voltage deviation index. | |
The best configuration of the distribution network. | |
The temporary configuration of the distribution network. |
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Before Sorting | After Sorting | , Then Set and | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Priority | Losses Reduction (%) | Decision | |||||||||
1 | 13 | 5 | 1 | 0.0153 | 3 | 1 | 14 | 10 | NA ** | Jump to | |
11 | 7 | 0.0182 | 2 | 2 | 13 | 7 | 3.568 | Update and jump to | |||
14 | 10 | 6 | 0.0169 | 4 | 3 | 13 | 1 | NA | NA | ||
14 | 10 | 0.0187 | 1 | 4 | 14 | 6 | |||||
15 | 7 | 3 | 0.0055 | 6 | 5 | 15 | 12 | ||||
16 | 12 | 0.0061 | 5 | 6 | 15 | 3 | |||||
2 | 7 | 9 | 5 | 0.0094 | 4 | 1 | 14 | 10 | NA | Jump to | |
11 | 13 | 0.0181 | 2 | 2 | 7 | 13 | NA | Jump to | |||
14 | 10 | 6 | 0.0167 | 3 | 3 | 14 | 6 | 8.854 | Update and jump to | ||
14 | 10 | 0.0186 | 1 | 4 | 7 | 5 | NA | NA | |||
15 | 7 | 3 | 0.0054 | 6 | 5 | 15 | 12 | ||||
16 | 12 | 0.0061 | 5 | 6 | 15 | 3 | |||||
3 | 6 | 8 | 5 | 0.0003 | 6 | 1 | 7 | 13 | NA | Jump to | |
10 | 14 | 0.0082 | 3 | 2 | 7 | 8 | NA | Jump to | |||
7 | 9 | 8 | 0.0137 | 2 | 3 | 6 | 14 | NA | Jump to | ||
11 | 13 | 0.0156 | 1 | 4 | 15 | 12 | NA | Jump to | |||
15 | 7 | 3 | 0.0032 | 5 | 5 | 15 | 3 | NA | Jump to | ||
16 | 12 | 0.0038 | 4 | 6 | 6 | 5 | NA | Terminate and display |
Distribution System | Feeders | Load (MVA) | ||
---|---|---|---|---|
16-node | 3 | 13 | 16 | 28.7 + 17.3 |
33-node | 1 | 32 | 37 | 3.7 + 2.3 |
70-node | 2 | 68 | 79 | 4.5 + 3.1 |
83-node | 11 | 83 | 96 | 28.4 + 20.7 |
135-node | 8 | 135 | 156 | 18.3 + 7.9 |
415-node | 55 | 415 | 480 | 141.8 + 103.5 |
880-node | 7 | 873 | 900 | 124.9 + 74.4 |
1760-node | 14 | 1746 | 1820 | 249.7 + 148.7 |
4400-node | 35 | 4365 | 4550 | 624.4 + 371.8 |
System | Ref. | Average Time (s) | |||
---|---|---|---|---|---|
16-node | Initial | 511.4 | 590.4 | 0.969 | NA |
[16] | 466.1 | 544.9 | 0.972 | 1.81 | |
[17] | 466.1 | 544.9 | 0.972 | 2.10 | |
Proposed | 466.1 | 544.9 | 0.972 | 0.10 | |
33-node | Initial | 211.0 | 143.0 | 0.904 | NA |
[18] | 139.6 | 102.3 | 0.938 | 4.64 | |
[19] | 139.6 | 102.3 | 0.938 | 160 | |
Proposed | 139.57 | 102.3 | 0.938 | 0.55 | |
70-node | Initial | 227.5 | 204.9 | 0.905 | NA |
[17] | 203.2 | 186.6 | 0.931 | 4.64 | |
[20] | 203.9 | 191.1 | 0.927 | 160 | |
Proposed | 201.4 | 185.1 | 0.931 | 0.70 | |
83-node | Initial | 532.0 | 1374.3 | 0.929 | NA |
[19] | 471.1 | 1252.1 | 0.952 | 36.1 | |
[7] | 469.9 | 1248.0 | 0.953 | 160 | |
Proposed | 470.06 | 1248.0 | 0.953 | 1.4 | |
136-node | Initial | 320.3 | 702.7 | 0.931 | NA |
[20] | 280.7 | 611.0 | 0.961 | 32.6 | |
[7] | 280.1 | 611.1 | 0.959 | 1800 | |
Proposed | 280.1 | 611.1 | 0.959 | 35.1 | |
415-node | Initial | 2660.0 | 6871.6 | 0.929 | NA |
[7] | 2359.9 | NA | NA | 1800 | |
[7] | 2350.7 | NA | NA | 1800 | |
Proposed | 2349.4 | 6240.0 | 0.953 | 70 | |
880-node | Initial | 1496.4 | 1396.5 | 0.956 | NA |
[10] | 461.4 | NA | 0.982 | 3192 | |
[8] | 461.0 | 566.7 | 0.992 | 1134 | |
Proposed | 457.03 | 563.3 | 0.992 | 310 | |
1760-node | Initial | 2992.2 | 2793.0 | 0.956 | NA |
Proposed | 822.4 | 1020.3 | 0.992 | 1400 | |
4400-node | Initial | 7482.2 | 6982.5 | 0.956 | NA |
Proposed | 1918.6 | 2412.7 | 0.9917 | 3600 |
Configuration (Tie-Lines) | Losses (kW) | |
---|---|---|
0 | 13, 14, 15 | 511.40 |
1 | 7, 14, 15 | 493.15 |
2 | 6, 7, 15 | 466.12 |
Configuration (Tie-Lines) | Losses (kW) | |
---|---|---|
0 | 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95 | 532.00 |
1 | 6, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95 | 512.54 |
11 | 6, 12, 33, 38, 41, 54, 61, 71, 82, 85, 88, 89, 91 | 470.06 |
Configuration (Tie-Lines) | Losses (kW) | |
---|---|---|
0 | 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155 | 320.36 |
1 | 109, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 154, 155 | 303.74 |
14 | 6, 34, 50, 89, 95, 105, 117, 125, 134, 136, 137, 140, 141, 143, 144, 145, 146, 147, 149, 150, 154 | 280.18 |
Configuration (Tie-Lines) | Losses (kW) | |
---|---|---|
0 | 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479 | 2660.0 |
1 | 6, 415, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479 | 2640.4 |
55 | 6, 12, 33, 38, 41, 54, 61, 71, 82, 89, 95, 116, 121, 124, 137, 144, 154, 165, 172, 178, 199, 204, 207, 220, 227, 237, 248, 255, 261, 282, 287, 290, 303, 310, 320, 331, 338, 344, 365, 370, 373, 386, 393, 403, 414, 417, 420, 421, 423, 430, 433, 434, 436, 443, 446, 447, 449, 456, 459, 460, 462, 469, 472, 473, 475 | 2349.4 |
Configuration (Tie-Lines) | Losses (kW) | |
---|---|---|
0 | 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899 | 1496.4 |
1 | 793, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899 | 1484.9 |
111 | 83, 129, 140, 158, 189, 281, 287, 305, 311, 408, 410, 451, 493, 595, 615, 629, 630, 636, 697, 814, 843, 884, 887, 888, 889, 895, 899 | 457.0 |
System | Configuration (Tie-Lines) |
---|---|
16-node | 6, 7, 15 |
33-node | 6, 9, 13, 31, 36 |
70-node | 12, 29, 44, 50, 65, 69, 74, 75, 76, 77, 78 |
83-node | 6, 12, 33, 38, 41, 54, 61, 71, 82, 85, 88, 89, 91 |
136-node | 6, 34, 50, 89, 95, 105, 117, 125, 134, 136, 137, 140, 141, 143, 144, 145, 146, 147, 149, 150, 154 |
415-node | 6, 12, 33, 38, 41, 54, 61, 71, 82, 89, 95, 116, 121, 124, 137, 144, 154, 165, 172, 178, 199, 204, 207, 220, 227, 237, 248, 255, 261, 282, 287, 290, 303, 310, 320, 331, 338, 344, 365, 370, 373, 386, 393, 403, 414, 417, 420, 421, 423, 430, 433, 434, 436, 443, 446, 447, 449, 456, 459, 460, 462, 469, 472, 473, 475 |
880-node | 83, 129, 140, 158, 189, 281, 287, 305, 311, 408, 410, 451, 493, 595, 615, 629, 630, 636, 697, 814, 843, 884, 887, 888, 889, 895, 899 |
1760-node | 83, 117, 128, 133, 166, 189, 243, 281, 288, 305, 311, 343, 406, 412, 425, 451, 458, 493, 585, 613, 627, 629, 633, 638, 647, 680, 697, 793, 814, 837, 843, 956, 991, 1005, 1016, 1030, 1040, 1062, 1096, 1110, 1138, 1155, 1160, 1185, 1188, 1281, 1284, 1323, 1330, 1365, 1468, 1488, 1502, 1503, 1507, 1511, 1570, 1675, 1687, 1716, 1718, 1757, 1761, 1763, 1765, 1772, 1784, 1788, 1789, 1790, 1799, 1809, 1811, 1814 |
4400-node | 79, 115, 133, 172, 189, 231, 237, 281, 283, 287, 392, 405, 417, 423, 447, 451, 493, 555, 611, 614, 626, 633, 639, 645, 695, 697, 729, 842, 863, 870, 915, 952, 961, 1001, 1012, 1017, 1039, 1061, 1104, 1116, 1154, 1160, 1178, 1186, 1279, 1282, 1357, 1426, 1465, 1483, 1500, 1508, 1517, 1518, 1561, 1570, 1666, 1687, 1711, 1716, 1743, 1829, 1864, 1879, 1918, 1960, 1989, 2027, 2030, 2033, 2052, 2069, 2070, 2127, 2151, 2160, 2197, 2204, 2236, 2241, 2324, 2340, 2359, 2360, 2373, 2377, 2381, 2384, 2393, 2443, 2475, 2547, 2563, 2588, 2605, 2608, 2698, 2739, 2750, 2762, 2791, 2859, 2899, 2924, 2927, 2930, 2995, 3029, 3037, 3044, 3068, 3075, 3112, 3214, 3231, 3243, 3249, 3266, 3312, 3433, 3461, 3487, 3491, 3575, 3621, 3632, 3650, 3681, 3773, 3779, 3797, 3803, 3900, 3902, 3943, 3985, 4087, 4107, 4121, 4122, 4128, 4189, 4306, 4335, 4367, 4371, 4376, 4378, 4382, 4388, 4391, 4403, 4407, 4409, 4410, 4418, 4419, 4420, 4427, 4434, 4435, 4445, 4446, 4457, 4462, 4463, 4472, 4484, 4487, 4488, 4489, 4495, 4499, 4500, 4501, 4503, 4505, 4509, 4517, 4519, 4522, 4523, 4527, 4529, 4543 |
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Mohamed Diaaeldin, I.; Abdel Aleem, S.H.E.; El-Rafei, A.; Abdelaziz, A.Y.; Zobaa, A.F. A Novel Graphically-Based Network Reconfiguration for Power Loss Minimization in Large Distribution Systems. Mathematics 2019, 7, 1182. https://doi.org/10.3390/math7121182
Mohamed Diaaeldin I, Abdel Aleem SHE, El-Rafei A, Abdelaziz AY, Zobaa AF. A Novel Graphically-Based Network Reconfiguration for Power Loss Minimization in Large Distribution Systems. Mathematics. 2019; 7(12):1182. https://doi.org/10.3390/math7121182
Chicago/Turabian StyleMohamed Diaaeldin, Ibrahim, Shady H. E. Abdel Aleem, Ahmed El-Rafei, Almoataz Y. Abdelaziz, and Ahmed F. Zobaa. 2019. "A Novel Graphically-Based Network Reconfiguration for Power Loss Minimization in Large Distribution Systems" Mathematics 7, no. 12: 1182. https://doi.org/10.3390/math7121182
APA StyleMohamed Diaaeldin, I., Abdel Aleem, S. H. E., El-Rafei, A., Abdelaziz, A. Y., & Zobaa, A. F. (2019). A Novel Graphically-Based Network Reconfiguration for Power Loss Minimization in Large Distribution Systems. Mathematics, 7(12), 1182. https://doi.org/10.3390/math7121182