Chinese Journal of Computational Physics ›› 2022, Vol. 39 ›› Issue (3): 361-370.DOI: 10.19596/j.cnki.1001-246x.8398
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Yanli ZOU(), Shuyi TAN, Xinyan LIU, Shaoze ZHANG, Haoqian LI
Received:
2021-05-14
Online:
2022-05-25
Published:
2022-09-02
Yanli ZOU, Shuyi TAN, Xinyan LIU, Shaoze ZHANG, Haoqian LI. Power System Critical Node Identification Based on Subnetwork Partition[J]. Chinese Journal of Computational Physics, 2022, 39(3): 361-370.
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URL: http://www.cjcp.org.cn/EN/10.19596/j.cnki.1001-246x.8398
节点有功功率 | 平均功率 | ||||
节点1 | 节点2 | 节点3 | 节点6 | 节点8 | |
1.8 | 1.89 | 1.8 | 3.22 | 1.8 | 2.1 |
Table 1 Active power and average power of generators in IEEE14 grid
节点有功功率 | 平均功率 | ||||
节点1 | 节点2 | 节点3 | 节点6 | 节点8 | |
1.8 | 1.89 | 1.8 | 3.22 | 1.8 | 2.1 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
1 | 0.141 | 0 | 0.094 | 0.627 | 0.276 | 0.016 | 0 | 0.061 | 0.084 | 0.276 | 0.276 | 0.276 | 0.087 |
0 | 0.75 | 0 | 0.339 | 0.325 | 0.143 | 0.06 | 0 | 0.219 | 0.211 | 0.143 | 0.143 | 0.143 | 0.21 |
0 | 0.108 | 1 | 0.565 | 0.047 | 0.02 | 0.1 | 0 | 0.356 | 0.318 | 0.02 | 0.02 | 0.02 | 0.314 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0.559 | 0 | 0 | 0 | 0.061 | 0.559 | 0.559 | 0.559 | 0.067 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0.821 | 1 | 0.363 | 0.324 | 0 | 0 | 0 | 0.32 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Table 2 Coefficient distribution matrix K of IEEE14 grid
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
1 | 0.141 | 0 | 0.094 | 0.627 | 0.276 | 0.016 | 0 | 0.061 | 0.084 | 0.276 | 0.276 | 0.276 | 0.087 |
0 | 0.75 | 0 | 0.339 | 0.325 | 0.143 | 0.06 | 0 | 0.219 | 0.211 | 0.143 | 0.143 | 0.143 | 0.21 |
0 | 0.108 | 1 | 0.565 | 0.047 | 0.02 | 0.1 | 0 | 0.356 | 0.318 | 0.02 | 0.02 | 0.02 | 0.314 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0.559 | 0 | 0 | 0 | 0.061 | 0.559 | 0.559 | 0.559 | 0.067 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0.821 | 1 | 0.363 | 0.324 | 0 | 0 | 0 | 0.32 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Fig.2 Subnet division result (Red boxes indicate generator nodes. Red dotted lines indicate inter network connections. Solid lines indicate internal connections.) (a)IEEE14 network; (b)IEEE57 network; (c)IEEE118 network
网络 | 模块度Q |
IEEE14 | 0.403 8 |
IEEE57 | 0.449 1 |
IEEE118 | 0.646 3 |
Table 3 Subnet partition modularity of IEEE grids
网络 | 模块度Q |
IEEE14 | 0.403 8 |
IEEE57 | 0.449 1 |
IEEE118 | 0.646 3 |
网络 | I1 | I2 | I3 | I4 |
IEEE14 | 0.739 3 | 0.817 8 | 0.756 2 | |
IEEE57 | 2.150 8 | 1.729 3 | 2.411 8 | 2.118 6 |
Table 4 Structure coefficients of subnets in IEEE grids
网络 | I1 | I2 | I3 | I4 |
IEEE14 | 0.739 3 | 0.817 8 | 0.756 2 | |
IEEE57 | 2.150 8 | 1.729 3 | 2.411 8 | 2.118 6 |
网络 | ||||
IEEE14 | 0.319 6 | 0.353 5 | 0.326 9 | |
IEEE57 | 0.255 7 | 0.205 6 | 0.286 8 | 0.251 9 |
Table 5 Normalized structure coefficients of subnets
网络 | ||||
IEEE14 | 0.319 6 | 0.353 5 | 0.326 9 | |
IEEE57 | 0.255 7 | 0.205 6 | 0.286 8 | 0.251 9 |
网络 | 子网1内节点 | 子网2内节点 | 子网3内节点 | 子网4内节点 |
IEEE14 | 1,2,3,4,5 | 7,8,9,10,14 | 6,11,12,13 | |
IEEE57 | 1,2,3,14,15,16,17,37,38,44,45,46,47 | 4,5,10,12,13, 18,19,20,21,22,23,24,25,30,31,48,49,50,51 | 9,11,32,33,34,35,36,39,40,41,42,43,53,54,55,56,57 | 6,7,8,26,27,28,29,52 |
Table 6 Nodes in subnets of IEEE grids
网络 | 子网1内节点 | 子网2内节点 | 子网3内节点 | 子网4内节点 |
IEEE14 | 1,2,3,4,5 | 7,8,9,10,14 | 6,11,12,13 | |
IEEE57 | 1,2,3,14,15,16,17,37,38,44,45,46,47 | 4,5,10,12,13, 18,19,20,21,22,23,24,25,30,31,48,49,50,51 | 9,11,32,33,34,35,36,39,40,41,42,43,53,54,55,56,57 | 6,7,8,26,27,28,29,52 |
序号 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
原节点编号 | 1 | 2 | 3 | 14 | 15 | 16 | 17 | 44 | 45 | 46 | 47 |
Table 7 Renumbering subnet nodes of C1 subnet in IEEE57
序号 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
原节点编号 | 1 | 2 | 3 | 14 | 15 | 16 | 17 | 44 | 45 | 46 | 47 |
Fig.3 Ranking of key nodes in subnets of IEEE57 grid (Node importance y is calculated with multi-attribute decision-making method[20].) (a)subnet C1; (b)subnet C2; (c)subnet C3; (d)subnet C4
排序 | 本文方法(SD-MA) | PageRank | 多属性决策法(MA)[ |
1 | 12 | 13 | 13 |
2 | 15 | 9 | 9 |
3 | 13 | 38 | 38 |
4 | 9 | 15 | 12 |
5 | 11 | 12 | 15 |
6 | 41 | 32 | 49 |
7 | 3 | 56 | 11 |
8 | 1 | 4 | 41 |
9 | 6 | 6 | 6 |
10 | 27 | 41 | 4 |
Table 8 IEEE 57 node importance ranking
排序 | 本文方法(SD-MA) | PageRank | 多属性决策法(MA)[ |
1 | 12 | 13 | 13 |
2 | 15 | 9 | 9 |
3 | 13 | 38 | 38 |
4 | 9 | 15 | 12 |
5 | 11 | 12 | 15 |
6 | 41 | 32 | 49 |
7 | 3 | 56 | 11 |
8 | 1 | 4 | 41 |
9 | 6 | 6 | 6 |
10 | 27 | 41 | 4 |
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