基于子网划分的电网关键节点识别

doi:10.19596/j.cnki.1001-246x.8398

摘要/Abstract

摘要：

结合电网拓扑结构和潮流追踪技术，提出一种基于子网划分的电网关键节点识别方法。首先，根据发电机节点的邻域信息和功率将发电机节点划分为不同的子集，然后根据电网的系数分配矩阵将负荷节点划分到为其提供最大功率的发电机节点子集中，完成子网划分。接着采用多属性决策法对每个子网的节点进行排序，进一步改进并计算每个子网的结构系数，作为衡量子网重要性的指标。根据子网重要性，从每个子网中提取特定比例的候选关键节点，对这些候选节点依据多属性决策法重新排序，得到关键节点的最终排序。以IEEE14、IEEE57和IEEE118三种节点系统为例进行分析，得到各个系统的子网划分结果和各个标准网络的重要节点排序结果。采用本文方法、PageRank法和多属性决策法分别进行关键节点排序，并对排序靠前的关键节点进行级联故障性能实验和网络效能实验。实验表明，本文算法选择的关键节点对整个网络的传播性能影响最大，优于其他两种关键节点识别方法。

关键词: 电力网络, 子网划分, 潮流追踪, 关键节点识别, 级联故障

Abstract:

With power grid topology and power flow tracing technology, a method for identifying key nodes of a power grid based on subnet division is proposed. Firstly, generator nodes are divided into subsets according to their neighborhood information and power. Then, with power flow tracking technology, a coefficient distribution matrix of the power grid is obtained. Next, a load node is divided into a generator node subset which offer the maximum power according to the coefficient distribution matrix. A multi-attribute decision-making method is used to sort the nodes in each subnet. The structure coefficient of subnet is further improved and calculated an index for measuring importance of the subnet. According to the importance of subnets, a specific proportion of candidate key nodes are extracted from each subnet. These candidate nodes are reordered with multi-attribute decision-making method to obtain the final ranking of the key nodes. Taking IEEE14, IEEE57 and IEEE118-node systems as examples, subnet division results and ranking results of important nodes of standard networks are obtained. Our method, PageRank method and multi-attribute decision-making method are used to sort key nodes, respectively. Cascade fault performance experiment and network efficiency performance are carried out on the key nodes with top ranking. It shows that the key nodes selected by the proposed algorithm have the greatest impact on propagation performance of the entire network.

Key words: power grid, subnet division, power flow tracing technology, identification of key nodes, cascading failure

邹艳丽, 谭秫毅, 刘欣妍, 张少泽, 李浩乾. 基于子网划分的电网关键节点识别[J]. 计算物理, 2022, 39(3): 361-370.

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.

图/表 13

图1 IEEE14系统(红色表示发电机节点，黑色表示负载节点。)

Fig.1 IEEE14 power grid (Red nodes denote generators and black nodes denote load nodes.)

表1 IEEE14网络发电机节点有功功率和平均功率

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	平均功率
1.8	1.89	1.8	3.22	1.8	2.1

表2 IEEE14网络系数分配矩阵K

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

图2 子网划分结果(红色方框表示发电机节点，红色虚线表示网间连接，实线表示子网内部连接。) (a)IEEE14网络；(b)IEEE57网络；(c)IEEE118网络

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

表3 IEEE网络子网划分模块度

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

表4 IEEE网络子网结构系数

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

表5 归一化处理后IEEE网络子网结构系数

Table 5 Normalized structure coefficients of subnets

网络	$\tilde I$^(C₁)	$\tilde I$^(C₂)	$\tilde I$^(C₃)	$\tilde I$^(C₄)
IEEE14	0.319 6	0.353 5	0.326 9
IEEE57	0.255 7	0.205 6	0.286 8	0.251 9

表6 IEEE网络各子网内的节点

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

表7 IEEE57 C1子网节点重新编写序号

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

图3 IEEE57网络各子网关键节点排序(节点重要度y为根据多属性决策法[20]计算的结果。) (a)子网C1；(b)子网C2；(c)子网C3；(d)子网C4

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

表8 IEEE 57节点重要度排序

Table 8 IEEE 57 node importance ranking

排序	本文方法(SD-MA)	PageRank	多属性决策法(MA)^[20]
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

图4 三种排序方式下IEEE57和IEEE118网络级联故障规模(a)IEEE57网络; (b)IEEE118网络

Fig.4 Network cascading fault scales of IEEE57 and IEEE118 grids under three sorting modes (a)IEEE57 network; (b)IEEE118 network

图5 三种排序方式下IEEE57和IEEE118网络效能(a)IEEE57网络, (b)IEEE118网络

Fig.5 Network performances of IEEE57 and IEEE118 grids under three sorting modes (a) IEEE57 network, (b) IEEE118 network

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