Robustness of Power Grids Structure and Braess Paradox Phenomenon: A Complex Network Theory Study

doi:10.19596/j.cnki.1001-246x.8279

Abstract

Abstract:

Based on complex network theory, a modified admittance model of a power system is constructed. Cascading failures of power grids are studied with topological and electrical characteristics of power grids. Cascading failures are made by removing transmission lines randomly. Effects of the number of nodes, average degree, number of power stations and distribution of power stations on system robustness are studied. Braess paradox phenomenon in the cascading failures of small world power grids is studied. It shows that robustness of a power grid is closely related to its topological structure. As the average degree is great, there exist several bifurcation points in the robustness curve of the nearest-neighbor coupled network and the small world network. In small world structure power grids, generally, the greater the average degree and the number of nodes, the more power stations, the better robustness of the power grid. Robustness of a power grid with distributed power stations is better than that with centralized distribution. In addition, the Braess phenomenon, which leads to the decrease of robustness due to the increase of network capacity, is explained.

Key words: complex network, cascading failures, admittance model, robustness, Braess paradox

CLC Number:

TM711

Haoqian LI, Yanli ZOU, Shaoze ZHANG, Xinyan LIU, Shuyi TAN. Robustness of Power Grids Structure and Braess Paradox Phenomenon: A Complex Network Theory Study[J]. Chinese Journal of Computational Physics, 2021, 38(4): 470-478.

Figures/Tables 10

Fig.1 Robustness of a WS small world network and a nearest-neighbor coupled network at (a) 〈k〉=4 and (b)〈k〉=6

Fig.2 Robustness of WS small world networks at different average degrees

Fig.3 Robustness of WS small world networks with different numbers of generators

Fig.4 Robustness of WS small world networks in two generator distribution modes

Fig.5 Robustness of WS small world networks with different number of nodes

Fig.6 A WS small world network with 〈k〉=4, N=118, Ng=40

Fig.7 Robustness of a WS small world network with 〈k〉=4, N=118, Ng=40

Fig.8 PPM-α after removing edges 61-96

Fig.9 Ratio of overload nodes and links as functions of capacity parameters α in stage T of the network after a single special link failure

Table 1 Key nodes in the network that operate normally at α=αL-Δα but overloaded at α=αL

节点编号	度	相对介数	节点编号	度	相对介数
1	4	0.562	81	5	0.544
3	4	0.595	89	5	0.531
12	4	0.504	90	5	0.586
17	5	0.485	96	5	0.875
38	6	0.952	101	5	0.562
41	5	0.805	104	5	0.808
56	5	0.609	111	5	0.731
70	6	0.937	113	5	0.485

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