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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 65, NO. 2, FEBRUARY 2018
CRITIC-Based Node Importance Evaluation in Skeleton-Network Reconfiguration of Power Grids Zhenzhi Lin, Fushuan Wen, Huifang Wang, Guanqiang Lin, Tianwen Mo, and Xiaojun Ye
Abstract—Seven centrality indexes are first presented for identifying important nodes with topological features of a complex network and electrical characteristics of a power system considered. Then, a criteria importance through intercriteria correlation-based multi-index decision-making method, in which entropy and the Spearman’s rank correlation coefficient are integrated for reflecting the differences and correlations among multiple indexes, respectively, is presented to comprehensively identify the importance degrees of nodes in a given power grid. Finally, the proposed indexes and method are applied to actual Guangdong power system in China, and the results are compared with those attained by single-attribute and multi-attribute evaluation methods. Index Terms—Power system, complex network, network reconfiguration, node importance evaluation, criteria importance through intercriteria correlation (CRITIC).
I. I NTRODUCTION OWER system operation at a boundary state and/or the destructive weather events could possibly lead to a complete blackout or large-area power interruption [1], [2]. An extreme weather event, the Typhoon ‘Rainbow’, attacked a large part of Guangdong power system in China on October 4, 2015, and led to large-area outage and huge economic cost. To prevent similar blackouts or outages from occurrence in the future, Guangdong Power Grid Corporation in China proposed an action plan to identify a skeleton-network including important nodes and branches for Guangdong power system. This action plan aims at preventing important nodes and transmission lines in the identified skeleton-network from faults and outages by implementing preventive measures, such as reinforcing some important power devices and transmission towers in this identified skeleton-network against strong typhoons or other extreme events. Then, power devices and transmission towers could be protected to the greatest extent under extreme events,
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Manuscript received April 30, 2017; accepted May 8, 2017. Date of publication May 12, 2017; date of current version January 29, 2018. This work was supported in part by the National Key Research and Development Program of China under 2016YFB0900105, in part by the National Natural Science Foundation of China under Grant 51377005, and in part by the project from Guangdong Power Grid Corporation under Grant GDKJQQ20153014. This brief was recommended by Associate Editor H. H.-C. Iu. (Corresponding author: Fushuan Wen.) Z. Lin, F. Wen, and H. Wang are with the School of Electrical Engineering, Zhejiang University, Hangzhou 310027, China (e-mail:
[email protected];
[email protected];
[email protected]). G. Lin, T. Mo, and X. Ye are with the Huizhou Power Supply Bureau, Guangdong Power Grid Corporation, Huizhou 516000, China (e-mail:
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCSII.2017.2703989
and hence facilitate transmission network reconfiguration after a complete or partial blackout [3]–[5]. Given this background, it is necessary to evaluate the importance degrees of nodes for determining the skeleton network of the power system concerned. In [6], the network reconfiguration efficiency is proposed and employed to identify the skeleton network for transmission network reconfiguration based on the average node importance degree of load nodes in the power network after node contraction and average clustering coefficient of all nodes in the original power network are carried out. In [7], an electrical characteristic, i.e., the charging capacitance of each candidate restoration path, is considered in the network reconfiguration efficiency index. In [8], the network reconfiguration is modeled as a multi-objective optimization problem, and the lexicographic method employed to solve the optimization model. In [9], an entropy based multi-index evaluation algorithm is proposed to identify the node importance considering the differences among various indexes. In [10], a node importance evaluation method is presented based on the PageRank algorithm. In [11], a Gini-coefficient based method is proposed to evaluate the node importance degree in a power system considering the differences among various indexes. Up to now, several indexes have been proposed to evaluate the importance degrees of nodes, while in some existing publications such as [6] and [10] only one index is employed and this is not enough to cover the topological and electrical characteristics of a complex power system. Furthermore, these indexes are presented to identify important nodes in a power system under normal operation states, and hence cannot be directly utilized for skeleton-network reconfiguration. On the other hand, some existing evaluation methods, such as the entropy theory and Gini-coefficient-based method, are proposed for integrating multiple indexes with differences among various indexes considered, but the possible correlations among the indexes are not taken into account. In operations research, the well established CRiteria Importance Through Intercriteria Correlation (CRITIC) method [12] can determine objective weights of relative importance degrees for multiple criteria decision-making (MCDM) problems considering the differences and correlations among various criteria. Given this background, several indexes are presented for node importance evaluation considering the topological and electrical characteristics of a power system, and a CRITIC based multi-index node importance evaluation method is presented with differences and correlations among multiple indexes well taken into account. The contributions of this brief are as follows: 1) seven indexes from different perspectives are defined and synthesized to identify important nodes for the skeleton-network reconfiguration with topological and electrical characteristics of a given power system considered;
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LIN et al.: CRITIC-BASED NODE IMPORTANCE EVALUATION IN SKELETON-NETWORK RECONFIGURATION OF POWER GRIDS
2) the CRITIC method is applied to identify the important nodes, with both the differences and correlations among multiple indexes well considered; 3) the proposed indexes and method are applied to the actual Guangdong power system in China for determining the skeleton-network so as to resist extreme weather scenarios. II. S KELETON -N ETWORK R ECONFIGURATION The main tasks of transmission network reconfiguration which is the second phase of power system restoration are to determine a desirable target power network (i.e., skeletonnetwork) and to optimize restoration paths for the skeletonnetwork determined [1]. A skeleton-network consists of power source nodes (black-start sources and non-black-start sources), important load nodes and transmission lines (or transformer branches) connecting these nodes. In determining a reasonable target skeleton-network, it is necessary to identify important nodes and associated transmission lines connecting these important nodes. Thus, how to identify important nodes is a key step of transmission network reconfiguration, and should be done at the beginning of transmission network reconfiguration. Because the number of nodes in a skeleton-network would be much less than that in the original power network, so the nodes with larger degrees of importance should be paid more attention. The network reconfiguration efficiency presented in [6], which is proportional to average node importance degree, is employed for optimizing the skeleton-network of a power system. The larger the average node importance degree is, the more efficient the skeleton-network will be. Thus, the node importance determination is one of the important steps of skeleton-network reconfiguration. With this in mind, several indexes are presented for identifying important nodes from the pure network topology and/or electrical characteristics for skeleton-network reconfiguration. III. M ULTI -I NDEX BASED N ODE I MPORTANCE I DENTIFICATION In complex network theory, a N-node power network could be described by a N × N adjacent matrix {Aij }, in which Aij will be 1 if there exists an edge between vertex i and vertex j. Based on this notation, seven indexes are defined for identifying the importance degrees of various nodes in a given power system [13]. A. Electrical Degree Centrality In the skeleton-network reconfiguration of a power system, the generators with larger generation capacities should be given priority to restart, and the load nodes with more important load demand should be re-supplied power first. The capacities of the generators and the amounts of important loads respectively represent the maximum power injected into and flowing out the power system, and could be deemed as the information to be transferred through the power network concerned [13]. Thus, for a power network with N nodes, the electrical degree centrality of node i is represented as SG,max −(SG,i +SL,i ) j∈(i) Aij − SG,max (1) e IEDC (i) = N−1 where (i) is the set of the adjacent nodes of node i; SG,max is the maximum generation capacity among the generators; SG,i and SL,i are respectively the generation capacity and load power at node i.
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B. Electrical Closeness Centrality In determining the restoration path of skeleton-network reconfiguration, it is expected that less transmission lines and transformer branches to be included in the related path so as to shorten the required restoration time, and less charging capacitance in the related transmission lines so as to reduce the possibility of over-voltage and hence negative impacts on the reconfiguration of the skeleton-network. Thus, according to the definition of closeness centrality [13] in complex network theory, the electrical closeness centrality is defined as N
IECC (i) = (N − 1)/
Q
C dmin,ij
(2)
j=1,j=i Q
C where dmin,ij denotes the number of transmission lines and transformer branches in the shortest electrical path with respect to line capacitance (i.e., the path with minimal total capacitance in the related lines) between node i and node j.
C. Electrical Betweenness Centrality In a power network, electric power might be transmitted through all possible paths between a power source and a load, rather than the shortest path. A new electrical betweenness index based on the power transfer distribution factor is proposed in [11] considering electric power transmission properties, and is defined as ⎞ ⎛ gl ⎝ (3) IEBC (i) = fij ⎠ g∈SE l∈SK
gl fij eq Zig
j∈(i)
eq eq eq eq = Zig − Zil − Zjg − Zjl /xij
= zii − zig − zig − zgg
(4) (5)
where SE and SK denote the power source set and the load gl set, respectively. fij denotes the power transferred from power source node g to load node l through the transmission line connecting node i and node j. xij denotes the reactance of transeq mission line Lij . Zig denotes the equivalent impedance between node i and node g. zig denotes the transfer impedance from node i to node g; zii and zgg are the driving-point impedances of node i and node g, respectively. It should be mentioned that black-start units should supply start-up power to nonblack-start units at the initial stage of the skeleton-network reconfiguration. Thus, the nodes with non-black-start units should be considered as power source nodes as well as load nodes, i.e., SE = BS + NBS and SK = NBS + LD , where BS , NBS and LD are the node sets of black-start units, non-black-start units and loads, respectively. D. Eigenvector Centrality Assume that λ and e = [e1 , e2 , . . . , eN ]T are respectively the dominant eigenvalue and dominant eigenvector of the N × N adjacency matrix A of a given network with N nodes. It can be concluded that [13] λei =
N
Aij ej , i = 1, 2, . . . , N
(6)
j=1
The eigenvector centrality of node i is defined as 1 Aij ej λ N
IEVC (i) =
j=1
(7)
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 65, NO. 2, FEBRUARY 2018
In the skeleton-network reconfiguration of a complex power network, this index is employed to evaluate the importance degree of a node from the pure topological perspective.
⎛
ESC Gvi = (NC − 1)/⎝2
⎞ XL ⎠ dmin,kj
(14)
1≤k
