Evaluation of the node importance of power communication network based on multi-factor evaluation indicators

The continuous development of smart grid has promoted the advancement of the power communication network. And what followed was the complexity of the topology of the power communication network being increasing. In order to evaluate the importance of the network node more accurately, an evaluation method based on the multi-factor evaluation indicators is proposed in this paper. This method integrates the service layer and the topology layer of the network, and then combines the node types, the load factors of the nodes and the probability of failure of the nodes and links as a comprehensive factor coefficient to evaluate the importance of the nodes. The simulation results show that the algorithm proposed in the paper can consider the indicators affecting the importance of the node of the power communication network more comprehensively. It can evaluate the importance of the node more effectively which has a good application value.


Service importance
The nodes of the power communication network carry various types of services. And the service importance of the node varies with the type of service the node assumes [16] . The feature indicator evaluation method is adopted in the paper because of the diversity of the service types undertaken by the nodes and the characteristic standards such as the bit error rate of each service of the power communication network to improve the accuracy of the evaluation results [17] .
In the characteristic set P = {P k } (k = 1, 2,…, K), P k represents the different characteristics of the service with a total of K and the service set S = {S l } (l = 1, 2,…, L) with a total of L. S is mapped into a characteristic importance evaluation value matrix B lk = [1, 2,…, B k ] according to the evaluation criteria of the characteristic standard P k . Then the relative importance matrix of the service Taking the sum of the elements of each row of the matrix A to obtain the comprehensive relative importance of service S l .
Normalizing the comprehensive relative importance to get the importance of service S l .
The typical service importance of a certain province is obtained based on the feature indicator evaluation method mentioned above with considering the service quality indicators (transmission delay, bit error rate, etc.) and the grid impact indicators (safety zone, bearer mode, etc.) of the node in the power communication network as shown in table 1 [18] .

Service-based point weight calculation
Define the network topology G (V, E), node set V = {v 1 , v 2 ,…, v n } in which n is the total number of nodes and the edge set E = {e 1 , e 2 ,…, e m } with the total number of edges m.
The tight connection between nodes in the power communication network is measured by the point weight which is defined as follows.
In equation (6), E i is the links connected to node i, and W j is the edge weight of the two adjacent nodes.
We can combine the types and quantities of services carried on the network link when calculating the edge weight between nodes and then define the service-based edge weight as follows.
In equation (7), m j is the total number of service types on the link e j , k jl is the number of l-type service running on the link e j , and σ l is the value of the service importance of the l-type service.
Therefore, redefining the point weight is as follows.
In equation (8), n i is the total number of links connected to node v i .

Node importance combining service layer and topology layer
The network cohesion is obtained based on the service-based point weight defined above. In equation (9), l is the average path length between nodes and 1 = n i i P P   is the sum of the point weight. So the node importance combining service layer and topology layer CBTNI(v i ) is as follows.
In equation (10), ә(G 0 ) and ә(G i ) are the network cohesions before and after the contraction of the node v i .

Introduction of factor coefficients
3.1. The factor coefficient based on the power factor CBTNI(v i ) can better assess the importance of nodes. However, the node importance varies due to the different node types in the actual power communication network. Therefore, the factor coefficient based on the power factor PF(v i ) is defined according to the different types of nodes.
The indicator set A = {ɑ m } (m = 1, 2, 3, 4) in the power factor is summarized firstly according to the actual situation when calculating PF(v i ). Among them, ɑ 1 、ɑ 2 、ɑ 3 and ɑ 4 represent the node level, the node size, the load level and the load size respectively [19] .
In equation (11) (13) According to the above method, the relative force matrix of each node under the four indicators is obtained in turn. Define the comprehensive relative force matrix of the nodes as follows. 4 ( The factor coefficient based on the power factor PF(v i ) is obtained by normalizing the elements in the matrix sum n b . In equation (15), p i represents the node failure rate of the node; k i is the number of links connected to the node and e j is the link failure rate (The rate of the link failure between the two nodes is equal to the average value of the two-node link failure rate).

The comprehensive factor coefficient
The introduction of the factor coefficient based on the power factor PF(v i ) and the factor coefficient based on the failure probability FP(v i ) makes the evaluation of the node importance more accurate. However, the weight of the power factor indicator and the failure probability indicator are different. The following conclusion can be drawn by consulting relevant experts and summarizing them: FP(v i ) is smaller than PF(v i ). The fuzzy analytic hierarchy process is used in this paper to calculate the weight of the two factor coefficients, and the comprehensive factor coefficient of the node CFC(v i ) is obtained.
A priority judgment matrix A is constructed for the power factor indicator and the failure probability indicator firstly, and the elements of the matrix are defined according to the following rules.
Then the priority judgment matrix A is as follows. 0.5 0.6 = 0.4 0.5 Applying the following equation to the priority judgment matrix A. 1 ( 1, 2, , ) That is, the sum of the row elements of the matrix A is determined and r T = (1.1, 0.9) T is obtained. Then making the following mathematical transformation on the matrix r T .
We can obtain a fuzzy consistent judgment matrix M. 2 2 0.5 0.55 The equation for calculating the indicator weights can be obtained by using the relationship between the elements of the matrix M and the weights.
In equation (21), α ≥ (n-1) / 2, and we make α = (n-1) / 2 in this paper. Then the weights of the power factor indicator and the failure probability indicator are respectively as follows.
The comprehensive factor coefficient CFC(v i ) is as follows in summary.

Comprehensive node importance
Based on the above analysis, the nodes are comprehensively evaluated from the four perspectives of service, network topology, power factor and failure probability factor. The comprehensive node importance CNI(v i ) is obtained by CBTNI(v i ) and CFC(v i ).
The flow chart of the algorithm for calculating the comprehensive importance is shown in figure 2.

Start
Abstracting the power communication network as a weighted network model Calculating the comprehensive importance of nodes by using the node importance combining service layer and topology layer and comprehensive factor coefficient End Calculating service importance and point weight based on power service Calculating the node importance combining service layer and topology layer through the network cohesion formula Calculating the factor coefficient based on the power factor and factor coefficient based on failure probability Using the fuzzy analytic hierarchy process to determine the weight of two factor coefficients and calculating the comprehensive factor coefficient

Case analysis
The power communication network topology in southeastern Sichuan Province is used as a model to verify the effectiveness of the algorithm proposed in this paper. As shown in figure 3, the network consists of 10 nodes and 14 links, in which node v 4 is the provincial dispatching center, node v 10 is the 220kV substation and the remaining nodes are the 500kV substations. The node set is v = {v 1 , v 2 ,…, v 10 }, the link set is e = {e 1 , e 2 ,…, e 14 }, and the service set is S={S 1    The node contraction method, the cross-layer fusion method [20] , the topology + power factor method [21] and the method proposed in the paper are compared and the comparison results of the four algorithms are shown in table 4. Combined with the topology model of the power communication network and the actual operation of the network, it can be known through the analysis that node v 4 is the provincial dispatching center with more service on it, so its node has the highest importance. Nodes v 1 、v 2 、v 3 、v 5 、v 6 、v 7 、v 8 and v 9 are all 500kV substations, but v 3 、v 5 、v 6 、v 7 and v 9 are connected to node v 4 which has a higher power factor. And the failure rate of the link connected to v 4 is large. So v 3 、v 5 、v 6 、v 7 and v 9 are more important than the nodes of v 1 and v 2 . v 3 and v 7 have more service on the link than v 5 、v 6 、v 8 and v 9 , and the node type and load factor of v 7 are higher than v 3 , so node v 7 is more important than node v 3 . v 6 and v 9 have a relatively high service volume, while v 6 is connected to v 4 and v 7 , v 9 is connected to v 4 and v 10 , node v 6 has a higher node type, load factor and failure probability, so node v 6 is more important than node v 9 . We can see from the topological position that both v 5 and v 8 are connected to node v 10 , and node v 8 has more service than node v 5 , but node v 5 is connected to node v 4 which makes node v 5 has a higher load factor and failure probability. Therefore, node v 5 has a relatively high node importance. It can be seen from figure 3 that the positions of nodes v 1 and v 2 are symmetrical. The node contraction method and the topology + power factor method cannot distinguish the importance of the two nodes, but the service carried on node v 1 is more than node v 2 . Therefore, the method proposed