CN106156862A - The evaluation methodology of importance degree distribution characteristics index in a kind of powerline network - Google Patents

Abstract

The present invention provides the evaluation methodology of importance degree distribution characteristics index in a kind of powerline network, and importance degree distribution characteristics index is the composite target characterizing powerline network physical reliability with fault rate；This comprises steps of determining that each node betweenness importance degree accounting in whole powerline network；The method using curve matching, is fitted pitch point importance accounting, determines powerline network importance degree distribution characteristics index.The evaluation methodology of importance degree distribution characteristics index in the powerline network that the present invention provides, wherein importance degree distribution characteristics index is the composite target of assessment powerline network physical layer topology performance, this index contains the information of network cutpoint, have and be more widely applied environment, it is not necessary to statistics network key point or cutpoint etc. are for the index parameter of individual node the most again.

Description

The evaluation methodology of importance degree distribution characteristics index in a kind of powerline network

Technical field

The invention belongs to field of power communication, it is specifically related to the evaluation methodology of importance degree distribution characteristics index in a kind of powerline network.

Background technology

Power communication planning, construction need to find out important optical fiber link section; if this link down; the impact that need to cause business is analyzed; or under communication system N-2 situation, cause a plurality of route protection passage entirely disconnected, safety stabilization control system is malfunctioning and the impact that produces electricity net safety stable calculates and analyzes.But, for a complicated communication network, the influence degree of node failures is different, is required for which equipment can not break down, which communication equipment breaks down must the guideline of the problem such as reparation immediately.Network reliability is said on the whole and is built closely related with the physical network such as network structure, network topology, needs to find out the key node of network, the analysis and evaluation impact influence degree to network reliability.

Typically can be characterized the relative Link Importance of nodes by the number of degrees of network node or betweenness, but this method can only assess the feature of individual node, it is impossible to reflect the index feature of whole network.

Node betweenness is defined as the shortest path number by this node, and transfinite the sensitivity of fault to network flow on major embodiment limit.Node betweenness can reflect the key node in network and hub node, for separable graph network, can indirectly reflect network cutpoint.For powerline network, the many employings many planes construction of backbone transport network, there are active and standby two core nodes in each area, and such framework mode determines the overall tendentiousness of core node and selects.Therefore electric power backbone communication network belongs to scales-free network, and its node degree and betweenness distribution can represent by power law form, and betweenness distribution characteristics can be used to characterize network-critical degree configuring condition.

Summary of the invention

In order to seek to reflect the index parameter in terms of whole network synthesis reliability, safety, the present invention provides the evaluation methodology of importance degree distribution characteristics index in a kind of powerline network, wherein importance degree distribution characteristics index is the composite target characterizing powerline network physical reliability with fault rate, it it is the composite target of assessment powerline network physical layer topology performance, it comprises the information of network cutpoint, have and be more widely applied environment, it is not necessary to statistics network key point or cutpoint etc. are for the index parameter of individual node the most again.

In order to realize foregoing invention purpose, the present invention adopts the following technical scheme that:

The present invention provides the evaluation methodology of importance degree distribution characteristics index in a kind of powerline network, described importance degree distribution characteristics index to be the composite target characterizing powerline network physical reliability with fault rate；Said method comprising the steps of:

Determine node betweenness and importance degree accounting thereof；

The method using curve matching, is fitted pitch point importance accounting, determines powerline network importance degree distribution characteristics index.

The determination process of the importance degree accounting of node betweenness is as follows: represent the node betweenness of certain set-point with B ', and it is constant, and B ' ∈ [B_min,B_max], B_maxAnd B_minRepresent powerline network interior joint betweenness maximum and minima respectively；

The importance degree accounting of node betweenness is defined as the nodes accounting at whole powerline network interior joint number of given betweenness, first calculates each node betweenness B in powerline network_N, it is then determined that accounting p (B >=B ') of the node total nodes of relative power communication network that node betweenness is not less than B '.

Powerline network importance degree distribution characteristics index determines that process is as follows:

Using cumulative distribution function method to determine that powerline network interior joint betweenness is distributed, the cumulative distribution function of definition B ' is P_cum(B '), it is expressed as:

$P_{\mathrm{cum}}\left(B^{\′}\right)=\underset{B=B^{\′}}{\overset{B_{\max }}{\mathrm{\Σ}}}p(B\≥B^{\′})---\left(1\right)$

For powerline network, node betweenness statistics meets power-law distribution, therefore:

$P_{\mathrm{cum}}\left(B^{\′}\right)=\underset{B_N=B^{\≤}}{\overset{B_{\max }}{\mathrm{\Σ}}}{B}_N^{-{\mathrm{\δ}}_N}---\left(2\right)$

Wherein, δ_NRepresent the distribution characteristics index of powerline network interior joint betweenness, δ_N＞ 0；B_NRepresent the betweenness of node N；

Formula (2) deformation is obtained:

${\mathrm{\δ}}_N=-\frac{\lg \left(P_{\mathrm{cum}}\left(B^{\′}\right)\right)}{\lg {\mathrm{\Σ}}_{B_N=B^{\′}}^{B_{\max }}{B}_N}---\left(3\right).$

Compared with prior art, the beneficial effects of the present invention is:

A. network-critical degree distribution characteristics index is an important indicator parameter for the distribution of network node betweenness, the key point distribution situation in network can be reflected, when network exists cutpoint, the betweenness of this node is of a relatively high, its must in network certain two node link by force path, therefore, network node betweenness index contains the information of network cutpoint, have and be more widely applied environment, it is not necessary to the single index such as statistics network key point or cutpoint the most again；

B. in actual applied environment, determine the distribution characteristics index relative difficulty of node betweenness, determine betweenness index to need network topology data and be fitted processing.Firstly the need of calculating all shortest paths between node, can be solved by the shortest path first such as dijkstra algorithm, BFS；Secondly, need to make curve matching further according to real data situation from betweenness cumulative distribution formula, simply determine the distribution characteristics index of powerline network interior joint betweenness.

Accompanying drawing explanation

Fig. 1 is powerline network topology diagram in the embodiment of the present invention.

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is described in further detail.

The present embodiment provides a kind of approximation to meet the 8 simple powerline networks of node of power-law distribution feature, uses importance degree distribution characteristics index to characterize this powerline network key node distribution situation, and its topological structure is as shown in Figure 1.

Eight network nodes of the present embodiment are A, B, C, D, E, F, G, H；

The importance degree distribution characteristics index number evaluation method of the present embodiment comprises the steps:

Step 1: determine node betweenness and importance degree accounting thereof；

In the present embodiment, calculate node betweenness to need first to calculate the shortest path between all non-conterminous nodes pair, dijkstra algorithm is used to draw 13, respectively BH, DF, ABC, AHG, CDE, GFE, ABCD, AHGF, BCDE, HGFE, EFGHA, DCGH, FGCB.

According to the definition in step 1, in network, betweenness and the importance degree accounting thereof of each node calculate as shown in table 1:

Table 1

Step 2: the method using curve matching, is fitted pitch point importance accounting, determines powerline network importance degree distribution characteristics index.

Cumulative distribution function method is used to determine that powerline network interior joint betweenness is distributed, then cumulative distribution function P of node betweenness B '_cum(B ') is expressed as:

$P_{\mathrm{cum}}\left(B^{\′}\right)=\underset{B=B^{\′}}{\overset{B_{\max }}{\mathrm{\Σ}}}p(B\≥B^{\′})---\left(1\right)$

Therefore, according to the result of table 1, convolution (1), P is drawn_cum(B ') is as shown in table 2:

Table 2

With δ_NRepresent powerline network interior joint betweenness distribution characteristics index；B_NRepresent the betweenness of node N.

Assume that this embodiment network node betweenness statistics meets power-law distribution, then P_cum(B ') is also shown as:

$P_{\mathrm{cum}}\left(B^{\′}\right)=\underset{B_N=B^{\≤}}{\overset{B_{\max }}{\mathrm{\Σ}}}{B}_N^{-{\mathrm{\δ}}_N}---\left(2\right)$

Wherein, δ_NRepresent the distribution characteristics index of powerline network interior joint betweenness, δ_N＞ 0；B_NRepresent the betweenness of node N；

Formula (2) deformation can be obtained:

${\mathrm{\δ}}_N=-\frac{\lg \left(P_{\mathrm{cum}}\left(B^{\′}\right)\right)}{\lg {\mathrm{\Σ}}_{B_N=B^{\′}}^{B_{\max }}{B}_N}---\left(3\right).$

Wherein, right in formula (3)Calculating, it is assumed that B_N=1, then:

$\underset{B_N-1}{\overset{B_{\max }}{\mathrm{\Σ}}}{B}_N=1+1+2+2+3+3+5+6=23---\left(4\right)$

All when obtainingAfter value (as shown in table 2), to each B ', the δ of correspondence can be drawn by formula (3)_N,.Owing to this network approximation meets power-law distribution feature, the corresponding betweenness distribution characteristics index δ of the most each B ' value_NHaving different, can affirm, when network size is bigger, value difference is different will be reduced.

Use single order method of least square to δ_NCarry out curve fitting, if y_i=lg (P_cum(B')),(occurrence is shown in Table 2), then formula (3) can be deformed into:

y_i=-δ_Nx_i (5)

Therefore substitute into single order method of least square computing formula (see formula 6, wherein N is B ' value number), final δ can be obtained_NFor:

${\text{\δ}}_N=-\frac{N\left(\mathrm{\Σ}{x}_i{y}_i\right)-\mathrm{\Σ}{x}_i{\mathrm{\Σy}}_i}{\mathrm{N\Σ}{x}_i^2-{\left(\mathrm{\Σ}{x}_i\right)}^2}---\left(6\right)$

Substituting into the numerical value in table 2, can be calculated this network-critical degree distribution exponent value is:

${\mathrm{\δ}}_N=-\frac{5\×(-0.36816)-5.7339\×(-0.75707)}{5\×6.8006-{5.73394}^2}=-2.16477---\left(7\right)$

According to the computing formula of betweenness characteristic index above, in actual application, need to be undertaken in two steps, the first step, determine betweenness value and the importance degree accounting thereof of all nodes；Second step, calculates node betweenness cumulative distribution, carries out curve fitting its importance degree accounting, draw powerline network interior joint importance degree distribution characteristics index.

Finally should be noted that: above example is only in order to illustrate that technical scheme is not intended to limit; the detailed description of the invention of the present invention still can be modified or equivalent by those of ordinary skill in the field with reference to above-described embodiment; these are without departing from any amendment of spirit and scope of the invention or equivalent, within the claims of the present invention all awaited the reply in application.

Claims (3)

1. the evaluation methodology of importance degree distribution characteristics index in a powerline network, it is characterised in that: described importance degree is distributed Characteristic index is the composite target characterizing powerline network physical reliability with fault rate；Said method comprising the steps of:

Determine node betweenness and importance degree accounting thereof；

The method using curve matching, is fitted pitch point importance accounting, determines powerline network importance degree distribution characteristics Index.

The evaluation methodology of importance degree distribution characteristics index in powerline network the most according to claim 1, its feature exists In: the determination process of the importance degree accounting of node betweenness is as follows: represent the node betweenness of certain set-point with B ', and it is constant, and B′∈[B_min,B_max], B_maxAnd B_minRepresent powerline network interior joint betweenness maximum and minima respectively；

The importance degree accounting of node betweenness is defined as the nodes accounting at whole powerline network interior joint number of given betweenness, First calculate each node betweenness B in powerline network_N, it is then determined that the node relative power communication network that node betweenness is not less than B ' Accounting p (B >=B ') of the total nodes of network.

The evaluation methodology of importance degree distribution characteristics index in powerline network the most according to claim 2, its feature exists In: powerline network importance degree distribution characteristics index determines that process is as follows:

Using cumulative distribution function method to determine that powerline network interior joint betweenness is distributed, the cumulative distribution function of definition B ' is P_cum(B '), it is expressed as:

$P_{\mathrm{cum}}\left(B^{\′}\right)=\underset{B=B^{\′}}{\overset{B_{\max }}{\mathrm{\Σ}}}p(B\≥B^{\′})---\left(1\right)$

For powerline network, node betweenness statistics meets power-law distribution, therefore:

$P_{\mathrm{cum}}\left(B^{\′}\right)=\underset{B_N=B^{\′}}{\overset{B_{\max }}{\mathrm{\Σ}}}{B}_N^{-{\mathrm{\δ}}_N}---\left(2\right)$

Wherein, δ_NRepresent the distribution characteristics index of powerline network interior joint betweenness, δ_N＞ 0；B_NRepresent Jie of node N Number；

Formula (2) deformation is obtained:

${\mathrm{\δ}}_N=-\frac{\lg \left(P_{\mathrm{cum}}\left(B^{\′}\right)\right)}{\lg {\mathrm{\Σ}}_{B_N=B^{\′}}^{B_{\max }}{B}_N}---\left(3\right).$