CN107622360A - A kind of critical circuits recognition methods for considering subjective and objective factor - Google Patents

A kind of critical circuits recognition methods for considering subjective and objective factor Download PDF

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Publication number
CN107622360A
CN107622360A CN201710986824.4A CN201710986824A CN107622360A CN 107622360 A CN107622360 A CN 107622360A CN 201710986824 A CN201710986824 A CN 201710986824A CN 107622360 A CN107622360 A CN 107622360A
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mrow
msub
node
msubsup
mfrac
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谭嫣
李力
邓卿
向丽玲
梁永清
华威
苏瑞文
文福拴
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Zhejiang University ZJU
Electric Power Dispatch Control Center of Guangdong Power Grid Co Ltd
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Zhejiang University ZJU
Electric Power Dispatch Control Center of Guangdong Power Grid Co Ltd
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Abstract

The present invention discloses a kind of critical circuits recognition methods for considering subjective and objective factor, there are n grid nodes to be evaluated for setting tool, m evaluation index is chosen altogether, and it is X that desired value of each node in each evaluation index, which forms Evaluations matrix, and R=[r are can obtain after standardization is done to Xij]m×n；The R obtained to standardization can obtain W=[w after assigning weightij]m×n=[λi×rij]m×n；Determine Positive ideal pointAnd Negative ideal pointThe evaluation vector that each index is selected to optimal desired value composition is defined as Positive ideal point, is conversely Negative ideal point；IfDue to all having carried out standardization to data, soFor null vector；Definition is evaluated the evaluation vector of node to Positive ideal pointDistance；Definition is evaluated the evaluation vector and Positive ideal point and the irrelevance of Negative ideal point of node；According to the T being calculatedjValue is ranked up to each node, and the value is smaller, shows that the node is more important；If the T of two or more nodesjBe worth it is equal, then with djIt is distinguish between, nearer apart from smaller explanation nodal distance ideal point, then the node is also more important.

Description

A kind of critical circuits recognition methods for considering subjective and objective factor
Technical field
The present invention relates to Power System Analysis field, more particularly, to a kind of key for considering subjective and objective factor Identification of lines method.
Background technology
The key node and branch road of power network are identified, and then targetedly crucial transformer station and transmission line of electricity entered Row is laid special stress on protecting, and the reliability to improving power system, the probability of happening for reducing massive blackout accident has highly important meaning Justice.
Existing technology includes the method based on Monte-Carlo Simulation, has computationally intensive, calculating time and calculating The problem of precision contradiction；Method based on Complex Networks Theory, by changing rest network after circuit or node in network Changing features degree identifies the fragile link in former network topology, and this method only investigated the topological property of network, do not count and Unique characteristics and operation constrain.
The content of the invention
The present invention is to overcome at least one defect described in above-mentioned prior art, there is provided one kind considers subjective and objective factor Critical circuits recognition methods.This method is fully extracted the information that objective data contains, and has taken into full account the subjectivity of expert again Opinion, the result for preferably meeting that equipment operation management is actual can be obtained.
To achieve the above object, the technical scheme is that：
A kind of critical circuits recognition methods for considering subjective and objective factor, its implementation process are：
The index of objective evaluation power network critical circuits is defined, including：
(1) the electric betweenness of circuit, is defined according to the following formula：
In formula,For when node between (i, j) to injecting unit power, the power component on circuit l；PGiSaved to generate electricity Point i active power weight, PDjFor load bus j active power weight, the power for taking node to inject or flow out respectively herein； SGAnd SDRespectively generating node and load bus set.
(2) efficiency fragile degree is transmitted.
Definition transmission efficiency is first：
In formula, n is network node number, and i, j are any two points in system, dijFor two nodes of connection it is most short electrically away from From.
Will transmission fragile degree ViIt is defined as former network and loses the transmission efficiency variable quantity after circuit i：
If ViValue is bigger, show to influence the transmission of the electric energy of electric power networks after circuit i failures it is also bigger, so as to show this Circuit location in electric power networks is more important.
(3) voltage class value
The voltage class of circuit is higher, it is however generally that the trend undertaken in a network is collected also heavier with the effect of distribution Will, the circuit of the different voltage class in the present invention is entered as：500kV values are 4,220kV values are 3,110kV values are 2, Below 110kV values are 1.
2nd, the weight design of subjective and objective factor is considered
(1) objective factor weight
Objective factor weight uses information entropy assessment, and step is：
Assuming that there is n objects to be evaluated, the m indexs for being used to evaluate, object j evaluation vector is xj=(x1j, x2j,...,xmj)T.It is hereby achieved that Evaluations matrix X=(x1,x2,...,xn), i.e. X=[xij]m×n, wherein, xijRepresent jth Desired value of the individual object in i-th of index；I=1,2 ..., m；J=1,2 ..., n.Comentropy and comentropy is given below The definition of power and property.
Evaluation index can be generally divided into profit evaluation model and the class of cost type two.Profit evaluation model desired value is the bigger the better, and cost type refers to Scale value is the smaller the better.Therefore following standardization is done to Evaluations matrix：
In formula,WithIt is illustrated respectively in x in i-th of indexijMaximum and minimum value.
R=[r can be obtained after standardization to original Evaluations matrix Xij]m×n, in formula, rij∈ [0,1], table Show desired value of j-th of object in i-th of index；I=1,2 ..., m；J=1,2 ..., n.
In the evaluation model with m evaluation index and n objects to be evaluated, the comentropy of i-th of evaluation index is determined Justice is：
In formula,And work as fijWhen=0, fijlnfij=0.
The information entropy weight of i-th of evaluation index is defined as：
(2) subjective factor weight
Subjective factor weight uses stratification, and step is：
1) multilevel iudge matrix U=[u is constructedij]m×m, uijExpression factor i opposing factors j importance, and uij=1/ uij, multilevel iudge matrix uses nine grades of scale systems.
2) Weight of Expert α=[α is defined1, α2... αm]T, wherein the Weight of Expert of i-th of evaluation index is
(3) comprehensive weight
With reference to objective, subjective factor, defining comprehensive weight is：
In formula, m is index sum to be evaluated.
3rd, the flow of overall algorithm is as follows：
(1) assume with n grid nodes to be evaluated, and have chosen m evaluation index altogether, then each node is respectively being commented It is X that desired value in valency index, which forms Evaluations matrix, and R=[r are can obtain after standardization is done to Xij]m×n。
(2) W=[w can be obtained after assigning weight to the R that above-mentioned standard handles to obtainij]m×n=[λi×rij]m×n。
(3) Positive ideal point is determinedAnd Negative ideal pointEach index is selected to the evaluation of optimal desired value composition Vector is defined as Positive ideal point, is conversely Negative ideal point.IfDue to all being standardized to data Processing, soFor null vector.
(4) define and be evaluated the evaluation vector of node to Positive ideal pointDistance be：
(5) irrelevance for defining the evaluation vector and Positive ideal point and Negative ideal point that are evaluated node is：
According to the T being calculatedjValue is ranked up to each node, and the value is smaller, shows that the node is more important.If two The T of individual or multiple nodesjBe worth it is equal, then with djIt is distinguish between, apart from smaller, illustrates that the nodal distance ideal point is nearer, thus The node is also more important.
Compared with prior art, the beneficial effect of technical solution of the present invention is：Description power system includes topological structure, set Standby parameter, running status, load attribute etc., during key equipment is identified, should fully extract objective data and accumulate The information contained, takes into full account the subjective opinion of expert again, can just obtain the result for preferably meeting that equipment operation management is actual.
Brief description of the drawings
Fig. 1 is the node system wiring diagram of 10 machine of New England 39.
Embodiment
Accompanying drawing being given for example only property explanation, it is impossible to be interpreted as the limitation to this patent；It is attached in order to more preferably illustrate the present embodiment Scheme some parts to have omission, zoom in or out, do not represent the size of actual product；
To those skilled in the art, it is to be appreciated that some known features and its explanation, which may be omitted, in accompanying drawing 's.Technical scheme is described further with reference to the accompanying drawings and examples.
A kind of critical circuits recognition methods for considering subjective and objective factor, its implementation process are：
The index of objective evaluation power network critical circuits is defined, including：
(1) the electric betweenness of circuit, is defined according to the following formula：
In formula,For when node between (i, j) to injecting unit power, the power component on circuit l；PGiSaved to generate electricity Point i active power weight, PDjFor load bus j active power weight, the power for taking node to inject or flow out respectively herein； SGAnd SDRespectively generating node and load bus set.
(2) efficiency fragile degree is transmitted.
Definition transmission efficiency is first：
In formula, n is network node number, and i, j are any two points in system, dijFor two nodes of connection it is most short electrically away from From.
Will transmission fragile degree ViIt is defined as former network and loses the transmission efficiency variable quantity after circuit i：
If ViValue is bigger, show to influence the transmission of the electric energy of electric power networks after circuit i failures it is also bigger, so as to show this Circuit location in electric power networks is more important.
(3) voltage class value
The voltage class of circuit is higher, it is however generally that the trend undertaken in a network is collected also heavier with the effect of distribution Will, the circuit of the different voltage class in the present invention is entered as：500kV values are 4,220kV values are 3,110kV values are 2, Below 110kV values are 1.
2nd, the weight design of subjective and objective factor is considered
(1) objective factor weight
Objective factor weight uses information entropy assessment, and step is：
Assuming that there is n objects to be evaluated, the m indexs for being used to evaluate, object j evaluation vector is xj=(x1j, x2j,...,xmj)T.It is hereby achieved that Evaluations matrix X=(x1,x2,...,xn), i.e. X=[xij]m×n, wherein, xijRepresent jth Desired value of the individual object in i-th of index；I=1,2 ..., m；J=1,2 ..., n.Comentropy and comentropy is given below The definition of power and property.
Evaluation index can be generally divided into profit evaluation model and the class of cost type two.Profit evaluation model desired value is the bigger the better, and cost type refers to Scale value is the smaller the better.Therefore following standardization is done to Evaluations matrix：
In formula,WithIt is illustrated respectively in x in i-th of indexijMaximum and minimum value.
R=[r can be obtained after standardization to original Evaluations matrix Xij]m×n, in formula, rij∈ [0,1], table Show desired value of j-th of object in i-th of index；I=1,2 ..., m；J=1,2 ..., n.
In the evaluation model with m evaluation index and n objects to be evaluated, the comentropy of i-th of evaluation index is determined Justice is：
In formula,And work as fijWhen=0, fijlnfij=0.
The information entropy weight of i-th of evaluation index is defined as：
(2) subjective factor weight
Subjective factor weight uses stratification, and step is：
1) multilevel iudge matrix U=[u is constructedij]m×m, uijExpression factor i opposing factors j importance, and uij=1/ uij, multilevel iudge matrix uses nine grades of scale systems.
2) Weight of Expert α=[α is defined1, α2... αm]T, wherein the Weight of Expert of i-th of evaluation index is
(3) comprehensive weight
With reference to objective, subjective factor, defining comprehensive weight is：
In formula, m is index sum to be evaluated.
3rd, the flow of overall algorithm is as follows：
(1) assume with n grid nodes to be evaluated, and have chosen m evaluation index altogether, then each node is respectively being commented It is X that desired value in valency index, which forms Evaluations matrix, and R=[r are can obtain after standardization is done to Xij]m×n。
(2) W=[w can be obtained after assigning weight to the R that above-mentioned standard handles to obtainij]m×n=[λi×rij]m×n。
(3) Positive ideal point is determinedAnd Negative ideal pointEach index is selected to the evaluation of optimal desired value composition Vector is defined as Positive ideal point, is conversely Negative ideal point.IfDue to all being standardized to data Processing, soFor null vector.
(4) define and be evaluated the evaluation vector of node to Positive ideal pointDistance be：
(5) irrelevance for defining the evaluation vector and Positive ideal point and Negative ideal point that are evaluated node is：
According to the T being calculatedjValue is ranked up to each node, and the value is smaller, shows that the node is more important.If two The T of individual or multiple nodesjBe worth it is equal, then with djIt is distinguish between, apart from smaller, illustrates that the nodal distance ideal point is nearer, thus The node is also more important.
Embodiment 1
The feature of proposed method is illustrated using the node system of 10 machine of New England 39 as shown in Figure 1 herein.This In have chosen the electric betweenness of node, the fragility of electrical grid transmission efficiency, node location importance, node power coefficient of concentration, 6 indexs of load loss rate and node reactive power nargin (are designated as I respectively1, I2, I3, I4, I5And I6) be used to identify in the system Key node.
First, value of each node in each index is calculated according to the definition of index respectively, it the results are shown in Table 1.
The comentropy and information entropy weight of 1 each index of table
Then, the Weight of Expert of each index is calculated using AHP methods, the multilevel iudge matrix that expert determines is shown in Table 2.And The I being calculated using AHP methods1~I6Weight of Expert be respectively：0.0493、0.0493、0.1183、0.1964、0.4391、 0.1476。
The AHP multilevel iudge matrixes of table 2
Be calculated each index comprehensive weight for λ=[0.0800,0.0580,0.1195,0.1556,0.4365, 0.1504]T.The assessment result obtained according to comprehensive weight is shown in Table 3 respectively.
Node significance level sequence of the table 3 based on comprehensive weight
As can be seen from Table 3：The node of the power network most critical identified is node 16, the reason for this is that：First, at node 16 In the center of network transmission, its electric betweenness value is 712, to be maximum in all nodes；Its node location importance is 1566, it ranked third in all nodes.Secondly, node 16 is the key node on topological structure of electric, once node 16 is lost, System meeting off-the-line causes electric power networks without connectedness, therefore the fragility of its network transmission efficiency is into 3 subsystems It is maximum in 0.3284, and all nodes.Again, one of node that node 16 and network re-active power are most concentrated, it is saved Point power coefficient of concentration is 0.6522, and (almost equal with the node 10 that ranked third) is ranked fourth in all nodes, illustrates node 16 be the node to be played an important role in network re-active power conveying and assigning process.Finally, although node 16 is not to generate electricity Machine node, but the load that node 16 itself is connected can be lost by losing node 16, and also generator node 33,34,35,36 is past Load bus conveying active power process will by extreme influence, thereby result in can supply load total amount decline can than lose Go a generator node even more serious.To sum up, under extreme disasters weather, power grid operation personnel can be according to above-mentioned node The ranking results of importance and the actual conditions of emergency first-aid repair, targetedly the key node high to importance meet an urgent need Prevent (such as windproof Scheme of Strengthening), so as to farthest prevent the generation that the failure of important node and system are had a power failure on a large scale.
Obviously, the above embodiment of the present invention is only intended to clearly illustrate example of the present invention, and is not pair The restriction of embodiments of the present invention.For those of ordinary skill in the field, may be used also on the basis of the above description To make other changes in different forms.There is no necessity and possibility to exhaust all the enbodiments.It is all this All any modification, equivalent and improvement made within the spirit and principle of invention etc., should be included in the claims in the present invention Protection domain within.

Claims (1)

  1. A kind of 1. critical circuits recognition methods for considering subjective and objective factor, it is characterised in that
    The index of objective evaluation power network critical circuits is defined, including：
    (101) the electric betweenness of circuit, is defined according to the following formula：
    <mrow> <msub> <mi>B</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <mi>l</mi> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>&amp;Element;</mo> <msub> <mi>S</mi> <mi>G</mi> </msub> </mrow> </munder> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <msub> <mi>S</mi> <mi>D</mi> </msub> </mrow> </munder> <msqrt> <msub> <mi>P</mi> <mrow> <mi>G</mi> <mi>i</mi> </mrow> </msub> </msqrt> <mo>|</mo> <msubsup> <mi>P</mi> <mi>l</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msubsup> <mo>|</mo> </mrow>
    In formula, Pl ijDuring for node to injecting unit power between circuit (i, j), the power component on circuit l；PGiFor generating node i Active power weight, PDjFor load bus j active power weight, the power for taking node to inject or flow out respectively herein；SG And SDRespectively generating node and load bus set；
    (102) efficiency fragile degree is transmitted：
    Definition transmission efficiency is first：
    <mrow> <msub> <mi>E</mi> <mn>0</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>&amp;NotEqual;</mo> <mi>j</mi> </mrow> </munder> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mfrac> </mrow>
    In formula, n is network node number, and i, j are any two points in system, dijTo connect the most short electrical distance of two nodes；
    Will transmission fragile degree ViIt is defined as former network and loses the transmission efficiency variable quantity after circuit i：
    <mrow> <msub> <mi>V</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>E</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>E</mi> <mi>i</mi> </msub> </mrow> <msub> <mi>E</mi> <mn>0</mn> </msub> </mfrac> </mrow>
    If ViValue is bigger, show to influence the transmission of the electric energy of electric power networks after circuit i failures it is also bigger, so as to show the circuit Location is more important in electric power networks；
    (103) voltage class value
    The circuit of different voltage class is entered as：500kV values are 4,220kV values are 3,110kV values are 2, below 110kV Value is 1；
    S2, the weight design for considering subjective and objective factor
    (201) objective factor weight
    Objective factor weight uses information entropy assessment, and step is：
    Assuming that there is n objects to be evaluated, the m indexs for being used to evaluate, object j evaluation vector is xj=(x1j,x2j,...,xmj )T；It is hereby achieved that Evaluations matrix X=(x1,x2,...,xn), i.e. X=[xij]m×n, wherein, xijRepresent j-th of object Desired value in i index；I=1,2 ..., m；J=1,2 ..., n；Be given below comentropy and information entropy weight definition and Property；
    Evaluation index can be generally divided into profit evaluation model and the class of cost type two；Profit evaluation model desired value is the bigger the better, cost type desired value It is the smaller the better；Therefore following standardization is done to Evaluations matrix：
    In formula,WithIt is illustrated respectively in x in i-th of indexijMaximum and minimum value；
    R=[r can be obtained after standardization to original Evaluations matrix Xij]m×n, in formula, rij∈ [0,1], represent the Desired value of the j object in i-th of index；I=1,2 ..., m；J=1,2 ..., n；
    In the evaluation model with m evaluation index and n objects to be evaluated, the comentropy of i-th of evaluation index is defined as：
    <mrow> <msub> <mi>H</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <mi>ln</mi> <mi> </mi> <mi>n</mi> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mi>ln</mi> <mi> </mi> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>m</mi> </mrow>
    In formula,And work as fijWhen=0, fijlnfij=0；
    The information entropy weight of i-th of evaluation index is defined as：
    <mrow> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>H</mi> <mi>i</mi> </msub> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>H</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
    (202) subjective factor weight
    Subjective factor weight uses stratification, and step is：
    1) multilevel iudge matrix U=[u is constructedij]m×m, uijExpression factor i opposing factors j importance, and uij=1/uij, compare Judgment matrix uses nine grades of scale systems；
    2) Weight of Expert α=[α is defined1, α2... αm]T, wherein the Weight of Expert of i-th of evaluation index is
    (203) comprehensive weight
    With reference to objective, subjective factor, defining comprehensive weight is：
    <mrow> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <msub> <mi>&amp;alpha;</mi> <mi>i</mi> </msub> </mrow> <mrow> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </msubsup> <msub> <mi>&amp;omega;</mi> <mi>k</mi> </msub> <msub> <mi>&amp;omega;</mi> <mi>k</mi> </msub> </mrow> </mfrac> </mrow>
    In formula, m is index sum to be evaluated；
    The critical circuits recognition methods implementation process for considering subjective and objective factor is：
    (1) assume with n grid nodes to be evaluated, and have chosen m evaluation index altogether, then each node refers in each evaluation It is X that the desired value put on, which forms Evaluations matrix, and R=[r are can obtain after standardization is done to Xij]m×n；
    (2) W=[w can be obtained after assigning weight to the R that above-mentioned standard handles to obtainij]m×n=[λi×rij]m×n；
    (3) Positive ideal point is determinedAnd Negative ideal pointThe evaluation vector that each index is selected to optimal desired value composition is determined Justice is Positive ideal point, is conversely Negative ideal point；IfDue to data have all been carried out with standardization, institute WithFor null vector；
    (4) define and be evaluated the evaluation vector of node to Positive ideal pointDistance be：
    <mrow> <msub> <mi>d</mi> <mi>j</mi> </msub> <mo>=</mo> <msqrt> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>m</mi> <mo>;</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    (5) irrelevance for defining the evaluation vector and Positive ideal point and Negative ideal point that are evaluated node is：
    <mrow> <msub> <mi>T</mi> <mi>j</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> <mo>+</mo> </msubsup> <mo>-</mo> <msub> <mi>W</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> <mo>+</mo> </msubsup> <mo>-</mo> <msubsup> <mi>X</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> <mo>-</mo> </msubsup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <msubsup> <mi>X</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> <mo>+</mo> </msubsup> <mo>-</mo> <msubsup> <mi>X</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> <mo>-</mo> </msubsup> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>w</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>p</mi> <mi>i</mi> </msub> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msubsup> <mi>p</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>m</mi> <mo>;</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    According to the T being calculatedjValue is ranked up to each node, and the value is smaller, shows that the node is more important；If two or more The T of individual nodejBe worth it is equal, then with djIt is distinguish between, apart from smaller, illustrates that the nodal distance ideal point is nearer, thus the node Also it is more important.
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CN109242308A (en) * 2018-09-05 2019-01-18 西南交通大学 The distribution network failure recovery scheme Interval evaluation method of meter and negative rules
CN109242308B (en) * 2018-09-05 2021-12-03 西南交通大学 Power distribution network fault recovery scheme interval evaluation method considering load uncertainty
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CN111444593B (en) * 2020-03-02 2022-05-03 浙江大学 Method for improving vulnerability of elements of electricity-gas comprehensive energy system
CN111697590A (en) * 2020-06-19 2020-09-22 上海交通大学 Entropy weight method-based power system key node identification method and system
CN112615365A (en) * 2020-12-08 2021-04-06 国网四川省电力公司经济技术研究院 Smart power grid vulnerability key point identification method and device
CN112487658A (en) * 2020-12-14 2021-03-12 重庆邮电大学 Method, device and system for identifying key nodes of power grid
CN112487658B (en) * 2020-12-14 2022-09-16 重庆邮电大学 Method, device and system for identifying key nodes of power grid
CN114357761A (en) * 2021-12-31 2022-04-15 中国电力工程顾问集团中南电力设计院有限公司 Wind generating set type selection method based on entropy weight ideal point method

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