CN105654245B - Power grid static voltage stability methods of risk assessment based on negative rules modeling - Google Patents

Power grid static voltage stability methods of risk assessment based on negative rules modeling Download PDF

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CN105654245B
CN105654245B CN201511031154.8A CN201511031154A CN105654245B CN 105654245 B CN105654245 B CN 105654245B CN 201511031154 A CN201511031154 A CN 201511031154A CN 105654245 B CN105654245 B CN 105654245B
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韩肖清
白杨
王鹏
秦文萍
贾燕冰
梁琛
任春光
王磊
许进
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Abstract

The present invention relates to the static electric voltage stability methods of risk assessment of power grid, specifically a kind of power grid static voltage stability methods of risk assessment based on negative rules modeling.The present invention solves the problems, such as existing static electric voltage stability methods of risk assessment assessment result inaccuracy.Based on the power grid static voltage stability methods of risk assessment of negative rules modeling, this method is realized using following steps: 1) establishing negative rules model；2) trend operational model is established；3) risk assessment index is established, and with the high operation risk region in risk indicator identification power grid.The present invention is suitable for the static electric voltage stability risk assessment of power grid.

Description

Power grid static voltage stability methods of risk assessment based on negative rules modeling
Technical field
It is specifically a kind of to be based on negative rules the present invention relates to the static electric voltage stability methods of risk assessment of power grid The power grid static voltage stability methods of risk assessment of modeling.
Background technique
In the actual moving process of power grid, Voltage Instability accident caused by quiescent voltage collapses can seriously affect power grid Steady stability operation, thereby results in huge economic loss, to seriously affect national product.Therefore, voltage loses in order to prevent The generation of steady accident needs to carry out risk assessment to the static electric voltage stability of power grid.Existing static electric voltage stability risk Appraisal procedure mainly includes the following two kinds: the first is certainty appraisal procedure, such appraisal procedure the problem is that: due to It can not count and the probability distribution of a variety of uncertain factors, its assessment result is caused to be difficult to objectively and comprehensively reflect the reality of power grid Thus border operation conditions causes assessment result inaccurate.It is for second that can count and the probability evaluation method of failure of uncertain factor, this Kind of appraisal procedure the problem is that: fail based on historical load changing rule, accurately and comprehensively count and be present in initial There is the uncertainty in the node serial number increased and load growth situation in load consumption, load, and lack and anticipate with physics Justice, can be from the risk indicator of reflection static voltage stability degree at all levels, therefore such probability evaluation method of failure also results in Assessment result inaccuracy.In consideration of it, it is necessary to invent a kind of completely new static electric voltage stability methods of risk assessment, it is existing to solve There is the problem of static electric voltage stability methods of risk assessment assessment result inaccuracy.
Summary of the invention
The present invention provides to solve the problems, such as existing static electric voltage stability methods of risk assessment assessment result inaccuracy A kind of power grid static voltage stability methods of risk assessment based on negative rules modeling.
The present invention is achieved by the following technical scheme: the power grid static voltage stability based on negative rules modeling Methods of risk assessment, this method are realized using following steps:
1) negative rules model is established；The negative rules model include: just lotus fluctuation probability Distribution Model, There is the node cluster identification model increased, load stochastic growth model in load；
2) it establishes trend operational model: determining in power grid occur according to the node cluster identification model that increasing occurs in load first The node serial number of load growth is acquired based on monte carlo simulation methodology first in just lotus fluctuation probability Distribution Model respectively later Load increment sample in lotus consumption sample and load stochastic growth model, finally by sample value carry out based on and synthetic load it is special The continuous tide operation of property；
3) risk assessment index is established, and with the high operation risk region in risk indicator identification power grid；The risk Evaluation index includes network limit load level risk indicator, node low pressure load risk indicator, line transmission power accounting wind Dangerous index, line threshold transmit nargin risk indicator.
In the step 1),
The method for establishing just lotus fluctuation probability Distribution Model specifically comprises the following steps:
1.1) taking clusters number is 2, generates the initial value of one group of Subject Matrix element at random；
1.2) first time fuzzy C-means clustering is carried out to historical load data；
1.3) Classification Index BWP in class between the class of the Calculation Estimation secondary cluster result；Specific formula for calculation is as follows:
In formula (1)-(3): BWP (j, i) Classification Index in class between class；B (j, i) is the infima species of i-th of sample of jth class Between distance；W (j, i) is the inter- object distance of i-th of sample of jth class；J and k is category；I, p and q is specimen number；M is cluster numbers Mesh；nkFor the number of samples in kth class；njFor the number of samples of jth class；For p-th of sample of kth class；For jth class i-th A sample；For q-th of sample of jth class；
1.4) one group of Subject Matrix element initial value is randomly generated again, repeats step 1.2) -1.3), until cluster number reaches Until the 1/2 of historical load data length；
1.5) enable clusters number add 1, generate the initial value of one group of Subject Matrix element at random, repeat step 1.2) -1.4), directly Until clusters number reaches the evolution value of historical load data length；
1.6) Classification Index in class is counted between whole classes；Classification Index maximum is BWP in class between selection classoptWhen it is corresponding Cluster result, as the Time segments division mode to unloaded power consumption time graph:
In formula (4): BWPoptThe Classification Index in class between the class of corresponding optimum cluster result；N is total sample number；Csize is The evolution value of load sample total length；
1.7) it to every type load power mode, calculates the related coefficient of all payload node power consumptions of the whole network and forms phase relation Matrix number；
1.8) utilize Cholesky method decomposition step 1.7) in the corresponding correlation matrix of every type load power mode, Obtain obeying the first lotus power consumption sample of multiple normal distribution；So far, first lotus fluctuation probability Distribution Model modeling finishes.
The node cluster identification model that increasing occurs in load is specifically expressed as follows:
In formula (5)-(6): ρxyFor the related coefficient of x and y；IxyFor the mutual information of x and y；Cov (x, y) is the association of x and y Variance；D (x) and D (y) is respectively the variance of x, y；P (x) and p (y) is respectively the marginal probability density of x, y；P (x, y) is x and y Joint probability density；
Load stochastic growth model is specifically expressed as follows:
In formula (7)-(9): D0 is the reference direction of load growth；D1 is the practical growing direction of load；(S1,S2,..., SNload) it is the one-dimensional vector being made of each payload node apparent energy；Nload is payload node number；It is carried for i-th The power factor (1≤i≤Nload) of lotus point；SΔbaseFor the power reference value of system；kLiFor load growth factor, kLiValue Set can be determined as the method described in step 1), can also be determined by the approximating method of probability distribution.
In the step 2),
Firstly, according to given threshold values ρ1、ρ2And I1、I2, determine occur the node serial number of load growth in power grid:
ρ1≤ρxy≤ρ2(10)；
I1≤Ixy≤I2(11)；
In formula (10)-(11): x and y is node serial number；ρ1And ρ2The respectively lower and upper limit of related coefficient；I1And I2 The respectively lower and upper limit of mutual information；
Later, the method introduced using step 1), acquire first lotus consumption sample in first lotus fluctuation probability Distribution Model and Load increment sample in load stochastic growth model, determines kLiValue set；
Trend operational model is specifically expressed as follows:
In formula (12)-(13): λ is the sustainable growth factor of load；PLi0、QLi0The respectively initial active, nothing of node i Function power load amount；For the power factor of node i；δijFor the phase angle difference of node i and j voltage；As i=j, Yii=Gii +jBiiFor node self-admittance；As i ≠ j, Yij=Gij+jBijFor node transadmittance；SΔbaseFor the power reference value of system；kLi For load growth factor, kGiFor power output growth factor related with power generation dispatching strategy；Integrated load model often uses constant current, perseverance The static equivalent model of impedance, invariable power type load and induction conductivity indicates, when meter and integrated load model, node admittance square The building method of battle array are as follows:
Yij=YIn+YZn+YMn(14)；
YIn=In0/Vn0(15)；
YZn=1/Zn(16)；
YMn=1/ (R+jX) (17)；
Z2m=(rm+r2/s)2+(xm+x2)2(20)；
Tm=l (α+(1- α) (1-s)p) (21)；
In formula (14)-(22): YIn、YZnAnd YMnRespectively constant current type, constant-impedance type and induction motor load is equivalent Admittance value；s,rm+jxmAnd r2/s+jx2The respectively revolutional slip of induction conductivity, excitation impedance and secondary side equivalent impedance；ViFor section The voltage magnitude of point i；L, α and p is respectively induction motor load rate, repose resistance square and mechanical load performance index；
Based on the negative rules model that step 1) is established, using Monte Carlo method one group of load sample of every acquisition, Just it is calculated using the trend operational model of meter and synthetic load, until having acquired whole load samples.
In the step 3),
Network limit load level risk indicator is specifically expressed as follows:
In formula (23)-(24): m is total number realization；PLtotal(Mi) and p (Mi) be respectively i-th kind of load scenarios system Ultimate load amount and its probability of appearance, the meaning of idle parameter is similar with active situation, repeats no more；
Node low pressure load risk indicator is specifically expressed as follows:
In formula (25)-(26):It is the minimum event sets of the whole network for i-node voltage；P (*) is event AijWhen generation The probability of system crash；Event result res (*) is the system maximum load amount after ultimate load desired value normalized；
Line transmission power accounting risk indicator is specifically expressed as follows:
In formula (27)-(28):It is highest for the ratio between the limit transmitted power of route l and system load amount in the whole network Event sets；P (*) is event LlkThe probability of system crash when generation；(p_transfer)lk(pcollapse)kRespectively thing The active power and system limits load capacity transmitted on route l when part k occurs；
Line threshold transmission nargin risk indicator is specifically expressed as follows:
In formula (29)-(30): p (*) is event LlMThe probability of system crash when generation；(Ls- 1) abundant for the line transmission limit Degree；PtFor route sending end amount of power transfer；SbaseFor power reference value.
It is of the present invention to be modeled based on negative rules compared with existing static electric voltage stability methods of risk assessment Power grid static voltage stability methods of risk assessment have following advantage: first, compared with certainty appraisal procedure, institute of the present invention State based on the power grid static voltage stability methods of risk assessment of negative rules modeling and a variety of uncertain factors Probability distribution so that assessment result can objectively and comprehensively reflect the actual operating state of power grid, so that assessment As a result more accurate.Second, the power grid of the present invention based on negative rules modeling is quiet compared with probability evaluation method of failure State voltage stabilization methods of risk assessment accurately and comprehensively meter and is present in original negative based on the historical load changing rule There is the uncertainty in the node serial number increased and load growth situation in lotus consumption, load, and thus having has physics meaning Justice, can from it is at all levels reflection static voltage stability degree risk indicator so that assessment result is more accurate.
The present invention efficiently solves the problems, such as existing static electric voltage stability methods of risk assessment assessment result inaccuracy, fits Static electric voltage stability risk assessment for power grid.
Detailed description of the invention
Fig. 1 is the power grid static voltage stability methods of risk assessment flow chart based on negative rules modeling.
Fig. 2 is that description Taiyuan 110kV power grid the whole network payload node load variations otherness " close by mutual information-correlation System ".
Fig. 3 is the load stochastic growth model of Taiyuan 110kV grid nodes 15,18 and 47.
Fig. 4 is the line transmission changed power situation in certain trend operation of Taiyuan 110kV power grid under constant power load model.
Fig. 5 is the line transmission changed power situation in certain trend operation of Taiyuan 110kV power grid under integrated load model.
Fig. 6 is Taiyuan 110kV power grid under three kinds of load increases, the core probability of network limit load level value-at-risk Density Distribution.
Specific embodiment
Based on the power grid static voltage stability methods of risk assessment of negative rules modeling, this method is using following step Suddenly it realizes:
1) negative rules model is established；The negative rules model include: just lotus fluctuation probability Distribution Model, There is the node cluster identification model increased, load stochastic growth model in load；
2) it establishes trend operational model: determining in power grid occur according to the node cluster identification model that increasing occurs in load first The node serial number of load growth is acquired based on monte carlo simulation methodology first in just lotus fluctuation probability Distribution Model respectively later Load increment sample in lotus consumption sample and load stochastic growth model, finally by sample value carry out based on and synthetic load it is special The continuous tide operation of property；
3) risk assessment index is established, and with the high operation risk region in risk indicator identification power grid；The risk Evaluation index includes network limit load level risk indicator, node low pressure load risk indicator, line transmission power accounting wind Dangerous index, line threshold transmit nargin risk indicator.
In the step 1),
The method for establishing just lotus fluctuation probability Distribution Model specifically comprises the following steps:
1.1) taking clusters number is 2, generates the initial value of one group of Subject Matrix element at random；
1.2) first time fuzzy C-means clustering is carried out to historical load data；
1.3) Classification Index BWP in class between the class of the Calculation Estimation secondary cluster result；Specific formula for calculation is as follows:
In formula (1)-(3): BWP (j, i) Classification Index in class between class；B (j, i) is the infima species of i-th of sample of jth class Between distance；W (j, i) is the inter- object distance of i-th of sample of jth class；J and k is category；I, p and q is specimen number；M is cluster numbers Mesh；nkFor the number of samples in kth class；njFor the number of samples of jth class；For p-th of sample of kth class；For jth class i-th A sample；For q-th of sample of jth class；
1.4) one group of Subject Matrix element initial value is randomly generated again, repeats step 1.2) -1.3), until cluster number reaches Until the 1/2 of historical load data length；
1.5) enable clusters number add 1, generate the initial value of one group of Subject Matrix element at random, repeat step 1.2) -1.4), directly Until clusters number reaches the evolution value of historical load data length；
1.6) Classification Index in class is counted between whole classes；Classification Index maximum is BWP in class between selection classoptWhen it is corresponding Cluster result, as the Time segments division mode to unloaded power consumption time graph:
In formula (4): BWPoptThe Classification Index in class between the class of corresponding optimum cluster result；N is total sample number；Csize is The evolution value of load sample total length；
1.7) it to every type load power mode, calculates the related coefficient of all payload node power consumptions of the whole network and forms phase relation Matrix number；
1.8) utilize Cholesky method decomposition step 1.7) in the corresponding correlation matrix of every type load power mode, Obtain obeying the unloaded power consumption sample of multiple normal distribution；So far, first lotus fluctuation probability Distribution Model modeling finishes；
The node cluster identification model that increasing occurs in load is specifically expressed as follows:
In formula (5)-(6): ρxyFor the related coefficient of x and y；IxyFor the mutual information of x and y；Cov (x, y) is the association of x and y Variance；D (x) and D (y) is respectively the variance of x, y；P (x) and p (y) is respectively the marginal probability density of x, y；P (x, y) is x and y Joint probability density；
Load stochastic growth model is specifically expressed as follows:
In formula (7)-(9): D0 is the reference direction of load growth；D1 is the practical growing direction of load；(S1,S2,..., SNload) it is the one-dimensional vector being made of each payload node apparent energy；Nload is payload node number；It is carried for i-th The power factor (1≤i≤Nload) of lotus point；SΔbaseFor the power reference value of system；kLiFor load growth factor, kLiValue Set can be determined as the method described in step 1), can also be determined by the approximating method of probability distribution.
In the step 2),
Firstly, according to given threshold values ρ1、ρ2And I1、I2, determine occur the node serial number of load growth in power grid:
ρ1≤ρxy≤ρ2(10)；
I1≤Ixy≤I2(11)；
In formula (10)-(11): x and y is node serial number；ρ1And ρ2The respectively lower and upper limit of related coefficient；I1And I2 The respectively lower and upper limit of mutual information；
Later, the method introduced using step 1), acquire first lotus consumption sample in first lotus fluctuation probability Distribution Model and Load increment sample in load stochastic growth model, determines kLiValue set；
Trend operational model is specifically expressed as follows:
In formula (12)-(13): λ is the sustainable growth factor of load；PLi0、QLi0The respectively initial active, nothing of node i Function power load amount；For the power factor of node i；δijFor the phase angle difference of node i and j voltage；As i=j, Yii=Gii +jBiiFor node self-admittance；As i ≠ j, Yij=Gij+jBijFor node transadmittance；SΔbaseFor the power reference value of system；kLi For load growth factor, kGiFor power output growth factor related with power generation dispatching strategy；Integrated load model often uses constant current, perseverance The static equivalent model of impedance, invariable power type load and induction conductivity indicates, when meter and integrated load model, node admittance square The building method of battle array are as follows:
Yij=YIn+YZn+YMn(14)；
YIn=In0/Vn0(15)；
YZn=1/Zn(16)；
YMn=1/ (R+jX) (17)；
Z2m=(rm+r2/s)2+(xm+x2)2(20)；
Tm=l (α+(1- α) (1-s)p) (21)；
In formula (14)-(22): YIn、YZnAnd YMnRespectively constant current type, constant-impedance type and induction motor load is equivalent Admittance value；s,rm+jxmAnd r2/s+jx2The respectively revolutional slip of induction conductivity, excitation impedance and secondary side equivalent impedance；ViFor section The voltage magnitude of point i；L, α and p is respectively induction motor load rate, repose resistance square and mechanical load performance index；
Based on the negative rules model that step 1) is established, using Monte Carlo method one group of load sample of every acquisition, Just it is calculated using the trend operational model of meter and synthetic load, until having acquired whole load samples.
In the step 3),
Network limit load level risk indicator is specifically expressed as follows:
In formula (23)-(24): m is total number realization；PLtotal(Mi) and p (Mi) be respectively i-th kind of load scenarios system Ultimate load amount and its probability of appearance, the meaning of idle parameter is similar with active situation, repeats no more；
Node low pressure load risk indicator is specifically expressed as follows:
In formula (25)-(26):It is the minimum event sets of the whole network for i-node voltage；P (*) is event AijWhen generation The probability of system crash；Event result res (*) is the system maximum load amount after ultimate load desired value normalized；
Line transmission power accounting risk indicator is specifically expressed as follows:
In formula (27)-(28):It is highest for the ratio between the limit transmitted power of route l and system load amount in the whole network Event sets；P (*) is event LlkThe probability of system crash when generation；(p_transfer)lk(pcollapse)kRespectively thing The active power and system limits load capacity transmitted on route l when part k occurs；
Line threshold transmission nargin risk indicator is specifically expressed as follows:
In formula (29)-(30): p (*) is event LlMThe probability of system crash when generation；(Ls- 1) abundant for the line transmission limit Degree；PtFor route sending end amount of power transfer；SbaseFor power reference value.
When it is implemented, making further specifically by taking 57 node 110kV power grid of Taiyuan as an example to technical solution of the present invention It is bright:
1) negative rules model is established:
By process described in step 1), just lotus fluctuation probability Distribution Model is obtained are as follows: the first lotus in the part of first payload node Sample value is (- 47.53, -46.9, -58.5, -62.5, -50.5, -55.7, -43.2, -58.5), the portion of second payload node Lotus sample value at the beginning of point is (- 2.2, -2.7, -3.4, -4.0, -3.5, -2.8, -3.1, -3.9), the first lotus sample of other payload nodes It is omitted.The method introduced by step 1), the time graph of unloaded power consumption is divided into two periods, in first period, the One and second payload node sample related coefficient be 0.77；In second period, the correlation of the first and second payload nodes Coefficient is 0.74；
By process described in step 1), the node cluster identification model that increasing occurs in load is expressed as Fig. 2: abscissa is description The mutual information of the whole network node load difference in change opposite sex two-by-two, ordinate are to describe the whole network node load difference in change is anisotropic two-by-two Related coefficient.The threshold values of artificial given " mutual information-related coefficient " is respectively 1.5-0.9,1-0.8,0-0, obtains following three A possibility that class node cluster, same class node load increases simultaneously, is larger: first kind node cluster, threshold values 1.5-0.9 to 3-1 it Between node serial number be 2,6,9,12,13,14,15,16,19,25,29,30,38,41,49,51,52,53,54,56,57；The Two class node clusters, threshold values are 1,3,5,8,20,27,28,32,35,47,50 in 1-0.8 to the node serial number between 1.5-0.9； Third class node cluster, threshold values are 10,17,18,23,31,33,42,43,44,55 in 0-0 to the node serial number between 1-0.8；
By process described in step 1), obtains the load stochastic growth model by taking node 15,18,47 as an example and be expressed as Fig. 3；
2) trend operational model is established, the continuous tide operation of meter and synthetic load characteristic is carried out, each route is recorded and passes Defeated power and the whole network node voltage.It in trend operation, enables in integrated load model, induction conductivity, constant-impedance, constant current and perseverance The ratio of the total initial load power of power load Zhan is respectively 0.5,0.2,0.1,0.2, and induction conductivity model chooses the country Typical induction conductivity numerical value is calculated (r1=0.04, x1=0.18, r2=0.02, x2=0.12, rm=0.35, xm= 3.5, α=0.15, p=2).Statistics only increases first kind node cluster, increases by one or two class node clusters and increase three classes section simultaneously respectively Trend operation result in the case of three kinds of point group.It is only shown in certain continuous tide operation herein, the function transmitted on route 1 and 15 Rate size, such as Fig. 4-Fig. 5；
3) risk assessment index is established, and risk assessment is carried out to continuous tide operation result based on risk assessment index. The horizontal risk indicator P of the corresponding ultimate load of three kinds of load increasescollapseRespectively 2312.3,2434.2,2447.7MW, QcollapseRespectively 1050.6,1315.2,1400.1MVar, PcollapseCore probability density distribution it is as shown in Figure 6.Three kinds negative Node low pressure load risk indicator operation result under lotus growth pattern is shown in Table 1；Line transmission under three kinds of load increases Power accounting risk indicator and line threshold transmission nargin risk indicator operation result are shown in Table 2；
1 node low pressure load value-at-risk of table
2 line power of table transmits risk
Analysis indexes operation result it is found that from cause system occur collapse of voltage angle say that 31 and 33 nodes are risky, And 31 node value-at-risk be much higher than 33 nodes；Route 1 and 15 is heavy duty elevated track transimission power accounting risk route, but The line threshold transmission nargin risk of route 1 is very low, just the opposite with route 15.

Claims (1)

1. a kind of power grid static voltage stability methods of risk assessment based on negative rules modeling, it is characterised in that: the party Method is realized using following steps:
1) negative rules model is established；The negative rules model includes: just lotus fluctuation probability Distribution Model, load There is the node cluster identification model increased, load stochastic growth model；
2) it establishes trend operational model: determining occur load in power grid according to the node cluster identification model that increasing occurs in load first The node serial number of growth acquires the first lotus consumption in just lotus fluctuation probability Distribution Model respectively based on monte carlo simulation methodology later Measure the load increment sample in sample and load stochastic growth model, finally by sample value carry out based on and synthetic load characteristic Continuous tide operation；
3) risk assessment index is established, and with the high operation risk region in risk indicator identification power grid；The risk assessment Index includes that network limit load level risk indicator, node low pressure load risk indicator, line transmission power accounting risk refer to Mark, line threshold transmit nargin risk indicator；
In the step 1),
The method for establishing just lotus fluctuation probability Distribution Model specifically comprises the following steps:
1.1) taking clusters number is 2, generates the initial value of one group of Subject Matrix element at random；
1.2) first time fuzzy C-means clustering is carried out to historical load data；
1.3) Classification Index BWP in class between the class of the Calculation Estimation secondary cluster result；Specific formula for calculation is as follows:
In formula (1)-(3): BWP (j, i) Classification Index in class between class；B (j, i) is the infima species spacing of i-th of sample of jth class From；W (j, i) is the inter- object distance of i-th of sample of jth class；J and k is category；I, p and q is specimen number；M is clusters number； nkFor the number of samples in kth class；njFor the number of samples of jth class；For p-th of sample of kth class；For i-th of sample of jth class This；For q-th of sample of jth class；
1.4) one group of Subject Matrix element initial value is randomly generated again, repeats step 1.2) -1.3), it is gone through until cluster number reaches Until the 1/2 of history load data length；
1.5) enable clusters number add 1, generate the initial value of one group of Subject Matrix element at random, repeat step 1.2) -1.4), Zhi Daoju Until class number reaches the evolution value of historical load data length；
1.6) Classification Index in class is counted between whole classes；Classification Index maximum is BWP in class between selection classoptWhen it is corresponding poly- Class is as a result, as the Time segments division mode to unloaded power consumption time graph:
In formula (4): BWPoptThe Classification Index in class between the class of corresponding optimum cluster result；N is total sample number；Csize is load The evolution value of sample total length；
1.7) it to every type load power mode, calculates the related coefficient of all payload node power consumptions of the whole network and forms related coefficient square Battle array；
1.8) utilize Cholesky method decomposition step 1.7) in the corresponding correlation matrix of every type load power mode, obtain Obey the unloaded power consumption sample of multiple normal distribution；So far, first lotus fluctuation probability Distribution Model modeling finishes；
The node cluster identification model that increasing occurs in load is specifically expressed as follows:
In formula (5)-(6): ρxyFor the related coefficient of x and y；IxyFor the mutual information of x and y；Cov (x, y) is the covariance of x and y； D (x) and D (y) is respectively the variance of x, y；P (x) and p (y) is respectively the marginal probability density of x, y；P (x, y) is the connection of x and y Close probability density；
Load stochastic growth model is specifically expressed as follows:
In formula (7)-(9): D0 is the reference direction of load growth；D1 is the practical growing direction of load；(S1,S2,...,SNload) be The one-dimensional vector being made of each payload node apparent energy；Nload is payload node number；For the function of i-th of point of load Rate factor, 1≤i≤Nload；SΔbaseFor the power reference value of system；kLiFor load growth factor, kLiThe set of value is by step It is rapid 1) described in method determine；
In the step 2),
Firstly, according to given threshold value ρ1、ρ2And I1、I2, determine occur the node serial number of load growth in power grid:
ρ1≤ρxy≤ρ2(10)；
I1≤Ixy≤I2(11)；
In formula (10)-(11): x and y is node serial number；ρ1And ρ2The respectively lower and upper limit of related coefficient；I1And I2Respectively For the lower and upper limit of mutual information；
Later, the method introduced using step 1) acquires first lotus consumption sample and load in first lotus fluctuation probability Distribution Model Load increment sample in stochastic growth model, determines kLiValue set；
Trend operational model is specifically expressed as follows:
In formula (12)-(13): λ is the sustainable growth factor of load；PLi0、QLi0The respectively initial active and reactive function of node i Rate load；For the power factor of node i；δijFor the phase angle difference of node i and j voltage；As i=j, Yii=Gii+jBii For node self-admittance；As i ≠ j, Yij=Gij+jBijFor node transadmittance；SΔbaseFor the power reference value of system；kLiIt is negative Lotus growth factor, kGiFor power output growth factor related with power generation dispatching strategy；Integrated load model uses constant current, constant-resistance The static equivalent model of anti-, invariable power type load and induction conductivity indicates, when meter and integrated load model, node admittance matrix Building method are as follows:
Yij=YIn+YZn+YMn(14)；
YIn=In0/Vn0(15)；
YZn=1/Zn(16)；
YMn=1/ (R+jX) (17)；
Z2m=(rm+r2/s)2+(xm+x2)2(20)；
Tm=l (α+(1- α) (1-s)p) (21)；
In formula (14)-(22): YIn、YZnAnd YMnThe respectively equivalent admittance of constant current type, constant-impedance type and induction motor load Value；s,rm+jxmAnd r2/s+jx2The respectively revolutional slip of induction conductivity, excitation impedance and secondary side equivalent impedance；ViFor node i Voltage magnitude；L, α and p is respectively induction motor load rate, repose resistance square and mechanical load performance index；
Based on the negative rules model that step 1) is established, using Monte Carlo method one group of load sample of every acquisition, later It is calculated using the trend operational model of meter and synthetic load, until having acquired whole load samples；
In the step 3),
Network limit load level risk indicator is specifically expressed as follows:
In formula (23)-(24): m is total number realization；PLtotal(Mi) and p (Mi) be respectively i-th kind of load scenarios system limits Load capacity and its probability of appearance；
Node low pressure load risk indicator is specifically expressed as follows:
In formula (25)-(26):It is the minimum event sets of the whole network for i-node voltage；P (*) is event AijSystem when generation The probability of collapse；Event result res (*) is the system maximum load amount after ultimate load desired value normalized；
Line transmission power accounting risk indicator is specifically expressed as follows:
In formula (27)-(28):For the highest event set of the ratio between the limit transmitted power of route l and system load amount in the whole network It closes；P (*) is event LlkThe probability of system crash when generation；(p_transfer)lk(pcollapse)kRespectively event k hair The active power and system limits load capacity transmitted on route l when raw；
Line threshold transmission nargin risk indicator is specifically expressed as follows:
In formula (29)-(30): p (*) is event LlMThe probability of system crash when generation；(LsIt -1) is line transmission limit nargin；Pt For route sending end amount of power transfer；SbaseFor power reference value.
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