CN106203805A - A kind of active power distribution network probabilistic reliability method of estimation and device - Google Patents

Abstract

The active power distribution network probabilistic reliability method of estimation of present invention offer and device, after getting the bearing power at each node of distribution network system and/or output power, the stochastic variable formed is transformed to incoherent first standard normal variable between each variable.Use point estimations to construct on the basis of the first standard normal variable corresponding to the sample matrix in stochastic variable space, carry out Failure Mode Effective Analysis for this sample matrix, obtain the probability density function of reliability index.The method and device consider that the bearing power at the output power of DG and each node can be converted into certain problem to the impact of reliability and solve by point estimations, calculate simple；Simultaneously, it is contemplated that Nataf converts and do not limited by input variable type, can effectively process the relativity problem of stochastic variable, point estimations and Nataf are converted and combines, thus realize by simple method, the accurate of active power distribution network probabilistic reliability being estimated.

Description

A kind of active power distribution network probabilistic reliability method of estimation and device

Technical field

The invention belongs to distribution system planning operation field, be specifically related to a kind of active power distribution network probabilistic reliability estimation side Method and device.

Background technology

There is numerous uncertain factor in distribution system in actual motion, such as system element fault, load power fluctuation Etc..In the last few years, along with Power Electronic Technique in renewable energy power generation is applied gradually ripe, more and more intermittent Distributed power source (DG) accesses power distribution network so that it is will face the impact that more randomness power swing causes during operation.Probability Power distribution network is powered reliably by Calculation of Reliability by various uncertain factors as input variable, these random factors of quantitative analysis Property impact, assessment distribution system reliability level, the weak link of beneficially discovery system and potential collision hazard, to power distribution network Planning and designing be significant.

The computational methods of power distribution network probabilistic reliability mainly have analytic method, Monte Carlo simulation approach and method of approximation etc., approximation Method is with point estimations as representative.Analytic method needs to simplify the object studied, and then carries out convolutional calculation and solve, and calculates Amount is big, and simplification process can cause certain error, is not suitable for analyzing challenge；Monte Carlo simulation approach can directly be simulated respectively Kind of uncertain factor, it is achieved simple, but need the most substantial amounts of sample calculation to obtain higher precision, computational accuracy and Contradiction is there is between computational efficiency.

Summary of the invention

The technical problem to be solved is how to use simple method to realize active power distribution network probability decision Property accurate estimation.

For this technical problem, the invention provides a kind of active power distribution network probabilistic reliability method of estimation, including:

S1: obtain the bearing power at each node of the distribution network system preset and/or output power, using as at random Variable；

S2: described stochastic variable is just being transformed between each variable incoherent first standard according to default transformation rule State variable；

S3: use point estimations, after structure's variable sampled value each in described first standard normal variable, is formed with institute State the first sample matrix that sampled value is element, and according to the inverse transformation of described default transformation rule by described first sample matrix Be converted to the second sample matrix for reliability assessment；

S4: use distribution network failure mode influences analytic process, calculate described second sample matrix each column vector can By property index and weight, and according to described reliability index corresponding to described reliability index and weight calculation the second sample matrix Moment of the orign, to obtain the probability density function of described reliability index according to described moment of the orign.

Preferably, described step S2 includes:

S21: use Nataf conversion that described stochastic variable is transformed to the second standard normal variable；

S22: according to semiempirical formula ρ_0ij=h ρ_ij(i=1,2 ..., m；J=1,2 ..., m) just calculating described second standard The first correlation matrix between each variable in state variable；

S23: according to Orthogonal Decomposition transformation for mulaDescribed second standard normal variable is transformed to described first Standard normal variable；

Wherein, ρ_ijIt it is the i-th row jth in the second correlation matrix ρ between each variable in described stochastic variable The variable of row, ρ_0ijIt is described first correlation matrix ρ₀In the variable of the i-th row jth row, h is empirical coefficient, by described the The marginal probability density of two correlation matrixs and described stochastic variable determines, L₀It is described first correlation matrix ρ₀Warp Cholesky obtains inferior triangular flap after decomposing, and Y is described second standard normal variable, and V is described first standard normal variable.

Preferably, described step S3 includes:

S31: use three point estimations, to each variable V in described first standard normal variable V_iAccording to formula v_i,k =μ_i+ξ_i,kσ_i(k=1,2,3) three sampled values of structure；

S32: with vector V_i,k=[μ₁,μ₂,μ₃,…,v_i,k,…μ_m]^TFormal construction comprise the column vector of described sampled value；

S33: by column vector V_i,kAccording to [V_1,1,V_1,2,V_1,3,…,V_m,1,V_m,2,V_m,3] form arrangement, described to obtain First sample matrix；

S34: after described first sample matrix is converted according to the inverse transformation that described Orthogonal Decomposition converts, according still further to Nataf inverse transformation converts, to obtain described second sample matrix；

Wherein, μ_iIt it is variable V_iAverage, σ_iIt it is variable V_iStandard deviation, ξ_i,kFor sampled value v_i,kPosition parameter, ξ_i,k Can be calculated by following formula:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_{i,k}=\frac{{\mathrm{\λ}}_{i,3}}{2}+{(-1)}^{3-k}\sqrt{{\mathrm{\λ}}_{i,4}-\frac{3}{4}{\mathrm{\λ}}_{i,4}^2},(k=1,2)\\ {\mathrm{\ξ}}_{i,k}=0,(k=3)\end{array}\right.$

λ_i,3And λ_i,4It is respectively variable V_iSkewness and kurtosis, V_i,kIt is to comprise variable V_iSampled value v_i,kColumn vector, and Vector V_i,kIn the average of other variable that other element is described first standard normal variable V.

Preferably, described step S4 includes:

S41: use distribution network failure mode influences analytic process, each column vector institute calculating described second sample matrix is right The described power distribution network answered reliability index and weight, described weights omega_i,kComputing formula as follows:

$\left\{\begin{array}{c}{\mathrm{\ω}}_{i,k}=\frac{{\left(-1\right)}^{3-k}}{{\mathrm{\ξ}}_{i,k}\left({\mathrm{\ξ}}_{i,1}-{\mathrm{\ξ}}_{i,2}\right)},\left(k=1,2\right)\\ {\mathrm{\ω}}_{i,k}=\frac{1}{m}\frac{1}{{\mathrm{\λ}}_{i,4}-{\mathrm{\λ}}_{i,3}^2},\left(k=3\right)\end{array}\right.$

S42: according to described reliability index and weight according to formulaCalculate described second sample The moment of the orign of the described reliability index that this matrix is corresponding；

S43: by described moment of the orign by Cornish-Fisher series expansion, the probability obtaining described reliability index is close Degree function；

Wherein, ω_i,kIt is the weight of every string, Z in described second sample matrix_i,kIt is each in described second sample matrix The reliability index that row are corresponding, E (Z^l) it is the moment of the orign that described second sample matrix is corresponding.

Preferably, described reliability index includes: the System average interruption frequency of each node of described distribution network system, described in join The average power off time of each node of network system and the average of each node of described distribution network system lack delivery.

On the other hand, present invention also offers a kind of active power distribution network probabilistic reliability estimation unit, including:

Acquisition module, for obtaining the bearing power at each node of default distribution network system and/or output power；

Modular converter, for being transformed between each variable incoherent by described stochastic variable according to default transformation rule First standard normal variable；

Sample architecture module, is used for using point estimations, adopts each structure's variable in described first standard normal variable After sample value, form the first sample matrix with described sampled value as element, and will according to the inverse transformation of described default transformation rule Described first sample matrix is converted to the second sample matrix for reliability assessment；

Analyze module, be used for using distribution network failure mode influences analytic process, calculate each of described second sample matrix The reliability index of column vector and weight, and according to described reliability index and weight calculation the second sample matrix corresponding described in The moment of the orign of reliability index, to obtain the probability density function of described reliability index according to described moment of the orign.

Preferably, described modular converter includes:

First converting unit, is used for using Nataf conversion that described stochastic variable is transformed to the second standard normal variable；

Computing unit, for according to semiempirical formula ρ_0ij=h ρ_ij(i=1,2 ..., m；J=1,2 ..., m) described in calculating The first correlation matrix between each variable in second standard normal variable；

Second converting unit, for according to Orthogonal Decomposition transformation for mulaDescribed second standard normal variable is become It is changed to described first standard normal variable；

Wherein, ρ_ijIt it is the i-th row jth in the second correlation matrix ρ between each variable in described stochastic variable The variable of row, ρ_0ijIt is described first correlation matrix ρ₀In the variable of the i-th row jth row, h is empirical coefficient, by described the The marginal probability density of two correlation matrixs and described stochastic variable determines, L₀It is described first correlation matrix ρ₀Warp Cholesky obtains inferior triangular flap after decomposing, and Y is described second standard normal variable, and V is described first standard normal variable.

Preferably, described sample architecture module includes:

First structural unit, uses three point estimations, to each variable V in described first standard normal variable V_iPress According to formula v_i,k=μ_i+ξ_i,kσ_i(k=1,2,3) three sampled values of structure；

Second structural unit, for vector V_i,k=[μ₁,μ₂,μ₃,…,v_i,k,…μ_m]^TFormal construction comprise described in adopt The column vector of sample value；

Arrangement units, for by column vector V_i,kAccording to [V_1,1,V_1,2,V_1,3,…,V_m,1,V_m,2,V_m,3] form arrangement, with Obtain described first sample matrix；

3rd converting unit, converts the inverse transformation that described first sample matrix converts according to described Orthogonal Decomposition After, convert according still further to Nataf inverse transformation, to obtain described second sample matrix；

Wherein, μ_iIt it is variable V_iAverage, σ_iIt it is variable V_iStandard deviation, ξ_i,kFor sampled value v_i,kPosition parameter, ξ_i,k Can be calculated by following formula:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_{i,k}=\frac{{\mathrm{\λ}}_{i,3}}{2}+{(-1)}^{3-k}\sqrt{{\mathrm{\λ}}_{i,4}-\frac{3}{4}{\mathrm{\λ}}_{i,4}^2},(k=1,2)\\ {\mathrm{\ξ}}_{i,k}=0,(k=3)\end{array}\right.$

λ_i,3And λ_i,4It is respectively variable V_iSkewness and kurtosis, V_i,kIt is to comprise variable V_iSampled value v_i,kColumn vector, and Vector V_i,kIn the average of other variable that other element is described first standard normal variable V.

Preferably, described analysis module includes:

First analytic unit, is used for using distribution network failure mode influences analytic process, calculates described second sample matrix Described power distribution network corresponding to each column vector reliability index and weight, described weights omega_i,kComputing formula as follows:

$\left\{\begin{array}{c}{\mathrm{\ω}}_{i,k}=\frac{{\left(-1\right)}^{3-k}}{{\mathrm{\ξ}}_{i,k}\left({\mathrm{\ξ}}_{i,1}-{\mathrm{\ξ}}_{i,2}\right)},\left(k=1,2\right)\\ {\mathrm{\ω}}_{i,k}=\frac{1}{m}\frac{1}{{\mathrm{\λ}}_{i,4}-{\mathrm{\λ}}_{i,3}^2},\left(k=3\right)\end{array}\right.$

Second analytic unit, for according to described reliability index and weight according to formula Calculate the moment of the orign of described reliability index corresponding to described second sample matrix；

3rd analytic unit, for by described moment of the orign by Cornish-Fisher series expansion, obtain described reliably The probability density function of property index；

Wherein, ω_i,kIt is the weight of every string, Z in described second sample matrix_i,kIt is each in described second sample matrix The reliability index that row are corresponding, E (Z^l) it is the moment of the orign that described second sample matrix is corresponding.

Preferably, described reliability index includes: the System average interruption frequency of each node of described distribution network system, described in join The average power off time of each node of network system and the average of each node of described distribution network system lack delivery.

The active power distribution network probabilistic reliability method of estimation of present invention offer and device, get each joint of distribution network system Bearing power at Dian and/or output power, be transformed to each by the stochastic variable that bearing power and/or output power form and become Incoherent first standard normal variable between amount.Point estimations is used to construct sample on the basis of the first standard normal variable Matrix, then obtain the second sample matrix by the inverse transformation of above-mentioned conversion, carry out failure mode effect for the second sample matrix Analyze, obtain the probability density function of reliability index.On the one hand the method and device consider that point estimations can be by the confession of DG The random factors such as the bearing power of electrical power and power distribution network node are converted into certain problem to the impact of reliability and solve, and calculate Simply；On the other hand do not limited by input variable type in view of Nataf conversion, only needed the marginal probability of known stochastic variable Density function and correlation matrix, can effectively process the relativity problem of stochastic variable, point estimations and Nataf is converted In conjunction with, thus realize by simple method, the accurate of active power distribution network probabilistic reliability being estimated.

Accompanying drawing explanation

In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing In having technology to describe, the required accompanying drawing used is briefly described, it should be apparent that, the accompanying drawing in describing below is this Some bright embodiments, for those of ordinary skill in the art, on the premise of not paying creative work, it is also possible to root Other accompanying drawing is obtained according to these accompanying drawings.

Fig. 1 is that the embodiment of the present invention provides active power distribution network probabilistic reliability method of estimation schematic flow sheet；

Fig. 2 is that the more specifically active power distribution network probabilistic reliability that the embodiment of the present invention provides estimates schematic flow sheet；

Fig. 3 is that the embodiment of the present invention provides active power distribution network probabilistic reliability estimation unit structured flowchart；

Fig. 4 is the module design signal that the embodiment of the present invention provides that more specifically active power distribution network probabilistic reliability is estimated Figure.

Detailed description of the invention

For making the purpose of the embodiment of the present invention, technical scheme and advantage clearer, below in conjunction with the embodiment of the present invention In accompanying drawing, the technical scheme in the embodiment of the present invention is clearly and completely described, it is clear that described embodiment is The a part of embodiment of the present invention rather than whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art The every other embodiment obtained under not making creative work premise, broadly falls into the scope of protection of the invention.

Fig. 1 is that the embodiment of the present invention provides active power distribution network probabilistic reliability method of estimation schematic flow sheet.See Fig. 1, The method includes:

S1: obtain the bearing power at each node of the distribution network system preset and/or output power, using as at random Variable；

S2: described stochastic variable is just being transformed between each variable incoherent first standard according to default transformation rule State variable；

S3: use point estimations, after structure's variable sampled value each in described first standard normal variable, is formed with institute State the first sample matrix that sampled value is element, and according to the inverse transformation of described default transformation rule by described first sample matrix Be converted to the second sample matrix for reliability assessment；

S4: use distribution network failure mode influences analytic process, calculate described second sample matrix each column vector can By property index and weight, and according to described reliability index corresponding to described reliability index and weight calculation the second sample matrix Moment of the orign, to obtain the probability density function of described reliability index according to described moment of the orign.

Bearing power and output power are all random variablees, and bearing power is mainly affected by power consumption, output power Main by for providing the power supply source of power supply to be affected at this node, secondly, they all can by these external worlds of such as weather, temperature because of The impact of element.

Each element in stochastic variable is taken from same active power distribution network, and therefore each element in stochastic variable is It is correlated with.In order to use point estimations that the reliability of active power distribution network is analyzed, need first by each in stochastic variable Variable becomes incoherent first standard normal variable.

Point estimations includes: moments estimation method, order statistics are mensuration, method of maximum likelihood, method of least square etc..Second sample moment Battle array is at the matrix of the same variable space with stochastic variable.

Certainly, when getting bearing power and/or output power, it is also possible to negative according to output power and each node Carry power and obtain probability density function and the correlation matrix of these stochastic variables, use in follow-up calculating.

The active power distribution network probabilistic reliability method of estimation that the present embodiment provides, gets at each node of distribution network system Bearing power and/or the probability density of output power and their correlation coefficient after, by bearing power and/or output power group The stochastic variable become is transformed to incoherent first standard normal variable between each variable.Use point estimations in the first standard Construct sample matrix on the basis of normal variate, then try to achieve the second sample matrix by the inversion of above-mentioned conversion, for second Sample matrix carries out Failure Mode Effective Analysis, obtains the probability density function of reliability index.On the one hand the method considers point The impact of reliability can be converted into by the estimation technique by the random factors such as the bearing power of the output power of DG and power distribution network node Certain problem solves, and calculates simple；On the other hand do not limited by input variable type in view of Nataf conversion, only needed Know marginal probability density function and the correlation matrix of stochastic variable, can effectively process the relativity problem of stochastic variable, Point estimations and Nataf are converted and combines, thus realize by accurate to active power distribution network probabilistic reliability of simple method Estimate.

Further, described step S2 includes:

S21: use Nataf conversion that described stochastic variable is transformed to the second standard normal variable；

S22: according to semiempirical formula ρ_0ij=h ρ_ij(i=1,2 ..., m；J=1,2 ..., m) just calculating described second standard The first correlation matrix between each variable in state variable；

S23: according to Orthogonal Decomposition transformation for mulaDescribed second standard normal variable is transformed to described first mark Quasi-normal variate；

Wherein, ρ_ijIt it is the i-th row jth in the second correlation matrix ρ between each variable in described stochastic variable The variable of row, ρ_0ijIt is described first correlation matrix ρ₀In the variable of the i-th row jth row, h is empirical coefficient, by described the The marginal probability density of two correlation matrixs and described stochastic variable determines, L₀It is described first correlation matrix ρ₀Warp Cholesky obtains inferior triangular flap after decomposing, and Y is described second standard normal variable, and V is described first standard normal variable.

It should be noted that the stochastic variable in the present invention comprises m element, it is the random vector of m dimension, is m × 1 Matrix.In like manner, the first standard normal variable and the second standard normal variable be the most respectively m dimension vector, be the most respectively a m × The matrix of 1.Owing to the first correlation matrix is between each element in m the element reacting the second standard normal variable The matrix of relation, is therefore the matrix of a m × m.In like manner, the second correlation matrix is m element of reaction stochastic variable In each element between the matrix of relation, be the most also the matrix of a m × m.

Through Nataf conversion and Orthogonal Decomposition, stochastic variable is transformed to incoherent first standard normal of each variable become Amount, analyzes this first standard normal variable with satisfied employing point analysis method.

Further, described step S3 includes:

S31: use three point estimations, to each variable V in described first standard normal variable V_iAccording to formula v_i,k =μ_i+ξ_i,kσ_i(k=1,2,3) three sampled values of structure；

S32: with vector V_i,k=[μ₁,μ₂,μ₃,…,v_i,k,…μ_m]^TFormal construction comprise the column vector of described sampled value；

S33: by column vector V_i,kAccording to [V_1,1,V_1,2,V_1,3,…,V_m,1,V_m,2,V_m,3] form arrangement, described to obtain First sample matrix；

S34: after described first sample matrix is converted according to the inverse transformation that described Orthogonal Decomposition converts, according still further to Nataf inverse transformation converts, to obtain described second sample matrix；

Wherein, μ_iIt it is variable V_iAverage, σ_iIt it is variable V_iStandard deviation, ξ_i,kFor sampled value v_i,kPosition parameter, ξ_i,k Can be calculated by following formula:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_{i,k}=\frac{{\mathrm{\λ}}_{i,3}}{2}+{(-1)}^{3-k}\sqrt{{\mathrm{\λ}}_{i,4}-\frac{3}{4}{\mathrm{\λ}}_{i,4}^2},(k=1,2)\\ {\mathrm{\ξ}}_{i,k}=0,(k=3)\end{array}\right.$

λ_i,3And λ_i,4It is respectively variable V_iSkewness and kurtosis, V_i,kIt is to comprise variable V_iSampled value v_i,kColumn vector, and Vector V_i,kIn the average of other variable that other element is described first standard normal variable V.

Use sample matrix relevant between point estimations one variable of structure as evaluating reliability of distribution network matrix, with Use distribution network failure mode influences analytic process that this sample matrix is analyzed, obtain the reliability index of distribution network system.

Further, described step S4 includes:

S41: use distribution network failure mode influences analytic process, each column vector institute calculating described second sample matrix is right The described power distribution network answered reliability index and weight, described weights omega_i,kComputing formula as follows:

$\left\{\begin{array}{c}{\mathrm{\ω}}_{i,k}=\frac{{\left(-1\right)}^{3-k}}{{\mathrm{\ξ}}_{i,k}\left({\mathrm{\ξ}}_{i,1}-{\mathrm{\ξ}}_{i,2}\right)},\left(k=1,2\right)\\ {\mathrm{\ω}}_{i,k}=\frac{1}{m}\frac{1}{{\mathrm{\λ}}_{i,4}-{\mathrm{\λ}}_{i,3}^2},\left(k=3\right)\end{array}\right.$

S42: according to described reliability index and weight according to formulaCalculate described second sample The moment of the orign of the described reliability index that this matrix is corresponding；

S43: by described moment of the orign by Cornish-Fisher series expansion, the probability obtaining described reliability index is close Degree function；

Wherein, ω_i,kIt is the weight of every string, Z in described second sample matrix_i,kIt is each in described second sample matrix The reliability index that row are corresponding, E (Z^l) it is the moment of the orign that described second sample matrix is corresponding.

Described reliability index includes: the System average interruption frequency of each node of described distribution network system, described power distribution network system Unite the average power off time of each node and the average of each node of described distribution network system lacks delivery.

By this analysis mode, can obtain such as System average interruption frequency (SAIFI), average power off time (SAIDI) and These indexs being used for weighing distribution network reliability of average scarce delivery (AENS).It is, of course, also possible to obtain by this method Other reliability index, the present embodiment does not limits.

As one more specifically example, see Fig. 2.To access wind power generating set and the distribution of photovoltaic generation unit As a example by net, the probabilistic reliability estimation flow of meter and input variable dependency is described in detail.Node each in system is born The output of lotus demand power and distributed power source as input variable, will reliability index be asked as output variable, then Power distribution network probabilistic reliability containing dependency stochastic variable calculates and can be expressed as:

Z=F (X)=F (X₁,X₂,…X_m)

In formula, X is input variable, is constituted including Wind turbines, the output of photovoltaic cells and node load power M n-dimensional random variable n；Z is output variable, represents the reliability index of load point and system；F (X) represents the mapping between them Relation, i.e. conventional evaluating reliability of distribution network process.

Certainly, meanwhile, it is also possible to the marginal probability density function of input variable X and correlation coefficient.Marginal probability is close Degree function and correlation coefficient can input during data initialization, it is also possible to according to input during subsequent calculations Variable X is calculated.

The power distribution network probabilistic reliability appraisal procedure comprising dependency stochastic variable that this programme proposes, uses Nataf to become Change and convectional reliability point estimations is improved, be converted to determine by the probability decision sex chromosome mosaicism of meter and dependency stochastic variable Sex chromosome mosaicism.For the system mode of determination corresponding to certain sample point, by analyzing based on distribution network failure mode influences (FMEA) method solves the reliability index of load point, thus estimates the reliability level of whole power distribution network.Specifically comprise the following steps that

1) the marginal probability density function of input system interior joint load power, wind speed and intensity of illumination and correlation coefficient square Battle array.

2) using Nataf conversion that above-mentioned relevant Non-normal Variable X is transformed to standard normal variable Y, formula is as follows:

$\{\begin{array}{c}\mathrm{\Φ}\left(y_i\right)=F_i\left(x_i\right),\\ y_i={\mathrm{\Φ}}^{-1}=\left(F_i\right(x_i\left)\right),\end{array},i=1,2,...,m$

Φ (y in formula_i) and Φ^-1(F_i(x_i)) it is respectively standard normal cumulative distribution function and inverse standard normal cumulative distribution Function, F_i(x_i) it is the cumulative distribution function of stochastic variable X.

3) variable Y is still that relevant, can calculate the correlation matrix of variable Y, formula according to semiempirical formula As follows:

ρ_0ij=h ρ_ij(i=1,2 ..., m；J=1,2 ..., m)

ρ in formula_ijAnd ρ_0ijIt is respectively ρ and ρ₀In element, h is empirical coefficient, and correlation coefficient and edge by variable X are general Rate density determines.

4) by Orthogonal Decomposition, relevant criterion normal variate Y being transformed to incoherent standard normal variable V, formula is such as Under:

$V=L_0^{-1}Y$

L in formula₀For correlation matrix ρ₀Inferior triangular flap is obtained after Cholesky decomposes.

5) in independent standard normal space, sample point and respective weights are asked for based on point estimations principle.

As a example by three point estimations, to each stochastic variable, (stochastic variable herein can take in standard normal variable V One row vector or column vector) construct 3 sampled values respectively, variable V is tieed up for m, as stochastic variable V_iTake sampled value v_i,k Time, other m-1 variable takes respective average, i.e. constitutes a sample point.Sampled value v_i,kIt is represented by:

v_i,k=μ_i+ξ_i,kσ_i(k=1,2,3)

μ in formula_iAnd σ_iIt is respectively stochastic variable V_iAverage and standard deviation, ξ_i,kFor sampled value v_i,kPosition parameter.Sampling Value v_i,kPosition parameter ξ_i,kAnd weights omega_i,kCan be calculated by following formula:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_{i,k}=\frac{{\mathrm{\λ}}_{i,3}}{2}+{(-1)}^{3-k}\sqrt{{\mathrm{\λ}}_{i,4}-\frac{3}{4}{\mathrm{\λ}}_{i,4}^2},(k=1,2)\\ {\mathrm{\ξ}}_{i,k}=0,(k=3)\end{array}\right.$

$\left\{\begin{array}{c}{\mathrm{\ω}}_{i,k}=\frac{{\left(-1\right)}^{3-k}}{{\mathrm{\ξ}}_{i,k}\left({\mathrm{\ξ}}_{i,1}-{\mathrm{\ξ}}_{i,2}\right)},\left(k=1,2\right)\\ {\mathrm{\ω}}_{i,k}=\frac{1}{m}\frac{1}{{\mathrm{\λ}}_{i,4}-{\mathrm{\λ}}_{i,3}^2},\left(k=3\right)\end{array}\right.$

λ in formula_i,3And λ_i,4It is respectively variable V_iSkewness and kurtosis.Sampled value v as k=3_i,3Take variable V_iAverage, It is identical for i.e. having m sample point, owing to the average of each stochastic variable forms, and therefore only 2m+1 sample in Practical Calculation Point.Owing to the average of standard normal distribution is 0, variance is 1, and the degree of bias is 0, and kurtosis is 3, and the sampled value of the most each variable isWith 0；Respective weights coefficient is respectively 1/6,1/6 and 1/m-1/3.

6) with vector V_i,k=[0 ..., 0, v_i,k,0,…0]^TThe sample matrix V of formal construction independent standard normal variable =[V_1,1,V_1,2,…,V_m,1,V_m,2,V_2m+1], based on Nataf inverse transformation, sample matrix V transformed to original variable space (actual On be to be multiplied by matrix L to sample matrix V₀After, the inverse transformation of namely orthogonal transformation, through Nataf inverse transformation by sample moment Battle array V becomes again to the variable space of stochastic variable X), the sample matrix X=[X of structure input variable_1,1,X_1,2,…,X_m,1,X_m,2, X_2m+1], i.e. the reliability assessment sample of system.

7) every string of Reliability evaluation sample matrix correspond to system mode X determined_i,k=(μ₁,…, μ_i-1,x_i,k,μ_i+1,…,μ_m), according to distribution network failure mode influences analytic process, try to achieve the reliability of power distribution network under this state and refer to Mark.As in figure 2 it is shown, every string is analyzed, use assessment sample columns pass judgment on, as i > 2m+1 time, it is determined that each Class has all carried out fail-safe analysis.

8) utilize result of calculation and the respective weights of all samples, calculate the numerical characteristic value of reliability index, calculated Journey is as follows:

$E\left(Z^l\right)\≈\underset{i=1}{\overset{m}{\Σ}}\underset{k=1}{\overset{3}{\Σ}}{\mathrm{\ω}}_{i,k}{\left(Z_{i,k}\right)}^l$

E (Z in formula^l) it is the l rank moment of the orign of Reliability Index, Z_i,kAnd ω_i,kIt is respectively input variable sample X_i,k= (μ₁,…,μ_i-1,x_i,k,μ_i+1,…,μ_m) result of calculation and respective weights.Thus can obtain expectation and the variance of reliability index For:

$\left\{\begin{array}{c}{\mathrm{\μ}}_Z=E\left(Z\right)\\ {\mathrm{\σ}}_Z=\sqrt{E\left(Z^2\right)-{\mathrm{\μ}}_Z^2}\end{array}\right.$

9) according to each rank moment of the orign of reliability index, its probability can be tried to achieve by Cornish-Fisher expansion progression and divide Cloth.

Point estimations is combined by the method for the present embodiment with Nataf conversion, on the basis of three point estimations, profit Make improvements with Nataf conversion, so that algorithm can process incomplete multivariate information, improve reliability assessment Accuracy.It is little that the method has sample size compared with convectional reliability appraisal procedure, calculates simple, and it is excellent that accuracy is high etc. Point.Using the reliability variation characteristic of the form representation system of probability distribution, the information of expression is more comprehensive, for distribution system Planning and designing significant.

Fig. 3 is that the embodiment of the present invention provides active power distribution network probabilistic reliability estimation unit structured flowchart.See Fig. 3, should Active power distribution network probabilistic reliability estimation unit 30, including:

Acquisition module 31, for obtaining the bearing power at each node of default distribution network system and/or for electric work The probability density of rate, and their correlation coefficient；Modular converter 32, is used for described stochastic variable according to default transformation rule It is transformed to incoherent first standard normal variable between each variable；

Sample architecture module 33, is used for using point estimations, to each structure's variable in described first standard normal variable After sampled value, form the first sample matrix with described sampled value as element, and according to the inverse transformation of described default transformation rule Described first sample matrix is converted to the second sample matrix for reliability assessment；

Analyze module 34, be used for using distribution network failure mode influences analytic process, calculate the every of described second sample matrix The reliability index of one column vector and weight, and according to institute corresponding to described reliability index and weight calculation the second sample matrix State the moment of the orign of reliability index, to obtain the probability density function of described reliability index according to described moment of the orign.

The active power distribution network probabilistic reliability estimation unit 30 that the present invention provides, acquisition module 31 gets distribution network system After bearing power at each node and/or output power, modular converter 32 bearing power and/or output power are formed with Machine change of variable is incoherent first standard normal variable between each variable.Sample architecture module 33 uses point estimations to exist Construct sample matrix on the basis of first standard normal variable, analyze module 34 for corresponding to the sample in stochastic variable space Matrix carries out Failure Mode Effective Analysis, obtains the probability density function of reliability index.On the one hand this device considers point estimation The impact of reliability can be converted into and determine by method by the random factors such as the bearing power of the output power of DG and power distribution network node Sex chromosome mosaicism solves, and calculates simple；On the other hand do not limited by input variable type in view of Nataf conversion, only need known with The marginal probability density function of machine variable and correlation matrix, can effectively process the relativity problem of stochastic variable, by point The estimation technique and Nataf conversion combine, thus realize being estimated the accurate of active power distribution network probabilistic reliability by simple method.

As one more specifically embodiment, seeing Fig. 4, the active power distribution network probabilistic reliability that the present embodiment provides is estimated Counter device is broadly divided into five parts, as follows:

Part I: data initialization.Input the to be studied stochastic variable affecting distribution network reliability, including becoming at random Amount marginal probability density function and between correlation matrix.

Part II: stochastic variable nonlinear transformation.This link uses the dependency of Nataf conversion process stochastic variable, Converted by Nataf and relevant non normal random variables is transformed to relevant criterion normal random variable, then by orthogonal transformation, will Relevant criterion normal variate is transformed to independent standard normal variable.

Part III: structure reliability assessment sample.This link based on Nataf inverse transformation to convectional reliability point estimations Improved, incoherent standard normal space is calculated sample point and weight coefficient thereof, use Nataf inverse transformation by sample This point is mapped in original variable space, tries to achieve the sample point of input variable, the sample of structure Reliability evaluation.

Part IV: set up evaluating reliability of distribution network model.This link uses the general side of evaluating reliability of distribution network Method, calculates the sample of structure in Part III.Each sample correspond to a system mode determined, according to power distribution network Failure Mode Effective Analysis method, can try to achieve the reliability index of power distribution network under this state.

Part V: output target stochastic variable.Result of calculation according to all samples and respective weights, estimate reliability The numerical characteristic value of index and probability distribution thereof.

Described reliability index includes: the System average interruption frequency of each node of described distribution network system, described power distribution network system Unite the average power off time of each node and the average of each node of described distribution network system lacks delivery.

The present embodiment using the stochastic variable that affects distribution network reliability as input, quantitative analysis in these input variables and Under the effect of its dependency, the Probability Characteristics of distribution Power System Reliability level.Consider that point estimations can be by DG output work The random factor such as rate and load power is converted into certain problem to the impact of reliability and solves, and calculates simple；And Nataf becomes Change and do not limited by input variable type, only need marginal probability density function and the correlation matrix of known stochastic variable, i.e. Can effectively process the relativity problem of stochastic variable, the present invention uses Nataf converter technique to enter convectional reliability point estimations Row improves.First sample point is asked in independent standard normal space；By Nataf inverse transformation, sample point is mapped to original change again In quantity space, the sample matrix of structure evaluating reliability of distribution network；Finally according under the determination state that each sample point is corresponding Distribution network reliability result of calculation and the reliability level Probability Characteristics of weight estimating system entirety thereof.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, for the skill of this area For art personnel, the present invention can have various modifications and variations.All within the spirit and principles in the present invention, that is made any repaiies Change, equivalent, improvement etc., should be included within the scope of the present invention.

Claims (10)

1. an active power distribution network probabilistic reliability method of estimation, it is characterised in that including:

S1: obtain the bearing power at each node of the distribution network system preset and/or output power, to become as random Amount；

S2: described stochastic variable is transformed to incoherent first standard normal between each variable according to default transformation rule and becomes Amount；

S3: use point estimations, after structure's variable sampled value each in described first standard normal variable, is formed and adopts with described Sample value is the first sample matrix of element, and is changed by described first sample matrix according to the inverse transformation of described default transformation rule For the second sample matrix for reliability assessment；

S4: use distribution network failure mode influences analytic process, calculate the reliability of each column vector of described second sample matrix Index and weight, and according to described reliability index corresponding to the second sample matrix described in described reliability index and weight calculation Moment of the orign, to obtain the probability density function of described reliability index according to described moment of the orign.

Method the most according to claim 1, it is characterised in that described step S2 includes:

S21: use Nataf conversion that described stochastic variable is transformed to the second standard normal variable；

S22: according to semiempirical formula ρ_0ij=h ρ_ij(i=1,2 ..., m；J=1,2 ..., m) calculate described second standard normal and become The first correlation matrix between each variable in amount；

S23: according to Orthogonal Decomposition transformation for mulaDescribed second standard normal variable is just being transformed to described first standard State variable；

Wherein, ρ_ijIt is the i-th row jth row in the second correlation matrix ρ between each variable in described stochastic variable Variable, ρ_0ijIt is described first correlation matrix ρ₀In i-th row jth row variable, h is empirical coefficient, by described second phase The marginal probability density closing coefficient matrix and described stochastic variable determines, L₀It is described first correlation matrix ρ₀Warp Cholesky obtains inferior triangular flap after decomposing, and Y is described second standard normal variable, and V is described first standard normal variable.

Method the most according to claim 2, it is characterised in that described step S3 includes:

S31: use three point estimations, to each variable V in described first standard normal variable V_iAccording to formula v_i,k=μ_i+ ξ_i,kσ_i(k=1,2,3) three sampled values of structure；

S32: with vector V_i,k=[μ₁,μ₂,μ₃,…,v_i,k,…μ_m]^TFormal construction comprise the column vector of described sampled value；

S33: by column vector V_i,kAccording to [V_1,1,V_1,2,V_1,3,…,V_m,1,V_m,2,V_m,3] form arrangement, to obtain described first Sample matrix；

S34: after described first sample matrix is converted according to the inverse transformation that described Orthogonal Decomposition converts, according still further to Nataf Inverse transformation converts, to obtain described second sample matrix；

Wherein, μ_iIt it is variable V_iAverage, σ_iIt it is variable V_iStandard deviation, ξ_i,kFor sampled value v_i,kPosition parameter, ξ_i,kCan pass through Following formula calculates:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_{i,k}=\frac{{\mathrm{\λ}}_{i,3}}{2}+{(-1)}^{3-k}\sqrt{{\mathrm{\λ}}_{i,4}-\frac{3}{4}{\mathrm{\λ}}_{i,4}^2},(k=1,2)\\ {\mathrm{\ξ}}_{i,k}=0,(k=3)\end{array}\right.$

λ_i,3And λ_i,4It is respectively variable V_iSkewness and kurtosis, V_i,kIt is to comprise variable V_iSampled value v_i,kColumn vector, and vector V_i,kIn the average of other variable that other element is described first standard normal variable V.

Method the most according to claim 3, it is characterised in that described step S4 includes:

S41: use distribution network failure mode influences analytic process, calculate corresponding to each column vector of described second sample matrix Described power distribution network reliability index and weight, described weights omega_i,kComputing formula as follows:

$\left\{\begin{array}{c}{\mathrm{\ω}}_{i,k}=\frac{{\left(-1\right)}^{3-k}}{{\mathrm{\ξ}}_{i,k}\left({\mathrm{\ξ}}_{i,1}-{\mathrm{\ξ}}_{i,2}\right)},\left(k=1,2\right)\\ {\mathrm{\ω}}_{i,k}=\frac{1}{m}\frac{1}{{\mathrm{\λ}}_{i,4}-{\mathrm{\λ}}_{i,3}^2},\left(k=3\right)\end{array}\right.$

S42: according to described reliability index and weight according to formulaCalculate described second sample moment The moment of the orign of the described reliability index that battle array is corresponding；

S43: by described moment of the orign by Cornish-Fisher series expansion, obtain the probability density letter of described reliability index Number；

Wherein, ω_i,kIt is the weight of every string, Z in described second sample matrix_i,kIt it is every string pair in described second sample matrix The reliability index answered, E (Z^l) it is the moment of the orign that described second sample matrix is corresponding.

5. according to the method described in Claims 1-4, it is characterised in that described reliability index includes: described power distribution network system Unite the System average interruption frequency of each node, the average power off time of each node of described distribution network system and described distribution network system The average of each node lacks delivery.

6. an active power distribution network probabilistic reliability estimation unit, it is characterised in that including:

Acquisition module, for obtaining the bearing power at each node of default distribution network system and/or output power, to make For stochastic variable；

Modular converter, for being transformed between each variable incoherent first by described stochastic variable according to default transformation rule Standard normal variable；

Sample architecture module, is used for using point estimations, to structure's variable sampled value each in described first standard normal variable After, form the first sample matrix with described sampled value as element, and according to the inverse transformation of described default transformation rule by described First sample matrix is converted to the second sample matrix for reliability assessment；

Analyze module, be used for using distribution network failure mode influences analytic process, calculate every string of described second sample matrix to Amount reliability index and weight, and according to the second sample matrix described in described reliability index and weight calculation corresponding described in The moment of the orign of reliability index, to obtain the probability density function of described reliability index according to described moment of the orign.

Device the most according to claim 6, it is characterised in that described modular converter includes:

First converting unit, is used for using Nataf conversion that described stochastic variable is transformed to the second standard normal variable；

Computing unit, for according to semiempirical formula ρ_0ij=h ρ_ij(i=1,2 ..., m；J=1,2 ..., m) calculate described second The first correlation matrix between each variable in standard normal variable；

Second converting unit, for according to Orthogonal Decomposition transformation for mulaDescribed second standard normal variable is transformed to Described first standard normal variable；

Wherein, ρ_ijIt is the i-th row jth row in the second correlation matrix ρ between each variable in described stochastic variable Variable, ρ_0ijIt is described first correlation matrix ρ₀In i-th row jth row variable, h is empirical coefficient, by described second phase The marginal probability density closing coefficient matrix and described stochastic variable determines, L₀It is described first correlation matrix ρ₀Warp Cholesky obtains inferior triangular flap after decomposing, and Y is described second standard normal variable, and V is described first standard normal variable.

Device the most according to claim 7, it is characterised in that described sample architecture module includes:

First structural unit, uses three point estimations, to each variable V in described first standard normal variable V_iAccording to public affairs Formula v_i,k=μ_i+ξ_i,kσ_i(k=1,2,3) three sampled values of structure；

Second structural unit, for vector V_i,k=[μ₁,μ₂,μ₃,…,v_i,k,…μ_m]^TFormal construction comprise described sampled value Column vector；

Arrangement units, for by column vector V_i,kAccording to [V_1,1,V_1,2,V_1,3,…,V_m,1,V_m,2,V_m,3] form arrangement, to obtain Described first sample matrix；

3rd converting unit, after described first sample matrix is converted according to the inverse transformation that described Orthogonal Decomposition converts, then Convert according to Nataf inverse transformation, to obtain described second sample matrix；

Wherein, μ_iIt it is variable V_iAverage, σ_iIt it is variable V_iStandard deviation, ξ_i,kFor sampled value v_i,kPosition parameter, ξ_i,kCan pass through Following formula calculates:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_{i,k}=\frac{{\mathrm{\λ}}_{i,3}}{2}+{(-1)}^{3-k}\sqrt{{\mathrm{\λ}}_{i,4}-\frac{3}{4}{\mathrm{\λ}}_{i,4}^2},(k=1,2)\\ {\mathrm{\ξ}}_{i,k}=0,(k=3)\end{array}\right.$

λ_i,3And λ_i,4It is respectively variable V_iSkewness and kurtosis, V_i,kIt is to comprise variable V_iSampled value v_i,kColumn vector, and vector V_i,kIn the average of other variable that other element is described first standard normal variable V.

Device the most according to claim 8, it is characterised in that described analysis module includes:

First analytic unit, is used for using distribution network failure mode influences analytic process, calculates each of described second sample matrix Described power distribution network corresponding to column vector reliability index and weight, described weights omega_ikComputing formula as follows:

$\left\{\begin{array}{c}{\mathrm{\ω}}_{i,k}=\frac{{\left(-1\right)}^{3-k}}{{\mathrm{\ξ}}_{i,k}\left({\mathrm{\ξ}}_{i,1}-{\mathrm{\ξ}}_{i,2}\right)},\left(k=1,2\right)\\ {\mathrm{\ω}}_{i,k}=\frac{1}{m}\frac{1}{{\mathrm{\λ}}_{i,4}-{\mathrm{\λ}}_{i,3}^2},\left(k=3\right)\end{array}\right.$

Second analytic unit, for according to described reliability index and weight according to formulaCalculate The moment of the orign of the described reliability index that described second sample matrix is corresponding；

3rd analytic unit, for described moment of the orign is passed through Cornish-Fisher series expansion, obtains described reliability and refers to Target probability density function；

Wherein, ω_i,kIt is the weight of every string, Z in described second sample matrix_i,kIt it is every string pair in described second sample matrix The reliability index answered, E (Z^l) it is the moment of the orign that described second sample matrix is corresponding.

10. according to the device described in claim 6 to 9, it is characterised in that described reliability index includes: described power distribution network The System average interruption frequency of each node of system, the average power off time of each node of described distribution network system and described power distribution network system The average of each node of uniting lacks delivery.