CN105808962A - Assessment method considering voltage probabilities of multiple electric power systems with wind power output randomness - Google Patents

Abstract

The invention discloses an assessment method considering voltage probabilities of multiple electric power systems with wind power output randomness. The assessment method comprises the following steps: determining a weight coefficient, a mean vector and a covariance coefficient matrix according to a wind power predicted value matrix and a wind power actual value sample matrix of a plurality of wind power plants; calculating first-order and second-order sensitivity vector matrixes from node voltages to the wind power predicted value matrix; determining cumulative distribution functions of the node voltage corresponding to each Gaussian component according to the first-order and second-order sensitivity vector matrixes, the mean vector and the covariance coefficient matrix; determining cumulative distribution functions of the node voltage corresponding to a Gaussian hybrid model according to each cumulative distribution function and the weight coefficient. According to the assessment method, the cumulative distribution functions of the node voltages can be determined through extracting the wind power predicted value matrix and the wind power actual value sample matrix of the plurality of wind power plants, so that the used time is short; the first-order and second-order sensitivity vector matrixes are calculated, so that the nonlinear relationship between the node voltages and the wind power is fully considered and the correctness is high.

Description

Consider the appraisal procedure of the power system voltage probability of multiple wind power output randomness

Technical field

The present invention relates to the technical field of wind energy turbine set power system, particularly relate to the appraisal procedure of a kind of power system voltage probability considering multiple wind power output randomness.

Background technology

In power system, wind power output has randomness, cannot accurate CDF (Cumulativedistributionfunction to the node voltage of power system, the cumulative distribution function of stochastic variable) and PDF (Probabilisticdensitydistribution, the probability density function of stochastic variable) be estimated.

In order to obtain CDF and the PDF of node voltage, currently mainly there is method and have two classes: linearization technique and Monte Carlo simulation.Wherein,

Linearization technique mainly by approximate for output variable (node voltage) linear function being write as input variable (wind power), then carrys out CDF and the PDF of computing node voltage further according to some probabilistic operation rules.But, the shortcoming of conventional linear method is the assumption that between node voltage and wind power obedience linear relationship, and what have ignored therebetween is non-linear, and accuracy is not high.

And the embodiment of Monte Carlo simulation is to be initially formed substantial amounts of wind power sample point, then calculate trend at each sample point, thus obtaining the sample of the node voltage of correspondence.Finally, the sample of node voltage is added up, obtains CDF and the PDF of node voltage.But, disadvantage is that of Monte Carlo Method carries out substantial amounts of sampling generation sample point, and carries out Load flow calculation at these sample points, calculates the time long.

Summary of the invention

It is an object of the invention to provide the appraisal procedure of a kind of power system voltage probability considering multiple wind power output randomness, can accurately obtain the cumulative distribution function of node voltage.

For achieving the above object, the invention provides following scheme:

A kind of appraisal procedure of the power system voltage probability considering multiple wind power output randomness, described appraisal procedure includes: step one: according to the wind power prediction value matrix of multiple wind energy turbine set and wind power actual value sample matrix, it is determined that weight coefficient, mean vector and the covariance coefficient matrix that in gauss hybrid models, each Gaussian component is corresponding；Step 2: computing node voltage is to the one order matrix of described wind power prediction value matrix and Second Order Sensitivity vector matrix；Step 3: the mean vector corresponding according to described one order matrix, described Second Order Sensitivity vector matrix, each Gaussian component described and covariance coefficient matrix determine the cumulative distribution function of node voltage corresponding to each Gaussian component；Step 4: according to the cumulative distribution function of node voltage corresponding to each Gaussian component and weight coefficient, it is determined that the cumulative distribution function of the node voltage corresponding to gauss hybrid models.

Optionally, in step one, the computational methods of described weight coefficient, mean vector and covariance coefficient matrix include respectively:

The wind power prediction value extracting W wind energy turbine set in Database Management System in Electrical Power System forms wind power prediction value matrix P:

P=[p₁,p₂,...,p_W]^T--------(1)；

The wind power actual value all extracting I sample in W corresponding electric field forms wind power actual value sample matrix, calculates the difference of i-th wind power actual value and corresponding wind power prediction value, it is thus achieved that the wind power prediction error sample X of i-th sample_i:

$X_i=\[x_i^1,x_i^2,...,x_i^W\]---\left(2\right)$

Wherein,The wind power prediction error of w wind energy turbine set in expression i-th sample, i=1,2 ... .I；

According to wind power prediction error sample X_iDetermined by expectation-maximization algorithm and organize weight coefficient, mean vector and covariance coefficient matrix more, wherein, form gauss hybrid models according to each group of weight coefficient, mean vector and covariance coefficient matrix, described gauss hybrid models comprises M Gaussian component, ω_m、μ_m、Σ_mWeight coefficient, mean vector and the covariance coefficient matrix that expression m-th Gaussian component is corresponding respectively.

Optionally, in step 2, each item of described one order matrix Δ is determined according to below equation:

Wherein, w₁∈ [1, W], Y_kRepresent the kth node voltage determined according to power flow equation,It is by w₁The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards；

The described Second Order Sensitivity each item of matrix Γ is determined according to below equation:

Wherein, w₂∈ [1, W],It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards.

Optionally, in step 3, the computational methods of the cumulative distribution function of the node voltage that each described Gaussian component is corresponding include:

According to formulaDetermine Z_mAnd L_m；Wherein, Z_mFor ∑_mCholesky matrix, Λ isEigenvalue composition diagonal matrix, L_mServe as reasonsRight characteristic vector composition matrix；

Extract the jth element a in Λ_j；

CalculateExtractIn jth element b_j；

According to formulaDetermining parameter c, wherein θ is the kth node voltage numerical value determined according to power flow equation when wind power prediction error is 0；

The cumulative distribution function Y of node voltage corresponding to m-th Gaussian component is determined according to below equation_kmQuantile

$\begin{array}{c}{F}_{Ym}^{-1}\left(\mathrm{\α}\right)={\mathrm{\Φ}}^{-1}\left(\mathrm{\α}\right)+\frac{1}{6}({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2-1)k_3+\frac{1}{24}({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^3-3{\mathrm{\Φ}}^{-1}(\mathrm{\α}\left)\right)k_4\\ -\frac{1}{36}(2{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^3-5{\mathrm{\Φ}}^{-1}(\mathrm{\α}\left)\right)k_3^2+\frac{1}{120}({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^4-6{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2+1)k_5\\ -\frac{1}{24}({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^4-5{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2+2)k_3{k}_4+\frac{1}{324}(12{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^4-53{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2+17)k_3^3\end{array}---\left(7\right);$

$k_r=\left\{\begin{array}{cc}c+\frac{1}{2}\underset{j}{\Σ}{a}_j& r=1\\ \frac{1}{2}\underset{j}{\Σ}\{(r-1)!a_j^r+r!b_j^2{a}_j^{r-2}\}& r\≥2\end{array}\right.---\left(8\right);$

Wherein, Φ^-1(α) for the quantile of standard normal function alpha；

CalculateInverse function, it is determined that the cumulative distribution function F of the node voltage corresponding to m-th Gaussian component_Ym(y)。

Optionally, in step 4, determine the cumulative distribution function F of node voltage corresponding to described gauss hybrid models according to below equation_Y(y):

$F_Y\left(y\right)=\underset{m=1}{\overset{M}{\Σ}}{\mathrm{\ω}}_m{F}_{Ym}\left(y\right)---\left(9\right).$

Optionally, described appraisal procedure also includes: step 5: determine the probability density function of node voltage corresponding to each Gaussian component according to described one order matrix, described Second Order Sensitivity vector matrix, each described Gaussian component correspondence mean vector and covariance coefficient matrix；Step 6: according to the probability density function of node voltage corresponding to Gaussian component each described and weight coefficient, it is determined that the probability density function of the node voltage corresponding to gauss hybrid models.

Optionally, in step 5, the computational methods of the probability density function of the node voltage that each described Gaussian component is corresponding include:

The parameter A in described probability density function, B, C and D is determined according to below equation:

$A=-\frac{t^2}{2}\underset{j}{\Σ}\frac{b_j^2}{1+a_j^2{t}^2}---\left(10\right);$

$B=t(y-c+t^2\underset{j=1}{\Σ}\frac{b_j^2{a}_j}{2(1+a_j^2{t}^2)})---\left(11\right);$

$C=\frac{1}{2}\underset{j=1}{\Σ}{\tan }^{-1}(-a_{j}t)---\left(12\right);$

$D=\underset{j=1}{\Π}{(1+a_j^2{t}^2)}^{\frac{1}{4}}---\left(13\right);$

The probability density function f of node voltage corresponding to m-th Gaussian component is determined according to below equation_Ym(y):

$f_{Ym}\left(y\right)=\frac{1}{\mathrm{\π}}\underset{0}{\overset{\mathrm{\∞}}{\∫}}\frac{e^{A}cos(B+C)}{D}dt---\left(14\right).$

Optionally, in step 6, determine the probability density function f of node voltage corresponding to described gauss hybrid models according to below equation_Y(y):

$f_Y\left(y\right)=\underset{m=1}{\overset{M}{\Σ}}{\mathrm{\ω}}_m{f}_{Ym}\left(y\right)---\left(15\right).$

Optionally, described power flow equation is:Wherein, P_HaveFor input active power, including a wind power prediction error, Q_NothingFor the reactive power of input, Y is the node voltage of output,Phase angle for output.

According to specific embodiment provided by the invention, the invention discloses techniques below effect:

The present invention extracts wind power prediction value matrix and the wind power actual value sample matrix of multiple wind energy turbine set in data base, to determine weight coefficient, mean vector and the covariance coefficient matrix that in gauss hybrid models, each Gaussian component is corresponding；Computing node voltage is to the one order matrix of wind power prediction value matrix and Second Order Sensitivity vector matrix, to take into full account the non-linear relation of node voltage and wind power；Further, the cumulative distribution function of the node voltage corresponding to gauss hybrid models is can determine that according to one order matrix, Second Order Sensitivity vector matrix and each Gaussian component correspondence mean vector and covariance coefficient matrix, weight coefficient, accuracy is high, convenience of calculation is quick, and the used time is short.

Accompanying drawing explanation

In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, the accompanying drawing used required in embodiment will be briefly described below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the premise not paying creative work, it is also possible to obtain other accompanying drawing according to these accompanying drawings.

Fig. 1 is the flow chart that the present invention considers the appraisal procedure of the power system voltage probability of multiple wind power output randomness.

Detailed description of the invention

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is clearly and completely described, it is clear that described embodiment is only a part of embodiment of the present invention, rather than whole embodiments.Based on the embodiment in the present invention, the every other embodiment that those of ordinary skill in the art obtain under not making creative work premise, broadly fall into the scope of protection of the invention.

It is an object of the invention to provide the appraisal procedure of a kind of power system voltage probability considering multiple wind power output randomness, the present invention extracts wind power prediction value matrix and the wind power actual value sample matrix of multiple wind energy turbine set in data base, to determine weight coefficient, mean vector and the covariance coefficient matrix that in gauss hybrid models, each Gaussian component is corresponding；Computing node voltage is to the one order matrix of wind power prediction value matrix and Second Order Sensitivity vector matrix, to take into full account the non-linear relation of node voltage and wind power；Further, the cumulative distribution function of the node voltage corresponding to gauss hybrid models is can determine that according to one order matrix, Second Order Sensitivity vector matrix and each Gaussian component correspondence mean vector and covariance coefficient matrix, weight coefficient, accuracy is high, convenience of calculation is quick, and the used time is short.

Understandable for enabling the above-mentioned purpose of the present invention, feature and advantage to become apparent from, below in conjunction with the drawings and specific embodiments, the present invention is further detailed explanation.

As described in Figure 1, the present invention considers that the appraisal procedure of the power system voltage probability of multiple wind power output randomness includes:

Step 110: according to the wind power prediction value matrix of multiple wind energy turbine set and wind power actual value sample matrix, it is determined that weight coefficient, mean vector and the covariance coefficient matrix that in gauss hybrid models, each Gaussian component is corresponding.

Step 120: computing node voltage is to the one order matrix of described wind power prediction value matrix and Second Order Sensitivity vector matrix.

Step 130: the mean vector corresponding according to described one order matrix, described Second Order Sensitivity vector matrix, each Gaussian component described and covariance coefficient matrix determine the cumulative distribution function of node voltage corresponding to each described Gaussian component.

Step 140: according to the cumulative distribution function of node voltage corresponding to Gaussian component each described and weight coefficient, it is determined that the cumulative distribution function of the node voltage corresponding to gauss hybrid models.

Step 150: the mean vector corresponding according to described one order matrix, described Second Order Sensitivity vector matrix, each described Gaussian component and covariance coefficient matrix determine the probability density function of node voltage corresponding to each Gaussian component.

Step 160: according to the probability density function of node voltage corresponding to Gaussian component each described and weight coefficient, it is determined that the probability density function of the node voltage corresponding to gauss hybrid models.

Wherein, in step 110, the computational methods of described weight coefficient, mean vector and covariance coefficient matrix include respectively:

Step 111: the wind power prediction value extracting W wind energy turbine set in Database Management System in Electrical Power System forms wind power prediction value matrix P:

P=[p₁,p₂,...,p_W]^T--------(1)。

Step 112: the wind power actual value all extracting I sample in W corresponding electric field forms wind power actual value sample matrix, calculate the difference of i-th wind power actual value and corresponding wind power prediction value, it is thus achieved that the wind power prediction error sample X of i-th sample_i:

Wherein,The wind power prediction error of w wind energy turbine set in expression i-th sample, i=1,2 ... .I.In the present embodiment, I value is 5000.

Step 113: according to wind power prediction error sample X_iDetermined by expectation-maximization algorithm and organize weight coefficient, mean vector and covariance coefficient matrix more, wherein, form gauss hybrid models according to each group of weight coefficient, mean vector and covariance coefficient matrix, described gauss hybrid models comprises M Gaussian component, ω_m、μ_m、∑_mWeight coefficient, mean vector and the covariance coefficient matrix that expression m-th Gaussian component is corresponding respectively.Described expectation-maximization algorithm and EM algorithm, be an algorithms most in use in mathematical statistics, do not repeat them here.

Described gauss hybrid models is represented (X represents wind power prediction error sample) by below equation:

$\left\{\begin{array}{c}f\left(x\right)=\underset{m=1}{\overset{M}{\Σ}}{\mathrm{\ω}}_{m}N\left(X\right|{\mathrm{\μ}}_m,{\mathrm{\Σ}}_m)\\ \underset{m=1}{\overset{M}{\Σ}}{\mathrm{\ω}}_m=1\\ N\left(X\right|{\mathrm{\μ}}_m,{\mathrm{\Σ}}_m)=\frac{1}{{\left(2\mathrm{\π}\right)}^{W/2}{\[\det \left({\mathrm{\Σ}}_m\right)\]}^{W/2}}{e}^{-\frac{1}{2}{(X-{\mathrm{\μ}}_m)}^T{{\mathrm{\Σ}}_m}^{-1}(X-{\mathrm{\μ}}_m)}\end{array}\right.$

The present invention considers that the appraisal procedure of the power system voltage probability of multiple wind power output randomness has taken into full account the non-linear relation of node voltage and wind power, and wherein, the quadratic function relation formula of node voltage and wind power prediction error sample is:Wherein, Y_kRepresenting the kth node voltage determined according to power flow equation, θ is the kth node voltage numerical value determined according to power flow equation when wind power prediction error is 0, and Δ is node voltage Y_kOne order matrix to wind power prediction value P, Γ is node voltage Y_kSecond Order Sensitivity matrix to wind power prediction value P.

Wherein, each item of described one order matrix Δ is determined according to below equation:

Wherein, w₁∈ [1, W], Y_kRepresent the kth node voltage determined according to power flow equation,It is by w₁The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards；

The described Second Order Sensitivity each item of matrix Γ is determined according to below equation:

Wherein, w₂∈ [1, W],It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards.Wherein,Take w₁The 1% of individual wind energy turbine set installed capacity,Take w₂The 1% of individual wind energy turbine set installed capacity.

Described power flow equation is:Wherein, P_HaveFor input active power, including a wind power prediction error, Q_NothingFor the reactive power of input, Y is the node voltage of output,Phase angle for output.

In step 130, the computational methods of the cumulative distribution function of the node voltage that each described Gaussian component is corresponding include:

Step 131: according to formulaDetermine Z_mAnd L_m；Wherein, Z_mFor Σ_mCholesky matrix, Λ isEigenvalue composition diagonal matrix, L_mServe as reasonsRight characteristic vector composition matrix.

Step 132: extract the jth element a in Λ_j；CalculateExtractIn jth element b_j；According to formulaDetermining parameter c, wherein θ is the kth node voltage numerical value determined according to power flow equation when wind power prediction error is 0.

Step 133: determine the cumulative distribution function Y of node voltage corresponding to m-th Gaussian component according to below equation_kmQuantile

$\begin{array}{c}{F}_{Ym}^{-1}\left(\mathrm{\α}\right)={\mathrm{\Φ}}^{-1}\left(\mathrm{\α}\right)+\frac{1}{6}({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2-1)k_3+\frac{1}{24}({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^3-3{\mathrm{\Φ}}^{-1}(\mathrm{\α}\left)\right)k_4\\ -\frac{1}{36}(2{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^3-5{\mathrm{\Φ}}^{-1}(\mathrm{\α}\left)\right)k_3^2+\frac{1}{120}({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^4-6{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2+1)k_5\\ -\frac{1}{24}({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^4-5{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2+2)k_3{k}_4+\frac{1}{324}(12{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^4-53{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2+17)k_3^3\end{array}---\left(7\right);$

$k_r=\left\{\begin{array}{cc}c+\frac{1}{2}\underset{j}{\Σ}{a}_j& r=1\\ \frac{1}{2}\underset{j}{\Σ}\{(r-1)!a_j^r+r!b_j^2{a}_j^{r-2}\}& r\≥2\end{array}\right.---\left(8\right);$

Wherein, Φ^-1(α) for the quantile of standard normal function alpha；

Step 134: calculateInverse function, it is determined that the cumulative distribution function F of the node voltage corresponding to m-th Gaussian component_Ym(y)。

In step 140, the cumulative distribution function F of node voltage corresponding to described gauss hybrid models is determined according to below equation_Y(y):

$F_Y\left(y\right)=\underset{m=1}{\overset{M}{\Σ}}{\mathrm{\ω}}_m{F}_{Ym}\left(y\right)---\left(9\right).$

In step 150, the computational methods of the probability density function of the node voltage that each described Gaussian component is corresponding include:

Step 151: determine the parameter A in described probability density function, B, C and D according to below equation:

$A=-\frac{t^2}{2}\underset{j}{\Σ}\frac{b_j^2}{1+a_j^2{t}^2}---\left(10\right);$

$B=t(y-c+t^2\underset{j=1}{\Σ}\frac{b_j^2{a}_j}{2(1+a_j^2{t}^2)})---\left(11\right);$

$C=\frac{1}{2}\underset{j=1}{\Σ}{\tan }^{-1}(-a_{j}t)---\left(12\right);$

$D=\underset{j=1}{\Π}{(1+a_j^2{t}^2)}^{\frac{1}{4}}---\left(13\right);$

Step 152: determine the probability density function f of node voltage corresponding to m-th Gaussian component according to below equation_Ym(y):

$f_{Ym}\left(y\right)=\frac{1}{\mathrm{\π}}\underset{0}{\overset{\mathrm{\∞}}{\∫}}\frac{e^{A}cos(B+C)}{D}dt---\left(14\right).$

In a step 160, the probability density function f of node voltage corresponding to described gauss hybrid models is determined according to below equation_Y(y):

$f_Y\left(y\right)=\underset{m=1}{\overset{M}{\Σ}}{\mathrm{\ω}}_m{f}_{Ym}\left(y\right)---\left(15\right).$

The present invention, by extracting the sample of limited quantity in data base, just can determine that the analytic expression of CDF and PDF, and convenience of calculation is quick, and the used time is short；Fully taking into account the non-linear relation between node voltage and wind power prediction error, accuracy is high simultaneously.

In this specification, each embodiment adopts the mode gone forward one by one to describe, and what each embodiment stressed is the difference with other embodiments, between each embodiment identical similar portion mutually referring to.

Principles of the invention and embodiment are set forth by specific case used herein, and the explanation of above example is only intended to help to understand method and the core concept thereof of the present invention；Simultaneously for one of ordinary skill in the art, according to the thought of the present invention, all will change in specific embodiments and applications.In sum, this specification content should not be construed as limitation of the present invention.

Claims (9)

1. the appraisal procedure of the power system voltage probability considering multiple wind power output randomness, it is characterised in that described appraisal procedure includes:

Step one: according to the wind power prediction value matrix of multiple wind energy turbine set and wind power actual value sample matrix, it is determined that weight coefficient, mean vector and the covariance coefficient matrix that in gauss hybrid models, each Gaussian component is corresponding；

Step 2: computing node voltage is to the one order matrix of described wind power prediction value matrix and Second Order Sensitivity vector matrix；

Step 3: the mean vector corresponding according to described one order matrix, described Second Order Sensitivity vector matrix, each Gaussian component described and covariance coefficient matrix determine the cumulative distribution function of node voltage corresponding to each described Gaussian component；

Step 4: according to the cumulative distribution function of node voltage corresponding to Gaussian component each described and weight coefficient, it is determined that the cumulative distribution function of the node voltage corresponding to gauss hybrid models.

2. the appraisal procedure of the power system voltage probability of the multiple wind power output randomness of consideration according to claim 1, it is characterised in that in step one, the computational methods of described weight coefficient, mean vector and covariance coefficient matrix include respectively:

The wind power prediction value extracting W wind energy turbine set in Database Management System in Electrical Power System forms wind power prediction value matrix P:

P=[p₁,p₂,...,p_W]^T--------(1)；

The wind power actual value all extracting I sample in W corresponding electric field forms wind power actual value sample matrix, calculates the difference of i-th wind power actual value and corresponding wind power prediction value, it is thus achieved that the wind power prediction error sample X of i-th sample_i:

$X_i=\[x_i^1,x_i^2,...,x_i^W\]---\left(2\right)$

Wherein,The wind power prediction error of w wind energy turbine set in expression i-th sample, i=1,2 ... .I；

According to wind power prediction error sample X_iDetermined by expectation-maximization algorithm and organize weight coefficient, mean vector and covariance coefficient matrix more, wherein, form gauss hybrid models according to each group of weight coefficient, mean vector and covariance coefficient matrix, described gauss hybrid models comprises M Gaussian component, ω_m、μ_m、∑_mWeight coefficient, mean vector and the covariance coefficient matrix that expression m-th Gaussian component is corresponding respectively.

3. the appraisal procedure of the power system voltage probability of the multiple wind power output randomness of consideration according to claim 2, it is characterised in that in step 2,

Each item of described one order matrix Δ is determined according to below equation:

Wherein, w₁∈ [1, W], Y_kRepresent the kth node voltage determined according to power flow equation,It is by w₁The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards；

The described Second Order Sensitivity each item of matrix Γ is determined according to below equation:

$\frac{{\∂}^2{Y}_k}{\∂p_{w_1}\∂p_{w_2}}=\frac{Y_k(p_{w_1}+{\mathrm{\Δp}}_{w_1},p_{w_2}+{\mathrm{\Δp}}_{w_2})+Y_k(p_{w_1},p_{w_2})-Y_k(p_{w_1},p_{w_2}+{\mathrm{\Δp}}_{w_2})-Y_k(p_{w_1}+{\mathrm{\Δp}}_{w_1},p_{w_2})}{{\mathrm{\Δp}}_{w_1}{\mathrm{\Δp}}_{w_2}}--$ $------\left(4\right);$ Wherein, w₂∈ [1, W],It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards,It is by w₁The wind power assignment of individual wind energy turbine set isAnd w₂The wind power assignment of individual wind energy turbine set isThe kth node voltage determined according to power flow equation afterwards.

4. the appraisal procedure of the power system voltage probability of the multiple wind power output randomness of consideration according to claim 3, it is characterised in that in step 3, the computational methods of the cumulative distribution function of the node voltage that each described Gaussian component is corresponding include:

According to formulaDetermine Z_mAnd L_m；Wherein, Z_mFor Σ_mCholesky matrix, Λ isEigenvalue composition diagonal matrix, L_mServe as reasonsRight characteristic vector composition matrix；

Extract the jth element a in Λ_j；

Calculate (Δ^T+μ_m ^TΓ)Z_mL_m ^-1, extract (Δ^T+μ_m ^TΓ)Z_mL_m ^-1In jth element b_j；

According to formulaDetermining parameter c, wherein θ is the kth node voltage numerical value determined according to power flow equation when wind power prediction error is 0；

The cumulative distribution function Y of node voltage corresponding to m-th Gaussian component is determined according to below equation_kmQuantile

$\begin{array}{c}{F}_{Ym}^{-1}\left(\mathrm{\α}\right)={\mathrm{\Φ}}^{-1}\left(\mathrm{\α}\right)+\frac{1}{6}\left({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2-1\right)k_3+\frac{1}{24}\left({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^3-3{\mathrm{\Φ}}^{-1}\left(\mathrm{\α}\right)\right)k_4\\ -\frac{1}{36}\left(2{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^3-5{\mathrm{\Φ}}^{-1}\left(\mathrm{\α}\right)\right)k_3^2+\frac{1}{120}\left({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^4-6{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2+1\right)k_5\\ -\frac{1}{24}\left({\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^4-5{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2+2\right)k_3{k}_4+\frac{1}{324}\left(12{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^4-53{\mathrm{\Φ}}^{-1}{\left(\mathrm{\α}\right)}^2+17\right)k_3^3\end{array}---\left(7\right);$

$k_r=\left\{\begin{array}{cc}c+\frac{1}{2}\underset{j}{\Σ}{a}_j& r=1\\ \frac{1}{2}\underset{j}{\Σ}\{(r-1)!a_j^r+r!b_j^2{a}_j^{r-2}\}& r\≥2\end{array}\right.---\left(8\right);$

Wherein, Φ^-1(α) for the quantile of standard normal function alpha；

CalculateInverse function, it is determined that the cumulative distribution function F of the node voltage corresponding to m-th Gaussian component_Ym(y)。

5. the appraisal procedure of the power system voltage probability of the multiple wind power output randomness of consideration according to claim 4, it is characterised in that in step 4, determines the cumulative distribution function F of node voltage corresponding to described gauss hybrid models according to below equation_Y(y):

$F_Y\left(y\right)=\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\ω}}_m{F}_{Ym}\left(y\right)---\left(9\right).$

6. the appraisal procedure of the power system voltage probability of the multiple wind power output randomness of consideration according to claim 4, it is characterised in that described appraisal procedure also includes:

Step 5: the mean vector corresponding according to described one order matrix, described Second Order Sensitivity vector matrix, each described Gaussian component and covariance coefficient matrix determine the probability density function of node voltage corresponding to each Gaussian component；

Step 6: according to the probability density function of node voltage corresponding to Gaussian component each described and weight coefficient, it is determined that the probability density function of the node voltage corresponding to gauss hybrid models.

7. the appraisal procedure of the power system voltage probability of the multiple wind power output randomness of consideration according to claim 6, it is characterised in that in step 5, the computational methods of the probability density function of the node voltage that each described Gaussian component is corresponding include:

The parameter A in described probability density function, B, C and D is determined according to below equation:

$A=-\frac{t^2}{2}\underset{j}{\Σ}\frac{b_j^2}{1+a_j^2{t}^2}---\left(10\right);$

$B=t(y-c+t^2\underset{j=1}{\Σ}\frac{b_j^2{a}_j}{2(1+a_j^2{t}^2)})---\left(11\right);$

$C=\frac{1}{2}\underset{j=1}{\Σ}{\tan }^{-1}(-a_{j}t)---\left(12\right);$

$D=\underset{j=1}{\Π}{(1+a_j^2{t}^2)}^{\frac{1}{4}}---\left(13\right);$

The probability density function f of node voltage corresponding to m-th Gaussian component is determined according to below equation_Ym(y):

$f_{Ym}\left(y\right)=\frac{1}{\mathrm{\π}}\underset{0}{\overset{\mathrm{\∞}}{\∫}}\frac{e^{A}cos(B+C)}{D}dt---\left(14\right).$

8. the appraisal procedure of the power system voltage probability of the multiple wind power output randomness of consideration according to claim 7, it is characterised in that in step 6, determines the probability density function f of node voltage corresponding to described gauss hybrid models according to below equation_Y(y):

$f_Y\left(y\right)=\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\ω}}_m{f}_{Ym}\left(y\right)---\left(15\right).$

9. the appraisal procedure of the power system voltage probability considering multiple wind power output randomness according to any one of claim 3-8, it is characterised in that described power flow equation isWherein, P_HaveFor input active power, including a wind power prediction error, Q_NothingFor the reactive power of input, Y is the node voltage of output,Phase angle for output.