CN105701590A - Wind power fluctuation probability distribution description method based on great likelihood estimation - Google Patents

Abstract

The present invention provides a wind power fluctuation probability distribution description method based on great likelihood estimation. The method comprises a step of collecting wind farm power output historical data in a time length T period, a step of sampling with a step length Delta t, and obtaining the wind farm power output historical data sequence {Pm'}; a step of calculating a normalized wind farm power output historical data sequence {Pm}, a step of carrying out sliding scanning of the normalized wind farm power output historical data sequence {Pm} with a window length as a time scale Delta T and a length as time length Delta t, and obtaining a sub sequence after one time of sliding scanning, a step of calculating the fluctuation range Zm of each sub sequence and obtaining a fluctuation range sequence {z1, z2, . . . zQ}; a step of using weighted mixed Gaussian distribution to carry out the fitting of the wind power fluctuation probability distribution, and a step of calculating the parameter of a weighted mixed Gaussian distribution function based on the great likelihood estimation of expectation maximization. According to the method, from the angle of probability, the influence of wind power random fluctuation on power system safe and stable operation is estimated, and the estimation of the influence of the wind power random fluctuation on the power system safe and stable operation is helped.

Description

A kind of wind power fluctuation probability distribution based on Maximum-likelihood estimation describes method

Technical field

The present invention relates to technical field of wind power generation, in particular it relates to a kind of wind power based on Maximum-likelihood estimation fluctuates, probability distribution describes method。

Background technology

China's wind generating technology sustained and rapid development in recent years, wind-electricity integration installed capacity increases rapidly, ends for the end of the year 2013, and China adding new capacity 16.1GW, accumulative installed capacity has reached 91.4GW, occupies first place in the world。Operation characteristic due to the uncertainty of wind-resources and Wind turbines itself, the output making wind energy turbine set has stochastic volatility, the operation of power system will be made a big impact by the fluctuation of wind power output, and temporary influence (as 1min fluctuates) will the control performance of test system AGC；Long period yardstick (as 15min, 1h fluctuate) will affect the in a few days Real-Time Scheduling of power system。Therefore, the wave characteristic studying wind power output will provide experience and foundation for power system peak-frequency regulation, operation control method etc.。

It is concentrated mainly on the statistics to stability bandwidth about the research of wind electricity volatility at present and describes on direction, and the probability distribution about wind power fluctuation is studied less at present, describe compared to the statistics of stability bandwidth in view of the probability distribution of wind power fluctuation describes, there is higher wind power stochastic wave simulation precision, therefore, it is necessary to carry out the research of the probability distribution fluctuated about wind power。

Summary of the invention

The main purpose of the embodiment of the present invention is in that to provide a kind of wind power fluctuation probability distribution based on Maximum-likelihood estimation to describe method, from the angle estimator wind-powered electricity generation stochastic volatility of probability, power system safety and stability is run the impact brought, be conducive to instructing electric power system dispatching to run。

To achieve these goals, the embodiment of the present invention provides a kind of wind power fluctuation probability distribution based on Maximum-likelihood estimation to describe method, including:

Step A, is collected from moment T_startBeginning, moment T_start+ T terminates, the output of wind electric field historical data during duration T；

Step B, is sampled the output of wind electric field historical data during described duration T with step-length for time scale △ t, obtains output of wind electric field historical data sequence { P_m'；Wherein,P_m' for T_startThe output of wind electric field historical data in+(m × Δ t) moment；

Step C, calculates output of wind electric field historical data P_m' and T_startThe installed capacity of wind-driven power P in+(m × Δ t) moment_installRatio, obtain normalized output of wind electric field historical data sequence { P_m}；Wherein,

Step D, with window length for time scale △ T, step-length is normalized output of wind electric field historical data sequence { P described in time scale △ t slip scan_m, often slip single pass obtains subsequence { P_m,P_m+1,P_m+2,......P_m+H, there are Q described subsequence；Wherein, $H=\frac{\mathrm{\ΔT}}{\mathrm{\Δt}},Q=\frac{T-\mathrm{\ΔT}}{\mathrm{\Δt}};$

Step E, calculates each subsequence { P according to below equation_m,P_m+1,P_m+2,......P_m+HFluctuating margin Z_m, obtain fluctuating margin sequence { z₁,z₂…z_Q}；

$z_m=\left\{\begin{array}{cc}{P}_{m\_\max }-P_{m\_\min },& T_{P_{m\_\max }}-T_{\mathrm{start}}>T_{P_{m\_\min }}-T_{\mathrm{start}}\\ P_{m\_\min }-P_{m\_\max },& T_{P_{m\_\max }}-T_{\mathrm{start}}<T_{P_{m\_\min }}-T_{\mathrm{start}}\end{array}\right.$

Wherein, P_{m_max}For subsequence { P_m,P_m+1,P_m+2,......P_m+HIn maximum, P_{m_min}For subsequence { P_m,P_m+1,P_m+2,......P_m+HIn minima,For P_{m_max}The corresponding moment,For P_{m_min}The corresponding moment；

Step F, with fluctuating margin sequence { z₁,z₂…z_QIn each fluctuating margin be observed value, adopt weighted blend Gauss Distribution Fitting wind power fluctuation probability distribution, obtain wind power fluctuation weighted blend gauss of distribution function；

Step G, based on the maximum likelihood estimation algorithm of expectation maximization, calculates the parameter of the weighted blend gauss of distribution function of described wind power fluctuation。

By means of technique scheme, first the present invention collects and analysis and arrangement historical data, adopt the probability distribution of Weighted Gauss mixing Probability Distribution Fitting wind power fluctuation, adopt based on expectation maximization (Expectation-Maximization, EM) maximum likelihood estimation algorithm carrys out appraising model parameter, from the angle estimator wind-powered electricity generation stochastic volatility of probability, power system safety and stability is run the impact brought, contribute to, from the angle estimator wind-powered electricity generation stochastic volatility of probability, power system safety and stability is run the impact brought, electric power system dispatching is instructed to run, improve power system wind-powered electricity generation receive ability and run security and stability。

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 the accompanying drawing used required during embodiment is described is briefly described, 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 that the wind power fluctuation probability distribution based on Maximum-likelihood estimation provided by the invention describes method flow schematic diagram；

The wind power fluctuation probability distribution contrast schematic diagram that Fig. 2 obtains when being long △ T respectively 15min, 30min, the 1h of window provided by the invention；

Fig. 3 is the long △ T of window provided by the invention is measured data during 15min and the wind power fluctuation probability distribution contrast obtained according to normal distyribution function, Extremal distribution function, this special distribution function of logic and weighted blend gauss of distribution function；

Fig. 4 is the long △ T of window provided by the invention is measured data during 30min and the wind power fluctuation probability distribution contrast obtained according to this special distribution function of normal distyribution function, Extremal distribution function and logic and weighted blend gauss of distribution function；

Fig. 5 is the long △ T of window provided by the invention is measured data during 1h and the wind power fluctuation probability distribution contrast obtained according to this special distribution function of normal distyribution function, Extremal distribution function and logic and weighted blend gauss of distribution function。

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。

The present invention provides a kind of wind power fluctuation probability distribution based on Maximum-likelihood estimation to describe method, as it is shown in figure 1, the method includes:

Step S1, is collected from moment T_startBeginning, moment T_start+ T terminates, the output of wind electric field historical data during duration T。

It is also preferred that the left the output of wind electric field historical data can collected in nearest a year, namely duration T is 1 year。

Step S2, is sampled the output of wind electric field historical data during described duration T with step-length for time scale △ t, obtains output of wind electric field historical data sequence { P_m'；Wherein,P_m' for T_startThe output of wind electric field historical data in+(m × Δ t) moment, i.e. P_m' come across T_start+ (m × Δ t) moment。

It is also preferred that the left time scale △ t value is 15 minutes。Such as, this step S2 chooses moment T_start15 minutes afterwards, 30 minutes, 45 minutes ... wait the output of wind electric field historical data in each moment。

Step S3, calculates output of wind electric field historical data P_m' and T_startThe installed capacity of wind-driven power P in+(m × Δ t) moment_installRatio, obtain normalized output of wind electric field historical data sequence { P_m, wherein,

$P_m=\frac{{P_m}^{\&prime;}}{P_{\mathrm{install}}}$ (formula 1)

Concrete, this step S3 utilizes output of wind electric field historical data P in the same time_m' and installed capacity of wind-driven power P_installRatio, be normalized, so that fluctuating margin in the same time does not have unified criterion。

Step S4, with window length for time scale △ T, step-length is normalized output of wind electric field historical data sequence { P described in time scale △ t slip scan_m, often slip single pass obtains subsequence { P_m,P_m+1,P_m+2,......P_m+H, there are Q described subsequence；Wherein, $H=\frac{\mathrm{\&Delta;T}}{\mathrm{\&Delta;t}},Q=\frac{T-\mathrm{\&Delta;T}}{\mathrm{\&Delta;t}};$

Concrete, this step utilizes window that window length is △ T to normalized output of wind electric field historical data sequence { P_mIt is scanned sampling, and this window slides with step-length for △ t, and often slip single pass obtains a subsequence。

Step S5, calculates each subsequence { P according to below equation_m,P_m+1,P_m+2,......P_m+HFluctuating margin Z_m, obtain fluctuating margin sequence { z₁,z₂…z_Q}；

$z_m=\left\{\begin{array}{cc}{P}_{m\_\max }-P_{m\_\min },& T_{P_{m\_\max }}-T_{\mathrm{start}}>T_{P_{m\_\min }}-T_{\mathrm{start}}\\ P_{m\_\min }-P_{m\_\max },& T_{P_{m\_\max }}-T_{\mathrm{start}}<T_{P_{m\_\min }}-T_{\mathrm{start}}\end{array}\right.$ (formula 2)

In formula 2, P_{m_max}For subsequence { P_m,P_m+1,P_m+2,......P_m+HIn maximum, P_{m_min}For subsequence { P_m,P_m+1,P_m+2,......P_m+HIn minima,For P_{m_max}The corresponding moment, T_{Pm_min}For P_{m_min}The corresponding moment。

Represent subsequence { P_m,P_m+1,P_m+2,......P_m+HIn maximum come across minima after, z_mFor on the occasion of。

Represent subsequence { P_m,P_m+1,P_m+2,......P_m+HIn maximum come across minima before, z_mFor negative value。

Step S6, with fluctuating margin sequence { z₁,z₂…z_QIn each fluctuating margin be observed value, adopt weighted blend Gauss Distribution Fitting wind power fluctuation probability distribution, obtain wind power fluctuation weighted blend gauss of distribution function。

Concrete, shown in weighted blend gauss of distribution function such as formula 3 and formula 4；

$f\left(x\right)=\underset{j=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{j}N({\mathrm{\&mu;}}_j,{\mathrm{\&sigma;}}_j^2)$ (formula 3)

$N({\mathrm{\&mu;}}_j,{\mathrm{\&sigma;}}_j^2)=\frac{1}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_j}{e}^{-\frac{1}{2{\mathrm{\&sigma;}}_j^2}{(x-{\mathrm{\&mu;}}_j)}^2}$ (formula 4)

In formula 3 and formula 4, k is model order, α_jFor the weight coefficient of Gaussian component, in expression weighted blend Gauss distribution, the probability of each composition appearance, meetsμ_j、σ_jThe respectively average of jth Gaussian component and standard deviation。

Make θ_j=[α_j,μ_j,σ_j], it is necessary to the parameter of estimation is Θ=[θ₁,θ₂,…θ_k], given observed value Z={z₁,z₂…z_Q, likelihood function is:

$L\left(Z\right|\mathrm{\&Theta;})=\underset{j=1}{\overset{k}{\mathrm{\&Pi;}}}f\left(x_j\right)$ (formula 5)

Taking the logarithm in both sides, obtains:

$l\left(\mathrm{\&Theta;}\right)=\ln \left[L\left(Z\right|\mathrm{\&Theta;})\right]=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\ln \underset{j=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{i}N({\mathrm{\&mu;}}_j,{\mathrm{\&sigma;}}_j^2)$ (formula 6)

Step S7, based on the maximum likelihood estimation algorithm of expectation maximization, calculates the parameter of the weighted blend gauss of distribution function of described wind power fluctuation。

Concrete, this step S7 comprises the steps:

Step S71, it is determined that initial value。

Clustered observing sample by k-means clustering algorithm, utilize cluster centre point of all categories as μ_j0, and calculateParameter alpha_j0The ratio of total number of samples is accounted for for Different categories of samples after cluster。

Step S72, estimating step。

α is calculated by formula 7_jPosterior probability

${\mathrm{\&beta;}}_j\left(Z^{\left(i\right)}\right)=\frac{{\mathrm{\&alpha;}}_{j}N(Z^{\left(i\right)};{\mathrm{\&mu;}}_j,{\mathrm{\&sigma;}}_j^2)}{\underset{j=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{j}N(Z^{\left(i\right)};{\mathrm{\&mu;}}_j,{\mathrm{\&sigma;}}_j^2)}$ (formula 7)

Step S73, maximization steps。

Weight coefficient, average and standard deviation matrix is updated respectively by formula 8～formula 10。

${\mathrm{\&alpha;}}_j^{\&prime;}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{j}N\left(Z^{\left(i\right)}\right),j=\mathrm{1,2},...k$ (formula 8)

${\mathrm{\&mu;}}_j^{\&prime;}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_j\left(Z^{\left(i\right)}\right)Z^{\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_j\left(Z^{\left(i\right)}\right)},j=\mathrm{1,2},...k$ (formula 9)

${\mathrm{\&sigma;}}_j^{2\&prime;}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_j{(Z^{\left(i\right)}-{\mathrm{\&mu;}}_j^{\&prime;})}^T(Z^{\left(i\right)}-{\mathrm{\&mu;}}_j^{\&prime;})}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_j\left(Z^{\left(i\right)}\right)},j=\mathrm{1,2},...k$ (formula 10)

Step S74, it is determined that convergence。Repeatedly carry out step S72 and step S73, constantly repeat to update, until | l (Θ)-l'(Θ) | < ε generally takes ε < 10⁵, l (Θ) is calculated by formula 6, l'(Θ) represent each iteration update after value of calculation。

In a kind of preferred embodiment, the wind power fluctuation probability distribution based on Maximum-likelihood estimation provided by the invention describes method, also includes:

Step S8, adopts residual sum of squares (RSS), root-mean-square, the effectiveness determining the weighted blend gauss of distribution function of wind power fluctuation described in factor evaluation and accuracy。

Concrete, this step S8 adopts residual sum of squares (RSS), root-mean-square, determines the factor evaluation weighted blend gauss of distribution function precision with other distribution function (including this special distribution of normal distribution, the extreme value distribution and logic) matching wind power fluctuation, verifies its effectiveness。

Residual sum of squares (RSS), root-mean-square, determine that the computational methods of coefficient are as follows:

First digital simulation data

${\hat{y}}_i=f\left({\stackrel{\&OverBar;}{C}}_i\right)$ (formula 11)

Residual sum of squares (RSS) computing formula is as follows:

$W_{\mathrm{SSE}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(y_i-{\hat{y}}_i)}^2$ (formula 12)

Root mean square calculation formula is as follows:

$W_{\mathrm{RMSE}}=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(y_i-{\hat{y}}_i)}^2}$ (formula 13)

Determine that coefficient formulas is as follows:

$W_{R-\mathrm{square}}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(y_i-{\stackrel{\&OverBar;}{y}}_i)}^2}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(y_i-{\hat{y}}_i)}^2}$ (formula 14)

In formula 11～formula 14, i=1,2 ... n, wherein n is the packet count of histogram frequency distribution diagram, y_iWith C_iThe respectively height of i-th Nogata post and center, f is the probability density function of matching, y_iMeansigma methods for all Nogata post height。

Calculate and add up the wind power fluctuation probability distribution obtained when being long △ T respectively 15min, 30min, the 1h of window shown in Fig. 2 according to measured data。

Measured data during 15min that to be the long △ T of window shown in Fig. 3 be and the wind power fluctuation probability distribution contrast obtained according to normal distyribution function, Extremal distribution function, this special distribution function of logic and weighted blend gauss of distribution function。

Measured data during 30min that to be the long △ T of window shown in Fig. 4 be and the wind power fluctuation probability distribution contrast obtained according to this special distribution function of normal distyribution function, Extremal distribution function and logic and weighted blend gauss of distribution function。

Measured data during 1h that to be the long △ T of window shown in Fig. 5 be and the wind power fluctuation probability distribution contrast obtained according to this special distribution function of normal distyribution function, Extremal distribution function and logic and weighted blend gauss of distribution function。

According to Fig. 3～Fig. 5 it can be seen that the wind power fluctuation weighted blend gauss of distribution function obtained according to the present invention has higher degree of accuracy compared to this special distribution function of normal distyribution function, Extremal distribution function and logic。

First the present invention collects and analysis and arrangement historical data, adopt the probability distribution of Weighted Gauss mixing Probability Distribution Fitting wind power fluctuation, the maximum likelihood estimation algorithm based on EM is adopted to carry out appraising model parameter, propose the index of evaluation model fitting precision, and carry out effectiveness and the accuracy of this model of contrast verification with multiple probability Distribution Model, contribute to, from the angle estimator wind-powered electricity generation stochastic volatility of probability, power system safety and stability is run the impact brought, instruct electric power system dispatching to run, improve power system wind-powered electricity generation and receive ability and run security and stability。

Particular embodiments described above; the purpose of the present invention, technical scheme and beneficial effect have been further described; it is it should be understood that; the foregoing is only specific embodiments of the invention; the protection domain being not intended to limit the present invention; all within the spirit and principles in the present invention, any amendment of making, equivalent replacement, improvement etc., should be included within protection scope of the present invention。

Claims (5)

1. one kind describes method based on the wind power fluctuation probability distribution of Maximum-likelihood estimation, it is characterised in that including:

Step A, is collected from moment T_startBeginning, moment T_start+ T terminates, the output of wind electric field historical data during duration T；

Step B, is sampled the output of wind electric field historical data during described duration T with step-length for time scale △ t, obtains output of wind electric field historical data sequence { P_m'；Wherein,P_m' for T_startThe output of wind electric field historical data in+(m × Δ t) moment；

Step C, calculates output of wind electric field historical data P_m' and T_startThe installed capacity of wind-driven power P in+(m × Δ t) moment_installRatio, obtain normalized output of wind electric field historical data sequence { P_m}；Wherein,

Step D, with window length for time scale △ T, step-length is normalized output of wind electric field historical data sequence { P described in time scale △ t slip scan_m, often slip single pass obtains subsequence { P_m,P_m+1,P_m+2,......P_m+H, there are Q described subsequence；Wherein, $H=\frac{\mathrm{\&Delta;T}}{\mathrm{\&Delta;t}},Q=\frac{T-\mathrm{\&Delta;T}}{\mathrm{\&Delta;t}};$

Step E, calculates each subsequence { P according to below equation_m,P_m+1,P_m+2,......P_m+HFluctuating margin Z_m, obtain fluctuating margin sequence { z₁,z₂…z_Q}；

$z_m=\left\{\begin{array}{cc}{P}_{m\_\max }-P_{m\_\min },& T_{P_{m\_\max }}-T_{\mathrm{start}}>T_{P_{m\_\min }}-T_{\mathrm{start}}\\ P_{m\_\min }-P_{m\_\max },& T_{P_{m\_\max }}-T_{\mathrm{start}}<T_{P_{m\_\min }}-T_{\mathrm{start}}\end{array}\right.$

Wherein, P_{m_max}For subsequence { P_m,P_m+1,P_m+2,......P_m+HIn maximum,

P_{m_min}For subsequence { P_m,P_m+1,P_m+2,......P_m+HIn minima,

For P_{m_max}The corresponding moment,

For P_{m_min}The corresponding moment；

Step F, with fluctuating margin sequence { z₁,z₂…z_QIn each fluctuating margin be observed value, adopt weighted blend Gauss Distribution Fitting wind power fluctuation probability distribution, obtain wind power fluctuation weighted blend gauss of distribution function；

Step G, based on the maximum likelihood estimation algorithm of expectation maximization, calculates the parameter of the weighted blend gauss of distribution function of described wind power fluctuation。

2. method according to claim 1, it is characterised in that also include after described step G: adopt residual sum of squares (RSS), root-mean-square, the effectiveness determining the weighted blend gauss of distribution function of wind power fluctuation described in factor evaluation and accuracy。

3. method according to claim 1, it is characterised in that described duration T is a year。

4. method according to claim 1, it is characterised in that described time scale △ t is 15 minutes。

5. method according to claim 1, it is characterised in that described time scale △ T is 15 minutes or 30 minutes or 60 minutes。