CN112685915B - Wind power output condition probability distribution modeling method - Google Patents
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Abstract
The invention belongs to the technical field of power systems, and mainly relates to a wind power output conditional probability distribution modeling method, which comprises the following steps: acquiring historical data of wind power output; preprocessing historical data to obtain the actual wind power output w t Wind power actual output w in adjacent time period t‑1 And predicting the force
As experimental data; actual output w of wind power t Wind power actual output w in adjacent time period t‑1 And predicting the force
Estimating a marginal cumulative probability distribution of (1); by wind power actual output w t Wind power actual output w in adjacent time period t‑1 And predicting the force
Is performed on the original data to obtain a marginal cumulative probability F (w t )，F(w t‑1 ) And
and obtaining the conditional cumulative probability distribution of wind power output through the Pair Copula theory. The method effectively improves the accuracy of modeling the probability distribution of the wind power output condition, and provides more reliable basis for power dispatching, standby planning and other works in the wind power system.
Description
Technical Field
The invention belongs to the technical field of power systems, and particularly relates to a wind power output conditional probability distribution modeling method.
Background
Is influenced by environmental pressure and energy crisis, and wind power development is rapid in recent years. However, the uncertainty of wind power restricts the utilization of wind power, and the annual wind discarding rate of China reaches 169 hundred million kilowatt-hours in 2019 and is 4.0 percent according to statistics. In order to reduce the abandoned wind, a plurality of standby units are added to the power grid to compensate wind power fluctuation, and extra standby cost is brought. Through more accurate modeling of uncertainty of wind power output, wind abandoning can be reduced, so that wind power development and operation cost is reduced, wind power competitiveness is enhanced, and market impact caused by canceling wind power patch in the future is met. Therefore, the method for accurately modeling the uncertainty of the wind power output is an effective means for improving the economy of the wind power-containing power system from the aspect of scheduling planning, and has important significance.
The uncertainty of wind power output mainly comes from insufficient accuracy of wind power output prediction. The prediction of the certainty has the defect that the uncertainty of the wind power output cannot be quantitatively described, and for the problems of planning, scheduling, operation, reliability and the like of a power system containing wind power, the accurate estimation of the fluctuation range of the wind power output is more needed to solve the problems, namely the accurate wind power output probability distribution is obtained. Compared with unconditional modeling, conditional modeling is more accurate by accounting other external information in a short time scale, and is mainly divided into a transverse research direction and a longitudinal research direction. Wind power output is represented in a plane rectangular coordinate system, as shown in fig. 1, the horizontal direction is autocorrelation on wind power output time sequence, the vertical direction is correlation between other input variables used for estimating wind power output range, such as wind power predicted output and actual output. Considering the influence of one type of correlation on one side reduces the accuracy of modeling the probability distribution of the wind power output condition.
Therefore, how to combine these two correlations and improve the accuracy of wind power output conditional probability distribution modeling is a technical problem to be solved by those skilled in the art.
Disclosure of Invention
The purpose of the invention is that: the wind power output condition probability distribution modeling method is used for solving the problem of improving the accuracy of wind power output condition probability distribution modeling and providing more reliable basis for power dispatching, standby planning and other works in a wind power system.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a wind power output conditional probability distribution modeling method comprises the following steps:
step 1: acquiring historical data of wind power output;
step 2: preprocessing historical data to obtain the actual wind power output w t Wind power actual output w in adjacent time period t-1 And predicting the force
As experimental data;
step 3: actual output w of wind power t Wind power actual output w in adjacent time period t-1 And predicting the force
Estimating a marginal cumulative probability distribution of (1);
step 4: by wind power actual output w t Wind power actual output w in adjacent time period t-1 And predicting the force
Is performed on the original data to obtain a marginal cumulative probability F (w t )，F(w t-1 ) And->
Step 5: f (w) is obtained by using Copula theory t ) And F (w) t-1 )，F(w t-1 ) And
optimal Copula function between
And->
Step 6: for a pair of
Obtaining F (w) by obtaining bias t ) Relative to F (w) t-1 ) Is a conditional cumulative probability distribution F (w t |w t-1 ) And F (w) t-1 ) Relative to->
Is a conditional cumulative probability distribution of (2)
Step 7: derived by the Pair Copula theory
By means of
And obtaining the conditional cumulative probability distribution of wind power generation.
Further, the specific implementation of step 3 is as follows:
step 301: the actual output w of wind power is obtained by adopting a nuclear density estimation method in a non-parameter method t Wind power actual output w in adjacent time period t-1 And predicting the force
Is estimated.
Further, the specific implementation of step 4 is as follows:
step 401: by wind power actual output w t Wind power actual output w in adjacent time period t-1 And predicting the force
Is transformed into [0,1 ] by probability integration of the raw data]Evenly distributed, obtaining marginal cumulative probability F (w t )，F(w t-1 ) And->
Further, the specific implementation of obtaining the optimal Copula function in step 5 is as follows:
step 501: using a number of different forms of Copula function pairs F (w t ) And F (w) t-1 )，F(w t-1 ) And
two by twoFitting the joint probability distribution between the two, and estimating corresponding parameters by adopting a maximum likelihood method;
step 502: calculating the Euclidean distance between the experimental Copula function and the theoretical Copula function obtained by parameter estimation, wherein the Euclidean distance is used as an evaluation index for selecting the optimal Copula function type, and the smaller the Euclidean distance is, the closer the joint probability distribution of the Copula function model and experimental data is;
step 503: recording an optimal Copula function
And->
Type and corresponding parameters of (a).
Further, step 6 includes the following steps:
step 601: repeating steps 5.1-5.3 to obtain F (w) t |w t-1 ) And
optimal Copula function between the two>
Further, in step 7
The specific deduction steps of (a) are as follows:
step 701: actual output w of wind power t Wind power actual output w in adjacent time period t-1 Predicting the force
Combined cumulative distribution function among the three>
Conduct derivation to obtain +.>
Wherein,,
is w t ，w t-1 And->
Is a joint probability density distribution of (1);
f(w t )，f(w t-1 ) And
w is respectively t ，w t-1 And->
Is a marginal probability density distribution of (1);
such as
Shown;
step 702: based on the Pair Copula theory, the joint probability density of wind power output and wind power output in adjacent time periods is obtained
Partial differentiation is carried out on the above to obtain the wind power output w t Wind power generation w relative to adjacent time period t-1 The conditional probability density of (2) is:
step 703: expanding to obtain wind power output w t Wind power generation w relative to adjacent time period t-1 And predicting the force
Conditional probability Density->
Integrating to obtain the wind power output w t Wind power generation w relative to adjacent time period t-1 And predictive force->
Conditional cumulative probability distribution +.>
The invention adopting the technical scheme has the following advantages:
1. according to the invention, by utilizing the Pair Copula theory, the wind power output conditional probability distribution modeling process considering two correlations is decomposed into a chain type transmission process of the traditional two-dimensional Copula function, so that the accurate estimation of the wind power output conditional probability distribution can be realized;
2. the execution process does not depend on any priori knowledge such as a prediction method, and the like, and the analyzed wind power output conditional probability distribution function is obtained based on historical data, so that the fluctuation range of wind power output under different confidence levels can be accurately reflected, the method can be effectively applied to the optimization of a traditional unit standby plan, and has important significance in improving the economy and safety of a wind power system;
3. the modeling method based on the time sequence self-correlation and the inter-force cross-correlation prediction has better effectiveness compared with the method which only considers one of the correlations.
Drawings
The invention can be further illustrated by means of non-limiting examples given in the accompanying drawings;
FIG. 1 is a schematic diagram of two types of wind power output probability distribution condition modeling methods;
FIG. 2 is a schematic diagram of a wind power output conditional probability distribution modeling method for accounting in time sequence autocorrelation and predicted force cross correlation;
FIG. 3 is a flowchart of a method for modeling wind power output conditional probability distribution that accounts for time-series autocorrelation and inter-force cross-correlation with predicted forces provided by the present invention;
FIG. 4 is a graph showing 95% confidence intervals for wind power generation using the method of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the drawings and the specific embodiments, wherein like or similar parts are designated by the same reference numerals throughout the drawings or the description, and implementations not shown or described in the drawings are in a form well known to those of ordinary skill in the art. In addition, directional terms such as "upper", "lower", "top", "bottom", "left", "right", "front", "rear", etc. in the embodiments are merely directions with reference to the drawings, and are not intended to limit the scope of the present invention.
1-3, a wind power output conditional probability distribution modeling method comprises the following steps:
step 1: acquiring historical data of wind power output;
step 2: preprocessing historical data to obtain the actual wind power output w t Wind power actual output w in adjacent time period t-1 And predicting the force
As experimental data;
step 3: actual output w of wind power t Wind power actual output w in adjacent time period t-1 And predicting the force
Estimating a marginal cumulative probability distribution of (1);
step 4: by wind power actual output w t Wind power actual output w in adjacent time period t-1 And predicting the force
Is performed on the original data to obtain a marginal cumulative probability F (w t )，F(w t-1 ) And->
Step 5: f (w) is obtained by using Copula theory t ) And F (w) t-1 )，F(w t-1 ) And
optimal Copula function between
And->
Step 6: for a pair of
Obtaining F (w) by obtaining bias t ) Relative to F (w) t-1 ) Is a conditional cumulative probability distribution F (w t |w t-1 ) And F (w) t-1 ) Relative to->
Is a conditional cumulative probability distribution of (2)
Step 7: derived by the Pair Copula theory
By->
And obtaining the conditional cumulative probability distribution of wind power generation.
Example 1: obtaining an optimal Copula function
Step 501: using a number of different forms of Copula function pairs F (w t ) And F (w) t-1 )，F(w t-1 ) And
fitting the joint probability distribution between every two, and estimating corresponding parameters by adopting a maximum likelihood method;
step 502: calculating the Euclidean distance between the experimental Copula function and the theoretical Copula function obtained by parameter estimation, wherein the Euclidean distance is used as an evaluation index for selecting the optimal Copula function type, and the smaller the Euclidean distance is, the closer the joint probability distribution of the Copula function model and experimental data is;
step 503: recording an optimal Copula function
And->
Type and corresponding parameters of (a).
Example 2:
the specific deduction steps of (a) are as follows:
step 701: actual output w of wind power t Wind power actual output w in adjacent time period t-1 Predicting the force
Combined cumulative distribution function among the three>
Conduct derivation to obtain +.>
Wherein,,
is w t ，w t-1 And->
Is a joint probability density distribution of (1);
f(w t )，f(w t-1 ) And
w is respectively t ，w t-1 And->
Is a marginal probability density distribution of (1);
such as
Shown;
step 702: based on the Pair Copula theory, the joint probability density of wind power output and wind power output in adjacent time periods is obtained
Partial differentiation is carried out on the above to obtain the wind power output w t Wind power generation w relative to adjacent time period t-1 The conditional probability density of (2) is:
step 703: expanding to obtain wind power output w t Wind power generation w relative to adjacent time period t-1 And predicting the force
Conditional probability Density->
Integrating to obtain the wind power output w t Wind power generation w relative to adjacent time period t-1 And predictive force->
Conditional cumulative probability distribution +.>
Example 3: the method is applied to an actual wind power plant and is specifically implemented as follows:
Step 3, obtaining the actual output w of the stroke electricity by utilizing the Pair Copula theory t Actual wind power output w relative to adjacent time period t-1 And predicting a conditional cumulative probability distribution of force
Step 4, using the kernel density estimation to obtain the actual output w of the wind power in the training data respectively t Wind power actual output w in adjacent time period t-1 And predicting the force
F (w) of three data sequences t )，F(w t-1 ) And->
Will F (w) t-1 ) And->
Substitution into
Obtain F (w) t ) And (3) carrying out probability integral inverse transformation to obtain the actual wind power output w t Is a conditional probability distribution of (c).
Step 5, in order to evaluate the effectiveness of the invention, a 95% confidence interval of wind power output in training data is obtained by utilizing inverse probability integration transformation, and as shown in fig. 4, the 95% confidence interval obtained by the invention can effectively cover the actual output of wind power.
The wind power output conditional probability distribution modeling method designed by the invention has the advantages that the time sequence autocorrelation of wind power output and the cross correlation between the actual output and the predicted output of wind power are counted, no priori knowledge such as a prediction method is needed, and the wind power output conditional probability distribution model based on the actual output value and the predicted value of the historical output is very good in supplement effect on the traditional wind power output point prediction, and has important significance on planning, scheduling, energy storage and capacity fixing of wind power.
The invention discloses a wind power output condition probability distribution modeling method. The description of the specific embodiments is only intended to aid in understanding the method of the present invention and its core ideas. It should be noted that it will be apparent to those skilled in the art that the present invention may be modified and practiced with several improvements and modifications without departing from the spirit of the invention, and that the improvements and modifications are intended to be within the scope of the appended claims.
Claims (5)
1. The wind power output conditional probability distribution modeling method is characterized by comprising the following steps of:
step 1: acquiring historical data of wind power output;
step 2: preprocessing historical data to obtain the actual wind power output w t Wind power actual output w in adjacent time period t-1 And predicting the force
As experimental data;
step 3: actual output w of wind power t Wind power actual output w in adjacent time period t-1 And predicting the force
Estimating a marginal cumulative probability distribution of (1);
step 4: by wind power actual output w t Wind power actual output w in adjacent time period t-1 And predicting the force
Is performed on the original data to obtain a marginal cumulative probability F (w t )，F(w t-1 ) And->
Step 5: f (w) is obtained by using Copula theory t ) And F (w) t-1 )，F(w t-1 ) And
optimal Copula function between
And->
Step 6: for a pair of
Obtaining F (w) by obtaining bias t ) Relative to F (w) t-1 ) Is a conditional cumulative probability distribution F (w t |w t-1 ) And F (w) t-1 ) Relative to->
Is a conditional cumulative probability distribution of (2)
Step 7: derived by the Pair Copula theory
By->
ObtainingThe conditional cumulative probability distribution of wind power generation;
wherein in step 7
The specific deduction steps of (a) are as follows:
step 701: actual output w of wind power t Wind power actual output w in adjacent time period t-1 Predicting the force
Combined cumulative distribution function among the three>
Conduct derivation to obtain +.>
Wherein,,
is w t ，w t-1 And->
Is a joint probability density distribution of (1);
f(w t )，f(w t-1 ) And
w is respectively t ，w t-1 And->
Is a marginal probability density distribution of (1);
such as
Shown;
step 702: based on the Pair Copula theory, the joint probability density of wind power output and wind power output in adjacent time periods is obtained
Partial differentiation is carried out on the above to obtain the wind power output w t Wind power generation w relative to adjacent time period t-1 The conditional probability density of (2) is:
step 703: expanding to obtain wind power output w t Wind power generation w relative to adjacent time period t-1 And predicting the force
Conditional probability Density->
Integrating to obtain the wind power output w t Wind power generation w relative to adjacent time period t-1 And predictive force->
Is a conditional cumulative probability distribution of (2)
2. The method for modeling a wind power output conditional probability distribution according to claim 1, wherein the specific implementation of the step 3 is as follows:
step 301: the actual output w of wind power is obtained by adopting a nuclear density estimation method in a non-parameter method t Wind power actual output w in adjacent time period t-1 And predicting the force
Is estimated.
3. The method for modeling a wind power output conditional probability distribution according to claim 1, wherein the specific implementation of the step 4 is as follows:
step 401: by wind power actual output w t Wind power actual output w in adjacent time period t-1 And predicting the force
Is transformed into [0,1 ] by probability integration of the raw data]Evenly distributed, obtaining marginal cumulative probability F (w t )，F(w t-1 ) And->
4. The method for modeling a wind power output conditional probability distribution according to claim 1, wherein the specific implementation of obtaining the optimal Copula function in the step 5 is as follows:
step 501: using a number of different forms of Copula function pairs F (w t ) And F (w) t-1 )，F(w t-1 ) And
fitting the joint probability distribution between every two, and estimating corresponding parameters by adopting a maximum likelihood method;
step 502: calculating the Euclidean distance between the experimental Copula function and the theoretical Copula function obtained by parameter estimation, wherein the Euclidean distance is used as an evaluation index for selecting the optimal Copula function type, and the smaller the Euclidean distance is, the closer the joint probability distribution of the Copula function model and experimental data is;
step 503: recording an optimal Copula function
And->
Type and corresponding parameters of (a).
5. The method for modeling a wind power output conditional probability distribution of claim 1, wherein the step 6 further comprises the steps of:
step 601: repeating steps 501-503 to obtain F (w) t |w t-1 ) And
optimum Copula function between the two
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