Wind power forecast error uncertainty modeling method and device

Abstract

The present invention provides a method and device for modeling wind power prediction error uncertainty, belonging to the field of wind power prediction. The method comprises: obtaining a wind power sample set and preprocessing the wind power sample set to obtain a wind power sample distribution domain; based on the wind power sample distribution domain, using a Gaussian fusion method and an improved online adaptive kernel density method to determine a joint probability density model of multiple random variables and a marginal distribution probability density model of the wind power prediction value random variable; determining a conditional probability density model of the wind power prediction error random variable based on the joint probability density model of the multiple random variables and the marginal distribution probability density model of the wind power prediction value random variable; and modifying the conditional probability density model based on the definition domain of the wind power sample distribution domain to obtain a modified conditional probability density model, and determining a confidence interval and point prediction value of the wind power prediction error. The present invention can reduce model overfitting and non-smoothing, thereby improving model accuracy.

Description

Technical Field

[0001] This invention relates to the field of wind power prediction technology, and in particular to a method and apparatus for modeling uncertainty in wind power prediction errors. Background Technology

[0002] Due to the high uncertainty faced by wind power generation, wind farms currently generally use wind power forecasting to improve the reliability of wind power grid connection. Wind power forecasting widely adopts physical models based on numerical weather prediction (NWP), statistical models with NWP data and historical data as inputs, and statistical models based on historical data. The probability of error in point prediction by various methods is 100%, and it has been proven that there are some random and systematic biases in the original NWP speed prediction. Therefore, it is necessary to model the uncertainty of new energy prediction errors.

[0003] Common uncertainty modeling methods include interval modeling, quantile regression modeling, scenario modeling, and probability density modeling. Among these, probability density modeling contains the most comprehensive information, and the results of other types can be obtained based on probability density models. Probabilistic modeling of uncertainty can be divided into parametric and non-parametric estimation methods. Parametric estimation requires making assumptions about the distribution type the data follows, and then determining the optimal distribution parameters based on the data. Commonly used parametric estimation methods include Gaussian distribution, exponential distribution, and beta distribution. Non-parametric estimation is less affected by the type of the underlying distribution, does not require assumptions about data characteristics or prior knowledge, and instead performs probability estimation based on the cumulative characteristics of the data itself. Commonly used non-parametric estimation methods include quantile regression, Gaussian mixture model, and kernel density estimation.

[0004] Currently, online adaptive kernel density estimation methods can be used to model the uncertainty of wind power prediction errors. This method enables data-driven adaptive component generation, avoiding the cumbersome bandwidth estimation of traditional adaptive kernel density methods, and achieves higher fitting accuracy for samples. Furthermore, with the addition of new data, it can automatically update the probability density function based solely on the newly added data, avoiding the need to re-identify and update the model using all historical data, resulting in faster model identification and adaptation to new data. However, this method suffers from several small-variance Gaussian components coexisting in densely distributed data areas, leading to model unsmoothness and overfitting. Additionally, this method assumes that the uncertain variables are unbounded, resulting in lower model accuracy when directly applied to bounded data problems. Summary of the Invention

[0005] This invention provides a method and apparatus for modeling the uncertainty of wind power prediction errors, in order to solve the problems that existing methods can lead to unsmooth models, overfitting, and low model accuracy.

[0006] In a first aspect, embodiments of the present invention provide a method for modeling the uncertainty of wind power prediction errors, including:

[0007] Obtain a wind power sample set and preprocess it to obtain the wind power sample distribution domain;

[0008] Based on the wind power sample distribution domain, a Gaussian fusion method is adopted, and an improved online adaptive kernel density method is used to determine the joint probability density model of multiple random variables and the marginal distribution probability density model of the random variables of wind power prediction values.

[0009] Based on the joint probability density model of multiple random variables and the marginal distribution probability density model of the random variable of wind power prediction value, the conditional probability density model of the random variable of wind power prediction error is determined.

[0010] Based on the domain of the wind power sample distribution, the conditional probability density model is modified to obtain the modified conditional probability density model. Based on the modified conditional probability density model, the confidence interval and point prediction value of the wind power prediction error are determined.

[0011] Secondly, embodiments of the present invention provide a wind power prediction error uncertainty modeling device, comprising:

[0012] The preprocessing module is used to acquire the wind power sample set and preprocess the wind power sample set to obtain the wind power sample distribution domain.

[0013] An improved module is used to determine the joint probability density model of multiple random variables and the marginal distribution probability density model of the random variables of wind power prediction values ​​based on the distribution domain of wind power samples, using the Gaussian fusion method and the improved online adaptive kernel density method.

[0014] The conditional probability density model determination module is used to determine the conditional probability density model of the random variable of wind power prediction error based on the joint probability density model of multiple random variables and the marginal distribution probability density model of the random variable of wind power prediction value.

[0015] The correction module is used to correct the conditional probability density model based on the domain of the wind power sample distribution field, to obtain the corrected conditional probability density model, and to determine the confidence interval and point prediction value of the wind power prediction error based on the corrected conditional probability density model.

[0016] This invention provides a method and apparatus for modeling uncertainty in wind power prediction errors. By preprocessing a wind power sample set, a wind power sample distribution domain is obtained, and its distribution characteristics are analyzed. A Gaussian fusion method is used to improve the shortcomings of the online adaptive kernel density method, reducing overfitting and unsmoothness of the model. Based on the domain of the wind power sample distribution domain, the conditional probability density model is modified to obtain a modified conditional probability density model, which solves the probability density leakage problem in bounded data modeling and improves model accuracy. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the implementation of a wind power prediction error uncertainty modeling method according to an embodiment of the present invention.

[0019] Figure 2 This is a flowchart illustrating the implementation of a wind power prediction error uncertainty modeling method provided in another embodiment of the present invention;

[0020] Figure 3 This is a schematic diagram of the process architecture for wind power prediction error modeling and prediction provided in an embodiment of the present invention;

[0021] Figure 4 This is a schematic diagram of a joint probability density model of wind power prediction value and wind power prediction error provided in an embodiment of this application;

[0022] Figure 5 This is a schematic diagram of the structure of a wind power prediction error uncertainty modeling device provided in an embodiment of the present invention. Detailed Implementation

[0023] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0024] To make the objectives, technical solutions, and advantages of the present invention clearer, specific embodiments will be described below in conjunction with the accompanying drawings.

[0025] Figure 1The implementation flowchart of the wind power prediction error uncertainty modeling method provided in the embodiments of the present invention is described in detail below:

[0026] Step 101: Obtain the wind power sample set and preprocess the wind power sample set to obtain the wind power sample distribution domain.

[0027] A wind power sample set can include multiple wind power samples. After preprocessing each wind power sample in the wind power sample set, a wind power sample distribution domain can be obtained. The wind power sample distribution domain can include multiple preprocessed wind power samples.

[0028] In some embodiments, the preprocessing of the wind power sample set in step 101 above to obtain the wind power sample distribution domain may include:

[0029] according to The wind power sample set is normalized to obtain the wind power sample distribution domain;

[0030] Among them, the i-th wind power sample in the wind power sample set This is the original value for the predicted power output of the i-th wind farm. This represents the original value of the prediction error for the i-th wind farm. S represents the original actual power output of the i-th wind farm; WF Let r be the installed capacity of the wind farm; and r be the normalized wind power sample corresponding to the i-th wind power sample. i =(x i ,y i ,z i ), x i Let y be the normalized predicted output value of the i-th wind farm. i Let z be the normalized prediction error value for the i-th wind farm. i z represents the normalized actual power output of the i-th wind farm; 1 ≤ i ≤ N, where N is the number of wind farm samples in the wind farm sample set; i =x i +y i ;x i ∈[0,1],y i ∈[-x i ,1-x i ], z i ∈[0,1].

[0031] In this embodiment, the wind power sample set is normalized using the installed capacity of wind farms to obtain a wind power sample distribution domain. The wind power sample distribution domain contains N normalized wind power samples.

[0032] Step 102: Based on the wind power sample distribution domain, adopt the Gaussian fusion method to improve the online adaptive kernel density method, and determine the joint probability density model of multiple random variables and the marginal distribution probability density model of the wind power prediction value random variable.

[0033] Among them, the improved online adaptive kernel density method may include Gaussian component activation, parameter update, model noise reduction, and Gaussian fusion. The multiple random variables in the joint probability density model of multiple random variables may include the wind power prediction value random variable X and the wind power prediction error random variable Y.

[0034] In some embodiments, based on the wind power sample distribution domain, adopting the Gaussian fusion method to improve the online adaptive kernel density method and determine the joint probability density model of multiple random variables includes:

[0035] Initialize the update count k, and determine the joint probability density model of the wind power prediction value random variable X and the wind power prediction error random variable Y after k updates

[0036] Obtain the (k + 1)-th normalized wind power sample r in the wind power sample distribution domain k+1 , and based on r k+1 and perform Gaussian component activation to obtain the set S of subscripts of the activated Gaussian components, and based on S, perform Gaussian component insertion or Gaussian component update processing;

[0037] Perform noise reduction processing on the current joint probability density model, and fuse the Gaussian components in the data intensive aggregation area to obtain the joint probability density model of the wind power prediction value random variable X and the wind power prediction error random variable Y after (k + 1) updates;

[0038] If k + 1 < N, add 1 to k to get the new k, and jump to the step of obtaining the (k + 1)-th normalized wind power sample r k+1 and execute it in a loop;

[0039] If k + 1 ≥ N, use the joint probability density model of the wind power prediction value random variable X and the wind power prediction error random variable Y after (k + 1) updates as the joint probability density model of multiple random variables; N is the number of wind power samples in the wind power sample set.

[0040] See Figure 2 , first, the update count k = 0 can be initialized. Each time it is updated, k increases by 1 until k + 1 ≥ N, and the update of the joint probability density model based on all normalized wind power samples is completed.

[0041] In a new model update, when r k+1After input, Gaussian component activation is first performed to obtain the set S of indices of the activated Gaussian components. Then, based on whether S is empty, it is determined whether to perform Gaussian component insertion or update. Next, model denoising is performed to reduce the number of Gaussian components in the model. After denoising, the model may still contain a large number of Gaussian components in densely distributed sample areas. To prevent overfitting, a Gaussian fusion method is used to fuse Gaussian components in densely clustered data areas, significantly reducing Gaussian components with very small variance, thus avoiding overfitting and unsmoothness.

[0042] In some embodiments, in, Let the weight of the j-th Gaussian component be determined after k updates. Let be the mean vector of the j-th Gaussian component after k updates. Let be the costandard deviation matrix of the j-th Gaussian component after k updates. Let c be the j-th Gaussian probability density function after k updates. (k) Let k be the number of Gaussian probability density functions after k updates. x∈R, y∈R, where x is the data corresponding to the random variable X of wind power prediction value, and y is the data corresponding to the random variable Y of wind power prediction error; Let X be the mean of the random variable X with the j-th Gaussian component after k updates. Let Y be the mean of the random variable Y with the j-th Gaussian component after k updates; Let X be the standard deviation of the j-th Gaussian component of the random variable after k updates. Let X and Y be the costandard deviations of the j-th Gaussian component random variables after k updates. Let Y and X be the costandard deviation of the j-th Gaussian component random variables after k updates. Let Y be the standard deviation of the j-th Gaussian component of the random variable after k updates.

[0043] Accordingly, the above is based on r k+1 and Perform Gaussian component activation to obtain the set S of indices of the activated Gaussian components, including:

[0044] according to j = 1, 2, ..., c (k) Calculate r k+1 The Mahalanobis distance between each Gaussian component; M j (r k+1 ) is r k+1 The Mahalanobis distance between the j-th Gaussian component and the j-th component;

[0045] According to r k+1 The Mahalanobis distances to each Gaussian component determine the set of indices S of the activated Gaussian components; where S = {j | j ∈ {1, 2, ..., c} (k)},M j (r k+1 ) <T j};T j is the activation threshold for the j-th Gaussian component.

[0046] The set S of indices of the activated Gaussian components contains the subscripts of r. k+1 The Mahalanobis distance is less than the threshold value T j The subscripts of the Gaussian components, which generate samples r. k+1 The probability is highest when their parameters are updated to adapt to the new sample data r. k+1 .

[0047] In some embodiments, the above-described Gaussian component insertion or Gaussian component update process based on S includes:

[0048] like Then according to For the cth (k+1) Initialize the c-th Gaussian component, and set the c-th Gaussian component... (k+1) A Gaussian component is inserted into the current joint probability density model; where... The c-th digit after k+1 updates (k+1) The mean vector of Gaussian components, The c-th digit after k+1 updates (k+1) The weights of the Gaussian components, The c-th digit after k+1 updates (k+1) The co-standard deviation matrix of the Gaussian components, where I is an identity matrix with the same dimension as the wind power sample. For the cth (k+1) The number of activations of each Gaussian component;

[0049] according to For c after k updates (k) The weights of each Gaussian component are regularized to obtain the weights of each Gaussian component after k+1 updates. Let be the weight of the j-th Gaussian component after k+1 updates;

[0050] like Then according to For j∈S, perform Gaussian component updates; where... Let the weight of the j-th Gaussian component be determined after k+1 updates. Let be the mean vector of the j-th Gaussian component after k+1 updates. Let be the costandard deviation matrix of the j-th Gaussian component after k+1 updates. Let be the activation count of the j-th Gaussian component after k+1 updates. For r k+1 Estimate the posterior probability of belonging to the j-th Gaussian component.

[0051] Among them, the cth (k+1) Each Gaussian component becomes a new Gaussian component. In the above formula,

[0052] To make r k+1 Substitution The value obtained; To make r k+1 Substitution The value obtained.

[0053] like After Gaussian component insertion, to ensure that the sum of the weights after the model update is still 1, the first c... (k) The weights of the Gaussian components are regularized. If The Gaussian components corresponding to the subscripts in S are updated. The update method used in this embodiment has locality, which avoids the influence of Gaussian components outside the set, thereby improving the model update speed and making the update more targeted.

[0054] In some possible implementations, the above-mentioned denoising process for the current joint probability density model includes:

[0055] Delete the Gaussian components that have been updated less frequently.

[0056] By dynamically identifying and removing Gaussian components with low update frequency, the signal-to-noise ratio of the model can be effectively improved and overfitting can be reduced.

[0057] The average number of updates to the model after k updates for:

[0058] After k update cycles, delete the Gaussian components that have been updated less frequently. The set S of Gaussian components to be deleted is... delete The definition is as follows: in, is the number of updates for the j-th Gaussian component; g∈(0,1) is a user-defined coefficient. The smaller the value, the higher the model complexity, and the more low-probability features are retained. Conversely, the lower the model complexity, the lower the fit to extreme and low-probability scenarios.

[0059] In some embodiments, fusing the Gaussian components of data-dense clusters includes:

[0060] Based on the eigenvalues ​​of the costandard deviation matrix, a set S of Gaussian components with anomalies in the costandard deviation matrix is ​​selected from the current joint probability density model. mix ;in, A is the number of Gaussian components in the current joint probability density model, f n (ω n ,μ n ,Σ n ) represents the nth Gaussian component in the current joint probability density model, ω n μ is the weight of the nth Gaussian component. n Let Σ be the mean vector of the nth Gaussian component. n Let λ be the co-standard deviation matrix of the nth Gaussian component. n,l For Σ n The l-th eigenvalue, d is the number of eigenvalues, and α is a preset coefficient, α∈(0,1); U n It is a matrix composed of eigenvectors; λ a,l Σ is the costandard deviation matrix of the a-th Gaussian component. a The l-th eigenvalue;

[0061] according to S mix Each Gaussian component in x is converted into its corresponding equivalent sample; n Let ω be the value of the equivalent sample corresponding to the nth Gaussian component. x This represents the weight of the equivalent sample;

[0062] The equivalent samples are used as the newly added sample set, according to s∈S c The current joint probability density model is locally updated; where S c ω is the set of indices of the Gaussian components for which this local update is needed; s The weight of the s-th Gaussian component before this local update; ω′ s The weight of the s-th Gaussian component after this local update; μ s Σ is the mean vector of the s-th Gaussian component before the local update; μ′ is the mean vector of the s-th Gaussian component after the local update; Σ s Σ′ is the co-standard deviation matrix of the s-th Gaussian component before this local update. s The co-standard deviation matrix of the s-th Gaussian component after this local update; τ′ s is the estimate of the posterior probability that the value of the equivalent sample belongs to the s-th Gaussian component; v is the number of samples in the generative model.

[0063] In this embodiment, since the probability density of the multidimensional Gaussian distribution is controlled by the eigenvectors of the covariance matrix for rotation and by the eigenvalues ​​for scaling, the eigenvalue λ can be selected... n,l Components smaller than a set value are used to filter out Gaussian components with excessively small distribution scales, i.e., to filter out Gaussian components with abnormal co-standard deviation matrices.

[0064] Due to S mix The Gaussian component in S has a small variance and a high distribution concentration. To integrate it with the nearby Gaussian components, S... mix The component in the vector is transformed into an equivalent sample located at its mean vector position, while having the same weight as the original component. Resetting the weights to zero removes the anomalous Gaussian components.

[0065] In the formula for local updates described above, S c ={s|s∈{1,2,...,b},M s (x n ) <T s}; s = 1, 2, ..., b; M s (x n ) is the equivalent sample x n The Mahalanobis distance to the s-th Gaussian component, where b is the number of Gaussian components in the current joint probability density model.

[0066] In some possible implementations, based on the wind power sample distribution domain, the process of determining the marginal distribution probability density model of the random variable of wind power prediction using the Gaussian fusion method and the improved online adaptive kernel density method is similar to the process of determining the joint probability density model of multiple random variables, except that the random variables are different. The process of determining the joint probability density model of multiple random variables can be referred to.

[0067] Specifically, based on the needs of marginal probability distribution calculation, wind power prediction sample data x is extracted from the total sample data. i (i = 1, ..., N). Calculate the marginal distribution of the random variable X, and establish a marginal distribution probability density model through the improved online adaptive kernel density estimation described above. This model is then used to analyze the wind power prediction sample data sequence x. i Inputting each of the variables (i = 1, ..., N) sequentially, the model is updated through a similar update process to the joint probability density model of multiple random variables described above. The final result is the marginal distribution probability density model of the random variable for wind power prediction, expressed as: N(x; μ) h ,σ h Let ω be the h-th Gaussian density function of the random variable X; h The weights of the h-th Gaussian density function are... μh σ is the mean of the h-th Gaussian density function; h Let H be the standard deviation of the h-th Gaussian density function; H is the number of Gaussian density functions.

[0068] Step 103: Determine the conditional probability density model of the random variable of wind power prediction error based on the joint probability density model of multiple random variables and the marginal distribution probability density model of the random variable of wind power prediction value.

[0069] Conditional probability is the probability distribution of the wind power prediction error random variable Y, based on the known wind power prediction value random variable X.

[0070] In some embodiments, step 103 above may include:

[0071] according to Determine the conditional probability density model f of the random variable for wind power prediction error Y|X (y|x); where f X,Y (x,y) is a joint probability density model of multiple random variables; f X (x) is the marginal distribution probability density model of the random variable of wind power prediction value.

[0072] Based on the definition of conditional probability, the conditional probability density model of the random variable of wind power prediction error can be determined using the above formula. The conditional probability density model of the random variable of wind power prediction error can also be called the conditional probability density function of the random variable of wind power prediction error.

[0073] Step 104: Based on the domain of the wind power sample distribution, the conditional probability density model is modified to obtain the modified conditional probability density model. Based on the modified conditional probability density model, the confidence interval and point prediction value of the wind power prediction error are determined.

[0074] In some embodiments, the conditional probability density model is modified based on the domain of the wind power sample distribution domain to obtain a modified conditional probability density model, including:

[0075] according to The out-of-domain portion (i.e., the extra-boundary portion or overflow portion) of the conditional probability density model is truncated, and the out-of-domain portion is superimposed onto the in-domain portion (i.e., the actual distribution domain) in a uniform distribution manner to obtain the modified conditional probability density model f′. Y|X (y|x);

[0076] Where y represents the data of the random variable Y for wind power prediction error; x represents the data of the random variable X for wind power prediction value; f Y|X (y|x) represents the conditional probability density model; u represents the cumulative probability outside the defined domain of the wind power sample distribution.

[0077] The wind power sample distribution domain has a defined domain, i.e., it is bounded, and the range of values ​​for the random variables within it is: Since the distribution domain length is equal to 1, the uniform distribution density value is equal to the cumulative probability value. The above equation uniformly superimposes u onto the original density function f within the domain. Y|X On (y|x), obtain the modified conditional probability density model f′. Y|X (y|x). This method avoids changing the peak position of the original distribution function and reasonably designs the probability distribution outside the domain, so that the cumulative probability value within the interval is 1.

[0078] In some embodiments, determining the confidence interval and point prediction value of wind power prediction error based on the modified conditional probability density model includes:

[0079] according to Determine the confidence interval of wind power prediction error at confidence level c [L] c U c ]; where f′ Y|X (y|x) is the modified conditional probability density model;

[0080] The expected value E(y|x) of the modified conditional probability density model is used as the point prediction value of the wind power prediction error.

[0081] Among them, L c U is the lower limit of the confidence interval. c This represents the upper limit of the confidence interval.

[0082] Because of f′ Y|X (y|x) is a one-dimensional Gaussian mixture density function. According to the definition of a confidence interval, its upper and lower limits at confidence level c are respectively: the cumulative probability density is equal to... The position of U can be determined using the above formula and a value-finding algorithm. c and L c The specific value.

[0083] Based on the modified conditional probability density model, the point prediction results of the error can be calculated. Let f′ Y|X The expected value E(y|x) is used as the point prediction value of the wind power prediction error.

[0084] After the actual prediction error occurs, the new wind power samples can be fed back to step 102 for real-time model updates.

[0085] This invention preprocesses a wind power sample set to obtain the wind power sample distribution domain and analyzes its distribution characteristics. It improves upon the shortcomings of the online adaptive kernel density method by using a Gaussian fusion method, reducing overfitting and unsmoothness of the model. By modifying the conditional probability density model based on the domain of the wind power sample distribution domain, a modified conditional probability density model is obtained, which solves the probability density leakage problem in bounded data modeling and improves model accuracy. Furthermore, based on the improved online adaptive kernel density method and the principle of conditional probability, a new method for constructing the conditional probability density model is proposed. Specifically, a method of probability density truncation and accumulation is proposed to address the probability density leakage problem in the original model during bounded data modeling. A method for obtaining prediction intervals and point prediction values ​​at a certain confidence level based on the conditional probability model is also proposed. In summary, the probability prediction accuracy and point prediction accuracy of the method in this application are superior to traditional methods, solving the technical problems of uncertainty modeling under unknown distribution types of wind power prediction errors, rapid online updating of prediction models, and insufficient wind power prediction accuracy. At the same time, this application comprehensively considers various factors and is convenient for engineering implementation, thus possessing good engineering promotion value.

[0086] In some possible implementations, the multiple random vectors in the above formula can be two-dimensional random vectors, or they can be three-dimensional or higher random vectors. The specific implementation methods are similar and will not be described in detail here.

[0087] Figure 3 This demonstrates the workflow architecture for modeling and predicting wind power forecasting errors. It includes model training, which focuses on sample preprocessing and model updating, and model prediction, which focuses on calculating the conditional probability density function of the prediction error. See also... Figure 3 In the model prediction, the power output prediction value is obtained through short-term power prediction of the wind farm. Ultimately, probability prediction results, interval prediction results, and point prediction results can be obtained.

[0088] Figure 4 The diagram shows a joint probability density model of the wind power prediction value and the wind power prediction error obtained after step 102. The two horizontal axes in the diagram are the wind power prediction value and the prediction error value, respectively, and the vertical axis is their joint probability density value. It can be seen that the joint distribution is multi-peaked, and the power output of WF1 is significantly greater than that of WF2 and WF3.

[0089] This embodiment constructs comparative examples to illustrate the superiority of this application and uses the following indicators to evaluate the prediction accuracy:

[0090] (1) Uncertainty prediction evaluation indicators

[0091] The accuracy of the prediction of the sample distribution is evaluated using the average coverage error (ACE) and regional sharpness (IS).

[0092]

[0093] ACE = PINC-PICP

[0094] In the formula, PICP is the average coverage rate, which reflects the probability that the confidence interval actually contains the real sample; PINC is the nominal confidence level, which is the nominal probability that the confidence interval contains the sample. , respectively, represent the upper and lower limits of the interval under PINC; 1(·) is the indicator function, which has a value of 1 when the condition of (·) is met, and a value of 0 otherwise; ACE is the average coverage error, which is the difference between the actual coverage and the nominal coverage (confidence level).

[0095]

[0096]

[0097] In the formula, IS represents the average interval sharpness at confidence level c. Let be the sharpness of the distribution for the i-th sample at confidence level c. The smaller the sharpness value, the further the sample is from the confidence interval, and the worse the distribution's ability to describe the sample.

[0098] (2) Evaluation Indicators for Deterministic Prediction

[0099] The sum of squared errors (SSE) and mean squared error (MSE) are used to evaluate the accuracy of point prediction.

[0100]

[0101] In the formula, SSE is the sum of squared errors. y i These are the model prediction and the actual sample value, respectively.

[0102]

[0103] In the formula, MSE is the mean square error.

[0104] The proposed method (oKDE) is compared with adaptive smoothing kernel density estimation (aKDE), Gaussian parameter estimation (GE), and the original oKDE without Gaussian fusion improvement and density leakage processing. The uncertainty prediction accuracy (0.9 confidence level) and deterministic prediction accuracy of each method are shown in Tables 1 and 2.

[0105] As shown in Table 1, the fitting distribution accuracy of the oKDE method proposed in this application is better than that of aKDE, GE and the original oKDE. This shows that the improved oKDE has a strong ability to fit the data distribution and has better adaptability to multi-peak distributions, which verifies the superiority of the method in wind power uncertainty prediction.

[0106] As shown in Table 2, the point prediction accuracy of the oKDE proposed in this application is similar to that of the original oKDE, and is generally higher than that of aKDE and GE, but sometimes slightly lower than that of aKDE. This indicates that the method in this application has good accuracy in deterministic wind power prediction.

[0107] The above calculation results show that the method of this application performs well in wind power probability prediction and also has good point prediction accuracy, which has practical application value.

[0108] Table 1 Comparison of Uncertainty Prediction Accuracy (0.9 Confidence Level)

[0109]

[0110]

[0111] Table 2 Comparison of Deterministic Prediction Accuracy

[0112]

[0113] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0114] The following are device embodiments of the present invention. For details not described in detail, please refer to the corresponding method embodiments described above.

[0115] Figure 5 A schematic diagram of the wind power prediction error uncertainty modeling device provided in an embodiment of the present invention is shown. For ease of explanation, only the parts related to the embodiment of the present invention are shown, and are described in detail below:

[0116] like Figure 5 As shown, the wind power prediction error uncertainty modeling device 50 includes: a preprocessing module 51, an improvement module 52, a conditional probability density model determination module 53, and a correction module 54.

[0117] The preprocessing module 51 is used to acquire a wind power sample set and preprocess the wind power sample set to obtain the wind power sample distribution domain.

[0118] Improved module 52 is used to determine the joint probability density model of multiple random variables and the marginal distribution probability density model of the random variables of wind power prediction values ​​based on the distribution domain of wind power samples, using the Gaussian fusion method and the improved online adaptive kernel density method.

[0119] The conditional probability density model determination module 53 is used to determine the conditional probability density model of the random variable of wind power prediction error based on the joint probability density model of multiple random variables and the marginal distribution probability density model of the random variable of wind power prediction value.

[0120] The correction module 54 is used to correct the conditional probability density model based on the domain of the wind power sample distribution domain, to obtain the corrected conditional probability density model, and to determine the confidence interval and point prediction value of the wind power prediction error based on the corrected conditional probability density model.

[0121] In one possible implementation, the wind power sample set is preprocessed in preprocessing module 51 to obtain the wind power sample distribution domain, including:

[0122] according to The wind power sample set is normalized to obtain the wind power sample distribution domain;

[0123] Among them, the i-th wind power sample in the wind power sample set This is the original value for the predicted power output of the i-th wind farm. This represents the original value of the prediction error for the i-th wind farm. S represents the original actual power output of the i-th wind farm; WF Let r be the installed capacity of the wind farm; and r be the normalized wind power sample corresponding to the i-th wind power sample. i =(x i ,y i ,z i ), x i Let y be the normalized predicted output value of the i-th wind farm. i Let z be the normalized prediction error value for the i-th wind farm. i z represents the normalized actual power output of the i-th wind farm; 1 ≤ i ≤ N, where N is the number of wind farm samples in the wind farm sample set; i =x i +y i ;x i ∈[0,1],y i ∈[-x i ,1-x i ], z i ∈[0,1].

[0124] In one possible implementation, in the improved module 52, based on the wind power sample distribution domain, a Gaussian fusion method is used to improve the online adaptive kernel density method to determine the joint probability density model of multiple random variables, including:

[0125] Initialize the update count k, and determine the joint probability density model of the wind power prediction value random variable X and the wind power prediction error random variable Y after k updates.

[0126] Obtain the (k + 1)-th normalized wind power sample r in the wind power sample distribution domain. k+1 , and based on r k+1 and perform Gaussian component activation to obtain the set S of subscripts of the activated Gaussian components, and based on S, perform Gaussian component insertion or Gaussian component update processing;

[0127] Perform noise reduction processing on the current joint probability density model, and fuse the Gaussian components in the data-intensive aggregation area to obtain the joint probability density model of the wind power prediction value random variable X and the wind power prediction error random variable Y after (k + 1) updates;

[0128] If k + 1 < N, increment k by 1 to get a new k, and jump to the step of obtaining the (k + 1)-th normalized wind power sample r in the wind power sample distribution domain k+1 and execute it in a loop;

[0129] If k + 1 ≥ N, use the joint probability density model of the wind power prediction value random variable X and the wind power prediction error random variable Y after (k + 1) updates as the joint probability density model of multiple random variables; N is the number of wind power samples in the wind power sample set.

[0130] In a possible implementation, in the improvement module 52, where, is the weight of the j-th Gaussian component after k updates, is the mean vector of the j-th Gaussian component after k updates, is the covariance matrix of the j-th Gaussian component after k updates, is the j-th Gaussian probability density function after k updates, c (k) is the number of Gaussian probability density functions after k updates,

[0131] Correspondingly, based on r k+1 and perform Gaussian component activation to obtain the set S of subscripts of the activated Gaussian components, including:

[0132] According to j = 1, 2, …, c (k) , calculate the Mahalanobis distance between r k+1 and each Gaussian component; M j (r k+1 ) is r k+1The Mahalanobis distance between the j-th Gaussian component and the j-th component;

[0133] According to r k+1 The Mahalanobis distances to each Gaussian component determine the set of indices S of the activated Gaussian components; where S = {j | j ∈ {1, 2, ..., c} (k)},M j (r k+1 ) <T j};T j is the activation threshold for the j-th Gaussian component.

[0134] In one possible implementation, in the improved module 52, based on S, Gaussian component insertion or Gaussian component update processing is performed, including:

[0135] like Then according to For the cth (k+1) Initialize the c-th Gaussian component, and set the c-th Gaussian component... (k+1) A Gaussian component is inserted into the current joint probability density model; where... The c-th digit after k+1 updates (k+1) The mean vector of Gaussian components, The c-th digit after k+1 updates (k+1) The weights of the Gaussian components, The c-th digit after k+1 updates (k+1) The co-standard deviation matrix of the Gaussian components, where I is an identity matrix with the same dimension as the wind power sample. For the cth (k+1) The number of activations of each Gaussian component;

[0136] according to For c after k updates (k) The weights of each Gaussian component are regularized to obtain the weights of each Gaussian component after k+1 updates. Let be the weight of the j-th Gaussian component after k+1 updates;

[0137] like Then according to For j∈S, perform Gaussian component updates; where... Let the weight of the j-th Gaussian component be determined after k+1 updates. Let be the mean vector of the j-th Gaussian component after k+1 updates. Let be the costandard deviation matrix of the j-th Gaussian component after k+1 updates. Let be the activation count of the j-th Gaussian component after k+1 updates. For r k+1 Estimate the posterior probability of belonging to the j-th Gaussian component.

[0138] In one possible implementation, in the improvement module 52, the Gaussian components of the data-dense clustering region are fused, including:

[0139] Based on the eigenvalues ​​of the costandard deviation matrix, a set S of Gaussian components with anomalies in the costandard deviation matrix is ​​selected from the current joint probability density model. mix ;in, A is the number of Gaussian components in the current joint probability density model, f n (ω n ,μ n ,Σ n ) represents the nth Gaussian component in the current joint probability density model, ω n μ is the weight of the nth Gaussian component. n Let Σ be the mean vector of the nth Gaussian component. n Let λ be the co-standard deviation matrix of the nth Gaussian component. n,l For Σ n The l-th feature value, d is the number of such feature values, and α is a preset coefficient;

[0140] according to S mix Each Gaussian component in x is converted into its corresponding equivalent sample; n Let ω be the value of the equivalent sample corresponding to the nth Gaussian component. x This represents the weight of the equivalent sample;

[0141] The equivalent samples are used as the newly added sample set, according to s∈S c The current joint probability density model is locally updated; where S c ω is the set of indices of the Gaussian components for which this local update is needed; s The weight of the s-th Gaussian component before this local update; ω′ s The weight of the s-th Gaussian component after this local update; μ s Σ is the mean vector of the s-th Gaussian component before the local update; μ′ is the mean vector of the s-th Gaussian component after the local update; Σ s Σ′ is the co-standard deviation matrix of the s-th Gaussian component before this local update. s The co-standard deviation matrix of the s-th Gaussian component after this local update; τ′ s is the estimate of the posterior probability that the value of the equivalent sample belongs to the s-th Gaussian component; v is the number of samples in the generative model.

[0142] In one possible implementation, the conditional probability density model determination module 53 is specifically used for:

[0143] according to Determine the conditional probability density model f of the random variable for wind power prediction error Y|X (y|x); where f X,Y (x,y) is a joint probability density model of multiple random variables; f X (x) is the marginal distribution probability density model of the random variable of wind power prediction value.

[0144] In one possible implementation, the conditional probability density model is modified in the correction module 54 based on the domain of the wind power sample distribution domain, resulting in a modified conditional probability density model, including:

[0145] according to The out-of-domain portion of the conditional probability density model is truncated, and the out-of-domain portion is superimposed onto the in-domain portion in a uniform distribution to obtain the modified conditional probability density model f′. Y|X (y|x);

[0146] Where y represents the data of the random variable Y for wind power prediction error; x represents the data of the random variable X for wind power prediction value; f Y|X (y|x) is the conditional probability density model; u is the cumulative probability outside the defined domain of the wind power sample distribution.

[0147] In one possible implementation, in correction module 54, based on the corrected conditional probability density model, the confidence interval and point prediction value of the wind power prediction error are determined, including:

[0148] according to Determine the confidence interval of wind power prediction error at confidence level c [L] c U c ]; where f′ Y|X (y|x) is the modified conditional probability density model;

[0149] The expected value of the modified conditional probability density model is used as the point prediction value of the wind power prediction error.

[0150] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0151] Those skilled in the art will recognize that the templates, units, and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0152] If the module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various wind power prediction error uncertainty modeling method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory, a random access memory, an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0153] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for modeling the uncertainty of wind power prediction errors, characterized in that, include: Obtain a wind power sample set and preprocess the wind power sample set to obtain the wind power sample distribution domain; Based on the wind power sample distribution domain, a Gaussian fusion method is used to improve the online adaptive kernel density method, thereby determining the joint probability density model of multiple random variables and the marginal distribution probability density model of the random variables of wind power prediction values. Based on the joint probability density model of the multiple random variables and the marginal distribution probability density model of the random variable of wind power prediction value, the conditional probability density model of the random variable of wind power prediction error is determined. Based on the defined domain of the wind power sample distribution domain, the conditional probability density model is modified to obtain the modified conditional probability density model. Based on the modified conditional probability density model, the confidence interval and point prediction value of the wind power prediction error are determined. Based on the aforementioned wind power sample distribution domain, a Gaussian fusion method and an improved online adaptive kernel density method are used to determine the joint probability density model of multiple random variables, including: Initialize the number of updates k, and determine the joint probability density model of the random variable X of wind power prediction value and the random variable Y of wind power prediction error after k updates. Obtain the (k+1)th normalized wind power sample r in the wind power sample distribution domain. k+1 And according to the r k+1 and stated Perform Gaussian component activation to obtain the set of indices S of the activated Gaussian components, and perform Gaussian component insertion or Gaussian component update processing based on S. The current joint probability density model is denoised, and the Gaussian components of the data-dense clustering area are fused to obtain the joint probability density model of the wind power prediction value random variable X and the wind power prediction error random variable Y after k+1 updates. If k + 1 < N, then increment k by 1 to obtain a new k, and jump to the step of obtaining the (k + 1)-th normalized wind power sample r in the wind power sample distribution domain k+1 and loop through the steps If k+1≥N, then the joint probability density model of the random variable X of wind power prediction value after k+1 updates and the random variable Y of wind power prediction error is taken as the joint probability density model of the multiple random variables; N is the number of wind power samples in the wind power sample set. in, Let the weight of the j-th Gaussian component be determined after k updates. Let be the mean vector of the j-th Gaussian component after k updates. Let be the costandard deviation matrix of the j-th Gaussian component after k updates. Let c be the j-th Gaussian probability density function after k updates. (k) Let k be the number of Gaussian probability density functions after k updates. Accordingly, the statement based on the r k+1 and stated Perform Gaussian component activation to obtain the set S of indices of the activated Gaussian components, including: according to Calculate the r k+1 and the Mahalanobis distance of each of the Gaussian components; M j (r k+1 ) is the r k+1 The Mahalanobis distance between the j-th Gaussian component and the j-th component; According to the r k+1 The Mahalanobis distances of the Gaussian components are used to determine the set of indices S of the activated Gaussian components; where S = {j | j ∈ {1, 2, ..., c} (k) },M j (r k+1 ) <T j };T j is the activation threshold for the j-th Gaussian component; The step of determining the conditional probability density model of the wind power prediction error random variable based on the joint probability density model of the multiple random variables and the marginal distribution probability density model of the wind power prediction value random variable includes: according to Determine the conditional probability density model f of the random variable for wind power prediction error Y|X (y|x); where f X,Y (x,y) is the joint probability density model of the multiple random variables; f X (x) is the marginal distribution probability density model of the random variable of the wind power prediction value; The conditional probability density model is modified based on the domain defined by the wind power sample distribution domain to obtain the modified conditional probability density model, including: according to The out-of-domain portion of the conditional probability density model is truncated, and the out-of-domain portion is superimposed onto the in-domain portion in a uniform distribution to obtain the modified conditional probability density model f′. Y|X (y|x); Where y is the data of the random variable Y of wind power prediction error; x is the data of the random variable X of wind power prediction value; and u is the cumulative probability outside the defined domain of the wind power sample distribution domain.

2. The wind power prediction error uncertainty modeling method according to claim 1, characterized in that, The preprocessing of the wind power sample set to obtain the wind power sample distribution domain includes: according to The wind power sample set is normalized to obtain the wind power sample distribution domain; Among them, the i-th wind power sample in the wind power sample set This is the original value for the predicted power output of the i-th wind farm. This represents the original value of the prediction error for the i-th wind farm. S represents the original actual power output of the i-th wind farm; WF Let r be the installed capacity of the wind farm; and r be the normalized wind power sample corresponding to the i-th wind power sample. i =(x i ,y i ,z i ), x i Let y be the normalized predicted output value of the i-th wind farm. i Let z be the normalized prediction error value for the i-th wind farm. i The normalized actual power output value of the i-th wind farm; 1≤i≤N, where N is the number of wind farm samples in the wind power sample set; z i =x i +y i ;x i ∈[0,1],y i ∈[-x i ,1-x i ], z i ∈[0,1].

3. The wind power prediction error uncertainty modeling method according to claim 1, characterized in that, The Gaussian component insertion or Gaussian component update process based on S includes: like Then according to For the cth (k+1) Initialize the c-th Gaussian component, and then initialize the c-th Gaussian component. (k+1) A Gaussian component is inserted into the current joint probability density model; where... The c-th digit after k+1 updates (k+1) The mean vector of Gaussian components, The c-th digit after k+1 updates (k+1) The weights of the Gaussian components, The c-th digit after k+1 updates (k+1) The co-standard deviation matrix of the Gaussian components, where I is an identity matrix with the same dimension as the wind power sample. For the cth (k+1) The number of activations of each Gaussian component; according to For c after k updates (k) The weights of each Gaussian component are regularized to obtain the weights of each Gaussian component after k+1 updates. Let be the weight of the j-th Gaussian component after k+1 updates; like Then according to Perform Gaussian component updates; where, Let the weight of the j-th Gaussian component be determined after k+1 updates. Let be the mean vector of the j-th Gaussian component after k+1 updates. Let be the costandard deviation matrix of the j-th Gaussian component after k+1 updates. Let be the activation count of the j-th Gaussian component after k+1 updates. For the r k+1 Estimate the posterior probability of belonging to the j-th Gaussian component.

4. The wind power prediction error uncertainty modeling method according to claim 1, characterized in that, The fusion of Gaussian components in densely clustered data areas includes: Based on the eigenvalues ​​of the costandard deviation matrix, a set S of Gaussian components with anomalies in the costandard deviation matrix is ​​selected from the current joint probability density model. mix ;in, A is the number of Gaussian components in the current joint probability density model, f n (ω n ,μ n ,Σ n ) represents the nth Gaussian component in the current joint probability density model, ω n μ is the weight of the nth Gaussian component. n Let Σ be the mean vector of the nth Gaussian component. n Let λ be the co-standard deviation matrix of the nth Gaussian component. n,l For Σ n The l-th feature value, d is the number of such feature values, and α is a preset coefficient; according to S mix Each Gaussian component in x is converted into its corresponding equivalent sample; n Let ω be the value of the equivalent sample corresponding to the nth Gaussian component. x This represents the weight of the equivalent sample; The equivalent samples are used as the newly added sample set, according to The current joint probability density model is locally updated; where S c ω is the set of indices of the Gaussian components for which this local update is needed; s The weight of the s-th Gaussian component before this local update; ω s ′ represents the weight of the s-th Gaussian component after this local update; μ s Σ is the mean vector of the s-th Gaussian component before the local update; μ′ is the mean vector of the s-th Gaussian component after the local update; Σ s Σ′ is the co-standard deviation matrix of the s-th Gaussian component before this local update. s τ is the co-standard deviation matrix of the s-th Gaussian component after this local update; s ′ represents the posterior probability estimate of the equivalent sample's value belonging to the s-th Gaussian component; v represents the number of samples in the generative model.

5. The wind power prediction error uncertainty modeling method according to any one of claims 1 to 4, characterized in that, The process of determining the confidence interval and point prediction value of wind power prediction error based on the modified conditional probability density model includes: according to Determine the confidence interval of wind power prediction error at confidence level c [L] c U c ]; where f′ Y|X (y|x) represents the modified conditional probability density model; The expected value of the modified conditional probability density model is used as the point prediction value of the wind power prediction error.

6. A device for modeling uncertainty in wind power prediction errors, characterized in that, The method for performing the wind power prediction error uncertainty modeling method according to any one of claims 1 to 5 includes: The preprocessing module is used to acquire a wind power sample set and preprocess the wind power sample set to obtain the wind power sample distribution domain. The improved module is used to determine the joint probability density model of multiple random variables and the marginal distribution probability density model of the random variables of wind power prediction values ​​based on the distribution domain of the wind power samples, using the Gaussian fusion method and the improved online adaptive kernel density method. The conditional probability density model determination module is used to determine the conditional probability density model of the wind power prediction error random variable based on the joint probability density model of the multiple random variables and the marginal distribution probability density model of the wind power prediction value random variable. The correction module is used to correct the conditional probability density model based on the domain of the wind power sample distribution domain, to obtain the corrected conditional probability density model, and to determine the confidence interval and point prediction value of the wind power prediction error based on the corrected conditional probability density model.

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