Wind power probability prediction method and device based on kernel density estimation and copula

Abstract

The present invention discloses a method and device for wind power probability prediction based on kernel density estimation and copula. This method obtains currently predicted wind power data and currently predicted wind speed data; inputs these data into a wind power probability prediction model to obtain the conditional probability density of the currently predicted wind power and its confidence interval. The wind power probability prediction model is modeled using a historical sample dataset, kernel density estimation, and a copula function. This technical solution improves the accuracy of wind power probability prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of wind power probability prediction, and in particular to a method and device for wind power probability prediction based on kernel density estimation and copula. Background Art

[0002] In recent years, with the decline of non-renewable energy and the advent of the "dual carbon" strategy, the application and development of clean energy has increased. Wind power, due to its technological maturity, ease of access, and scalability, has been widely developed and applied. Wind power exhibits significant intermittent and fluctuating characteristics, making accurate wind power forecasting crucial for its large-scale grid integration and the safe operation of power systems. Current research on wind power forecasting focuses on point-based prediction techniques, but point-based predictions fail to provide information on the fluctuation range and distribution of wind power. Probabilistic wind power forecasting can demonstrate this fluctuation range and distribution, providing additional information for wind power-inclusive grid planning, operation, and safety and stability analysis.

[0003] Wind power probabilistic forecasting can be divided into parametric and non-parametric methods. Parametric probabilistic forecasting utilizes prior information, artificially assuming that wind power satisfies a certain probability distribution model. The known information is then used to estimate the distribution model parameters, ultimately yielding a parameterized probability distribution. Wind power exhibits strong random volatility, and its distribution often exhibits significant polymorphism and fat-tail characteristics, making it difficult to accurately model using simple parametric distribution models. Therefore, non-parametric models are more suitable for quantifying wind power uncertainty. Wind power distribution is strongly correlated with factors such as wind speed and historical wind power. Therefore, in practice, wind power probabilistic forecasting often requires its conditional probability distribution. A commonly used approach is to use the non-parametric method of kernel density estimation to construct univariate or multivariate marginal density functions for wind speed, historical wind power, and predicted wind power. These functions are then directly divided according to the definition of the conditional probability density to obtain the final conditional probability density function. However, these methods ignore the interdependencies among wind speed, historical wind power, and predicted wind power, thereby reducing the accuracy and precision of wind power probabilistic forecasts. Summary of the Invention

[0004] The present invention provides a method and device for wind power probability prediction based on kernel density estimation and copula, which improves the accuracy of wind power probability prediction.

[0005] An embodiment of the present invention provides a method for wind power probability prediction based on kernel density estimation and copula, comprising the following steps:

[0006] Acquiring a current prediction data set, wherein the current prediction data set includes currently predicted wind power data and currently predicted wind speed data;

[0007] The wind power data and wind speed data are input into a wind power probability prediction model to obtain the conditional probability density of the currently predicted wind power and the confidence interval of the conditional probability density; the wind power probability prediction model is obtained by modeling based on a historical sample data set, a kernel density estimation method, and a Copula function.

[0008] Furthermore, the wind power probability prediction model is established based on the historical sample data set, the kernel density estimation method and the Copula function, including the following steps:

[0009] Establishing marginal probability distribution models of actual wind power, predicted wind power, and actual wind speed respectively based on a historical sample data set and a kernel density estimation method; the historical sample data set includes historical actual wind power data, historical predicted wind power data, and historical actual wind speed data;

[0010] On the basis of the marginal probability distribution models of the actual wind power, the predicted wind power and the actual wind speed, a first joint probability distribution model and a second joint probability distribution model are established according to a Copula function;

[0011] A wind power probability prediction model is established based on the first joint probability distribution model and the second joint probability distribution model.

[0012] Furthermore, a first joint probability distribution model of the marginal probability distribution model of the actual wind power, the marginal probability distribution model of the predicted wind power, and the marginal probability distribution model of the actual wind speed is established according to the Copula function;

[0013] A second joint probability distribution model of the marginal probability distribution model of the predicted wind power and the marginal probability distribution model of the actual wind speed is established according to the Copula function.

[0014] Furthermore, the marginal probability distribution model of the actual wind power is:

[0015]

[0016] In the formula, x is the historical actual wind power data, n is the total number of samples, and x i is the i-th sample data, and h is the bandwidth value.

[0017] Furthermore, the bandwidth value is determined according to the rule of thumb and the grid search method.

[0018] Furthermore, the first joint probability distribution model is specifically:

[0019]

[0020] Where, f X (x), f Y (y) and f Z (z) are the marginal probability density functions of actual wind power, predicted wind power and actual wind speed, respectively, and F X (x), F F (f) and F Z (z) are the marginal probability distribution functions of actual wind power, predicted wind power and actual wind speed, respectively, and c is the probability density function of the Copula function.

[0021] Furthermore, the wind power probability prediction model is specifically as follows:

[0022]

[0023] Where, is the current predicted wind power data, is the current predicted wind speed data, for The corresponding marginal probability distribution function is, for The corresponding marginal probability distribution function.

[0024] Furthermore, the current prediction data set and the historical sample data set are preprocessed, including the following steps:

[0025] Linear interpolation is used to fill missing values ​​in the data set;

[0026] For outliers in the data set that exceed the parameter limit, replace the outliers according to the parameter limit;

[0027] The box plot method is used to identify outliers in the processed data set and the linear interpolation method is used to replace the identified outliers.

[0028] Another embodiment of the present invention provides a wind power probability prediction device based on kernel density estimation and copula, comprising a prediction data acquisition module and a wind power probability prediction module;

[0029] The prediction data acquisition module is used to acquire a current prediction data set, wherein the current prediction data set includes currently predicted wind power data and currently predicted wind speed data;

[0030] The wind power probability prediction module is used to input the wind power data and wind speed data into the wind power probability prediction model to obtain the conditional probability density of the currently predicted wind power and the confidence interval of the conditional probability density; the wind power probability prediction model is obtained by modeling based on the historical sample data set, kernel density estimation method and Copula function.

[0031] The embodiments of the present invention have the following beneficial effects:

[0032] The present invention provides a method and device for wind power probability prediction based on kernel density estimation and copula. The method, based on historical wind power data, historical predicted wind power data, historical actual wind speed data, and predicted wind speed data, utilizes kernel density estimation and Copula theory to estimate the probability distribution of wind power under wind speed and predicted power conditions. The method uses historical wind power, predicted wind power, and wind speed as variables and uses kernel density estimation to estimate the marginal distribution of each variable. Then, based on Copula theory, the joint distribution of multiple variables is estimated to obtain a wind power probability prediction model (i.e., a conditional probability prediction model). Finally, the wind power probability prediction model calculates the conditional probability density and fluctuation range of wind power under specified predicted wind power and specified predicted wind speed (i.e., current predicted wind power data and current predicted wind speed data). Therefore, by using Copula theory to estimate the joint probability distribution of multiple variables when establishing a wind power probability prediction model based on a historical sample data set, kernel density estimation, and Copula functions, the accuracy and precision of the model for wind power probability prediction are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 1 is a flow chart of a method for wind power probability prediction based on kernel density estimation and copula provided by an embodiment of the present invention;

[0034] Figure 2 It is a structural diagram of a wind power probability prediction device based on kernel density estimation and copula provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0035] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0036] like Figure 1 As shown, an embodiment of the present invention provides a wind power probability prediction method based on kernel density estimation and copula, comprising the following steps:

[0037] Step S101: obtaining a current prediction data set, where the current prediction data set includes currently predicted wind power data and currently predicted wind speed data.

[0038] Step S102: Input the wind power data and wind speed data into a wind power probability prediction model to obtain the conditional probability density of the currently predicted wind power and the confidence interval of the conditional probability density; the wind power probability prediction model is obtained by modeling based on a historical sample data set, a kernel density estimation method, and a Copula function.

[0039] As one embodiment, the wind power probability prediction model is established according to the following steps:

[0040] Step A01: Based on a historical sample data set and a kernel density estimation method, marginal probability distribution models of actual wind power, predicted wind power, and actual wind speed are respectively established; the historical sample data set includes historical actual wind power data, historical predicted wind power data, and historical actual wind speed data, and there is a corresponding relationship between the historical actual wind power, historical predicted wind power data, and historical actual wind speed data.

[0041] Select Gaussian function As a kernel function for kernel density estimation, the kernel function meets the requirements of symmetry, regularity and attenuation.

[0042] A marginal probability distribution model of actual wind power is established based on the historical actual wind power data and the kernel function:

[0043]

[0044] A marginal probability distribution model for predicting wind power is established based on the historical predicted wind power data and the kernel function:

[0045]

[0046] A marginal probability distribution model of actual wind speed is established based on the historical actual wind speed data and the kernel function:

[0047]

[0048] In marginal probability distribution models (1)-(3), x, y, and z are historical actual wind power data, historical predicted wind power data, and historical actual wind speed data, respectively. n is the total number of samples, i represents the i-th sample data, and h is the bandwidth value. The present invention uses kernel density estimation to estimate the marginal probability distributions of x, y, and z, respectively. The kernel density estimation method is to estimate a reasonable density function through the kernel density estimator.

[0049] The bandwidth value h determines the edge probability distribution model and The smoothness of the kernel density. If h is large, more data points will affect the probability density calculation here, and the corresponding curve of the model will be smoother at this point, but its deviation from the actual probability density curve will be larger. If h is small, fewer data points will affect the probability density calculation here, and the corresponding curve of the model will be steeper at this point, but its deviation from the actual probability density curve will be smaller. Therefore, in order to more accurately perform kernel density estimation, the selection of bandwidth h is particularly important.

[0050] Preferably, the bandwidth value h is determined according to the rule of thumb and the grid search method, specifically:

[0051] First, calculate the bandwidth range according to the rule of thumb. The optimal bandwidth calculation formula for the rule of thumb is:

[0052]

[0053] Where d is the dimension of the kernel density estimate and σ is the standard deviation of the random variable (i.e., x, y, or z).

[0054] The bandwidth value is calculated according to the rule of thumb and the bandwidth value interval is set to [0.8h, 1.2h]. Then the grid search method is used to search within the bandwidth value interval to determine the optimal bandwidth value.

[0055] Step A02: On the basis of the marginal probability distribution models of the actual wind power, the predicted wind power and the actual wind speed, a first joint probability distribution model and a second joint probability distribution model are established according to a Copula function.

[0056] Based on the marginal probability distribution models (1), (2) and (3), the joint probability distribution of x, y and z is estimated according to the Copula function:

[0057] F XYZ (x,y,z)=C(F X (x),F Y (y),F Z (z)) (5);

[0058] Where C is the Copula function of the dependency structure between the actual wind power and the predicted wind power of the wind farm.

[0059] Then, by taking the derivative of both sides of formula (5), we can obtain the first joint probability distribution model:

[0060]

[0061] Where, f X (x), f Y (y) and f Z(z) are the marginal probability density functions of actual wind power, predicted wind power and actual wind speed, respectively, and F X (x), F F (f) and F Z (z) are the marginal probability distribution functions of actual wind power, predicted wind power and actual wind speed, respectively; c is the probability density function of the Copula function, They represent the partial differentials of y and z, respectively. X, Y, and Z represent the random variables of actual wind power, predicted wind power, and actual wind speed, respectively. x, y, and z are the specific values ​​of the corresponding random variables.

[0062] Based on the marginal probability distribution models (2) and (3), the joint probability distribution of y and z is estimated according to the Copula function:

[0063] F YZ (y,z)=C(F Y (y),F Z (z)) (7);

[0064] Then, by taking the derivative of both sides of formula (7), we can obtain the second joint probability distribution model:

[0065]

[0066] Step A03: Establish a wind power probability prediction model based on the first joint probability distribution model and the second joint probability distribution model:

[0067]

[0068] Where, is the current predicted wind power data, is the current predicted wind speed data, for The corresponding marginal probability distribution function is, for The corresponding marginal probability distribution function.

[0069] When using the wind power probability prediction model for prediction, the currently predicted wind power data and the currently predicted wind speed data are input into the wind power probability prediction model to obtain the conditional probability density of the currently predicted wind power and the confidence interval of the conditional probability density.

[0070] Among them, the commonly used calculation method of the confidence interval is as follows:

[0071] P r (c1≤μ≤c2)=1-α (10)

[0072] α is the significance level (such as 0.05 or 0.10); Pr represents the probability; c1 and c2 are the lower and upper confidence limits of the random variable μ at the specified significance level.

[0073] The present invention adopts interval coverage PICP, average bandwidth As an evaluation indicator, the prediction effect of the wind power probability prediction model is verified. PICP represents the number of wind power actual values ​​that fall within the prediction interval. On the basis of meeting a certain confidence level 1-α, the closer its value is to 1-α, the better the prediction effect. It indicates the overall width of the estimated interval. When the same confidence level is met, the smaller the value, the narrower the prediction interval, which means that the prediction interval is closer to the actual value.

[0074]

[0075]

[0076] Where N is the total number of wind power to be predicted, i = 1, 2, ..., N; U i is the lower limit of the predicted value of the power i to be predicted, L i is the upper limit of the predicted value of the power i to be predicted; A i is an indicative function. When the actual value of wind power at the time i to be predicted falls within the prediction interval, A i The value is 1, otherwise it is 0.

[0077]

[0078] Where n is the number of test samples; ΔP pj is the jth estimation interval.

[0079] As one embodiment, the current prediction dataset (i.e., the designated prediction dataset) and the historical sample dataset are preprocessed according to the following steps:

[0080] Linear interpolation is used to fill missing values ​​in the data set;

[0081] For abnormal values ​​in the data set that exceed the parameter limits, the abnormal values ​​are replaced according to the parameter limits; the parameter limits are specifically the upper and lower limits of installed capacity, rated power and wind speed;

[0082] The box plot method is then used to identify outliers in the processed data set, and the linear interpolation method is used to replace the identified abnormal data.

[0083] By preprocessing the data set, the accuracy of estimating the marginal probability distribution of single variables and the joint probability distribution of multiple variables can be improved.

[0084] This method uses historical wind power data, historical forecasted wind power data, historical actual wind speed data, and forecasted wind speed data, and utilizes kernel density estimation and Copula theory to estimate the probability distribution of wind power under wind speed and forecasted power conditions. The method uses historical wind power, forecasted wind power, and wind speed as variables, and uses kernel density estimation to estimate the marginal distribution of each single variable. It then estimates the joint distribution of multiple variables based on Copula theory. Finally, based on a conditional probability forecast model, it calculates the conditional probability density and fluctuation range of wind power under specified forecasted wind power and forecasted wind speed, and evaluates the forecast range using two metrics: interval bandwidth and interval coverage.

[0085] Based on the above-mentioned embodiments of the invention, the present invention provides corresponding device embodiments, such as Figure 2 As shown;

[0086] Another embodiment of the present invention provides a wind power probability prediction device based on kernel density estimation and copula, comprising a prediction data acquisition module and a wind power probability prediction module;

[0087] The prediction data acquisition module is used to acquire a current prediction data set, wherein the current prediction data set includes currently predicted wind power data and currently predicted wind speed data;

[0088] The wind power probability prediction module is used to input the wind power data and wind speed data into the wind power probability prediction model to obtain the conditional probability density of the currently predicted wind power and the confidence interval of the conditional probability density; the wind power probability prediction model is obtained by modeling based on the historical sample data set, kernel density estimation method and Copula function.

[0089] For the convenience and brevity of description, the device embodiment of the present invention includes all the implementation methods in the above-mentioned wind power probability prediction method embodiment based on kernel density estimation and copula, which will not be repeated here.

[0090] Exemplarily, the computer program may be divided into one or more modules, which are stored in the memory and executed by the processor to implement the present invention. The one or more modules may be a series of computer program instruction segments capable of performing specific functions, and the instruction segments are used to describe the execution process of the computer program in the terminal device.

[0091] The terminal device may be a computing device such as a desktop computer, a notebook computer, a PDA, a cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0092] The processor may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc. The processor is the control center of the terminal device, connecting various parts of the entire terminal device using various interfaces and lines.

[0093] The memory can be used to store the computer programs and / or modules. The processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory. The memory can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system, at least one application required for a function (such as a sound playback function, an image playback function, etc.); the data storage area can store data created based on the use of the mobile phone (such as audio data, a phone book, etc.). In addition, the memory can include a high-speed random access memory and can also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, at least one disk storage device, a flash memory device, or other volatile solid-state storage device.

[0094] Wherein, if the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium (i.e., the above-mentioned readable storage medium). Based on this understanding, the present invention implements all or part of the process in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and when the computer program is executed by the processor, it can implement the steps of the above-mentioned various method embodiments. Wherein, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium, etc.

[0095] It should be noted that the device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed across multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present embodiment. In addition, in the drawings of the device embodiments provided by the present invention, the connection relationship between the modules indicates that there is a communication connection between them, which may be specifically implemented as one or more communication buses or signal lines. A person of ordinary skill in the art can understand and implement the present invention without inventive effort.

[0096] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications are also considered to be within the scope of protection of the present invention.

[0097] Those skilled in the art will appreciate that all or part of the processes in the above embodiments can be implemented by instructing the relevant hardware through a computer program. The program can be stored in a computer-readable storage medium, and when executed, the program can include the processes in the above embodiments. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

Claims

1. A wind power probability prediction method based on kernel density estimation and copula, characterized in that: The following steps are involved: Acquiring a current prediction data set, wherein the current prediction data set includes currently predicted wind power data and currently predicted wind speed data; Inputting the current prediction data set into a wind power probability prediction model to obtain the conditional probability density of the current predicted wind power and the confidence interval of the conditional probability density; wherein the wind power probability prediction model is to establish marginal probability distribution models of actual wind power, predicted wind power and actual wind speed respectively based on a historical sample data set and a kernel density estimation method; the historical sample data set includes historical actual wind power data, historical predicted wind power data and historical actual wind speed data; On the basis of the marginal probability distribution models of the actual wind power, the predicted wind power and the actual wind speed, a first joint probability distribution model and a second joint probability distribution model are established according to a Copula function; The method is established based on the first joint probability distribution model and the second joint probability distribution model; The first joint probability distribution model is specifically: Where x, y and z are historical actual wind power data, historical forecast wind power data and historical actual wind speed data respectively, and f X (x), f Y (y) and f Z (z) are the marginal probability density functions corresponding to x, y and z respectively, F X (x), F Y (y) and F Z (x) are the marginal probability distribution functions corresponding to x, y and z respectively, c is the probability density function of the Copula function, Respectively, they represent the partial differentials of y and x, X, Y, and Z represent the random variables of actual wind power, predicted wind power, and actual wind speed, respectively, and x, y, and z are the specific values ​​of the corresponding random variables; The second joint probability distribution model is specifically: The wind power probability prediction model is specifically: Where, is the current predicted wind power data, is the current predicted wind speed data, for The corresponding marginal probability distribution function is, for The corresponding marginal probability distribution function.

2. The wind power probability prediction method based on kernel density estimation and copula according to claim 1 is characterized in that: Establishing a first joint probability distribution model of the marginal probability distribution model of the actual wind power, the marginal probability distribution model of the predicted wind power, and the marginal probability distribution model of the actual wind speed according to the Copula function; A second joint probability distribution model of the marginal probability distribution model of the predicted wind power and the marginal probability distribution model of the actual wind speed is established according to the Copula function.

3. The wind power probability prediction method based on kernel density estimation and copula according to claim 2 is characterized in that: The marginal probability distribution model of the actual wind power is: In the formula, x is the historical actual wind power data, n is the total number of samples, and x i is the i-th sample data, and h is the bandwidth value.

4. The wind power probability prediction method based on kernel density estimation and copula according to claim 3 is characterized in that: The bandwidth value is determined based on the rule of thumb and grid search method.

5. The wind power probability prediction method based on kernel density estimation and copula according to any one of claims 1 to 4, characterized in that: Preprocessing the current prediction data set and the historical sample data set includes the following steps: Linear interpolation is used to fill missing values ​​in the data set; For outliers in the data set that exceed the parameter limit, replace the outliers according to the parameter limit; The box plot method is used to identify outliers in the processed data set and the linear interpolation method is used to replace the identified outliers.

6. A wind power probability prediction device based on kernel density estimation and copula, characterized in that: It includes a forecast data acquisition module and a wind power probability forecast module; The prediction data acquisition module is used to obtain the currently predicted wind power data and the currently predicted wind speed data; The wind power probability prediction module is used to input the wind power data and wind speed data into the wind power probability prediction model to obtain the conditional probability density of the currently predicted wind power and the confidence interval of the conditional probability density; wherein, the wind power probability prediction model is to establish marginal probability distribution models of actual wind power, predicted wind power and actual wind speed respectively based on a historical sample data set and a kernel density estimation method; the historical sample data set includes historical actual wind power data, historical predicted wind power data and historical actual wind speed data; On the basis of the marginal probability distribution models of the actual wind power, the predicted wind power and the actual wind speed, a first joint probability distribution model and a second joint probability distribution model are established according to a Copula function; The method is established based on the first joint probability distribution model and the second joint probability distribution model; The first joint probability distribution model is specifically: Where x, y and z are historical actual wind power data, historical forecast wind power data and historical actual wind speed data respectively, and f X (x), f Y (y) and f Z (z) are the marginal probability density functions corresponding to x, y and z respectively, F X (x), F Y (y) and F Z (z) are the marginal probability distribution functions corresponding to x, y and z respectively, c is the probability density function of the Copula function, Respectively, they represent the partial differentials of y and z, X, Y, and Z represent the random variables of actual wind power, predicted wind power, and actual wind speed, respectively, and x, y, and z are the specific values ​​of the corresponding random variables; The second joint probability distribution model is specifically: The wind power probability prediction model is specifically: Where, is the current predicted wind power data, is the current predicted wind speed data, for The corresponding marginal probability distribution function is, for The corresponding marginal probability distribution function.

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