Ultra-short-term wind power probability prediction method based on nonparametric stochastic differential equation

Abstract

The invention discloses an ultra-short-term wind power probability prediction method based on a nonparametric stochastic differential equation. The method comprises the following steps: firstly, constructing a nonparametric stochastic differential equation used for describing short-time random fluctuation of wind power output, and combining Gaussian process regression and approximate difference operation to realize adaptive inference of the nonparametric stochastic differential equation under limited wind power observation data; in order to meet the requirements of stochastic differential equation inference and solution for sample resolution and calculation efficiency, a stochastic differential equation is combined with a deep neural network, and a wind power stochastic process path interpolator and a stochastic differential equation numerical integrator are constructed based on a double-layer attention recurrent neural network. A two-stage training algorithm is provided to realize collaborative optimization of network parameters; and finally, through the probability transition characteristic of a stochastic differential equation, the time-varying probability distribution of the wind power in the prediction time is calculated by using the trained network. According to the invention, wind power probability prediction with super time resolution can be realized.

Description

Technical Field

[0001] The invention relates to an ultra-short-term wind power probability prediction method based on a non-parametric stochastic differential equation, and belongs to the field of renewable energy probability prediction. Background Art

[0002] Although wind power, photovoltaic power and other new energy power generation forms have significant advantages such as clean, economical and low carbon, their output is random, intermittent and volatile. Therefore, the operation of the power system under the high proportion of new energy penetration faces strong uncertainty. Accurate and reliable prediction can realize the quantitative estimation of new energy output and provide forward-looking information for the operation and control of the power system. Traditional deterministic prediction methods can only output the single-point expected value of the prediction object at a future moment, and cannot quantify its inherent uncertainty and objective prediction errors. In contrast, probabilistic prediction can effectively quantify prediction uncertainty and provide more comprehensive new energy output probability information for power system operation. However, existing ultra-short-term wind power probability prediction research mostly relies on massive data drive or simplified distribution assumptions, and fails to fully reveal the random fluctuation characteristics of wind power output and its evolution mechanism, which restricts the improvement of prediction performance. In addition, the prediction results are also limited by the time resolution of sample data, and its application value in power system operation and control has not been fully utilized. Therefore, in view of the non-stationary time-varying characteristics of wind power generation, it is necessary to propose an ultra-short-term wind power probability prediction method with mechanism interpretability and model generalization ability. Summary of the invention

[0003] In order to overcome the shortcomings of the prior art, the present invention proposes a super short-term wind power probability prediction method based on non-parametric stochastic differential equations. The method is as follows: first, a non-parametric stochastic differential equation is constructed to describe the short-term random fluctuation of wind power output, and Gaussian process regression and approximate difference operation are combined to realize the adaptive inference of non-parametric stochastic differential equations under limited wind power observation data; in order to meet the requirements of sample resolution and computational efficiency for the inference and solution of stochastic differential equations, the stochastic differential equation is combined with a deep neural network, and a cascaded wind power random process path interpolator and a stochastic differential equation numerical integrator are constructed based on a double-layer attention recurrent neural network, and a two-stage training algorithm is proposed to realize the coordinated optimization of network parameters; finally, through the probability transfer characteristics of stochastic differential equations, the time-varying probability distribution of wind power within the prediction time is calculated using the trained network. This method can accurately characterize the short-term random fluctuation characteristics of wind power output, realize the probability prediction of wind power with super time resolution and mechanism interpretability, and improve the interpretation ability and application value of the prediction under the premise of ensuring the reliability of the prediction.

[0004] The technical solution adopted by the present invention is as follows:

[0005] A method for ultra-short-term wind power probability prediction based on non-parametric stochastic differential equations is implemented by a wind power probability prediction model based on non-parametric stochastic differential equations. The method for constructing the wind power probability prediction model based on non-parametric stochastic differential equations includes the following steps:

[0006] (1) A nonparametric stochastic differential equation is constructed to describe the random process of wind power output. The wind power output fluctuation in a short period of time is a continuous time random process, which is expressed by a nonparametric stochastic differential equation:

[0007]

[0008] In the formula, d is the differential operation symbol; X t represents the state of the wind power output random process at time t; W t is a standard Wiener process; f(·) and g(·) represent the drift term and diffusion term of the stochastic differential equation, respectively, which are nonlinear functions of the wind power output state. Without assuming the functional form of the drift term and the diffusion term in advance, it is constructed as two Gaussian process models:

[0009]

[0010] In the formula, x and x′ are any two possible state values ​​of wind power generation; and They represent the Gaussian processes that the drift term and the diffusion term obey, respectively, and are determined by the mean function and the covariance function; m f (·) and m g (·) are the mean functions of the drift term and the diffusion term, respectively. In order to satisfy the generality of the stochastic differential equation, the prior mean functions of the drift term and the diffusion term are set to zero functions, that is: m f (x) = 0, m g (x) = 0; ∑ f (·,·) and ∑ g (·,·) represent the covariance functions of drift term and diffusion term respectively. In order to satisfy the nonlinear and smooth characteristics of drift term and diffusion term, radial basis kernel function is used to characterize the covariance function:

[0011]

[0012] In the formula, Radial basis kernel function The hyperparameters, l f and l g is the level factor, and is the vertical factor.

[0013] (2) Constructing a wind power output stochastic process path interpolator and a stochastic differential equation numerical integrator based on a two-layer attention recurrent neural network

[0014] In order to meet the demand for high-resolution samples in nonparametric stochastic differential equation inference, a two-layer attention recurrent neural network is constructed for sparse wind power observation data to simulate the wind power output random process path interpolator and generate ultra-time resolution wind power output random diffusion path samples. Considering the influence of time and meteorological factors on the random fluctuation characteristics of wind power output, wind power, observation time, predicted wind speed and predicted temperature are selected as input features of the path interpolator. The length of the observation time window is set to T, and the input feature time series within the observation time window is selected to form the input feature matrix:

[0015]

[0016] Where X is the K×T dimensional input feature matrix; K is the spatial dimension of the input feature; x K represents the input feature time series in the K-dimensional space; x T Represents the characteristic vector composed of the input features of each dimension at time T. The input-output port model of the constructed wind power output random process path interpolator is:

[0017]

[0018] In the formula, represents a path interpolator with parameter η; and denote the posterior estimates of the drift term and diffusion term of the stochastic differential equation respectively; A set of random diffusion path samples of wind power output generated by the path interpolator, where the time resolution of any random diffusion path sample is Δt.

[0019] The two-layer attention recurrent neural network structure used in the constructed path interpolator is as follows:

[0020] a) Spatial Attention Encoder

[0021] The spatial attention layer introduces the spatial attention mechanism to adaptively reconstruct the input features of different dimensions, and uses a recurrent neural network to encode the reconstructed input features to capture the temporal dependency of the feature sequence. The constructed spatial attention encoder model is expressed as:

[0022] h t = r(h t-1 ,x t )

[0023]

[0024] Where r(·) represents the recurrent neural unit function; x t is the input feature vector at time t; h t-1 ,h t are the encoder hidden layer state vectors at time t-1 and t respectively; v e ,W e and U e is the parameter to be optimized of the spatial attention module in the encoder; tanh(·) is the hyperbolic tangent activation function; represents the attention weight of the k-th dimension input feature at time t, is its normalized value; is the reconstructed feature vector at time t under spatial attention weighting. The reconstructed feature vector is input into the recurrent neural network. is the updated encoder hidden layer state vector at time t-1 and t.

[0025] b) Temporal Attention Decoder

[0026] The temporal attention layer introduces the temporal attention mechanism to adaptively reconstruct the encoder hidden layer states at different times, and also uses a recurrent neural network to decode the reconstructed encoder hidden layer states. The constructed temporal attention decoder model is expressed as:

[0027]

[0028] Where, d t-1 is the decoder hidden layer state vector at time t-1; v f ,W f and U f are the parameters to be optimized for the temporal attention module in the decoder; represents the attention weight of the encoder hidden layer state at time i and the decoder output at time t, is its normalized value; c t Reconstruct the state vector of the encoder hidden layer at time t under the weight of temporal attention; is the random diffusion path sample of wind power output at time t-1,t; W y ,b y ,v y ,b v are the parameters to be optimized for the recurrent neural network module in the decoder.

[0029] Affected by the chaotic characteristics of the atmosphere, the stochastic differential equations of the random process of wind power output are usually nonlinear and have no analytical solution in theory. Therefore, another two-layer attention recurrent neural network model is constructed as a stochastic differential equation numerical integrator to fit the numerical integral of the stochastic differential equation within the prediction time window, corresponding to the state estimation of wind power output. The input-output port model of the constructed stochastic differential equation numerical integrator is:

[0030]

[0031] In the formula, It is the time series state estimation of wind power output within the prediction time window of length H, and its time resolution is Δt; A numerical integrator with a parameter of φ is represented. In order to simplify the model training process and improve the model training efficiency, the numerical integrator adopts the same double-layer attention recurrent neural network structure as the path interpolator.

[0032] (3) using a wind power output random process path interpolator to generate ultra-time-resolution wind power output random diffusion path samples, optimizing the parameters of a Gaussian process model based on the wind power output random diffusion path samples, inferring a non-parametric stochastic differential equation based on the Gaussian process model after parameter optimization, and updating the wind power output random process model;

[0033] From the nonparametric stochastic differential equation established in step (1), we can find that there is an implicit relationship between its drift term and diffusion term and the state of the random process:

[0034]

[0035] In the formula, E[·] represents the mean operation; Represents the limit operation when Δt approaches 0. Using the sample average approximation method, the random diffusion path sample set of wind power output generated by the path interpolator in step (2) is approximated by the implicit relationship mentioned above to obtain the drift term and diffusion term corresponding to the sample points of different random diffusion paths, and then construct the training data set D of the Gaussian process model of the drift term and diffusion term. F ,D G , recorded as: D F ={(x i ,f i )1,…,N},D G ={(x i ,g i )1,…,N}, where N is the training set D F ,D G The number of sample points, x i ,f i and g iare the i-th random diffusion path sample point and its corresponding drift term and diffusion term respectively.

[0036] Using the stochastic gradient descent algorithm, we use the training set D F ,D G Optimize the hyperparameters θ of the Gaussian process model for drift and diffusion terms f ,θ g According to the Bayesian principle, the posterior estimates of the drift term and the diffusion term under any wind power output state are obtained, which can be expressed as:

[0037]

[0038] In the formula, and They represent the posterior estimates of the drift term and the diffusion term at state x respectively; and They are and The variance of and is the drift term and diffusion term vector; and Represents the covariance vector between the drift term and the diffusion term corresponding to the state x and all random diffusion path sample points; and Represents the covariance matrix between the drift term and the diffusion term corresponding to different random diffusion path sample points.

[0039] The non-parametric stochastic differential equation is inferred based on the a posteriori estimates of the drift term and the diffusion term functions, and the wind power output stochastic process model is updated:

[0040]

[0041] The stochastic differential equation satisfies the probability statistical characteristics of the wind power output random diffusion path samples generated by the wind power output random process path interpolator in step (2).

[0042] (4) Constructing a wind power probability prediction model based on non-parametric stochastic differential equations

[0043] The wind power output stochastic process path interpolator and the stochastic differential equation numerical integrator in step (2) and the wind power output stochastic process model in step (3) are connected in series to obtain the wind power probability prediction model based on non-parametric stochastic differential equations. The wind power probability prediction model based on non-parametric stochastic differential equations takes the time-varying probability distribution of wind power within the prediction time window as output, and its specific calculation process is:

[0044] Combining the wind power output state estimation output by the numerical integrator and the wind power output stochastic process model updated in step (3), the time-varying probability distribution of wind power in the prediction time window is derived, which is expressed as:

[0045]

[0046] In the formula, It is the wind power output state estimation at the future time h, h+1; Indicates the mean The variance is The normal distribution of .

[0047] (5) A two-stage training algorithm is used to achieve the coordinated optimization of the internal network parameters of the wind power probability prediction model based on non-parametric stochastic differential equations

[0048] a) Phase 1

[0049] According to the state probability transfer characteristics of the wind power output random process, the training loss function of the wind power output random process path interpolator is constructed and expressed as:

[0050]

[0051] In the formula, is the training loss of the path interpolator; log[·] is the logarithmic operation; is the posterior probability of the random diffusion path sample under the posterior estimation of the drift term and the diffusion term; is the likelihood probability of the wind power observation data under the obtained random diffusion path samples. In the first stage, the alternating iteration method is used to train the wind power output random process path interpolator and the wind power output random process model. In each iteration process, first, with the goal of minimizing the above loss function, the ADAM algorithm is used to train the double-layer attention recurrent neural network inside the path interpolator on a given training data set to achieve its optimal parameter estimation. Then, the optimized path interpolator is used to update the wind power output random diffusion path sample set, and then the sample set is approximate difference operation and Gaussian process regression are performed to update the posterior estimation of the drift term and diffusion term and the wind power output random process model.

[0052] b) Second stage

[0053] The path interpolator trained in the first stage generates random diffusion path samples of wind power output within the prediction time window. According to the updated wind power output random process model and the set of wind power output random diffusion path samples within the prediction time window, the training loss function of the stochastic differential equation numerical integrator is constructed, which is expressed as:

[0054]

[0055] In the formula, is the training loss function of the wind power probability prediction model; ρ α (·) represents the quantile loss function with the prediction quantile level α; is the predicted quantile of wind power at the α quantile level at the future time h; is the actual state of wind power output at the future time h. With the goal of minimizing the above loss function, the ADAM optimization algorithm is used to train the double-layer attention recurrent neural network inside the numerical integrator to obtain its optimal parameter estimation.

[0056] The beneficial effects of the present invention are:

[0057] A super short-term wind power probability prediction method based on non-parametric stochastic differential equations is proposed. Stochastic differential equations are used to characterize the short-term random fluctuation characteristics of wind power output, and wind power probability prediction with mechanism explainability and ultra-time resolution is realized; a non-parametric stochastic differential equation inference method based on the Gaussian process model is proposed, which avoids the prior assumptions of the drift term and diffusion term function form of the traditional stochastic differential equation inference, and improves the adaptability of the stochastic differential equation to the random fluctuation characteristics of time-varying wind power output; combined with the attention mechanism and the recurrent neural network, a wind power output random process path interpolator and a stochastic differential equation numerical integrator are constructed respectively, which solves the Gaussian process regression problem under sparse wind power observation conditions and the numerical solution problem of nonlinear stochastic differential equations. Under the premise of ensuring the reliability of the prediction, the method of the present invention improves the application value of wind power probability prediction in power system operation decision-making. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 The flowchart of the method for constructing an ultra-short-term wind power probability prediction model is shown in FIG.

[0059] Figure 2 The invention discloses a double-layer attention recurrent network structure adopted by the wind power output random process path interpolator and the non-parametric stochastic differential equation numerical integrator.

[0060] Figure 3 Wind power probability prediction intervals and random diffusion paths under different confidence levels, and their corresponding real wind power observation results. DETAILED DESCRIPTION

[0061] The present invention will be further described below in conjunction with the accompanying drawings.

[0062] The ultra-short-term wind power probability prediction method based on non-parametric stochastic differential equations of the present invention relies on a wind power probability prediction model based on non-parametric stochastic differential equations. The method for constructing a wind power probability prediction model based on non-parametric stochastic differential equations is as follows: Figure 1, specifically including the following steps:

[0063] (1) Constructing a training data set D = {(X i ,y i )1,…,N D}, X i is the input feature matrix of the model, which is composed of the time series of wind power, observation time, predicted wind speed and predicted temperature in the observation time window of length T, with a time resolution of ΔT; i is the time series of wind power within the prediction time window of length H.

[0064] (2) Construct a nonparametric stochastic differential equation for the random process of wind power output in each observation time window. The drift term and diffusion function are modeled using Gaussian processes to obtain a random process model of wind power output. The specific expression is:

[0065]

[0066]

[0067] In the formula, d is the differential operation symbol; X t Indicates the output state of wind power at time t; W t is a standard Wiener process; f(·) and g(·) represent the drift term and diffusion term of the stochastic differential equation, respectively. x and x′ are any two possible state values ​​of wind power generation; and is the Gaussian process followed by the drift term and diffusion term; m f (·) and m g (·) is the mean function of the drift term and the diffusion term, which is assumed to be a zero function a priori, that is: m f (x) = 0, m g (x) = 0; ∑ f (·,·) and ∑ g (·,·) is the covariance function of the drift term and the diffusion term, which is assumed to be a radial basis kernel function a priori.

[0068] (3) Construct a wind power output stochastic process path interpolator and a stochastic differential equation numerical integrator based on a two-layer attention recurrent neural network;

[0069] A two-layer attention recurrent neural network is constructed to simulate the path interpolator of the random process of wind power output, and the Xavier Glorot method is used to initialize the network parameters. The path interpolator takes the feature matrix described in step (1) as input and outputs the random diffusion path samples of wind power output with a time resolution of Δt<<ΔT. Its internal network structure is shown in the attached figure. Figure 2 shown.

[0070] A two-layer attention recurrent neural network is constructed to simulate the numerical integrator of the nonparametric stochastic differential equation, and the network parameters are initialized using the Xavier Glorot method. The numerical integrator takes the feature matrix described in step (1) as input and outputs a wind power output state estimate with a length of H and a time resolution of Δt. Its internal network structure is shown in the attached figure. Figure 2 shown.

[0071] (4) Using the sample average approximation method, the following approximate difference operation is performed on the wind power output random diffusion path samples generated by the wind power output random process path interpolator to update the drift term and diffusion term at each wind power output random diffusion path sample point:

[0072]

[0073] In the formula, E[·] represents the mean operation; It represents the limiting operation when Δt approaches 0.

[0074] (5) Construct the Gaussian process model training data set for drift term and diffusion term in each observation time window respectively, denoted as D F ={(X t ,f t )|1,…,T},D G ={(X t ,g t )|t=1,…,T}. In the training data set D F ,D G The stochastic gradient descent algorithm is used to optimize the hyperparameters θ of the drift term and diffusion term Gaussian process f ,θ g According to the Bayesian principle, the posterior estimates of the drift term and diffusion term function under any wind power output state are obtained. Based on the Gaussian process model after parameter optimization, the non-parametric stochastic differential equation is inferred and the wind power output stochastic process model is updated:

[0075]

[0076] (6) The wind power output stochastic process path interpolator and stochastic differential equation numerical integrator constructed in step (3) and the wind power output stochastic process model constructed in step (5) are connected in series to form the wind power probability prediction model based on non-parametric stochastic differential equations. The prediction model uses the time-varying probability distribution of wind power within the prediction time window as output, and its calculation method is: combining the wind power output state estimation output by the stochastic differential equation numerical integrator and the wind power output stochastic process model in step (5), deriving the time-varying probability distribution of wind power within the prediction time window, expressed as:

[0077]

[0078] In the formula, It is the wind power output state estimation at the future time h, h+1;

[0079] Indicates the mean The variance is The normal distribution of .

[0080] (7) A two-stage training algorithm is used to train a wind power probability prediction model based on non-parametric stochastic differential equations on the training data set D. The steps of the two-stage training algorithm are:

[0081] (7.1) The path interpolator and wind power output random process model of the wind power output random process are trained by the alternating iteration method. The semi-supervised learning loss function of the path interpolator is:

[0082]

[0083] In the formula, is the training loss of the path interpolator, log[·] represents the logarithmic operation; is the posterior probability of the obtained random diffusion path sample in the drift term and diffusion term; is the likelihood probability of the sparse observation data of wind power under the obtained random diffusion path samples. In each iteration, the ADAM algorithm is first used to optimize the parameters of the double-layer attention recurrent neural network inside the path interpolator on a given training data set with the goal of minimizing the above loss function, and the optimized path interpolator is used to update the set of random diffusion path samples of wind power output. Then, approximate difference operation and Gaussian process regression are performed on the updated set of random diffusion path samples of wind power output to update the posterior estimates of the drift term and diffusion term and the random process model of wind power output.

[0084] (7.2) Based on the wind power output random process model optimized in step (7.1) and the set of wind power output random diffusion path samples within the prediction time window generated by the path interpolator trained in step (7.1), the stochastic differential equation numerical integrator is trained, and its supervised learning loss function is:

[0085]

[0086] In the formula, is the training loss of the numerical integrator, ρ α (·) represents the quantile loss function with the prediction quantile level α; is the predicted quantile of wind power at the future time h and quantile level α; is the wind power output state at the future time h. In the second stage, the ADAM optimization algorithm is used to train the double-layer attention recurrent neural network inside the numerical integrator with the goal of minimizing the loss function to obtain its optimal parameter estimation.

[0087] Select Texas, USA The effectiveness of the proposed method is verified by using real wind power observation data and numerical meteorological forecasts of wind speed and temperature in the spring of 2013. The temporal resolution of the dataset is 5 minutes, and the prediction model is trained and verified on it, where the training samples account for 60% of the seasonal dataset and the remaining 40% are test samples. The prediction lead time is 1 hour.

[0088] Figure 3 The wind power probability prediction interval and random diffusion path at the confidence level of 10%-90% obtained by the method of the present invention under the data set, and the corresponding real wind power observation, can be seen that the prediction interval obtained by the method of the present invention can well cover the real wind power output, with good sharpness and reliability, and has a super time resolution of 4 seconds compared to the real wind power observation with a time resolution of 5 minutes. In addition, the method can output probability prediction results of other time resolutions, and is also applicable to the probability prediction of other new energy power generation power and load, and has a wide range of applicability.

Claims

1. A method for ultra-short-term wind power probability prediction based on non-parametric stochastic differential equations, characterized by: The probability prediction method relies on a wind power probability prediction model based on a non-parametric stochastic differential equation. The method for constructing the prediction model includes the following steps: (1) Construct a nonparametric stochastic differential equation to describe the random process of wind power output and obtain a random process model of wind power output; (2) Based on a two-layer attention recurrent neural network, a wind power output stochastic process path interpolator and a stochastic differential equation numerical integrator are constructed; (3) using a wind power output random process path interpolator to generate ultra-time-resolution wind power output random diffusion path samples, optimizing the parameters of a Gaussian process model based on the wind power output random diffusion path samples, inferring the non-parametric stochastic differential equation based on the Gaussian process model after parameter optimization, and updating the wind power output random process model; (4) connecting in series the wind power output random process path interpolator and the stochastic differential equation numerical integrator described in step (2), and the wind power output random process model described in step (3), to obtain the wind power probability prediction model based on the non-parametric stochastic differential equation; (5) A two-stage training algorithm is used to achieve the coordinated optimization of the internal network parameters of the wind power probability prediction model based on non-parametric stochastic differential equations.

2. The ultra-short-term wind power probability prediction method based on non-parametric stochastic differential equations according to claim 1 is characterized in that: In step (1), the wind power output random process model is represented by a non-parametric stochastic differential equation: In the formula, d is the differential operation symbol; X t represents the state of the wind power output random process at time t; W t is a standard Wiener process; f(·) and g(·) represent the drift term and diffusion term of the stochastic differential equation, respectively; without assuming the functional form of the drift term and the diffusion term in advance, it is constructed as two Gaussian process models: In the formula, x and x′ are any two possible state values ​​of wind power generation; and They represent the Gaussian processes followed by the drift term and the diffusion term respectively; m f (·) and m g (·) are the mean functions of drift term and diffusion term respectively; ∑ f (·,·) and ∑ g (·,·) represent the covariance functions of the drift term and diffusion term, respectively.

3. The ultra-short-term wind power probability prediction method based on non-parametric stochastic differential equations according to claim 2 is characterized in that: In the step (2): Based on a two-layer attention recurrent neural network, a wind power output random process path interpolator and a stochastic differential equation numerical integrator are constructed. The input-output port model of the wind power output random process path interpolator is: In the formula, represents the path interpolator with parameter η; X is the input feature matrix; and denote the posterior estimates of the drift term and diffusion term of the stochastic differential equation respectively; A set of random diffusion path samples of wind power output generated by the path interpolator, where the time resolution of any random diffusion path sample is Δt; The method for constructing the input feature matrix X is: Select wind power, observation time, predicted wind speed and predicted temperature as the input features of the path interpolator, set the length of the observation time window to T, select the input feature time series within the observation time window, and form the input feature matrix: Where X is the K×T dimensional input feature matrix; K is the spatial dimension of the input feature; x K Represents the input feature time series in the K-dimensional space; x T Represents the feature vector composed of the input features of each dimension at time T; The input-output port model of the stochastic differential equation numerical integrator is: In the formula, It is the time series state estimation of wind power output within the prediction time window of length H, and its time resolution is Δt; represents a numerical integrator with parameter φ.

4. The ultra-short-term wind power probability prediction method based on non-parametric stochastic differential equations according to claim 3 is characterized in that: In the step (3), the parameters of Gaussian process regression are optimized based on the random diffusion path samples of wind power output, the non-parametric stochastic differential equation is inferred based on the Gaussian process regression after parameter optimization, and the wind power output random process model is updated. The specific method is as follows: Firstly, the sample average approximation method is used to perform approximate difference operation on the sample set of wind power output random diffusion path to obtain the drift term and diffusion term corresponding to different random diffusion path sample points. The specific calculation formula is as follows: In the formula, E[·] represents the mean operation; It means taking the limit operation when Δt approaches 0; Then, construct the training data set D of the drift term and diffusion term Gaussian process model F ,D G , recorded as: D F ={(x i ,f i )|1,…,N},D G ={(x i ,g i )|1,…,N}, where N is the training set D F ,D G The number of sample points, x i ,f i and g i are the i-th random diffusion path sample point and its corresponding drift term and diffusion term respectively; Next, the stochastic gradient descent method is used to train the D F ,D G Optimize the hyperparameters θ of the Gaussian process model for drift and diffusion terms f ,θ g , and obtain the posterior estimates of the drift term and the diffusion term under any possible wind power output state: In the formula, and They represent the posterior estimates of the drift term and the diffusion term at state x respectively; and for and Variance of; f=[f1,…,f N ] T and g=[g1,…,g N ] T is the drift term and diffusion term vector; and Represents the covariance vector between the drift term and the diffusion term corresponding to the state x and all random diffusion path sample points; and Represents the covariance matrix between the drift term and the diffusion term corresponding to different random diffusion path sample points; and is the radial basis kernel function; Finally, the non-parametric stochastic differential equation is inferred based on the posterior estimation of the drift term and the diffusion term function, and the wind power output stochastic process model is updated:

5. The ultra-short-term wind power probability prediction method based on non-parametric stochastic differential equations according to claim 4 is characterized in that: In the step (4): The wind power probability prediction model based on non-parametric stochastic differential equations takes the time-varying probability distribution of wind power in the prediction time window as output, and its specific calculation process is: Combining the wind power output state estimation output by the stochastic differential equation numerical integrator and the wind power output stochastic process model in step (3), the time-varying probability distribution of wind power within the prediction time window is derived, which is expressed as: In the formula, It is the wind power output state estimation at the future time h, h+1; Indicates the mean The variance is The normal distribution of .

6. The ultra-short-term wind power probability prediction method based on non-parametric stochastic differential equations according to claim 5 is characterized in that: The step (5) is specifically as follows: Phase 1: The alternating iteration method is used to jointly train the wind power output random process path interpolator and the wind power output random process model; the semi-supervised learning loss function of the path interpolator is: In the formula, is the training loss of the path interpolator, log[·] represents the logarithmic operation; is the posterior probability of the obtained random diffusion path sample under the obtained posterior estimates of the drift term and diffusion term; is the likelihood probability of wind power observation data under the obtained random diffusion path sample; In each iteration, the ADAM algorithm is first used to optimize the parameters of the double-layer attention recurrent neural network inside the path interpolator on a given training data set with the goal of minimizing the semi-supervised learning loss function, and the optimized path interpolator is used to update the random diffusion path sample set of wind power output; then, approximate difference operation and Gaussian process regression are performed on the updated random diffusion path sample set of wind power output, and the posterior estimates of the drift term and the diffusion term and the random process model of wind power output are updated; The second stage: The path interpolator trained in the first stage generates random diffusion path samples of wind power output within the prediction time window. Based on the wind power output random process model optimized in the first stage and the set of wind power output random diffusion path samples within the prediction time window, the stochastic differential equation numerical integrator is trained. The supervised learning loss function is: In the formula, is the training loss of the numerical integrator, ρ α (·) represents the quantile loss function with the prediction quantile level α; is the predicted quantile of wind power at the future time h and quantile level α; is the wind power output state at the future time h; in the second stage, the ADAM optimization algorithm is used to train the double-layer attention recurrent neural network inside the numerical integrator with the goal of minimizing the supervised loss function to obtain its optimal parameter estimation.

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