A non-parametric stochastic differential equation based ultra-short-term wind power probability forecasting method

Abstract

The application discloses a kind of ultra-short-term wind power probability prediction methods based on non-parametric stochastic differential equation.The method is: first, construct the non-parametric stochastic differential equation for describing the short-time random fluctuation of wind power output, and combine Gaussian process regression and approximate difference operation, realize the adaptive inference of non-parametric stochastic differential equation under limited wind power observation data;To meet the needs of sample resolution and calculation efficiency for stochastic differential equation inference and solution, combine stochastic differential equation with deep neural network, construct wind power random process path interpolator and stochastic differential equation numerical integrator based on double-layer attention recurrent neural network, and propose two-stage training algorithm to realize the collaborative optimization of network parameters;Finally, through the probability transfer characteristics of stochastic differential equation, the time-varying probability distribution of wind power in the prediction time is calculated using the trained network.The application can realize the wind power probability prediction with ultra-time resolution.

Description

TECHNICAL FIELD

[0001] The application relates to a kind of ultra-short-term wind power probability prediction methods based on non-parametric stochastic differential equation, belong to renewable energy probability prediction field. BACKGROUND

[0002] Although new energy generation forms such as wind power and photovoltaic have significant advantages such as cleanliness, economy and low carbon, the output thereof has randomness, intermittency and volatility. Therefore, under high proportion of new energy penetration, power system operation faces strong uncertainty. Accurate and reliable prediction can realize quantitative estimation of new energy output and provide forward-looking information for power system operation control. Traditional deterministic prediction method can only output single-point expected value of prediction object at future time, and cannot quantify inherent uncertainty and objective prediction error. In contrast, probability 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 researches mostly rely on massive data driving or simplified distribution assumption, and cannot fully reveal the random fluctuation characteristics and evolution mechanism of wind power output, which restricts the improvement of prediction performance. In addition, the prediction result is also limited by the time resolution of sample data, and its application value in power system operation control has not been fully played. 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 explainability and model generalization ability. SUMMARY

[0003] In order to overcome the deficiencies of the prior art, the application proposes an ultra-short-term wind power probability prediction method based on non-parametric stochastic differential equation. The method is as follows: firstly, a non-parametric stochastic differential equation for describing short-time random fluctuation of wind power output is constructed, and Gaussian process regression and approximate difference operation are combined to realize adaptive inference of non-parametric 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, the stochastic differential equation is combined with deep neural network, a cascaded wind power random process path interpolator and stochastic differential equation numerical integrator are constructed based on double-layer attention recurrent neural network, and a two-stage training algorithm is proposed to realize collaborative optimization of network parameters; finally, the time-varying probability distribution of wind power in the prediction time is calculated by using the trained network through the probability transfer characteristics of the stochastic differential equation. The method can accurately describe the short-time random fluctuation characteristics of wind power output, realize wind power probability prediction with ultra-time resolution and mechanism explainability, and improve the explanation ability and application value of prediction under the premise of ensuring the reliability of prediction.

[0004] The technical scheme adopted by the application is as follows:

[0005] The application discloses a kind of based on nonparametric stochastic differential equation's ultra-short-term wind power probability prediction method, relies on a kind of based on nonparametric stochastic differential equation's wind power probability prediction model implementation, the construction method of the based on nonparametric stochastic differential equation's wind power probability prediction model includes the following steps:

[0006] (1) construct the nonparametric stochastic differential equation for describing wind power output random process, obtain the wind power output fluctuation of wind power output random process model short time as continuous time random process, using nonparametric stochastic differential equation is expressed as:

[0007]

[0008] In the formula, d is differential operator symbol;X t Indicate the state of wind power output random process at t time;W t It is standard wiener process;f (·) and g (·) respectively indicate the drift term and diffusion term of random differential equation, and it is the nonlinear function of wind power output state. Without prior assumption of the function form of drift term and diffusion term, 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 Gaussian process that drift term and diffusion term are subjected to respectively, determined by mean function and covariance function;m f (·) and m g (·) respectively the mean function of drift term and diffusion term. To meet the universality of random differential equation, the prior mean function of drift term and diffusion term is all set to zero function, i.e.: m f (x)=0, m g (x)=0;∑ f (·,·) and ∑ g (·,·) respectively the covariance function of drift term and diffusion term. To meet the nonlinear and smoothness characteristics of drift term and diffusion term, radial basis kernel function is used to represent covariance function:

[0011]

[0012] In the formula, Respectively radial basis kernel function Hyperparameter of l f And l g Horizontal factor, And Vertical factor.

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

[0014] To meet the demand of non-parametric stochastic differential equation inference for high-resolution samples, a double-layer attention recurrent neural network is constructed for wind power sparse observation data to simulate a wind power output random process path interpolator and generate a super-time-resolution wind power output random diffusion path sample. 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 in the observation time window are selected to form an input feature matrix:

[0015]

[0016] In the formula, X is a 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 Kth spatial dimension; x T represents a feature vector composed of input features at T time points. The input-output port model of the constructed wind power output random process path interpolator is:

[0017]

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

[0019] The double-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 a spatial attention mechanism to adaptively weight and reconstruct input features of different dimensions, and a recurrent neural network is used to encode the reconstructed input features to capture the time dependence of the feature sequence. The model of the constructed spatial attention encoder is represented as:

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

[0023]

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

[0025] b) Time Attention Decoder

[0026] The temporal attention layer introduces a temporal attention mechanism to adaptively weight and reconstruct the encoder hidden layer states at different time points. A recurrent neural network is then used to decode the reconstructed encoder hidden layer states. The constructed temporal attention decoder model is represented as follows:

[0027]

[0028] In the formula, d t-1 v is the decoder hidden layer state vector at time t-1; f W f and U f These are the parameters to be optimized for the temporal attention module in the decoder; This represents the attention weights of the encoder hidden layer state at time i and the decoder output at time t. Its normalized value; c t Reconstruct the hidden state vector of the encoder at time t under time attention weighting; These are random diffusion path samples of wind power output at times t-1 and t. W y ,b y ,v y ,b v These 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 equation of the wind power output random process is usually nonlinear, which has no analytical solution in theory. Therefore, another double-layer attention recurrent neural network model is constructed as a numerical integrator of the stochastic differential equation for fitting the numerical integration of the stochastic differential equation in the prediction time window, corresponding to the state estimation of the wind power output. The input-output port model of the constructed numerical integrator of the stochastic differential equation is:

[0030]

[0031] wherein, is the time series state estimation of the wind power output in the prediction time window with a length of H, and the time resolution is Δt; , which is a numerical integrator with φ as a parameter. 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) generating a super time resolution wind power output random diffusion path sample by using the wind power output random process path interpolator, optimizing the parameters of the Gaussian process model based on the wind power output random diffusion path sample, 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;

[0033] From the non-parametric stochastic differential equation established in step (1), it can be seen that there is an implicit relationship between the drift term and the diffusion term and the state of the random process:

[0034]

[0035] wherein, E[·] represents the mean value operation; represents the limit operation when Δt approaches 0. By using the sample mean approximation method, the wind power output random diffusion path sample set generated by the path interpolator in step (2) is subjected to approximate difference operation according to the above implicit relationship, so as to obtain the drift term and the diffusion term corresponding to different random diffusion path sample points, and further to construct the training data set D F ,D G of the drift term and the diffusion term Gaussian process model, denoted as: D F ={(x i ,f i )1,…,N} and D G ={(x i ,g i )1,…,N}, wherein N is the number of sample points of the training set D F ,D G , x i ,f i and g irespectively, are the drift term and diffusion term of the i-th random diffusion path sample point and its corresponding.

[0036] The random gradient descent algorithm is used to train the drift term and diffusion term Gaussian process model on the training set D F ,D G The hyperparameters θ f ,θ g of the drift term and diffusion term Gaussian process model are optimized.

[0037]

[0038] In the formula, and respectively represent the posterior estimates of the drift term and diffusion term at state x. and are the variances of and respectively. and are the drift term and diffusion term vectors. and represent the covariance vectors between the state x and the drift term and diffusion term corresponding to all random diffusion path sample points. and represent the covariance matrices between the drift term and diffusion term corresponding to different random diffusion path sample points.

[0039] Based on the posterior estimates of the drift term and diffusion term functions described above, the non-parametric stochastic differential equation is inferred, and the wind power output stochastic process model is updated:

[0040]

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

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

[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 the non-parametric stochastic differential equation. The wind power probability prediction model based on the non-parametric stochastic differential equation outputs the time-varying probability distribution of the wind power in the prediction time window, and its specific calculation process is as follows:

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

[0045]

[0046] wherein, is the wind power output state estimation at future h, h+1 time; represents a normal distribution with mean and variance .

[0047] (5) The two-stage training algorithm is adopted to realize the collaborative optimization of the network parameters in the internal network of the wind power probability prediction model based on the non-parametric stochastic differential equation

[0048] a) The first stage

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

[0050]

[0051] wherein, is the training loss of the path interpolator; log[·] is the logarithm 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 sample. The alternating iteration method is adopted in the first stage to train the wind power output stochastic process path interpolator and the wind power output stochastic process model. In each iteration process, firstly, the double-layer attention recurrent neural network in the internal network of the path interpolator is trained by using the ADAM algorithm on the given training data set to realize the optimal parameter estimation, with the objective of minimizing the above loss function. Then, the random diffusion path sample set of the wind power output is updated by using the optimized path interpolator, and then the sample set is subjected to the approximate difference operation and the Gaussian process regression to update the posterior estimation of the drift term and the diffusion term and the wind power output stochastic process model.

[0052] b) The second stage

[0053] The wind power output random diffusion path sample in the prediction time window is generated by the path interpolator trained in the first stage, and a training loss function of the numerical integrator of the stochastic differential equation is constructed according to the updated wind power output stochastic process model and the wind power output random diffusion path sample set in the prediction time window, and is expressed as:

[0054]

[0055] In the formula, is the training loss function of the wind power probability prediction model; p α (·) represents the quantile loss function of the prediction quantile level a; is the prediction quantile of the wind power at the future h time a quantile level; is the real state of the wind power output at the future h time. By minimizing the above loss function, the double-layer attention recurrent neural network inside the numerical integrator is trained using the ADAM optimization algorithm to obtain its optimal parameter estimation.

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

[0057] A kind of super short-term wind power probability prediction method based on non-parametric stochastic differential equation is presented, the short-time random fluctuation characteristics of wind power output are described using stochastic differential equation, and wind power probability prediction with mechanism explainability and super time resolution is realized;A non-parametric stochastic differential equation inference method based on Gaussian process model is proposed, which avoids the prior assumption of the function form of the drift term and diffusion term function in traditional stochastic differential equation inference, and improves the adaptability of stochastic differential equation to time-varying wind power output random fluctuation characteristics;Combined with attention mechanism and recurrent neural network, wind power output random process path interpolator and stochastic differential equation numerical integrator are constructed respectively, solving the Gaussian process regression problem under sparse wind power observation condition and the numerical solution problem of nonlinear stochastic differential equation.The method of the present application improves the application value of wind power probability prediction in power system operation decision-making under the premise of ensuring prediction reliability. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 It is the construction method flow chart of super short-term wind power probability prediction model.

[0059] Figure 2 It is the double-layer attention recurrent network structure used by wind power output random process path interpolator and non-parametric stochastic differential equation numerical integrator of the present application.

[0060] Figure 3 It is the wind power probability prediction interval and random diffusion path under different confidence levels, and the corresponding real wind power observation results. DETAILED DESCRIPTION

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

[0062] A kind of super short-term wind power probability prediction method based on non-parametric stochastic differential equation of the present application is realized by a kind of wind power probability prediction model based on non-parametric stochastic differential equation.The construction method of the kind of wind power probability prediction model based on non-parametric stochastic differential equation is as follows Figure 1, specifically comprising the following steps:

[0063] (1) Constructing the training data set D = {(X i ,y i )1,…,N D} of the wind power probability prediction model based on the non-parametric stochastic differential equation, 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 with length T, and the time resolution is ΔT; y i is the time series of wind power in the prediction time window with length H.

[0064] (2) Constructing the non-parametric stochastic differential equation of the wind power output random process in each observation time window, and modeling the drift term and diffusion function by Gaussian process to obtain the wind power output random process model. The specific expression is:

[0065]

[0066]

[0067] In the formula, d is the differential operator symbol; X t represents 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 are Gaussian processes obeyed by the drift term and diffusion term; m f (·) and m g (·) are the mean functions of the drift term and diffusion term, which are assumed to be zero functions, i.e. m f (x) = 0, m g (x) = 0; ∑ f (·,·) and ∑ g (·,·) are the covariance functions of the drift term and diffusion term, which are assumed to be radial basis kernel functions.

[0068] (3) Constructing the wind power output random process path interpolator and the numerical integrator of the stochastic differential equation based on the double-layer attention recurrent neural network;

[0069] The double-layer attention recurrent neural network is constructed to simulate the path interpolator of the wind power output random process, 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 wind power output random diffusion path sample with time resolution Δt << ΔT, and the internal network structure is shown in the accompanying drawing Figure 2 .

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

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

[0072]

[0073] In the formula, E[·] represents the average value operation; This represents the limit operation when Δt approaches 0.

[0074] (5) Construct training datasets for the Gaussian process models of the drift and diffusion terms within each observation time window, denoted as D. F ={(X t ,f t )|1,…,T},D G ={(X t ,g t )|t=1,…,T}. In the training dataset D F D G The hyperparameter θ of the Gaussian process with drift and diffusion terms is optimized using the stochastic gradient descent algorithm. f θ g Based on Bayes' principle, posterior estimates of the drift and diffusion terms under arbitrary wind power output conditions are obtained. The nonparametric stochastic differential equations are inferred from the parameter-optimized Gaussian process model, 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 nonparametric stochastic differential equations. The prediction model outputs the time-varying probability distribution of wind power within the prediction time window. The calculation method is as follows: Combining the wind power output state estimate output by the stochastic differential equation numerical integrator and the wind power output stochastic process model in step (5), the time-varying probability distribution of wind power within the prediction time window is derived, as follows:

[0077]

[0078] wherein, is the wind power state estimation at future h, h+1 time instant;

[0079] denotes a normal distribution with mean and variance .

[0080] (7) Train the wind power probability prediction model based on non-parametric stochastic differential equation on training dataset D by using two-stage training algorithm. The steps of two-stage training algorithm are:

[0081] (7.1) Train the path interpolator of wind power stochastic process and wind power stochastic process model by using alternating iterative method. The semi-supervised learning loss function of path interpolator is:

[0082]

[0083] wherein, is the training loss of path interpolator, log[·] denotes taking logarithm operation; is the posterior probability of obtained stochastic diffusion path sample under drift term and diffusion term; is the likelihood probability of wind power sparse observation data under obtained stochastic diffusion path sample. In each iteration process, firstly, minimize the above loss function as the goal, optimize the double-layer attention recurrent neural network parameters inside path interpolator on given training dataset by using ADAM algorithm, and update the wind power stochastic diffusion path sample set by using optimized path interpolator. Then, update the wind power stochastic diffusion path sample set by using approximate difference operation and Gaussian process regression, update the posterior estimation of drift term and diffusion term and wind power stochastic process model.

[0084] (7.2) Train the stochastic differential equation numerical integrator based on the wind power stochastic process model optimized in step (7.1) and the wind power stochastic diffusion path sample set generated in prediction time window by path interpolator trained in step (7.1), and the supervised learning loss function is:

[0085]

[0086] wherein, is the training loss of numerical integrator, ρ α (·) denotes quantile loss function with prediction quantile level α; is the prediction quantile of wind power at future h time instant and α quantile level; The wind power output state at a future h time is taken as a first stage.

[0087] The Texas The effectiveness of the method is verified by using the real wind power observation data and numerical weather prediction of wind speed and temperature of a wind farm in spring 2013, and the prediction model is trained and verified on the data set with a time resolution of 5 minutes, wherein the training sample accounts for 60% of the seasonal data set, and the remaining 40% is the test sample, and the prediction time is 1 hour.

[0088] Figure 3 The wind power probability prediction interval at a 10%-90% confidence level obtained by the method of the application on the data set is shown, and the corresponding random diffusion path and real wind power observation are shown, and it can be seen that the prediction interval obtained by the method of the application can well cover the real wind power output, has good sharpness and reliability, and has a super time resolution of 4 seconds compared with 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 probability prediction of other new energy power generation and load, and has wide applicability.

Claims

1. A non-parametric stochastic differential equation based ultra-short-term wind power probability forecasting method, characterized in that: The probability prediction method relies on a wind power probability prediction model based on a non-parametric stochastic differential equation, and the construction method of the prediction model comprises the following steps: (1) Constructing a non-parametric stochastic differential equation for describing the wind power output random process to obtain a wind power output random process model; (2) Constructing a wind power output random process path interpolator and a stochastic differential equation numerical integrator based on a double-layer attention recurrent neural network; (3) Generating a super-time resolution wind power output random diffusion path sample using the wind power output random process path interpolator, optimizing the Gaussian process model based on the wind power output random diffusion path sample, inferring the non-parametric stochastic differential equation based on the parameter-optimized Gaussian process model, and updating the wind power output random process model; (4) Connecting the wind power output random process path interpolator and the stochastic differential equation numerical integrator in step (2) and the wind power output random process model in step (3) in series to obtain the wind power probability prediction model based on the non-parametric stochastic differential equation; (5) Realizing the collaborative optimization of the network parameters in the wind power probability prediction model based on the non-parametric stochastic differential equation by using a two-stage training algorithm.

2. The non-parametric stochastic differential equation based ultra-short term wind power probability forecasting method according to claim 1, characterized in that, In step (1), the wind power output random process model is represented by a non-parametric stochastic differential equation: where d is the differential operator; X t denotes the state of the wind power output stochastic 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 diffusion term in advance, they are constructed as two Gaussian process models: where x and x' are any two possible state values of the wind power generation; and Gaussian processes that the drift and diffusion terms follow, respectively; m f (·) and m g (·) are the mean functions of the drift and diffusion terms, respectively; ∑ f (·,·) and ∑ g (·,·) are the covariance functions of the drift and diffusion terms, respectively.

3. The non-parametric stochastic differential equation based ultra-short term wind power probability forecasting method according to claim 2, characterized in that, In step (2), the wind power output random process path interpolator and the stochastic differential equation numerical integrator are constructed based on a double-layer attention recurrent neural network, and the input-output port model of the wind power output random process path interpolator is: The construction method of the input feature matrix X is: wherein, denotes a path interpolator with parameter η; X is an input feature matrix; and denote the posterior estimates of the drift and diffusion terms of the stochastic differential equation, respectively; is a set of stochastic diffusion path samples of wind power output generated by the path interpolator, wherein the time resolution of any stochastic diffusion path sample is Δt; The input features of the path interpolator are selected as wind power, observation time, predicted wind speed, and predicted temperature, the length of the observation time window is set as T, the input feature time series in the observation time window is selected, and the input feature matrix X is constructed: The input-output port model of the stochastic differential equation numerical integrator is: where X is a K x T dimensional input feature matrix; K is the spatial dimension of the input features; x K represents the input feature time series in the Kthdimensional space; x T x represents the feature vector composed of each dimension input feature at time T; In step (3), the Gaussian process regression is parameter-optimized based on the wind power output random diffusion path sample, the non-parametric stochastic differential equation is inferred based on the parameter-optimized Gaussian process regression, and the wind power output random process model is updated, and the specific method is as follows: In the formula, is the time series state estimation of the wind power output in a prediction time window with length H, and the time resolution is Δt; denotes a numerical integrator with parameter φ.

4. The non-parametric stochastic differential equation based ultra-short term wind power probability forecasting method according to claim 3, characterized in that, Firstly, the sample average approximation method is used to perform approximate difference operation on the wind power output random diffusion path sample set to obtain the drift term and the diffusion term corresponding to different random diffusion path sample points, and the specific calculation formula is as follows: 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 random process model is updated: In the formula, E[·] represents a mean value operation; represents a limit operation as Δt approaches 0; Then, a training data set D of the Gaussian process model of the drift term and the diffusion term is constructed F ,D G F = {(x i ,f i )|1,…,N}, D G = {(x i ,g i )|1,…,N}, where N is the number of sample points of the training set D F ,D G , 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;​ Then, the random gradient descent method is used to optimize the hyperparameters θ of the drift and diffusion Gaussian process models on the training set D F ,D G The hyperparameters θ of the drift and diffusion Gaussian process models are optimized f ,θ g The posterior estimates of the drift and diffusion at any possible wind power output state are obtained where and denote the posterior estimates of the drift and diffusion terms at state x, respectively; and are and the variances; f = [f1,..., f N ] T and g = [g1,..., g N ] T are the drift and diffusion term vectors; and denote the covariance vectors between the drift and diffusion terms at state x and all the random diffusion path sample points; and denote the covariance matrices between the drift and diffusion terms at different random diffusion path sample points; and are the radial basis kernel functions; In step (4), the wind power probability prediction model based on the non-parametric stochastic differential equation takes the time-varying probability distribution of wind power in the prediction time window as the output, and the specific calculation process is as follows:

5. The non-parametric stochastic differential equation based ultra-short term wind power probability forecasting method according to claim 4, characterized in that, The time-varying probability distribution of wind power in the prediction time window is derived based on the wind power output state estimation output by the stochastic differential equation numerical integrator and the wind power output random process model in step (3), and is represented as: Step (5) is specifically: ​ In the formula, is the wind power output state estimation at future time h, h+1; represents a normal distribution with mean and variance .

6. The non-parametric stochastic differential equation based ultra-short term wind power probability forecasting method according to claim 5, characterized in that, ​ The first stage: the alternating iterative method is used to train the wind power output random process path interpolator and the wind power output random process model; a semi-supervised learning loss function of the path interpolator is: wherein is the training loss of the path interpolator, log[·] denotes the logarithm operation; is the posterior probability of the resulting stochastic diffusion path sample under the resulting posterior estimates of the drift and diffusion terms; is the likelihood probability of the wind power observation data under the resulting stochastic diffusion path sample; In each iteration process, firstly, the ADAM algorithm is used to optimize the parameters of the double-layer attention recurrent neural network inside the path interpolator on the given training data set, with the objective of minimizing the semi-supervised learning loss function, and the updated wind power output random diffusion path sample set is updated by using the optimized path interpolator; then, the updated wind power output random diffusion path sample set is subjected to approximate difference operation and Gaussian process regression, and the posterior estimation of the drift term and the diffusion term and the wind power output random process model are updated; The second stage: the wind power output random diffusion path sample in the prediction time window is generated by the path interpolator trained in the first stage, and the random differential equation numerical integrator is trained based on the wind power output random process model optimized in the first stage and the wind power output random diffusion path sample set in the prediction time window, and a supervised learning loss function of the random differential equation numerical integrator is: In the formula, is the training loss of the numerical integrator, p α (·) represents the quantile loss function of predicting quantile level a; is the predicted quantile of wind power at future h time, a quantile level; is the wind power state at future h time; the second stage adopts the ADAM optimization algorithm to train the double-layer attention recurrent neural network inside the numerical integrator to obtain the optimal parameter estimation, with the objective of minimizing the supervised learning loss function.

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