A wind power prediction method based on Gaussian process regression

Abstract

A wind power prediction method based on Gaussian process regression, a target wind turbine wind power prediction model is established, historical data is obtained, the obtained wind speed, wind direction, temperature, air pressure and humidity data of the target wind turbine are substituted into the output model of the wind turbine, so that N groups of wind power data of the target wind turbine are obtained, and the prediction of the wind power is realized; the historical data of the wind turbine in the region is interpolated, the environment field of the target wind turbine is obtained, the Gaussian process regression is adopted, the generator wind power prediction model is obtained, and an effective means for wind power prediction under small sample data is provided.

Description

Technical Field

[0001] This invention belongs to the field of wind power prediction technology, and in particular relates to a wind power prediction method based on Gaussian process regression. Background Technology

[0002] my country has a wide distribution of wind energy resources, which have received widespread attention and vigorous development in recent years. However, due to the extreme volatility of wind, wind power output is unstable, with a large gap between peak and off-peak daily output. The generated wind power cannot be absorbed in time, which easily leads to the phenomenon of "wind curtailment" and causes a large waste of energy.

[0003] The safe and stable operation of the power system requires real-time energy balance. However, wind power output is greatly affected by the external environment, making accurate wind power forecasting necessary. Utilizing forecast data to improve system dispatch capabilities can effectively reduce investment in energy storage equipment and flexibly adjust the power source. Therefore, accurate wind power forecasting can enhance the grid's ability to accommodate the randomness of wind power generation, reduce the impact of wind power fluctuations on grid stability, help power sectors develop more rational dispatch plans, reduce wind curtailment, and significantly improve energy utilization efficiency.

[0004] In practice, due to issues such as short establishment time of wind power sources and improper storage of historical sample data, the sample size is often small, making it difficult to establish an effective prediction model for wind power sources or to guarantee the accuracy of predictions. Inefficient wind power prediction directly affects the stability and security of grid connection, and may lead to a large amount of wind curtailment, resulting in a significant waste of energy.

[0005] The paper "A Wind Power Probability Density Prediction Method Based on Data Mining and Nonlinear Quantile Regression" from Hefei University of Technology combines support vector machines and quantile regression to achieve a good fit to the nonlinear relationship of wind power. However, this method requires a large amount of data and is difficult to adapt to situations with limited historical sample data. Therefore, it is necessary to establish a wind power prediction model based on relevant field source data to improve prediction accuracy under small sample conditions. Summary of the Invention

[0006] In order to overcome the shortcomings of the prior art, the present invention aims to disclose a wind power prediction method based on Gaussian process regression. By interpolating historical data of wind turbines in the region, the environmental field of the target wind turbine is obtained, and Gaussian process regression is used to obtain the wind power prediction model of the generator, thereby providing an effective means for wind power prediction under small sample data.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows:

[0008] A wind power prediction method based on Gaussian process regression includes the following steps:

[0009] (1) Establish a target wind turbine power prediction model with wind speed, wind direction, temperature, air pressure, and humidity as input variables and wind power as output variable:

[0010] Y = F(X1,X2,...,X5) (1)

[0011] Where: Y is the wind power prediction variable; X1, X2, ..., X5 represent the variables of wind speed, wind direction, temperature, air pressure and humidity at the target wind turbine, respectively;

[0012] (2) Suppose there are n wind turbines with sufficient historical wind power output data in the target wind turbine area, and their historical datasets are D1, D2, ..., D... n The sample size is N, where D i ={X i 1,X i 2,…,X i 5,Y i}, i = 1, 2, ..., n; X i 1,X i 2,…,X i 5 represent the historical wind speed, wind direction, temperature, air pressure, and humidity data at the i-th wind turbine in the vicinity of the region, respectively. Y i Y represents the historical wind power data at the i-th wind turbine in the vicinity of the region, and Y i =[y i 1,y i 2,…,y i N ];

[0013] (3) Assume that the output model F(·) of all wind turbines in the region is consistent, and use the historical datasets D1, D2, ..., D n Merge into D A ={X A 1,X A 2,…,X A 5,Y A} and used as the model training dataset, where the input variable data is The output variable data is Y A ={Y 1 ,Y 2 ,…,Y n}, Y i =[y i 1, y i 2,…,y iN Based on input variable data, output variable data, and fused dataset D A The output model F(·) of the wind turbine was established by using the Gaussian process regression method. The input variables are the influencing factors of wind speed, wind direction, temperature, air pressure and humidity, and the output variable is the wind power generation.

[0014] (4) Based on the dataset E1, E2, ..., E of n wind turbines within the target wind turbine area n E i ={S i ,X i 1,X i 2,…,X i 5}, S i Let be the position variable of the i-th wind turbine, which is also the input variable of the environmental field interpolation function. As output variables; for N sets of historical data, interpolation functions G for N environmental fields are established using a Gaussian process regression model. m (·), m=1,2,…,N, interpolate the wind speed, wind direction, temperature, air pressure and humidity data at the target wind turbine N times to obtain the distribution law of the environmental field data E at the location of the target wind turbine under N states;

[0015] (5) Based on the environmental field data E={X1,X2,…,X5} of the target wind turbine, which includes wind speed, wind direction, temperature, air pressure and humidity, substitute it into the output model F(·) of the wind turbine in step (4) to obtain the wind power prediction of the target wind turbine.

[0016] The Gaussian process regression method mentioned in step (3) specifically refers to:

[0017] Gaussian process regression uses a Gaussian process as the model prior, which is represented by the determination of the mean function and covariance function, i.e., equation (2), where the mean function represents the surrogate model for the objective function, and the covariance function represents the uncertainty of the model:

[0018]

[0019] Where m(x) = E[f(x)] is the mean function; It is the covariance function;

[0020] The prior mean function is represented as a linear combination of a set of basis functions:

[0021] m(x)=s T (x)β (3)

[0022] Among them, s T (x)=[s1(x),s2(x),...,sp [x] is a vector composed of basis functions; β is a p×1 regression parameter vector; the prior mean function is set to 0;

[0023] The covariance function determines the interdependence between samples and is represented by a kernel function, with the expression:

[0024]

[0025] Where, σ 2 Here is the variance parameter; The kernel is the correlation kernel, and θ is the parameter vector;

[0026] Covariance functions include the squared exponential covariance function, the Matern 3 / 2 covariance function, and the Matern 5 / 2 covariance function, which are represented as follows:

[0027] (1) Squared exponential covariance function

[0028]

[0029] Where θ is a scale parameter, representing the degree of dependence on the distance between observation points;

[0030] (2) Matern 3 / 2 covariance function

[0031]

[0032] Where θ is the scale parameter;

[0033] (3) Matern 5 / 2 covariance function

[0034]

[0035] Where θ is the scale parameter;

[0036] Based on the definition of Gaussian process prior, let the prior mean function be 0 and the prior covariance function be... Then the training data X A ={X A 1,XA2,…,X A 5}, of which The probability distributions of the predicted data x = [x1, x2, ..., x5] are expressed as follows:

[0037] F(X A )~N(0,K+Δ) (8)

[0038] F(x)~N(0,k t (x,x)) (9)

[0039] Where, K = [kt (x A p ,x A q )] p,q＝1,...,N ,Δ=σ n 2 I;

[0040] Based on formulas (8) and (9), their joint Gaussian distribution is expressed as:

[0041]

[0042] Where, k t (x)=k t (x,x), k t T (x)=[k t (x,x A m )] m＝1,...,N ;

[0043] Based on the marginal distribution properties of the joint Gaussian distribution, the predicted data x follows a distribution:

[0044]

[0045] in:

[0046]

[0047]

[0048] As can be seen from formula (11), there are other necessary parameters and hyperparameters in the model, which are obtained by the maximum likelihood method. First, a negative log-likelihood function based on the conditional probability of the training samples is established and the partial derivatives with respect to the hyperparameters are obtained. The negative log-likelihood function is expressed as:

[0049] L(θ) = -log p(Y) A |X A ,θ) (14)

[0050] In the formula: θ is the set of hyperparameters;

[0051] Then, the partial derivatives are minimized using the conjugate gradient method or Newton's method to obtain the optimal solution for the hyperparameters.

[0052] Step (4) specifically involves:

[0053] The input variable of the environmental field interpolation function is the position variable S of n wind turbines within the target wind turbine area. i Excluding the target wind turbine, the output variables are wind speed, wind direction, temperature, air pressure, humidity, and environmental field [X]. i 1,Xi 2,…,X i [5]; For a set of historical data, using the data of n wind turbines in the region as training data, let the location of the target wind turbine be s. t The environmental field G1(s) at the target wind turbine under this state is obtained by using a Gaussian process regression model. t ) = [xst 1 1,xst 1 2,…,xst 1 5]; then repeat the above steps for the remaining historical data to establish N Gaussian process regression models and obtain the environmental field [G2(s)] at the target wind turbine. t ), G3(s t ),…,G N (s t Thus, the distribution law of the environmental field data E at the location of the target wind turbine in N states is obtained.

[0054] Compared with the prior art, the beneficial technical effects of the present invention are as follows:

[0055] 1. This invention optimizes the environmental prediction accuracy of target wind turbines based on spatial correlation prediction. It uses a Gaussian process regression model to interpolate the historical dataset of wind turbines in the region, establishing a more accurate environmental field model and providing data support for wind power prediction of target wind turbines.

[0056] 2. This invention integrates historical data within the target wind turbine area to establish a wind turbine output model F(·) based on Gaussian process regression, which can be well combined with the obtained environmental field, facilitating rapid acquisition of wind power prediction results. Attached Figure Description

[0057] Figure 1 This is a flowchart of the technical solution of the present invention. Detailed Implementation

[0058] The present invention will now be described in detail with reference to the accompanying drawings.

[0059] Reference Figure 1 A wind power prediction method based on Gaussian process regression includes the following steps:

[0060] (1) Modeling of wind power prediction problem

[0061] Considering the influence of wind speed, wind direction, temperature, air pressure, and humidity on wind turbine power generation, a target wind turbine power prediction model is established with wind speed, wind direction, temperature, air pressure, and humidity as input variables and wind power as the output variable:

[0062] Y = F(X1,X2,...,X5) (2)

[0063] Where: Y is the wind power prediction variable; X1, X2, ..., X5 represent the variables of wind speed, wind direction, temperature, air pressure and humidity at the target wind turbine, respectively.

[0064] (2) Suppose there are n wind turbines with sufficient historical wind power output data in the target wind turbine area, and their historical datasets are D1, D2, ..., D... n The sample size is N, where D i ={X i 1,X i 2,…,X i 5,Y i}, i = 1, 2, ..., n; X i 1,X i 2,…,X i 5 represent the historical wind speed, wind direction, temperature, air pressure, and humidity data at the i-th wind turbine in the vicinity of the region, respectively. Y i Y represents the historical wind power data at the i-th wind turbine in the vicinity of the region, and Y i =[y i 1,y i 2,…,y i N ];

[0065] (3) Training of wind power prediction model based on Gaussian process regression

[0066] Assuming all wind turbines in the region have the same output model, the historical datasets D1, D2, ..., D... n Merge into D A ={X A 1,X A 2,…,X A 5,Y A} and used as the model training dataset, where the input variable data is The output variable data is Y A ={Y 1 ,Y 2 ,…,Y n}, Y i =[y i 1,y i 2,…,y i N Based on input variable data, output variable data, and fused dataset D AA Gaussian process regression method was used to establish the output model F(·) of the wind turbine, where the input variables are the influencing factors of wind speed, wind direction, temperature, air pressure, and humidity, and the output variable is the wind power generation capacity; specifically:

[0067] The Gaussian process regression model uses the Gaussian process as the model prior, and is represented by the determination of the mean function and covariance function, i.e., equation (2), where the mean function represents the surrogate model for the objective function, and the covariance function represents the uncertainty of the model:

[0068]

[0069] Where m(x) = E[f(x)] is the mean function; It is the covariance function;

[0070] The prior mean function can usually be represented as a linear combination of a set of basis functions:

[0071] m(x)=s T (x)β (3)

[0072] Among them, s T (x)=[s1(x),s2(x),...,s p [x] is a vector composed of basis functions; β is a vector of regression parameters of p×1; in fact, for ease of calculation, the prior mean function is usually set to 0.

[0073] The covariance function determines the interdependence between samples. The greater the distance between the predicted data and the known data, the larger the covariance, and the more uncertain the result. In fact, the choice of covariance function has a significant impact on the regression results and is an important component of the Gaussian process model. It is usually represented by a kernel function, and the general expression is:

[0074]

[0075] Where, σ 2 Here is the variance parameter; Let θ be the correlation kernel and θ be the parameter vector.

[0076] Covariance functions include the squared exponential covariance function, the Matern 3 / 2 covariance function, and the Matern 5 / 2 covariance function, which are represented as follows:

[0077] (1) Squared exponential covariance function

[0078]

[0079] Here, θ is a scale parameter, representing the degree of dependence of the distance between observation points.

[0080] (2) Matern 3 / 2 covariance function

[0081]

[0082] Where θ is the scale parameter.

[0083] (3) Matern 5 / 2 covariance function

[0084]

[0085] Where θ is the scale parameter.

[0086] Based on the definition of Gaussian process prior, let the prior mean function be 0 and the prior covariance function be... Then the training data X A ={XA1,X A 2,…,X A 5}, of which The probability distributions of the predicted data x = [x1, x2, ..., x5] are expressed as follows:

[0087] F(X A )~N(0,K+Δ) (8)

[0088] F(x)~N(0,k t (x,x)) (9)

[0089] Where, K = [k t (x A p ,x A q )] p,q＝1,...,N ,Δ=σ n 2 I.

[0090] Based on formulas (8) and (9), their joint Gaussian distribution is expressed as:

[0091]

[0092] Where, k t (x)=k t (x,x), k t T (x)=[k t (x,x A m )] m＝1,...,N .

[0093] Based on the marginal distribution properties of the joint Gaussian distribution, the predicted data x follows a distribution:

[0094]

[0095] in:

[0096]

[0097]

[0098] As can be seen from formula (11), there are other necessary parameters and hyperparameters in the model. These parameters are often not known in advance and need to be estimated based on the training data. They are obtained by the maximum likelihood method. First, a negative log-likelihood function based on the conditional probability of the training samples is established and the partial derivatives with respect to the hyperparameters are obtained. The negative log-likelihood function is expressed as:

[0099] L(θ) = -log p(Y) A |X A ,θ) (14)

[0100] In the formula: θ is the set of hyperparameters.

[0101] Then, the partial derivatives are minimized using the conjugate gradient method or Newton's method to obtain the optimal solution for the hyperparameters.

[0102] (4) Constructing the regional environmental field distribution of the target wind turbine based on Gaussian process regression

[0103] Based on the dataset E1, E2, ..., E of n wind turbines within the target wind turbine area n E i ={S i ,X i 1,X i 2,…,X i 5}, S i Let be the position variable of the i-th wind turbine, which is also the input variable of the environmental field interpolation function. As output variables; for N sets of historical data, interpolation functions G for N environmental fields are established using a Gaussian process regression model. m (·), m=1,2,…,N, interpolate the wind speed, wind direction, temperature, air pressure, and humidity data at the target wind turbine location N times to obtain the distribution law of the environmental field data E at the target wind turbine location under N states; specifically:

[0104] The input variable for this environmental field interpolation function is the position variable S of n wind turbines (excluding the target wind turbine) within the target wind turbine area. i The output variables are wind speed, wind direction, temperature, air pressure, and humidity environmental field [X]. i 1,X i 2,…,X i5]. Using a set of historical data, with the data of n wind turbines in the region as training data, let the location of the target wind turbine be s. t The environmental field G1(s) at the target wind turbine under this state is obtained by using a Gaussian process regression model. t ) = [xst 1 1,xst 1 2,…,xst 1 5).

[0105] Then, repeat the above steps for the remaining historical data to establish N Gaussian process regression models and obtain the environmental field [G2(s)] at the target wind turbine. t ),G3(s t ),…,G N (s t )];

[0106] Thus, the distribution patterns of the environmental field data E at the location of the target wind turbine under N states are obtained.

[0107] (5) Target wind turbine power prediction

[0108] Based on the environmental field data E={X1,X2,…,X5} of the target wind turbine obtained in step (3), the output model F(·) of the wind turbine obtained in step (4) is substituted into it to obtain N sets of wind power data of the target wind turbine, thereby realizing the prediction of wind power.

Claims

1. A wind power prediction method based on Gaussian process regression, characterized in that, Includes the following steps: (1) Establish a target wind turbine power prediction model with wind speed, wind direction, temperature, air pressure, and humidity as input variables and wind power as output variable: Y = F(X1,X2,...,X5) (1) Where: Y is the wind power prediction variable; X1, X2, ..., X5 represent the variables of wind speed, wind direction, temperature, air pressure and humidity at the target wind turbine, respectively; (2) Suppose there are n wind turbines with sufficient historical wind power output data in the target wind turbine area, and their historical datasets are D1, D2, ..., D... n The sample size is N, where D i ={X i 1,X i 2,…,X i 5,Y i }, i = 1, 2, ..., n; X i 1,X i 2,…,X i 5 represent the historical wind speed, wind direction, temperature, air pressure, and humidity data at the i-th wind turbine in the vicinity of the region, respectively. j = 1, 2, ..., 5; Y i Y represents the historical wind power data at the i-th wind turbine in the vicinity of the region, and Y i =[y i 1,y i 2,…,y i N ]; (3) Assume that the output model F(·) of all wind turbines in the region is consistent, and use the historical datasets D1, D2, ..., D n Merge into D A ={X A 1,X A 2,…,X A 5,Y A } and used as the model training dataset, where the input variable data is j = 1, 2, ..., 5 The output variable data is Y A ={Y 1 ,Y 2 ,…,Y n }, Y i =[y i 1,y i 2,…,y i N ]; Based on input variable data, output variable data, and fused dataset D A The output model F(·) of the wind turbine was established by using the Gaussian process regression method. The input variables are the influencing factors of wind speed, wind direction, temperature, air pressure and humidity, and the output variable is the wind power generation. (4) Based on the dataset E1, E2, ..., E of n wind turbines within the target wind turbine area n E i ={S i ,X i 1,X i 2,…,X i 5}, S i Let be the position variable of the i-th wind turbine, which is also the input variable of the environmental field interpolation function. As output variables; for N sets of historical data, interpolation functions G for N environmental fields are established using a Gaussian process regression model. m (·), m=1,2,…,N, interpolate the wind speed, wind direction, temperature, air pressure and humidity data at the target wind turbine N times to obtain the distribution law of the environmental field data E at the location of the target wind turbine under N states; (5) Based on the environmental field data E={X1,X2,…,X5} of the target wind turbine, which includes wind speed, wind direction, temperature, air pressure and humidity, substitute it into the output model F(·) of the wind turbine in step (3) to obtain the wind power prediction of the target wind turbine.

2. The wind power prediction method based on Gaussian process regression according to claim 1, characterized in that, The Gaussian process regression method mentioned in step (3) specifically refers to: Gaussian process regression uses a Gaussian process as the model prior, which is represented by the determination of the mean function and covariance function, i.e., equation (2), where the mean function represents the surrogate model for the objective function, and the covariance function represents the uncertainty of the model: Where m(x) = E[f(x)] is the mean function; It is the covariance function; The prior mean function is represented as a linear combination of a set of basis functions: m(x)=s T (x)β (3) Among them, s T (x)=[s1(x),s2(x),...,s p [x] is a vector composed of basis functions; β is a p×1 regression parameter vector; the prior mean function is set to 0; The covariance function determines the interdependence between samples and is represented by a kernel function, with the expression: Where, σ 2 Here is the variance parameter; The kernel is the correlation kernel, and θ is the parameter vector; Covariance functions include the squared exponential covariance function, the Matern 3 / 2 covariance function, and the Matern 5 / 2 covariance function, which are represented as follows: (1) Squared exponential covariance function Where θ is a scale parameter, representing the degree of dependence on the distance between observation points; (2) Matern 3 / 2 covariance function Where θ is the scale parameter; (3) Matern 5 / 2 covariance function Where θ is the scale parameter; Based on the definition of Gaussian process prior, let the prior mean function be 0 and the prior covariance function be... Then the training data X A ={X A 1,X A 2,…,X A 5}, of which j = 1, 2, ..., 5 The probability distributions of the predicted data x = [x1, x2, ..., x5] are expressed as follows: F(X A )~N(0,K+Δ) (8) F(x)~N(0,k t (x,x)) (9) where K = [k t (x A p ,x A q )] p,q＝1,...,N , Δ = σ n 2 I; Based on formulas (8) and (9), their joint Gaussian distribution is expressed as: Where, k t (x)=k t (x,x), k t T (x)=[k t (x,x A m )] m＝1,...,N ; Based on the marginal distribution properties of the joint Gaussian distribution, the predicted data x follows a distribution: in: As can be seen from formula (11), there are other necessary parameters and hyperparameters in the model, which are obtained by the maximum likelihood method. First, a negative log-likelihood function based on the conditional probability of the training samples is established and the partial derivatives with respect to the hyperparameters are obtained. The negative log-likelihood function is expressed as: L(θ)=-log p(Y A |X A ,i) (14) In the formula: θ is the set of hyperparameters; Then, the partial derivatives are minimized using the conjugate gradient method or Newton's method to obtain the optimal solution for the hyperparameters.

3. The wind power prediction method based on Gaussian process regression according to claim 1, characterized in that, Step (4) specifically involves: The input variable for this environmental field interpolation function is the position variable S of n wind turbines within the target wind turbine area. i Excluding the target wind turbine, the output variables are wind speed, wind direction, temperature, air pressure, humidity, and environmental field [X]. i 1,X i 2,…,X i [5]; For a set of historical data, using the data of n wind turbines in the region as training data, let the location of the target wind turbine be s. t The environmental field G1(s) at the target wind turbine under this state is obtained by using a Gaussian process regression model. t )=[xst 1 1,xst 1 2,…,xst 1 5]; then repeat the above steps for the remaining historical data to establish N Gaussian process regression models and obtain the environmental field [G2(s)] at the target wind turbine. t ),G3(s t ),…,G N (s t Thus, the distribution law of the environmental field data E at the location of the target wind turbine in N states is obtained.

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