Photovoltaic power prediction method for Gaussian mixture error probability distribution compensation based on initial value optimization

Abstract

The invention discloses a photovoltaic power prediction method for Gaussian mixture error probability distribution compensation based on initial value optimization, and the method comprises the steps: carrying out the fitting of a distribution rule of a photovoltaic power preliminary prediction error through employing a Gaussian mixture model (GMM) based on initial value optimization according to a photovoltaic prediction error, and carrying out the calculation of the distribution rule of the photovoltaic power preliminary prediction error; and compensating a predicted value of the error to a point prediction result to realize interval prediction of photovoltaic output. As environmental factors such as illumination intensity, temperature, visibility and the like have great influence on a prediction result of photovoltaic power generation output, historical photovoltaic output data are divided into a plurality of different weather scenes by adopting a K-means clustering algorithm (K-means) based on an irradiance index, an optimal initial value data set selected by inputting a whale optimization algorithm (WOA), and the prediction result of the photovoltaic power generation output is predicted by using a prediction result of the photovoltaic power generation output according to the optimal initial value data set selected by the whale optimization algorithm (WOA). And then a Gaussian mixture distribution model is adopted and an expectation maximization (EM) method is combined to solve a model optimal parameter so as to carry out modeling analysis on probability distribution of photovoltaic prediction errors, and a model fitting result is used to correct a photovoltaic power generation power point prediction value under a specified confidence level interval so as to obtain a final prediction interval. According to the scheme provided by the invention, simulation analysis is carried out by taking photovoltaic power data of a certain photovoltaic power station in Jiangsu province as an example, and a result shows that the method provided by the invention has better fitness and reliability.

Description

Technical Field

[0001] The invention relates to photovoltaic power prediction technology, and in particular to a photovoltaic power prediction method based on initial value optimization and Gaussian mixture error probability distribution compensation. Background Art

[0002] In recent years, countries around the world have devoted themselves to the plan of realizing the transformation to new energy. Whether the renewable clean energy such as solar energy and wind energy can be used efficiently is gradually becoming the key to solving the world energy crisis. With its unique geographical advantages, my country has rapidly expanded the scale of photovoltaic power generation. Although photovoltaic power generation is regarded as an important part of achieving low carbon, due to the discontinuity and uncertainty of its output, the large-scale grid connection of photovoltaics has also brought related problems such as operation stability and reasonable scheduling planning to the modern power system, and the reasonable planning and scheduling of photovoltaic power is more significant. In order to ensure the power quality of the power grid after photovoltaic grid connection, it is necessary to accurately predict the photovoltaic output. Therefore, how to accurately predict the output power of photovoltaic power stations is of great significance to improving the operating efficiency of photovoltaic power stations and even the planning and operation of the entire system.

[0003] At present, most of the research focuses on the point prediction of power. However, the volatility of solar radiation and the weak anti-interference of photovoltaic power generation equipment make the error of point prediction impossible to be completely ignored. Direct point prediction contains limited information and cannot describe the fluctuation and multi-peak characteristics of photovoltaic power. Therefore, it is necessary to design a new method to meet the actual needs. Summary of the invention

[0004] In response to the above problems, the present invention proposes to use a Gaussian mixture distribution model to describe the distribution characteristics of the photovoltaic output prediction error after weather classification. The K-means clustering algorithm based on the irradiance index is used to classify the original environmental data according to the characteristics of different meteorological conditions. In order to solve the problem that there are abnormal fluctuation points in the initial value data set of the model, the whale optimization algorithm is introduced to perform adaptive optimization. Then, the Gaussian probability density function is combined with the expectation maximization algorithm to solve the model parameters and fit the distribution of prediction errors in different scenarios, and compare and analyze them with the fitting results of several traditional distribution models. Finally, the evaluated error value is fed back to compensate for the point prediction result to determine the interval range of photovoltaic power generation prediction at a specified confidence level.

[0005] S1: Weather division: The present invention first analyzes the error distribution after the traditional point prediction, and finds that its error distribution is greatly affected by different weather conditions. Therefore, the K-means algorithm based on the irradiance index is introduced to cluster the original environmental data and divide it into multiple weather groups with obvious characteristics. The K-means algorithm is an unsupervised real-time clustering algorithm. Its core is to generate the initial data set center point based on the specified number of clusters, and divide each point in the original data into the cluster represented by the closest cluster center. After all points are assigned, the center point of the cluster is recalculated according to the difference relationship between all points in a cluster, and each object is reassigned to its closest cluster for iteration until the convergence condition or the specified number of iterations is reached.

[0006] The purpose of the K-means algorithm iteration process is to find the number of clusters that minimize the square error function value. Its definition is as follows:

[0007]

[0008] Where E is the sum of squared errors of all objects in the database, k is the number of clusters initially specified, p is a point in space, and also represents a given original data point, m i It is cluster C i Under this criterion, the data in each cluster generated can be kept as compact and independent as possible.

[0009] Regarding the classification indicators of the algorithm, compared with the commonly used classification scheme based on the functional relationship between the difference between the predicted value and the actual value, the present invention uses two basic indicators based on the average solar irradiance and the average fluctuation of the irradiance to cluster the collected photovoltaic data. Under this scheme, the characteristics of the data distribution under various weather conditions can be concentrated on one graph. Compared with the traditional classification method, the data distribution characteristics of each weather category and the location of each cluster center point are more intuitive.

[0010] S2: Optimization of the initial value of the model: Since the initial value of the Gaussian distribution model is determined by its mean and variance, the selection of these two values ​​is determined by the selected input data set. When selecting the data set of the model input variable, due to the randomness of the environmental data, the input data may contain some abnormally fluctuating data points, which in turn leads to deviations in the model's fitting effect on the data. Or due to the limitation of the number of data sets, the model parameters are prone to converge to the local optimal solution. Here, the whale optimization algorithm is introduced to perform global optimization on the data combination of the model input, and eliminate abnormal fluctuation points on the basis of ensuring the multi-peak characteristics of the overall data; the whale optimization algorithm takes random individuals in the population as the target prey, and based on the random characteristics of the initial data, after ensuring that there are no abnormal points in each data set, the maximum information entropy value of the data set is taken as the fitness target. In each subsequent iteration, assuming that the current best candidate whale is the target prey, other whales will surround and shrink towards this position to form the target data set. The mathematical model is as follows:

[0011] X(t+1)=X * (t)-A·D

[0012]

[0013] In the formula, X* represents the current best candidate whale position vector, X represents the position vector, t represents the current iteration number, D represents the step vector of the whale individual approaching X*, and the j-th dimension component D of D is j From the formula, X j * and X j They represent the j-th dimension components of X* and X respectively, and A and C are coefficients. A represents a random number on [-2, 2], and C represents a random number on [0, 2]. Their definitions are as follows:

[0014] A=2a·ra

[0015] C=2·r

[0016] Where r is a random number in [0, 1]; a is called the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases. The definition of a is as follows:

[0017]

[0018] In the formula, t max is the maximum number of iterations.

[0019] Whales can attack prey through bubble nets, and can also use the encirclement and contraction mechanism to approach prey. In order to implement the two mechanisms at the same time, a probability of P0 = 50% is selected to update the position of the whale. The mathematical model is as follows:

[0020]

[0021] Where D' represents the distance vector between the whale and X*, and the j-th dimension component of D' is D' j =|X* j (t)-X j (t)|, b is a constant coefficient used to define the shape of the logarithmic spiral, and l takes a random number on [-1, 1].

[0022] In the iterative update process of the whale population position, when |A|<1, the whale returns to the first step to update the position; when |A|≥1, the whale is forced to move to the randomly selected reference whale position vector X rand Update the position as shown below:

[0023] D=|C·X rand -X(t)|

[0024] X(t+1)=X rand -A.D

[0025] S3: Establishment of Gaussian distribution model and parameter solution: Use Gaussian mixture model to fit the probability distribution of prediction errors at different levels, and obtain the results of interval prediction based on this. By changing the corresponding parameters within the Gaussian mixture model, such as the number of components, weight coefficients, mean, and covariance matrix of each component, different probability density distributions can be accurately characterized. For the non-convex optimization problem existing in the Gaussian distribution model, the expectation maximization method is used to solve the parameters in the model. This method is specifically implemented by iteratively calculating and updating the parameters of the model; the probability density function of a single Gaussian distribution can be represented by a specific mathematical model, as shown in the formula:

[0026]

[0027] In the formula, μ and σ 2 are the mean and variance of the Gaussian distribution.

[0028] The Gaussian mixture distribution composed of weighted combinations of multiple single Gaussian distribution functions is expressed as:

[0029]

[0030] Where θ is the parameter set of the mean and variance of each Gaussian component, θ={θ1,θ2,θ3,…,θ k}; a k is the weight coefficient assigned to the kth Gaussian component; satisfying a k ≥0 and in It is expressed as the probability density function of Gaussian distribution, and its expression is:

[0031]

[0032] After selecting the initial value, the model parameters are solved. According to the existing power prediction error data, the parameters can be determined by the maximum likelihood estimation method. The objective equation of the Gaussian mixture model is expressed as:

[0033]

[0034] In view of the non-convex optimization problem in the above formula, the expectation maximization method is used to solve the parameters in the model. This method is implemented by iteratively calculating and updating the parameters of the model. When facing the problem of solving model parameters, it is usually preferred to select a type of parameters that have a greater impact on the model fitting results. In the above Gaussian mixture distribution model, it is obvious that determining the total number of Gaussian components k is the key point in selecting the GMM model. In theory, k can be set to a larger value so that as many Gaussian distribution functions as possible can be used to make the final prediction results more accurate. When solving the model parameters, only the components with larger weight coefficients need to be considered, and the part with smaller weights needs to be discarded. Therefore, when setting the k value, it is necessary to ensure that the weight coefficients corresponding to each of the k Gaussian components are as large as possible, and there should be no meaningless calculations caused by parameter iterations of too many components with small weight coefficients.

[0035] The algorithm first gives an initial value for the weight parameter:

[0036]

[0037] All mean vectors μ k The calculated values ​​at the center of the data density are selected in turn. The diagonal elements of all covariance matrices should be equal to the side length of the matrix containing the measured data set, and when both sub-diagonal elements are 0, the iteration process of the entire algorithm can be guaranteed to be faster.

[0038] According to the given initial value of the weight parameter, a Gaussian component is randomly selected, and a specific distribution prediction is formed according to the density function PDF corresponding to the selected random component. Therefore, a hidden variable Z can be introduced m To characterize the observed quantity X m The subordinate relationship with the Gaussian density function PDF, that is, which Gaussian component forms this observation, is as follows: m (Z m ) indicates the probability of this relationship occurring:

[0039]

[0040] Then, based on the obtained results, the parameters in GMM are updated and iterated according to the following formula.

[0041]

[0042]

[0043]

[0044] The above iterative process is repeated until the GMM parameters of two iterations are basically the same or the maximum number of iterations is reached, and the optimal model parameters that satisfy the above optimization equation are obtained.

[0045] S4: Case analysis and verification: The historical photovoltaic power data and corresponding environmental data of a photovoltaic power station in Jiangsu Province were simulated and calculated, and compared with the fitting results of the traditional probability distribution model. The results show that the proposed method has good adaptability and reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0047] Figure 1 A flowchart of a photovoltaic power prediction method based on initial value optimization and Gaussian mixture error probability distribution compensation provided by the present invention;

[0048] Figure 2 It is a distribution diagram of prediction errors of the point prediction model when analyzing errors of the present invention;

[0049] Figure 3 It is a K-means clustering scatter plot based on irradiance of the present invention;

[0050] Figure 4 is the optimized initial data distribution diagram of the present invention;

[0051] Figure 5 is a randomly selected data distribution diagram of the present invention;

[0052] Figure 6 It is a comparison of the error distribution model fitting results under different weather conditions of the present invention;

[0053] Figure 7 is the prediction result after the error distribution probability correction of the present invention; DETAILED DESCRIPTION

[0054] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] The purpose of the present invention is to provide a photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation with initial value optimization to solve the problems existing in the above-mentioned prior art and to be able to reliably and accurately predict the power size of photovoltaic output.

[0056] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail in combination with the accompanying drawings and specific embodiments. The original data uses the actual regional photovoltaic output data recorded by a photovoltaic power station in Jiangsu Province from March 1 to October 1, 2020. It also includes the environmental monitoring data of the photovoltaic array area. The sampling period is 15 minutes and the effective recording time is 241 days.

[0057] The present invention provides a photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation based on initial value optimization, such as Figure 1 As shown, the Gaussian mixture distribution model based on initial value optimization and its implementation steps are as follows:

[0058] (I) Point prediction error analysis and weather clustering:

[0059] The EMD-KPCA-LSTM point prediction method is used to predict photovoltaic output. The prediction model is built using MATLAB R2021 for simulation. The training set and test set ratios for the point prediction part are 0.8 and 0.2 respectively. The results are rounded, and the first 192 days are taken as the training set and the last 49 days as the test set. Under different humidity, the error distribution of the prediction results is as follows Figure 2 shown.

[0060] Depend on Figure 2 It can be seen that under low ambient humidity, due to the adaptability of the long short-term memory network model itself to the processing of time series environmental data, under the condition that the input variables remain unchanged, the overall prediction accuracy is high and the error change range is not large. However, when the ambient humidity value gradually increases, that is, when it is in an external environment such as rainy days, the error has a large-scale continuous mutation and is in a trend of gradually increasing. It is not difficult to see that the change in weather conditions has a great impact on the accuracy of point predictions, and the fluctuation range of the error in a high humidity environment is much larger than that in a dry environment. A single point prediction cannot accurately control it. Therefore, it is necessary to pre-group the original environmental data according to its fluctuations and discuss the error changes in different groups.

[0061] The data clustering results are as follows Figure 3 As shown, compared with the commonly used classification scheme based on the functional relationship between the difference between the predicted value and the actual value, the present invention uses two basic indicators based on the average solar irradiance and the average fluctuation of irradiance to cluster the collected photovoltaic data. According to the dense piles of several points distributed on the scatter plot obtained after the photovoltaic data clustering, the weather conditions are roughly divided into three typical weather scenes: sunny days, cloudy days, and thunderstorm days. Due to the particularity of each region, very individual meteorological conditions such as sunny to cloudy, sunny to rainy, etc. or extreme weather phenomena are not considered for the time being. The sample data after K-means clustering can be divided into three groups, namely 104 sunny days, 75 cloudy days and 62 rainy days. The probability distribution model of the corresponding prediction error is established under these three weather types, and the error probability distribution result under the specified confidence level is fitted.

[0062] (II) Optimization of initial value of model input

[0063] The model input was optimized before data normalization. The error value was less than 6 as the threshold function and the variance of the data set was the largest as the objective function. The number of whales was set to 46 and the maximum number of iterations was t max It is set to 200. In order to reflect the advantages of introducing the WOA algorithm, a set of optimized data sets in the "cloudy day" group is taken for comparative analysis with a randomly selected data set.

[0064] Figure 4 This is the dataset optimized by the whale algorithm. Figure 5 The data distribution in the data set does not contain abnormally fluctuating data points, and the overall numerical distribution does not tend to be mediocre. There are still multi-peak characteristics and fluctuations. It is suitable as the initial data set for testing the fitting fitness of the probability distribution model for multi-type error distribution, and also makes the results after model fitting more reliable and convincing. The example results show that this method has good practicality and reliability.

[0065] (III) Gaussian mixture model parameter solution and error fitting

[0066] Through multiple simulations and empirical selection, under the premise of ensuring that each Gaussian density function decomposed by the model has a large weight coefficient, the number of Gaussian distribution model sub-functions is selected as 3. The third-order Gaussian mixture distribution model containing these three Gaussian component functions is applied to fit the error probability distribution in each scene after classification. Table 1 gives the final results of the main parameters of each component in the Gaussian mixture distribution model after iteration under different weather scenarios.

[0067] Table 1 Parameter values ​​of Gaussian mixture distribution model under different weather conditions

[0068]

[0069] In order to verify the adaptability of the scheme to multi-peak error data, the fitting results of several typical single probability distribution models (normal distribution, logistic distribution, t distribution) and Gaussian mixture distribution models for error distribution under three different weather conditions were compared and analyzed horizontally, and the adaptability of these fitting curves to the error distribution probability was evaluated. The model evaluation indicators were further calculated and the data are listed in Table 2.

[0070] Figure 6 The figure shows the comparison of the fitting effect of the above four distribution models on the error distribution under three climate conditions: thunderstorm, cloudy and clear. Figure 6 It is not difficult to see that among the different types of error distributions, the error under sunny conditions is more consistent with the normal distribution model, but in other cases, the normal distribution model has a poor fit. The lack of recognition of multi-peak data causes the distribution of the probability fitting center to be concentrated on a single error value, and it is impossible to accurately predict the probability of error distribution. The centralized advantages of the t distribution model and the logistic distribution over the normal distribution are both reflected in the fitting of the tail data, but there is still a large deviation in the fitting when facing multi-peak conditions. Compared with these three distribution models, the Gaussian mixture distribution can quickly identify the local maximum points and adjust the extreme value distribution of the probability distribution curve to reflect them when facing multi-peak data, and the overall fitting effect is better.

[0071] Table 2 Evaluation indicators of each distribution model under different weather conditions

[0072]

[0073] According to the three fitting utility evaluation criteria listed in Table 2, as the error type evolves from normal distribution, t distribution, and Logistic distribution to GMM distribution, the MAE and RMSE values ​​gradually show a decreasing trend, and at the same time, the R2 value shows a gradually increasing trend. The analysis results show that GMM outperforms the other three models in model fitting ability, especially when the weather conditions are cloudy and thunderstorms, the error distribution shows significant multi-peak and asymmetric characteristics. Compared with the best performing logistic distribution in the traditional distribution, the RMSE of the GMM model is reduced by 43% and 44%, the MAE is reduced by 20% and 28%, and the R2 value is increased by 19% and 9%.

[0074] After obtaining the interval distribution model of the forecast error, the fitting result is substituted back into the point forecast value to correct the forecast value. Figure 7The figure shows the prediction result interval after the error distribution is corrected. The confidence level is 0.9. In the prediction results of the randomly selected time period, the final prediction interval coverage rate CP basically reaches 100%, which has higher accuracy and reliability than the traditional photovoltaic power prediction scheme.

[0075] The present invention uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the method and core ideas of the present invention. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation with initial value optimization, characterized in that: The steps include: S1: Weather classification: First, the error distribution after traditional point prediction is analyzed. It is found that its error distribution is greatly affected by different weather conditions. Therefore, the K-means algorithm based on irradiance index is introduced to cluster the original environmental data and divide it into multiple weather groups with obvious characteristics. S2: Optimization of model initial values: Since the initial values ​​of the Gaussian distribution model are determined by its mean and variance, the selection of these two values ​​is determined by the selected input data set. When selecting the data set of the model input variables, due to the randomness of the environmental data, the input data may contain some abnormally fluctuating data points, which may lead to deviations in the model's fitting effect on the data; or due to the limitation of the number of data sets, the model parameters are prone to converge to the local optimal solution. Here, the whale optimization algorithm is introduced to perform global optimization on the data combination of the model input, and eliminate abnormal fluctuation points on the basis of ensuring the multi-peak characteristics of the overall data; S3: Establishment of Gaussian distribution model and parameter solution: Use Gaussian mixture model to fit the probability distribution of prediction errors at different levels, and obtain the results of interval prediction based on this; By changing the corresponding parameters inside the Gaussian mixture model, the parameters include: number of components, weight coefficients, averages and covariance matrices of each component, different probability density distributions can be accurately characterized. For the non-convex optimization problem existing in the Gaussian distribution model, the expectation maximization method is used to solve the parameters in the model. This method is specifically implemented by iteratively calculating and updating the parameters of the model; S4: Case analysis and verification: Simulation calculations were performed using historical photovoltaic power data and corresponding environmental data, and compared with the fitting results of the traditional probability distribution model.

2. The photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation with initial value optimization according to claim 1 is characterized in that: In step S1, weather classification is completed by the following method: K-means algorithm is an unsupervised real-time clustering algorithm. Its core is to generate the initial data set center point based on the specified number of clusters, and divide each point in the original data into the cluster represented by the nearest cluster center. After all points are assigned, the center point of a cluster is recalculated based on the difference relationship between all points in a cluster, and then each object is reassigned to its closest cluster for iteration until the convergence condition or the specified number of iterations is reached; The purpose of the K-means algorithm iteration process is to find the number of clusters that minimize the square error function value. Its definition is as follows: Where E is the sum of squared errors of all objects in the database, k is the number of clusters initially specified, p is a point in space, and also represents a given original data point, m i It is cluster C i Under this criterion, the data in each cluster finally generated can be kept as compact and independent as possible.

3. The photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation with initial value optimization according to claim 2 is characterized in that: The relationship between the average irradiance value and the irradiance fluctuation value is used to reflect the weather environment in which the error occurs, and this indicator is used as the criterion for dividing the error groups.

4. The photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation with initial value optimization according to claim 1 is characterized in that: The specific optimization scheme of the model initial value in step S2 is: In view of the complexity of data distribution, the whale optimization algorithm is used to screen and optimize it. The whale optimization algorithm takes random individuals in the population as target prey. According to the random characteristics of the initial data, after ensuring that there are no abnormal points in each data set, the maximum information entropy value of the data set is taken as the fitness target; in each subsequent iteration process, it is assumed that the current best candidate whale is the target prey, and other whales will surround and shrink towards this position to form the target data set.

5. The photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation based on initial value optimization according to claim 4 is characterized in that: The whale optimization algorithm cited above takes into account that whales can attack prey through bubble nets and approach prey using a surrounding and contraction mechanism; in order to implement the two mechanisms simultaneously, a probability index of P0=50% is selected to update the position of the whale; During the iterative update process of the whale population position, when the absolute value of the coefficient |A|<1, the whale returns to the first step to update the position; when |A|≥1, the whale is forced to iterate to update the position to the randomly selected reference whale position vector.

6. The photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation with initial value optimization according to claim 1 is characterized in that: The steps for establishing the Gaussian distribution model in step S3 are: The probability density function of a single Gaussian distribution can be expressed by a specific mathematical model, as shown in the formula: In the formula, μ and σ 2 are the mean and variance of the Gaussian distribution respectively; The Gaussian mixture distribution composed of weighted combinations of multiple single Gaussian distribution functions is expressed as: Where θ is the parameter set of the mean and variance of each Gaussian component, θ={θ1,θ2,θ3,…,θ k }; a k is the weight coefficient assigned to the kth Gaussian component; satisfying a k ≥0 and in It is expressed as the probability density function of Gaussian distribution, and its expression is:

7. The photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation with initial value optimization according to claim 6 is characterized in that: The objective function is determined before the solution process begins. Based on the existing power prediction error data, the objective equation of the Gaussian mixture model is expressed as a non-convex optimization problem as follows:

8. The photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation with initial value optimization according to claim 6 is characterized in that: In view of the non-convex optimization problem in the above formula, the expectation maximization method is used to solve the parameters in the model. This method is implemented by iteratively calculating and updating the parameters of the model. In the above Gaussian mixture distribution model, determining the total number k of Gaussian components is the key point in selecting the GMM model. Setting k to a larger value allows as many Gaussian distribution functions as possible to make the final prediction result more accurate. When solving the model parameters, only the components with larger weight coefficients need to be considered, and the smaller weights are discarded.

9. The photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation with initial value optimization according to claim 6 is characterized in that: The expectation maximization method is used for the non-convex optimization problem of the objective function of the Gaussian mixture distribution model. The following scheme is used to select and deal with it to ensure the convergence of the algorithm. First, an initial value of the weight parameter is given, and all mean vectors μ k The calculated values ​​at the center of the data density are selected in turn. The diagonal elements of all covariance matrices should be equal to the side length of the matrix containing the measured data set, and when both sub-diagonal elements are 0, the iteration process of the entire algorithm can be guaranteed to be faster.

10. The photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation with initial value optimization according to claim 6, characterized in that: The expectation maximization method for solving non-convex optimization problems adopts the following iterative process: randomly select Gaussian components according to the given initial value of the weight parameter, and form a specific distribution prediction based on the density function PDF corresponding to the selected random component; introduce a hidden variable Z m To characterize the observed quantity X m The subordinate relationship with the Gaussian density function PDF, that is, which Gaussian component forms this observation, is as follows: m (Z m ) indicates the probability of this relationship occurring: Then, the parameters in the GMM are updated and iterated according to the obtained results; the above iterative process is repeated until the GMM parameters of two iterations are basically the same or the maximum number of iterations is reached, and the optimal model parameters that satisfy the above optimization equation are obtained.

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