A photovoltaic power prediction method based on initial value optimization of Gaussian mixture error probability distribution compensation

Abstract

The application discloses a photovoltaic power prediction method based on initial value optimization and Gauss mixed error probability distribution compensation, and the method comprises the following steps: for the error of photovoltaic prediction, a Gauss mixed distribution model (GMM) based on initial value optimization is used to fit the distribution rule of the preliminary photovoltaic power prediction error, and then the prediction value of the error is compensated to the result of point prediction to realize interval prediction of photovoltaic output. Since environmental factors such as illumination intensity, temperature and visibility have a great influence on the prediction result of photovoltaic power generation output, a K-means clustering algorithm based on irradiance index (K-means) is used to divide historical photovoltaic output data into multiple different weather scenes, the optimal initial value data set selected by inputting a Whale Optimization Algorithm (WOA) is used, then a Gauss mixed distribution model is used in combination with an expectation maximum algorithm (EM) to obtain optimal parameters of the model, and the probability distribution of photovoltaic prediction error is modeled and analyzed, and under a specified confidence level interval, the model fitting result is used to correct the photovoltaic power point prediction value, so that the final prediction interval is obtained. The scheme provided by the application takes photovoltaic power data of a photovoltaic power station in Jiangsu Province as an example for simulation analysis, and the result shows that the method has better fitness and reliability.

Description

Technical Field

[0001] The present invention relates to photovoltaic power prediction technology, 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 been committed to transitioning to new energy sources. The efficient utilization of renewable energy sources such as solar and wind power is becoming crucial to resolving the global energy crisis. my country, leveraging its unique geographical advantages, has rapidly expanded photovoltaic power generation. While considered a crucial component of achieving low-carbon development, the discontinuous and uncertain nature of its output has led to large-scale grid-connected photovoltaic power systems, raising challenges related to operational stability and proper scheduling. The proper planning and scheduling of photovoltaic power is particularly significant. Accurate prediction of photovoltaic output is essential to ensure grid power quality after photovoltaic grid integration. Therefore, accurate prediction of photovoltaic power station output is crucial for improving operational efficiency and, ultimately, the planning and operation of the entire system.

[0003] Currently, most research focuses on point-based power prediction. However, the volatility of solar radiation and the weak interference immunity of photovoltaic power generation equipment make point-based prediction errors difficult to completely ignore. Direct point-based predictions contain limited information and fail to capture the fluctuations and multimodal characteristics of photovoltaic power. Therefore, it is necessary to design a new method to meet practical 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 different meteorological conditions. In order to solve the problem of 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 under different scenarios. It is then compared and analyzed 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 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 based on 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. It is defined 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 the 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 variables, 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 convergence to local optimal solutions. 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 uses random individuals in the population as 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, the 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] Where X* represents the current best candidate whale position vector, X represents the position vector, t represents the current number of iterations, 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 Denote 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 the range [0, 1]; a is called the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases. a is defined as follows:

[0017]

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

[0019] Whales can attack prey using a bubble net or approach them using a constriction mechanism. To enable both mechanisms to operate simultaneously, a probability of P0 = 50% is chosen to update the whale's position. 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] During 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 under different degrees, 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] Where μ and σ 2 are the mean and variance of the Gaussian distribution, respectively.

[0028] The Gaussian mixture distribution composed of a weighted combination 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 weighting 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 values, the model parameters are solved. Based on 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] To address the non-convex optimization problem in the above equation, the expectation maximization method is used to solve the model parameters. This method is implemented by iteratively calculating and updating the model parameters. When faced with the problem of solving model parameters, priority is usually given to selecting a class of parameters that have a greater impact on the model fitting results. In the above-mentioned Gaussian mixture distribution model, determining the total number of Gaussian components, k, is obviously the key point in selecting the GMM model. Theoretically, 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 smaller weights need 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 unnecessary computational effort caused by iterating the parameters 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 meet 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 following briefly introduces the drawings required for use in the embodiments. 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 any 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 This is a distribution diagram of the prediction error of the point prediction model when analyzing the error 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 graph 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 error distribution probability correction of the present invention; DETAILED DESCRIPTION

[0054] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts 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 reliably and accurately predict the power size of photovoltaic output.

[0056] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, the present invention is further described in detail with reference to the accompanying drawings and specific embodiments. The original data used is the actual regional photovoltaic output data recorded by a photovoltaic power station in Jiangsu Province between March 1 and October 1, 2020. It also includes 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] (1) 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 used as the training set and the last 49 days are used as the test set. Under different humidity conditions, 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 processing time-series environmental data, when the input variables remain unchanged, the overall prediction accuracy is high and the error change 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 shows a large-scale continuous mutation and the overall trend is gradually increasing. It is not difficult to see the great impact of weather changes on the accuracy of point predictions. In addition, the fluctuation range of the error in high humidity environments is much greater than that in dry conditions. A single point prediction cannot accurately control it. Therefore, it is necessary to pre-group the original environmental data according to its fluctuation and discuss the error changes within 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 clusters the collected photovoltaic data based on two basic indicators: the average solar irradiance and the average fluctuation of the irradiance. According to the dense distribution of several points on the scatter plot obtained after the photovoltaic data clustering, the weather conditions are roughly divided into three typical weather scenes: sunny, cloudy, and thunderstorm. 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. After K-means clustering, the sample data can be divided into three groups, namely 104 sunny days, 75 cloudy days and 62 rainy days. Under these three weather types, the probability distribution model of the corresponding prediction error is established, and the error probability distribution result under the specified confidence level is obtained by fitting.

[0062] (2) Optimization of initial value of model input

[0063] Before data normalization, the model input was optimized. 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 Set to 200. In order to reflect the advantages of 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 this dataset does not contain abnormally fluctuating data points, while the overall numerical distribution does not tend to be mediocre. It still has multimodal characteristics and fluctuations. This makes it suitable as an initial dataset for testing the fitness of probability distribution models for multi-type error distributions. It also makes the results of model fitting more reliable and convincing. The results of the example show that this method has good practicality and reliability.

[0065] (3) 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. By applying the third-order Gaussian mixture distribution model containing these three Gaussian component functions, the error probability distribution under each scene after classification is fitted and analyzed. Table 1 shows 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] To verify the adaptability of this scheme to multimodal error data, we conducted a comparative analysis of the error distribution fitting results of several typical single probability distribution models (normal, logistic, and t-distribution) and a Gaussian mixture distribution model under three different weather conditions. We also evaluated the adaptability of these fitting curves to the error distribution probability. We further calculated model evaluation metrics and list the data in Table 2.

[0070] Figure 6 The figure shows the comparison of the fitting effect of the four distribution models on the error distribution under three climatic conditions: thunderstorm, cloudy and clear. Figure 6 It is not difficult to see that among the different types of error distributions, the error under clear weather conditions is more consistent with the normal distribution model, but in other cases, the normal distribution model fits poorly. Insufficient recognition of multi-peak data results in the distribution of the probability fit center being concentrated on a single error value, making it impossible to accurately predict the error distribution probability. The t-distribution model and the logistic distribution have advantages over the normal distribution in fitting tail data, but the fit still has significant deviations when dealing with multi-peak data. Compared with these three distribution models, the Gaussian mixture distribution can quickly identify local maxima points when dealing with multi-peak data and adjust the extreme value distribution of the probability distribution curve to reflect them, resulting in a better overall fit.

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

[0072]

[0073] According to the three goodness-of-fit 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 downward trend, while the R² value shows a gradual upward trend. The analysis results show that GMM outperforms the other three models in model fitting ability, especially in cloudy and thunderstorm weather conditions, where the error distribution exhibits significant multimodal and asymmetric characteristics. Compared with the logistic distribution, the best performing traditional distribution, the GMM model's RMSE decreases by 43% and 44%, MAE decreases by 20% and 28%, and R² increases by 19% and 9%, respectively.

[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, with a confidence level of 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 traditional photovoltaic power prediction schemes.

[0075] The present invention uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A photovoltaic power prediction method based on initial value optimization and Gaussian mixture error probability distribution compensation, characterized by: The steps include: S1: Weather classification: First, we analyze the error distribution of traditional point predictions. We find that the error distribution is greatly affected by different weather conditions. Therefore, we introduce the K-means algorithm based on the irradiance index 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 for 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 convergence to local optimal solutions. Here, the whale optimization algorithm is introduced to perform global optimization on the data combination of the model input, eliminating abnormal fluctuation points while ensuring the multimodal 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 under different degrees, and obtain the results of interval prediction based on this. By changing the corresponding parameters within the Gaussian mixture model, including the number of components, weight coefficients, mean, and covariance matrix of each component, different probability density distributions can be accurately characterized. In response to 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 implemented by iteratively calculating and updating the model parameters. 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; 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: Where μ and σ 2 are the mean and variance of the Gaussian distribution respectively; The Gaussian mixture distribution composed of a weighted combination 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 weighting 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:

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: 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 cluster center closest to it. After all points are assigned, the center point of a cluster is recalculated based on the difference relationship between all points in a cluster. Each object is then reassigned to its closest cluster and iterated until the convergence condition is reached 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, which is defined 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 the 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.

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 for 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. Based on the random characteristics of the initial data, after ensuring that there are no outliers in each data set, the maximum information entropy value of the data set is taken as the fitness target; in each subsequent iteration process, the current best candidate whale is assumed to be 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 with initial value optimization according to claim 4 is characterized in that: The aforementioned whale optimization algorithm takes into account that whales can attack prey through bubble nets and also approach prey using a surrounding and contraction mechanism. In order to implement both mechanisms simultaneously, a probability index of P0 = 50% is selected to update the whale's position. During the iterative update process of the whale population position, when the absolute value of the coefficient |A| is less than 1, the whale returns to the first step to update its position; when |A| ≥ 1, the whale is forced to iterate to update its position to a randomly selected reference whale position vector.

6. The photovoltaic power prediction method based on initial value optimization and Gaussian mixture error probability distribution compensation according to claim 1 is characterized in that: Before the solution process begins, the objective function is determined. 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:

7. The photovoltaic power prediction method based on initial value optimization and Gaussian mixture error probability distribution compensation according to claim 1 is characterized in that: In response to 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 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 for the use of as many Gaussian distribution functions as possible 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 smaller weight components are discarded.

8. 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 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 are 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.

9. The photovoltaic power prediction method based on Gaussian mixture error probability distribution compensation with initial value optimization according to claim 1, 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 based on the obtained results; the above iterative process is repeated until the GMM parameters of the two iterations are basically the same or the maximum number of iterations is reached, and the optimal model parameters that meet the above optimization equation are obtained.

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