Photovoltaic prediction error evaluation method based on Gaussian mixture model

Abstract

The invention provides a photovoltaic prediction error evaluation method based on a Gaussian mixture model, and the method comprises the steps: carrying out the prediction of photovoltaic power generation power through a neural network prediction model, carrying out the normalization processing of a predicted power value and an actual value, and constructing a data sample set; gMM clustering analysis is carried out on the constructed data sample set, and the data sample set is divided into different groups according to the data characteristics and similarity of the data sample set to carry out partition processing. And finally, analyzing the data sample set of the photovoltaic output prediction error by adopting a Gaussian mixture model, and comparing the data sample set with normal distribution and t distribution, and the result shows that the fitting effect of the Gaussian mixture model on the photovoltaic prediction error is the best, is superior to that of a single model, can be more flexibly adapted to the multi-modal characteristic of data, and has a good application prospect. The method is of great significance in realizing dynamic scheduling of photovoltaic output and adapting to real-time changing power demands.

Description

Technical Field

[0001] The present invention belongs to the field of photovoltaic power prediction, and specifically relates to a photovoltaic prediction error evaluation method based on a Gaussian mixture model. Background Art

[0002] As the concept of sustainable development has gained popularity, the scale of global solar energy development has gradually expanded, technology has continued to advance, and costs have significantly decreased, showing a good development prospect. However, photovoltaic power generation is greatly affected by meteorology and is intermittent and volatile. These characteristics have brought huge impacts and challenges to the power system after a high proportion of photovoltaic access. Therefore, accurate prediction of photovoltaic output is of great significance to the operation of the power generation system.

[0003] At present, prediction methods are mainly divided into two categories: traditional and modern. Traditional methods such as time series and regression analysis can meet the requirements for photovoltaic output prediction to a certain extent, but it is difficult to capture the intermittent and volatile nature of photovoltaic output, and they are data-dependent and lack adaptive capabilities. Modern methods such as fuzzy prediction, neural networks, and probabilistic prediction have improved prediction accuracy, with errors controlled at 8%-40%, but the extent of improvement is greatly affected by the environment, data quality, and models.

[0004] In order to more accurately dispatch the operation of the power grid and reduce the adverse effects of photovoltaic output changes on the power system, it is particularly important to study the probability interval prediction of photovoltaic power generation prediction errors. Through probabilistic prediction, a probability distribution containing prediction errors can be provided, which is convenient for better understanding the uncertainty of the prediction results and obtaining prediction results within a range rather than single point estimates, so as to better plan and dispatch power resources. However, there are few studies on probabilistic prediction error models in China, and most of them are single models. When processing complex data sets, a single model may not be able to capture all the features of the data, lacks robustness, and has limited adaptability. It is necessary to introduce a hybrid model to improve the probability interval of photovoltaic power generation prediction errors.

[0005] The technical differences between this application and the prior art are as follows:

[0006] This patent is compared with Patent No. 2016100477838, a method for analyzing wind power real-time prediction errors based on mixed Gaussian distribution. The differences are:

[0007] 1. The research object selected by this patent is the prediction error of photovoltaic power data, while the research object selected by the comparative patent is the prediction error of wind power.

[0008] 2. Before constructing the Gaussian mixture model, this patent uses the GMM clustering algorithm to partition the prediction error into power levels. Subsequently, the three partition results after clustering are used as input data for the Gaussian mixture model. In contrast, the comparative patent does not use a clustering algorithm to preprocess the prediction error, but directly inputs the original prediction error value into the Gaussian mixture model. The introduction of this preprocessing step in this patent helps to improve the model's ability to recognize error features, and can more accurately reflect the prediction error of each power partition segment, so as to better perform power scheduling. The failure of the comparative patent to use a clustering algorithm may cause data containing multiple features in the prediction error value to be mixed together, which will mask the potential patterns and structures in the data, thereby affecting the performance of the Gaussian mixture model. In addition, the training process of the Gaussian mixture model involves the expectation maximization (EM) algorithm. Failure to use a clustering algorithm will cause the model to be overly dependent on the specific features of the training data, thereby reducing the model's generalization ability on unseen data. When the data set is large, more computing resources and time are required.

[0009] 3. This patent provides a comprehensive perspective to evaluate the performance of different models by comparing the Gaussian mixture model with the single normal model and the t-distribution model in terms of power error fitting. This approach not only enriches the research content, but also enhances the persuasiveness of the conclusion. The comparative patent only contains the analysis of the Gaussian mixture model and lacks comparison with other models. Therefore, this patent provides in-depth insights in theory, making the Gaussian mixture model results a more comprehensive and reliable choice.

[0010] This patent is compared with the wind power prediction error segmented fitting method based on Gaussian mixture model in Patent No. 2019103674973. The differences are:

[0011] 1. The research object selected by this patent is the prediction error of photovoltaic power data, while the research object selected by the comparative patent is the prediction error of wind power.

[0012] 2. This patent uses the GMM algorithm to partition the photovoltaic prediction error algorithm, while the comparative patent directly divides the wind power prediction value into intervals through the prediction data distribution scatter plot, but lacks the basis for division and is not persuasive. And the direct interval division through the scatter plot may not fully capture the statistical characteristics of the data, resulting in the inaccurate analysis results of the Gaussian mixture model and the inability to accurately reflect the accuracy of the prediction interval. In addition, this method may be sensitive to the selection of initial parameters, resulting in a decrease in model accuracy, and it is easy to fall into the local optimal solution when using the EM algorithm, and the convergence speed is slow. In contrast, this patent uses the GMM algorithm to partition the photovoltaic prediction error, which has obvious advantages. The GMM algorithm can not only capture more types of cluster shapes, but also provide the probability of each point belonging to each cluster, providing more information for the model when understanding the data. In addition, the GMM algorithm can handle overlapping clusters because it assigns data points to clusters based on probability rather than hard boundaries, which enables it to more accurately reflect the complexity of the data and is more credible in theory.

[0013] 3. This patent compares the power error fitting of the Gaussian mixture model with the single normal model and the t-distribution model, while the comparative patent only has the error fitting of the Gaussian mixture model. In comparison, this patent is richer and more convincing, and more intuitively reflects the advantages of the Gaussian mixture model.

[0014] This patent is compared with Patent No. 2022103070547, a photovoltaic power prediction error compensation method based on weather conditions. The differences are:

[0015] 1. This patent and the comparative patent have different focuses. This patent focuses on using a mixed Gaussian model to conduct an in-depth analysis of the photovoltaic power prediction error, aiming to reveal the statistical characteristics and distribution laws of the error through the model. The comparative patent focuses on how to effectively compensate for the photovoltaic power prediction error so that the actual output power is closer to the predicted output power, and pays more attention to the compensation aspect of energy storage. Although both patents revolve around photovoltaic power prediction errors, the research focuses and objectives are different. This patent provides a theoretical basis and scientific basis for the understanding and compensation of photovoltaic power prediction errors through the analysis of mixed Gaussian models.

[0016] 2. The workflow of this patent is also very different from that of the comparative patent. This patent first uses the LSTM prediction model to predict photovoltaic power, and then partitions the photovoltaic power prediction error through the GMM algorithm. The partitioned results are used as the input of the Gaussian mixture model and compared with a single model to highlight the advantages of the Gaussian mixture model. In contrast, the comparative patent first classifies the weather under different conditions, and then inputs the results into the LSSVM prediction model to obtain the prediction error and fit the Gaussian model. Finally, in the energy storage link, the firefly algorithm is used to obtain the optimal solution to compensate for the prediction error.

[0017] 3. This patent selected the GMM clustering algorithm in the data preprocessing process. The GMM clustering algorithm can not only perform detailed partitioning of photovoltaic prediction errors and enhance the persuasiveness of the model, but also intuitively demonstrate the advantages of the Gaussian mixture model in processing complex data distribution. The comparative patent did not mention what method was used to divide different photovoltaic weather conditions. The lack of clustering algorithm as a theoretical support resulted in the lack of strong credibility of its subsequent model when processing data.

[0018] 4. This patent compares the Gaussian mixture model with the normal distribution model and the t distribution model respectively, while the comparative patent only compares it with the normal distribution model. In comparison, this patent is richer in content. Summary of the invention

[0019] In order to solve the above technical problems, the present invention proposes a photovoltaic prediction error evaluation method based on a Gaussian mixture model. The present invention evaluates the probability interval of photovoltaic power generation prediction error by introducing a Gaussian mixture model to better achieve stable operation of the power system.

[0020] To achieve the above object, the technical solution adopted by the present invention is:

[0021] A photovoltaic prediction error evaluation method based on a Gaussian mixture model comprises the following steps:

[0022] 1) Obtain the time series power data of the photovoltaic power station and predict the time series photovoltaic power data through the LSTM neural network;

[0023] 2) For each i time point or observation point, the predicted actual value P 1i and the predicted value P 2i Subtract the power data error value ΔP before and after the prediction. i , and normalize the data error value;

[0024] 3) Arrange the normalized data errors into an error data sequence, and construct the results into a data sample set;

[0025] 4) GMM is used to perform cluster analysis on the constructed data sample set to obtain photovoltaic power error data under different power partition characteristics;

[0026] 5) For the error data under different power partition characteristics, partition them;

[0027] 6) The error data after partition processing are used as the input of the Gaussian mixture model to obtain the error fitting under different power partitions;

[0028] 7) Compare the power error fitting under the Gaussian mixture model with the single normal model and t-distribution model, and take reasonable measures to implement the photovoltaic power zoning scheduling strategy.

[0029] Furthermore, in step 1), the time series power data of the photovoltaic power station is the photovoltaic output of the region throughout the year. The actual power generation power is collected every 15 minutes, and the collected data is used as the data observation point. The time series power is predicted through the LSTM neural network, and a dynamic parameter adjustment strategy is adopted during the training process to obtain the optimal training parameters.

[0030] Furthermore, in step 2), after predicting the photovoltaic power generation power by using the LSTM neural network prediction model, the predicted power value and the actual value are normalized;

[0031] Calculate the prediction error:

[0032] ΔP i =P 2i -P 1i

[0033] Normalize the prediction error values:

[0034]

[0035] Where i represents the i-th observation data, ΔP i That is, the error between the true value and the predicted value of the i-th observation data, ΔP min Represents all ΔP i Minimum value in the data, ΔP max Represents all ΔP i The maximum value in the data, P Ii is the result after normalizing the error of the i-th observation data.

[0036] Further, in step 3), the normalized prediction error time series power P I =P I1 ,P I2 ,...P Ik , k = 35040, which is constructed as the input sample set for GMM clustering.

[0037] Furthermore, in the step 4), during the clustering process of GMM, the input sample data to be tested is a mixture of several Gaussian distributions, and each observation point in the mixture is considered to be generated by one of the multiple Gaussian distributions, each distribution has a certain weight, and the sum of the weights is 1;

[0038] In the clustering process of GMM, each Gaussian distribution represents a potential cluster, that is, a partition, which is defined by the mean vector μ and the covariance matrix Σ;

[0039] GMM estimates the mean vector and covariance matrix of the Gaussian distribution and calculates the maximum likelihood estimation function to achieve clustering of prediction error data.

[0040] Furthermore, in step 5), after clustering the data based on GMM, the clustered data can be partitioned according to the clustering result and divided into three partitions;

[0041] The first partition is the prediction error sample set θ for the 0-10MW power range a ;

[0042] The second partition is the prediction error sample set θ for the 10-30MW power range b ;

[0043] The third partition is the prediction error sample set θ for the 30-50MW power range c .

[0044] Furthermore, the Gaussian mixture model in step 6) is a probability distribution model, indicating that each power partition data is composed of a linear combination of multiple Gaussian distributions, and each Gaussian distribution has its corresponding probability density function. By adjusting the number of fitted Gaussian distributions and the parameters of each distribution, i.e., the number of samples in the distribution partition, the mean, variance and mixing coefficient of the Gaussian distribution of each power partition are accurately calculated, thereby more accurately describing the probability density distribution of the prediction error data in the partition;

[0045] Among them, the probability density function of each partition Gaussian mixture is expressed as a weighted sum of multiple Gaussian distributions:

[0046]

[0047] y represents the prediction error sample set of one of the known partitions, θ={θ1,θ2,θ3,...,θ k}, k represents the number of Gaussian mixture models in the partition power; each k corresponds to a θ k , μ k With σ kRespectively represent the mean and variance of the kth Gaussian model; α k represents the weight coefficient of the kth Gaussian mixture model, α k ≥0 and

[0048] Furthermore, in step 6), the Gaussian mixture model fitting result is compared with the normal distribution and the t distribution.

[0049] Normal distribution of partition prediction errors The curve is symmetrical about its mean, that is, the mean, median, and mode are equal. The prediction error distribution curve of each partition is symmetrical on both sides and has only one peak.

[0050] t distribution The curve is also single and symmetrical, and the shape of the prediction error t distribution curve changes with the change of the degrees of freedom df.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] Compared with a single model, the Gaussian mixture model is more suitable for processing data with multimodal distribution. In photovoltaic power generation prediction, it can be used to capture the complex distribution characteristics of prediction errors, thereby providing more accurate prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a flow chart of a photovoltaic prediction error evaluation method based on a Gaussian mixture model of the present invention;

[0054] Figure 2 It is a Gaussian mixture model prediction error distribution diagram based on all prediction error data of the present invention;

[0055] Figure 3 It is a quantitative fitting diagram of a partition-Gaussian mixture model of the present invention;

[0056] Figure 4 This is a partition-Gaussian mixture model fitting result diagram of the present invention;

[0057] Figure 5 It is a quantitative fitting diagram of the partition two Gaussian mixture model of the present invention;

[0058] Figure 6 This is a figure showing the fitting results of the partition two Gaussian mixture model of the present invention;

[0059] Figure 7 It is a quantitative fitting diagram of the partition three-Gaussian mixture model of the present invention;

[0060] Figure 8 This is a figure showing the fitting results of the partition three-Gaussian mixture model of the present invention;

[0061] Fig. 9It is a comparison diagram of the prediction error distribution of the Gaussian mixture model of a partition part of the present invention and a single model;

[0062] Fig.10 It is a comparison diagram of the prediction error distribution of the two-part Gaussian mixture model of the present invention and a single model;

[0063] Fig.11 It is a comparison diagram of the prediction error distribution of the three-part Gaussian mixture model of the present invention and a single model. DETAILED DESCRIPTION

[0064] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0065] like Figure 1 As shown, a photovoltaic prediction error evaluation method based on a Gaussian mixture model includes: predicting photovoltaic power with a neural network, calculating and normalizing data errors, constructing a data sample set, GMM clustering analysis, error data partitioning processing, fitting prediction errors with a Gaussian mixture model, and comparing with a single model.

[0066] Specifically, in the process of LSTM neural network prediction of photovoltaic power, the historical power generation data of photovoltaic power stations are selected as input features, and the input data is preprocessed: including data cleaning (removing outliers, missing values, etc.), normalization (scaling data to the same range) and other operations to improve the training efficiency and prediction accuracy of the model. The model includes an input layer (the number of neurons is set to 1 according to the input features), an LSTM layer (controls the input, output and forgetting of information through memory units and gating mechanisms, selectively remembering or forgetting past information), a fully connected layer (connecting neurons to the output of the LSTM layer, generating predicted values ​​through weighted summation and sigmoid activation function) and an output layer (the number of neurons is set to 1 for single quantity prediction).

[0067] During the model training process, the mean absolute error (MAE) is selected as the loss function to measure the difference between the predicted value and the true value. The model weights are continuously updated through the Adam optimization algorithm to minimize the loss function.

[0068] The predicted result is subtracted from the true value, the prediction error is calculated, and the predicted power value is normalized with the actual value to construct it as a sample set of data.

[0069] In the GMM clustering process, each Gaussian distribution represents a potential cluster, that is, a partition, which is defined by the mean vector μ and the covariance matrix Σ;

[0070] The mean vector μ is used to describe the center position of the Gaussian distribution, that is, the center point of the partition. Each prediction error Gaussian distribution has its own mean vector, which represents the average position of the prediction error data points in the partition.

[0071] The covariance matrix Σ is used to describe the shape and size of the partitioned Gaussian distribution, and the probability density function value of the data point under the Gaussian distribution is calculated.

[0072] In the process of fitting data errors with the Gaussian mixture model, the probability density function of each partitioned Gaussian mixture can be expressed as the weighted sum of multiple Gaussian distributions in the partition:

[0073]

[0074] y represents the prediction error sample set of one of the known partitions, θ={θ1,θ2,θ3,...,θ k}, k represents the number of Gaussian mixture models in the partition power; each k corresponds to a θ k , μ k With σ k Respectively represent the mean and variance of the kth Gaussian model; α k represents the weight coefficient of the kth Gaussian mixture model, α k ≥0 and

[0075] Among them, one of the Gaussian distribution PDFs in a single partition can be expressed as:

[0076]

[0077] In the process of solving the model, since the generation of samples is related to latent variables, and latent variables cannot be directly observed, the EM algorithm is used to solve it. The EM algorithm is divided into two steps:

[0078] Step E: Calculate the posterior probability that each data point belongs to each partitioned Gaussian distribution, that is, find the conditional probability value of the data point under the implicit variable (the variable that connects the prediction error and the result in the model).

[0079] M step: Update the parameters to maximize the likelihood function.

[0080] The E step and the M step are executed alternately until the convergence condition is reached. When the change beta between two consecutive iterations of the log-likelihood function value is less than 0.0001, the algorithm stops.

[0081] like Figure 2 As shown, this method includes the following specific steps:

[0082] Step 1: Taking the historical data of photovoltaic output of a certain park in Xinjiang in 2023 as the data set, the LSTM neural network prediction model is used to predict the photovoltaic historical time series data;

[0083] Step 2: For each i time point or observation point, the predicted actual value P1i and the predicted value P 2i Subtract the power data error value ΔP before and after the prediction. i , and normalize the data error value.

[0084] Step 3: Use the normalized value as the input of the Gaussian mixture model to obtain the Gaussian mixture model diagram of the full-year forecast error, as shown in Figure 2 shown.

[0085] Figure 3 , 4 , 5, 6, 7, and 8 are respectively the Gaussian mixture model prediction error distribution diagrams of the three partition parts of the present invention: Fig. 9 , 10 1 and 11 are comparison diagrams of the prediction error distribution of the Gaussian mixture model of the three partition parts of the present invention and a single model, including the prediction error distribution diagram of the Gaussian mixture model of the three partition parts. The number of Gaussian models selected for the three partitions is 6; the number of distribution partitions is 50.

[0086] The model results under this parameter setting are shown in the following table.

[0087]

[0088]

[0089] Zone 2 Miu(mean) sigma2 (variance) Pi (mixing coefficient) Gaussian Model 1 0.3079 0.0043 0.1904 Gaussian Model 2 0.4308 6.5686e-04 0.4049 Gaussian Model 3 0.5800 0.0082 0.1083 Gaussian Model 4 0.3651 6.5283e-04 0.1336 Gaussian Model 5 0.4778 0.0020 0.1580 Gaussian Model 6 0.9389 0.0018 0..0048

[0090] Zone 3 Miu(mean) sigma2 (variance) Pi (mixing coefficient) Gaussian Model 1 0.4002 6.0383e-05 0.4966 Gaussian Model 2 0.3123 0.0132 0.0592 Gaussian Model 3 0.4417 0.0176 0.0328 Gaussian Model 4 0.3872 0.0019 0.1370 Gaussian Model 5 0.4728 0.0011 0.0540 Gaussian Model 6 0.4225 1.0767e-04 0.2204

[0091] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. A photovoltaic prediction error evaluation method based on a Gaussian mixture model, characterized in that: The following steps are involved: 1) Obtain the time series power data of the photovoltaic power station and predict the time series photovoltaic power data through the LSTM neural network; 2) For each i time point or observation point, the predicted actual value P 1i and the predicted value P 2i Subtract the power data error value ΔP before and after the prediction. i , and normalize the data error value; 3) Arrange the normalized data errors into an error data sequence, and construct the results into a data sample set; 4) GMM is used to perform cluster analysis on the constructed data sample set to obtain photovoltaic power error data under different power partition characteristics; 5) For the error data under different power partition characteristics, partition them; 6) The error data after partition processing are used as the input of the Gaussian mixture model to obtain the error fitting under different power partitions; 7) Compare the power error fitting under the Gaussian mixture model with the single normal model and t-distribution model, and take reasonable measures to implement the photovoltaic power zoning scheduling strategy.

2. The photovoltaic prediction error evaluation method based on Gaussian mixture model according to claim 1, characterized in that: The time series power data of the photovoltaic power station in step 1) is the photovoltaic output of the region throughout the year. The actual power generation power is collected every 15 minutes, and the collected data is used as the data observation point. The time series power is predicted through the LSTM neural network, and a dynamic parameter adjustment strategy is adopted during the training process to obtain the optimal training parameters.

3. The photovoltaic prediction error evaluation method based on Gaussian mixture model according to claim 1, characterized in that: In step 2), after predicting the photovoltaic power generation power by using the LSTM neural network prediction model, the predicted power value and the actual value are normalized; Calculate the prediction error: ΔP i =P 2i -P 1i Normalize the prediction error values: Where i represents the i-th observation data, ΔP i That is, the error between the true value and the predicted value of the i-th observation data, ΔP min Represents all ΔP i Minimum value in the data, ΔP max Represents all ΔP i The maximum value in the data, P Ii is the result after normalizing the error of the i-th observation data.

4. The photovoltaic prediction error evaluation method based on Gaussian mixture model according to claim 1, characterized in that: The step 3) is for the normalized prediction error time series power P I =P I1 ,P I2 ,...P Ik , k = 35040, which is constructed as the input sample set for GMM clustering.

5. The photovoltaic prediction error evaluation method based on Gaussian mixture model according to claim 1, characterized in that: In the step 4), during the clustering process of GMM, the input sample data to be tested is a mixture of several Gaussian distributions, and each observation point in the mixture is considered to be generated by one of the multiple Gaussian distributions, each distribution has a certain weight, and the sum of the weights is 1; In the clustering process of GMM, each Gaussian distribution represents a potential cluster, that is, a partition, which is defined by the mean vector μ and the covariance matrix ∑; GMM estimates the mean vector and covariance matrix of the Gaussian distribution and calculates the maximum likelihood estimation function to achieve clustering of prediction error data.

6. The photovoltaic prediction error evaluation method based on Gaussian mixture model according to claim 1, characterized in that: After the data is clustered based on GMM in step 5), the clustered data can be partitioned according to the clustering results and divided into three partitions; The first partition is the prediction error sample set θ for the 0-10MW power range a ; The second partition is the prediction error sample set θ for the 10-30MW power range b ; The third partition is the prediction error sample set θ for the 30-50MW power range c .

7. The photovoltaic prediction error evaluation method based on Gaussian mixture model according to claim 1, characterized in that: The Gaussian mixture model in step 6) is a probability distribution model, indicating that each power partition data is composed of a linear combination of multiple Gaussian distributions, and each Gaussian distribution has its corresponding probability density function. By adjusting the number of fitted Gaussian distributions and the parameters of each distribution, i.e., the number of samples in the distribution partition, the mean, variance and mixing coefficient of the Gaussian distribution of each power partition are accurately calculated, thereby more accurately describing the probability density distribution of the prediction error data in the partition; Among them, the probability density function of each partition Gaussian mixture is expressed as a weighted sum of multiple Gaussian distributions: y represents the prediction error sample set of one of the known partitions, θ={θ1,θ2,θ3,...,θ k }, k represents the number of Gaussian mixture models in the partition power; each k corresponds to a θ k , μ k With σ k Respectively represent the mean and variance of the kth Gaussian model; α k represents the weight coefficient of the kth Gaussian mixture model, α k ≥0 and 8. The photovoltaic prediction error evaluation method based on Gaussian mixture model according to claim 1, characterized in that: The step 6) compares the Gaussian mixture model fitting result with the normal distribution and the t distribution; Normal distribution of partition prediction errors The curve is symmetrical about its mean, that is, the mean, median, and mode are equal, and the prediction error distribution curve of each partition is symmetrical on both sides and has only one peak; t distribution The curve is also single and symmetrical, and the shape of the prediction error t distribution curve changes with the change of the degrees of freedom df.

Images