Interval prediction method of fusion improved kernel density estimation and lstm-pinn under photovoltaic data two-stage classification

Abstract

This application discloses a design method for an interval prediction method that integrates improved kernel density estimation and LSTM-PINN under a two-stage classification of photovoltaic data. This includes establishing the overall architecture of the proposed photovoltaic power interval prediction method; designing a two-stage weather classification method based on meteorological characteristics in the data preprocessing stage; designing a point prediction method integrating physical constraints using a long short-term memory network in the point prediction stage; and designing an improved kernel density estimation interval prediction method driven by multiple meteorological variables in the interval prediction stage. The goal of this application is to achieve highly reliable photovoltaic power interval prediction under complex weather conditions. By introducing a meteorological characteristic-driven time-series prediction method and the concept of physical mechanism constraints, the existing prediction process is optimized, and further, quantitative analysis of prediction uncertainty is achieved, aiming to improve prediction accuracy while enhancing the reliability and stability of the prediction results.

Description

Technical Field

[0001] This application relates to the field of new energy power generation prediction, specifically to the interval prediction method of fusion improved kernel density estimation and LSTM-PINN under the two-stage classification of photovoltaic data. Background Technology

[0002] As a crucial component of renewable energy, photovoltaic (PV) power generation has become one of the fastest-growing new energy forms globally due to its cleanliness, environmental friendliness, and flexible installation. With the large-scale grid connection and rapid development of PV power generation, constructing a new power system dominated by new energy sources like PV is an inevitable trend for optimizing the energy structure and achieving a green and low-carbon transformation. However, PV power generation is significantly constrained by natural conditions. The dynamic changes in meteorological factors such as solar irradiance, temperature, and humidity result in significant fluctuations, intermittency, and uncertainty in its output. As PV power plants in a region exhibit a clustered distribution with significant differences in geographical environment and meteorological conditions, the differences in output characteristics among different plants intensify. Single-point prediction results are no longer sufficient to fully reflect the actual fluctuation range of PV power, increasing the pressure on grid dispatch and posing a severe challenge to the safe and stable operation of the power system. Therefore, PV power range prediction technology, capable of quantifying and predicting uncertainties, has become a key technology supporting large-scale PV grid connection and consumption, optimizing system reserve capacity, and ensuring reliable power supply.

[0003] Traditional point forecasting methods, such as those based on physical models and those based on statistical models, have limitations in handling the complex nonlinear relationships and uncertainties of photovoltaic (PV) power output. While physical model-based methods offer physical interpretation, their prediction accuracy is highly dependent on the acquisition of high-quality meteorological data; whereas statistical model methods struggle to accurately capture dynamic changes under complex weather conditions. In recent years, deep learning methods, represented by long short-term memory (LSTM) networks, have made significant progress in time series forecasting, effectively capturing the long-term dependence characteristics in PV power sequences. However, without physical mechanism constraints, purely data-driven models may produce predictions that violate the fundamental physical laws of PV power generation under complex weather conditions such as cloudy or rainy days, such as the monotonically positive correlation between power output and irradiance.

[0004] On the other hand, to characterize the uncertainty of photovoltaic power prediction, interval prediction methods have gradually become a research hotspot. Common interval prediction methods include quantile regression and kernel density estimation (KDE). Quantile regression can construct prediction intervals without relying on assumptions about the error distribution, but its interval coverage depends to some extent on the model structure and feature selection. Kernel density estimation methods are widely used in prediction error modeling because they do not require a pre-defined data distribution and can flexibly characterize arbitrary probability distributions. However, traditional kernel density estimation methods usually use fixed bandwidth parameters, which are difficult to adapt to the dynamic changes in the prediction error distribution under different meteorological conditions. Moreover, existing methods often ignore the joint driving effect of multi-dimensional meteorological variables such as solar irradiance, temperature, and humidity on the prediction error distribution during bandwidth selection, resulting in poor generalization ability and reliability of interval estimation in complex weather scenarios.

[0005] Therefore, this application proposes an interval prediction method that integrates improved kernel density estimation and LSTM-PINN under two-stage classification of photovoltaic data. It can effectively combine the advantages of physical mechanisms and data-driven models under various meteorological conditions, improve the accuracy and physical rationality of point prediction, and construct a more reliable photovoltaic power prediction interval through a kernel density estimation method driven by multiple meteorological variables. Summary of the Invention

[0006] To address the aforementioned issues, this application discloses an interval prediction method that integrates improved kernel density estimation and LSTM-PINN under two-stage classification of photovoltaic data. This interval prediction method can effectively improve the prediction accuracy of photovoltaic power points under complex meteorological conditions, make the predicted values ​​conform to physical mechanisms, and quantify the prediction uncertainty.

[0007] To achieve the above objectives, the following technical solution is adopted:

[0008] The specific steps of the interval prediction method combining improved kernel density estimation and LSTM-PINN under two-stage classification of photovoltaic data are as follows:

[0009] Step 1: Formulate the overall architecture of the photovoltaic power interval prediction method proposed in this application. The overall architecture of the photovoltaic power interval prediction method includes a data preprocessing stage, a point prediction stage, and an interval prediction stage.

[0010] Step 2: In the data preprocessing stage, design a two-stage weather classification method based on meteorological characteristics;

[0011] Step 3: In the point prediction stage, design a point prediction method for long short-term memory networks that incorporates physical constraints;

[0012] Step 4: In the interval forecasting stage, design an improved kernel density estimation interval forecasting method driven by multiple meteorological variables.

[0013] Step 5: Verify the effectiveness of the method by setting up an experimental scenario.

[0014] Compared with the prior art, this application has the following advantages:

[0015] 1. In the data preprocessing stage, a two-stage weather classification method based on K-means++ is proposed. By optimizing the initial centroid selection, the differences between samples are effectively reduced, and the accuracy of the classification results is improved. Compared with traditional classification methods, the method in this application can improve the adaptability of the prediction model under different weather conditions.

[0016] 2. In the point prediction stage, an LSTM-PINN photovoltaic power point prediction method incorporating physical constraints is proposed. By embedding the physical mechanism constraints of photovoltaic power generation into the loss function, not only is the accuracy of point prediction improved, but the physical rationality of the prediction results is also ensured. Compared with traditional single-point prediction methods, the proposed method can avoid unreasonable predictions under extreme weather conditions by traditional pure data-driven models.

[0017] 3. In the interval forecasting stage, an improved kernel density estimation interval forecasting method based on multiple meteorological variables is proposed. By introducing meteorological variables such as irradiance, temperature, and humidity to jointly drive the selection of adaptive bandwidth, it can more accurately characterize the probability distribution of forecast errors under different meteorological conditions, thereby constructing a forecast interval with higher coverage and greater reliability. Compared with traditional interval forecasting methods, the proposed method can solve the problem of interference from meteorological variables on forecast errors. Attached Figure Description

[0018] Figure 1 This is a photovoltaic range prediction scenario diagram for this application;

[0019] Figure 2 This is the overall framework diagram for photovoltaic range prediction in this application;

[0020] Figure 3 This is a schematic diagram illustrating the improvement of the prediction loss of the LSTM-PINN model in this application;

[0021] Figure 4(a) shows a comparison of the point prediction results under clear weather conditions;

[0022] Figure 4(b) shows a comparison of the point prediction results under cloudy conditions;

[0023] Figure 4(c) is a comparison of the in-situ prediction results under cloudy / rainy weather conditions;

[0024] Figure 5(a) shows the comparison of interval predictions under clear weather conditions;

[0025] Figure 5(b) shows a comparison of interval predictions under cloudy conditions;

[0026] Figure 5(c) shows the comparison of interval predictions under cloudy / rainy weather conditions. Detailed Implementation

[0027] The present application will be further explained below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the present application. It should be noted that the terms "front", "rear", "left", "right", "up" and "down" used in the following description refer to the directions in the accompanying drawings, and the terms "inner" and "outer" refer to the directions toward or away from the geometric center of a specific component, respectively.

[0028] Example 1

[0029] like Figure 1 As shown, this application designs a photovoltaic range prediction scenario diagram, including a data preprocessing module, a point prediction module, and a range prediction module. The goal of this application is to achieve highly reliable photovoltaic power range prediction under complex weather conditions. By introducing a meteorological feature-driven time-series prediction method and the concept of physical mechanism constraints, the existing prediction process is optimized, and further quantitative analysis of prediction uncertainty is achieved, aiming to improve prediction accuracy while enhancing the reliability and stability of prediction results.

[0030] Step 1 specifically includes the following steps:

[0031] Step 11, the data preprocessing stage is used to classify the sample points for weather and to provide time-series input features for the point prediction stage;

[0032] Step 12, the point prediction stage is used to embed physical constraints into the long short-term memory network for training, and output the photovoltaic power point prediction value of each sample point;

[0033] Step 13, the interval prediction stage is used to construct the photovoltaic power prediction interval for each sample point based on the improved kernel density estimation driven by multiple meteorological variables.

[0034] Step 2: Design a two-stage weather classification method based on meteorological characteristics during the data preprocessing stage.

[0035] like Figure 2 As shown, after completing the overall architecture design, the data preprocessing stage is designed.

[0036] Step 2 specifically includes the following steps:

[0037] Step 21: Selection of meteorological features and data preprocessing

[0038] In the process of weather classification, the selection of meteorological features directly affects the rationality and physical meaning of the clustering results. Based on the mechanism of photovoltaic power generation and existing research results, this application selects solar irradiance, ambient temperature, and humidity as the main features for weather classification.

[0039] ;

[0040] middle, For the first Three-dimensional feature values ​​of each sample point For the first Solar irradiance at each sample point For the first The ambient temperature of each sample point For the first Humidity at each sample point;

[0041] Step 22, Outlier Detection and Replacement

[0042] The interquartile range method was used to detect outliers in three meteorological characteristics: solar irradiance, ambient temperature, and humidity. It is the first quartile. It is the 3rd quartile, and the interquartile range is... The outlier detection rule is as follows:

[0043] ;

[0044] Meteorological characteristic values ​​that do not meet the outlier criteria are replaced with the median of that characteristic.

[0045] Step 23, Min-Max Normalization

[0046] The processed meteorological data were normalized using the Min–Max normalization method to unify the scale of three meteorological characteristics: solar irradiance, ambient temperature, and humidity. The normalization expression is as follows:

[0047] ;

[0048] ;

[0049] ;

[0050] in, , and The first The normalized values ​​of irradiance, ambient temperature, and humidity for each sample point. , These are the maximum and minimum values ​​of irradiance, respectively. , These represent the maximum and minimum ambient temperatures, respectively. and These are the maximum and minimum humidity values, respectively; the... Normalized three-dimensional feature values ​​of each sample point The expression is:

[0051] ;

[0052] After outlier detection, replacement, and normalization preprocessing in steps 21 to 23, a standardized meteorological feature dataset for weather classification is obtained.

[0053] Traditional K-means clustering algorithm is widely used in weather classification problems due to its simplicity and high computational efficiency. However, this algorithm is sensitive to the selection of initial cluster centers; random initialization can easily lead to unstable clustering results, or even getting trapped in local optima, affecting classification accuracy. To address the sensitivity of the K-means clustering algorithm to the selection of initial cluster centers, this application introduces the K-means++ clustering strategy to perform weather classification in two stages.

[0054] Step 24, Two-stage weather classification based on K-means++

[0055] Phase 1: During initialization, the K-means++ strategy is used to initialize cluster centers: a sample point is randomly selected as the initial centroid, and the minimum distance from the sample point to the existing centroid is used as the initial centroid. The probability distribution is constructed based on the squared distance. The formula for the probability distribution is:

[0056] ;

[0057] in For the first The probability that a sample point is selected as the new centroid. This is the first The distance from each sample point to the nearest cluster center For the total number of sample points, repeat the process of selecting the initial centroid until a centroid is selected. An initial centroid, in which The number of cluster categories is preset; this application These correspond to sunny days, rainy days, and cloudy days, respectively.

[0058] In the second stage, the standard K-means iterative process is used to cluster the samples: First, the distance from each sample to each cluster center is calculated, and the sample is assigned to the nearest cluster; then, the centroid position of each cluster is recalculated; the clustering and centroid updating are repeated until the cluster centers converge or the maximum number of iterations is reached. After classification, time-series sample points are constructed, using the following formula:

[0059] ;

[0060] in: The time input matrix of the LSTM This represents the length of the time window.

[0061] Step 3: Design a point prediction method for Long Short-Term Memory networks that incorporates physical constraints during the point prediction stage.

[0062] like Figure 2 and Figure 3 As shown, after completing the design of the data preprocessing stage, the next step is to design the point prediction stage.

[0063] Step 3 specifically includes the following steps:

[0064] Step 31, Definition of Photovoltaic Physical Relationships: The basic physical relationship between the output power of a photovoltaic module and irradiance and temperature is expressed as follows:

[0065] ;

[0066] in, This represents the actual output power. For reference rated power, Solar irradiance, For reference irradiance, For component temperature, For reference temperature, Temperature coefficient;

[0067] Step 32, Construction of the physical loss function:

[0068] In the training process of traditional LSTM networks, the concept of Physics-Informed Neural Networks (PINN) is introduced, and the physical relationship between photovoltaic power and meteorological factors is embedded as a constraint term in the loss function, forming a joint optimization objective that combines data-driven and physical mechanisms.

[0069] The optimization objective of the prediction model is set as the total loss of prediction error. Its expression is:

[0070] ;

[0071] in, To the total loss of prediction error, For data-driven loss terms, For the irradiance and temperature constraint loss terms, For monotonicity-constrained loss terms, These are the weighting coefficients for the irradiance and temperature constraint loss terms. The weighting coefficients of the monotonicity constraint loss term satisfy... , and ;

[0072] The total loss of prediction error Multi-objective optimization is achieved by weighted fusion of three types of loss terms. The formulas for each loss term are as follows:

[0073] ;

[0074] in, For data-driven loss terms, The total number of sample points. For the first The true power value of each sample point For the first Predicted power values ​​for each sample point;

[0075] ;

[0076] in:

[0077] ;

[0078] in, This represents the loss due to irradiance and temperature confinement. No. The theoretical physical power value of each sample point For reference rated power, For reference irradiance, For the first Component temperature at each sample point;

[0079] ;

[0080] in This represents the monotonicity constraint loss. It is the partial derivative of predicted power with respect to irradiance;

[0081] Step 33, LSTM-PINN model training;

[0082] In each training batch, the LSTM-PINN model first encodes the multidimensional temporal input, then uses its gating structure to selectively memorize and update long-term and short-term dependencies, extracting key temporal features of photovoltaic power changes. The state update formula for the LSTM-PINN model is:

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] ;

[0088] ;

[0089] in, , , These are the input gate, forget gate, and output gate, respectively. and These represent the current cell state and the candidate cell state, respectively. The output of the hidden layer at the current moment and This is the output of the hidden layer from the previous time step. For the current input,

[0090] , , For trainable parameters, Pick , , , These correspond to the parameters of the input gate, forget gate, output gate, and candidate cell state, respectively. It is the Sigmoid activation function.

[0091] Based on historical power and meteorological input characteristics, the LSTM-PINN model learns the nonlinear mapping relationship from input time series to photovoltaic power output. The predicted photovoltaic power point value for each sample point is expressed as follows:

[0092] ;

[0093] in: It is the mapping function of the LSTM-PINN model. The time input matrix of the LSTM This represents the total loss due to prediction error.

[0094] Step 4: In the interval forecasting stage, based on the adaptive selection of the bandwidth matrix according to meteorological characteristics, an improved kernel density estimation interval forecasting method driven by multiple meteorological variables is designed.

[0095] like Figure 2 As shown, after completing the design of the point prediction stage, the next step is to design the interval prediction stage.

[0096] Step 4 specifically includes the following steps:

[0097] Step 41, Prediction error calculation, let the first... The prediction error for each sample point is:

[0098] ;

[0099] in, For the first Prediction error per sample point For the first Predicted power values ​​for each sample point;

[0100] Step 42, Global Reference Bandwidth Calculation:

[0101] Unlike traditional kernel density estimation methods that use fixed bandwidth and model based solely on the overall distribution of error samples, the method in this application fully considers the influence of meteorological conditions on the distribution of prediction errors, and introduces irradiance, temperature, and humidity as conditional variables into the error probability distribution modeling process.

[0102] Considering the significant differences in photovoltaic power prediction errors under various meteorological conditions, this application introduces bandwidths for three meteorological variables: irradiance, temperature, and humidity. Furthermore, it integrates the three-dimensional bandwidths of these three meteorological variables into a one-dimensional weighted bandwidth. To fully account for the differences in physical mechanisms, scale ranges, and the degree of influence of different meteorological characteristics on photovoltaic power, a three-dimensional diagonal bandwidth matrix is ​​adopted. :

[0103] ;

[0104] in, Corresponding to the first Bandwidth of irradiance, ambient temperature, and humidity dimensions for each sample point;

[0105] Calculate the global reference bandwidth for each meteorological characteristic based on Silverman's rule of thumb. :

[0106] ;

[0107] in: For the first Standard deviation of meteorological characteristics For meteorological features dimension, Take 1-3;

[0108] Step 43, Adaptive bandwidth calculation

[0109] To avoid the problem of over-smoothing or unstable estimation caused by fixed bandwidth under complex weather conditions, this application introduces an adaptive bandwidth mechanism for each meteorological dimension.

[0110] Calculate the nearest point for each point in each dimension The average distance between neighboring points, Use experience points ,in Take the integer, when If the value is less than 1, round it up to 1. The sample point of the th sample point Up to the latest Average distance of neighboring points The expression is:

[0111] ;

[0112] in, For the first The sample point of the th sample point The set of neighboring points of dimension, For the index of neighboring points, For the first The sample point of the th sample point The meteorological characteristic value of the dimension, For the first The neighboring points of the sample point. The meteorological characteristic value of the dimension, The parameter is the number of nearest neighbors;

[0113] The median of the average distance is taken as the distance threshold for distinguishing between dense and sparse points, as shown in the following expression:

[0114] ;

[0115] in, For the first The distance threshold used to distinguish between dense and sparse points in meteorological features. For the first The average distance between each sample point in the dimension This represents the total number of sample points;

[0116] By classifying based on a distance threshold, each dimension can yield a set of dense points and a set of sparse points, as shown in the following expression:

[0117] ;

[0118] ;

[0119] in, For the first The set of dense points in the dimension, For the first The set of sparse points in dimension 1 Using the sample point index, the small and large bandwidth coefficients are calculated for points in both the dense and sparse point sets, respectively. The small bandwidth coefficient is then used to... and large bandwidth coefficient Through the small bandwidth coefficient Multiplying by the global reference bandwidth yields a smaller bandwidth, which is then used through the large bandwidth coefficient. Multiplying by the global reference bandwidth yields the larger bandwidth; the expression is as follows:

[0120] Small bandwidth coefficient :

[0121] ;

[0122] Large bandwidth coefficient :

[0123] ;

[0124] Small bandwidth :

[0125] ;

[0126] High bandwidth :

[0127] ;

[0128] in: For each point in the dense set of points, the first... The average distance of the dimension, For each point in the sparse point set, the first... The average distance of the dimension;

[0129] For each sample point, based on its dense or sparse point set and the corresponding calculated small or large bandwidth coefficient, each dimension of the bandwidth is selected. The final expression for the three-dimensional diagonal bandwidth matrix is ​​as follows:

[0130] ;

[0131] in, For the first The bandwidth ultimately selected for the first dimension of each sample point. For the first The bandwidth ultimately selected in the second dimension for each sample point. For the first The final selected bandwidth for the third dimension of each sample point corresponds to the final bandwidth for the dimensions of irradiance, ambient temperature, and humidity, respectively.

[0132] Step 44: 3D bandwidth to 1D weighted bandwidth: Convert the 3D diagonal bandwidth matrix obtained in step 43 to one-dimensional weighted bandwidth. Substituting the bandwidth of each dimension into the Gaussian kernel function, we obtain the first... The sample point of the th sample point Gaussian kernel function of dimension :

[0133] ;

[0134] in: Let be the required independent variable for prediction error. No. Prediction error per sample point For the first The sample point of the th sample point Dimensional bandwidth;

[0135] The first Multiplying the Gaussian kernel functions of each sample point in each dimension yields the weather similarity weight for that sample point. :

[0136] ;

[0137] A multidimensional kernel function is constructed using a product kernel, and weather similarity weights are utilized. By applying a weighted average to the error kernel functions, the probability density function of the final one-dimensional weighted KDE is obtained. The expression is:

[0138] ;

[0139] in: It is the first Bandwidth of prediction error per sample point;

[0140] Step 45, Prediction Interval Construction: Substitute the one-dimensional weighted KDE into the cumulative distribution function to obtain the first... Cumulative distribution function of points Its expression is as follows:

[0141] ;

[0142] Let the cumulative distribution function described above be applied to a 95% confidence interval, and we obtain the expressions for the upper and lower bounds of the prediction interval:

[0143] ;

[0144] ;

[0145] in, This is the lower bound of the prediction error. This represents the upper limit of the prediction error;

[0146] Take a grid set within the range of the minimum to maximum prediction error for all sample points, substitute it into the cumulative distribution function to calculate its value, and find the two prediction errors closest to 0.025 and 0.975, which are then considered as... and , and then and Adding the predicted value, we obtain the final prediction interval, which is expressed as follows:

[0147] ;

[0148] ;

[0149] Final prediction range :

[0150] ;

[0151] in, and These are the upper and lower limits of the predicted power.

[0152] Step 5: Verify the effectiveness of the photovoltaic power range prediction method constructed in steps 1 to 4 by setting up an experimental scenario.

[0153] This application selects historical operating data from actual photovoltaic power plants in Australia as the research object. The data has a time resolution of 5 minutes and includes meteorological variables such as photovoltaic output power, solar irradiance, ambient temperature, and humidity. The data covers the complete seasonal cycle and can reflect the output variation characteristics under different meteorological conditions. To ensure experimental fairness, the dataset is divided according to time order, with 80% of the data used for model training and 20% used for testing and validation.

[0154] (1) To verify the effectiveness of the LSTM-PINN model, the following methods were selected for comparison: SVR, traditional LSTM, and LSTM-PINN. The evaluation metrics used were MAE and RMSE.

[0155] SVR has a large error in the range of violent fluctuations; traditional LSTM can capture time dependence, but it has overshoot under extreme weather conditions; the method proposed in this application is smoother and more physically reasonable in the fluctuation phase.

[0156] As shown in Figures 4(a), 4(b), and 4(c), the LSTM-PINN method proposed in this application exhibits good prediction accuracy and physical consistency under different weather conditions. Compared with benchmark models such as LSTM and SVR, the method in this application is close to LSTM in terms of MAE and RMSE, and improves by an average of about 15% to 20% compared with SVR.

[0157] (2) To quantify the uncertainty of the forecast, the following interval forecasting methods were selected for comparison: normal distribution method, traditional fixed bandwidth KDE, and the improved three-dimensional meteorological feature KDE of this application. Among them, Figure 5(a) is a comparison of interval forecasts under sunny conditions; Figure 5(b) is a comparison of interval forecasts under cloudy conditions; and Figure 5(c) is a comparison of interval forecasts under overcast / rainy conditions.

[0158] Experiments show that the interval coverage rate of the normal distribution method is the lowest among the three methods; the interval coverage rate of the traditional KDE method is slightly higher than that of the normal distribution method, but far lower than that of the method proposed in this application; the interval coverage rate of the method proposed in this application is much higher than that of the other two methods, as shown in Figures 5(a), 5(b), and 5(c), with a prediction interval coverage rate 2% to 4% higher than other methods at the 95% confidence interval. Therefore, the above experimental results indicate that the method proposed in this application has stronger uncertainty characterization ability and interval prediction performance.

[0159] The technical means disclosed in this application are not limited to the technical means disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features.

Claims

1. A method for interval prediction that integrates improved kernel density estimation and LSTM-PINN under two-stage classification of photovoltaic data, characterized in that... Specifically, the following steps are included: Step 1: Develop the overall architecture of the photovoltaic power range prediction method. The overall architecture of the photovoltaic power range prediction method includes the data preprocessing stage, the point prediction stage, and the range prediction stage. Step 2: In the data preprocessing stage, design a two-stage weather classification method based on meteorological characteristics; Step 3: In the point prediction stage, design a point prediction method for long short-term memory networks that incorporates physical constraints; Step 4: In the interval forecasting stage, based on the adaptive selection of the bandwidth matrix according to meteorological characteristics, an improved kernel density estimation interval forecasting method driven by multiple meteorological variables is designed. Step 5: Verify the effectiveness of the photovoltaic power range prediction method constructed in steps 1 to 4 by setting up an experimental scenario.

2. The interval prediction method for photovoltaic data under two-stage classification, which integrates improved kernel density estimation and LSTM-PINN, as described in claim 1, is characterized in that... Step 1 specifically includes the following steps: Step 11, the data preprocessing stage is used to classify the sample points for weather and to provide time-series input features for the point prediction stage; Step 12, the point prediction stage, is used to embed physical constraints into the long short-term memory network for training and output the photovoltaic power point prediction value for each sample point; Step 13, the interval prediction stage, is used to construct the photovoltaic power prediction interval for each sample point by using improved kernel density estimation driven by multiple meteorological variables.

3. The interval prediction method for photovoltaic data under two-stage classification, which integrates improved kernel density estimation and LSTM-PINN, as described in claim 2, is characterized in that... Step 2 specifically includes the following steps: Step 21, meteorological feature selection and data preprocessing: solar irradiance, ambient temperature, and humidity are selected as the main features for weather classification. ； in, For the first Three-dimensional feature values ​​of each sample point For the first Solar irradiance at each sample point For the first The ambient temperature of each sample point For the first Humidity at each sample point; Step 22, outlier detection and replacement: The interquartile range method is used to detect outliers in three meteorological characteristics: solar irradiance, ambient temperature, and humidity. It is the first quartile. It is the 3rd quartile, and the interquartile range is... The outlier detection rule is as follows: ； Meteorological characteristic values ​​that do not meet the outlier criteria are replaced with the median of that characteristic. Step 23, Min-Max Normalization: The meteorological data after outlier detection and replacement in Step 22 are normalized using the Min-Max normalization method to unify the scale of the three meteorological characteristics: solar irradiance, ambient temperature, and humidity. The normalization expression is as follows: ； ； ； in, , and The first The normalized values ​​of irradiance, ambient temperature, and humidity for each sample point. , These are the maximum and minimum values ​​of irradiance, respectively. , These represent the maximum and minimum ambient temperatures, respectively. and These are the maximum and minimum humidity values, respectively; the... Normalized three-dimensional feature values ​​of each sample point The expression is: ; After outlier detection, replacement, and normalization preprocessing in steps 21 to 23, a standardized meteorological feature dataset for weather classification is obtained; Step 24: Two-stage weather classification based on K-means++: Phase 1: During initialization, the K-means++ strategy is used to initialize cluster centers: a sample point is randomly selected as the initial centroid, and the minimum distance from the sample point to the existing centroid is used as the initial centroid. The probability distribution is constructed based on the squared distance. The formula for the probability distribution is: ； in For the first The probability that a sample point is selected as the new centroid. For the first The distance from each sample point to the nearest cluster center For the total number of sample points, repeat the process of selecting the initial centroid until a centroid is selected. There are initial centroids; among which The preset number of cluster categories; In the second stage, the standard K-means iterative process is used to cluster the sample points: First, the distance from each sample point to each cluster center is calculated, and it is assigned to the nearest category; then, the centroid position of each category of sample points is recalculated; the clustering and centroid updating are repeated until the cluster centers converge or the maximum number of iterations is reached. After the classification is completed, time-series sample points are constructed, and the specific formula is as follows: ； in, The time input matrix of the LSTM This represents the length of the time window.

4. The interval prediction method for photovoltaic data under two-stage classification, which integrates improved kernel density estimation and LSTM-PINN, as described in claim 3, is characterized in that... Step 3 specifically includes the following steps: Step 31, Definition of Photovoltaic Physical Relationships: The basic physical relationship between the output power of a photovoltaic module and irradiance and temperature is expressed as follows: ； in, This represents the actual output power. For reference rated power, Solar irradiance, For reference irradiance, For component temperature, For reference temperature, Temperature coefficient; Step 32, Construction of the physical loss function: The physical relationship between photovoltaic power and meteorological factors is embedded into the loss function as a constraint term, forming a joint optimization objective that combines data-driven and physical mechanisms. The optimization objective of the prediction model is set as the total loss of prediction error. Its expression is: ； in, To the total loss of prediction error, For data-driven loss terms, For the irradiance and temperature constraint loss terms, For monotonicity-constrained loss terms, These are the weighting coefficients for the irradiance and temperature constraint loss terms. The weighting coefficients of the monotonicity constraint loss term satisfy... , and ; The total loss of prediction error Multi-objective optimization is achieved by weighted fusion of three types of loss terms. The formulas for each loss term are as follows: ; in, For data-driven loss terms, The total number of sample points. For the first The true power value of each sample point For the first Predicted power values ​​for each sample point; ; in: ; in, This represents the loss due to irradiance and temperature confinement. No. The theoretical physical power value of each sample point For reference rated power, For reference irradiance, For the first Component temperature at each sample point; ； in, For monotonicity-constrained loss, To predict the partial derivative of power with respect to irradiance; Step 33, LSTM-PINN model training; the state update formula for the LSTM-PINN model is: ； ； ； ； ； ； in, , , These are the input gate, forget gate, and output gate, respectively. This represents the current cell state. This represents the current state of the candidate cells. This is the output of the hidden layer at the current moment. This is the output of the hidden layer from the previous time step. For the current input, , , For trainable parameters, Pick , , , These correspond to the parameters of the input gate, forget gate, output gate, and candidate cell state, respectively. It is the Sigmoid activation function; Based on historical power and meteorological input characteristics, the LSTM-PINN model learns the nonlinear mapping relationship from input time series to photovoltaic power output. The predicted photovoltaic power point value for each sample point is expressed as follows: ; in, For the mapping function of the LSTM-PINN model, The time input matrix of the LSTM To the total loss of prediction error, This represents the length of the time window.

5. The interval prediction method for photovoltaic data under two-stage classification, which integrates improved kernel density estimation and LSTM-PINN, as described in claim 4, is characterized in that... Step 4 specifically includes: Step 41, Prediction Error Calculation: Let the first... The prediction error for each sample point is: ； in, For the first Prediction error per sample point For the first Predicted power values ​​for each sample point; Step 42, Global Reference Bandwidth Calculation: Using a three-dimensional diagonal bandwidth matrix : ； in: Corresponding to the first Bandwidth of irradiance, ambient temperature, and humidity dimensions for each sample point; Calculate the global reference bandwidth based on Silverman's rule of thumb for solar irradiance, ambient temperature, and humidity. : ； in, For the first Standard deviation of meteorological characteristics For meteorological features dimension, Take 1-3; Step 43, Adaptive bandwidth calculation: For each point in each dimension, calculate the nearest bandwidth. The average distance between neighboring points, For the nearest neighbor count parameter, Use experience points ,in Take the integer, when If the value is less than 1, round it up to 1. The sample point of the th sample point Up to the latest Average distance of neighboring points The expression is: ； in, For the first The sample point of the th sample point The set of neighboring points of dimension, For the index of neighboring points, For the first The sample point of the th sample point The meteorological characteristic value of the dimension, For the first The sample point of the th sample point The neighboring point The meteorological characteristic values ​​of the dimension; The median of the average distance is taken as the distance threshold for distinguishing between dense and sparse points, as shown in the following expression: ； in For the first The distance threshold used to distinguish between dense and sparse points in meteorological features. For the first The average distance between each sample point in the dimension This represents the total number of sample points; By classifying based on a distance threshold, each dimension can yield a set of dense points and a set of sparse points, as shown in the following expression: ； ； in, For the first The set of dense points in the dimension, For the first The set of sparse points in dimension 1 Using the sample point index, the small and large bandwidth coefficients are calculated for points in both the dense and sparse point sets, respectively. The small bandwidth coefficient is then used to... and large bandwidth coefficient Through the small bandwidth coefficient Multiplying by the global reference bandwidth yields a smaller bandwidth, which is then used with a larger bandwidth coefficient. Multiplying by the global reference bandwidth yields the larger bandwidth; the expression is as follows: Small bandwidth coefficient : ； Large bandwidth coefficient : ； Small bandwidth : ； High bandwidth : ； in, For each point in the dense set of points, the first... The average distance of the dimension, For each point in the sparse point set, the first... The average distance of the dimension; For each sample point, the bandwidth is then selected in each dimension according to the above conditions, resulting in a three-dimensional diagonal bandwidth matrix. The expression is as follows: ; in, For the first The bandwidth ultimately selected for the first dimension of each sample point. For the first The bandwidth ultimately selected in the second dimension for each sample point. For the first The final selected bandwidth for the third dimension of each sample point corresponds to the final bandwidth for the dimensions of irradiance, ambient temperature, and humidity, respectively. Step 44: 3D bandwidth to 1D weighted bandwidth: Convert the 3D diagonal bandwidth matrix obtained in step 43 to one-dimensional weighted bandwidth. Substituting the bandwidth of each dimension into the Gaussian kernel function, we obtain the first... The sample point of the th sample point Gaussian kernel function of dimension : ； in, Let be the required independent variable for prediction error. No. Prediction error per sample point For the first The sample point of the th sample point The bandwidth ultimately chosen by the dimension; The first Multiplying the Gaussian kernel functions of each sample point in each dimension yields the weather similarity weights. : ； A multidimensional kernel function is constructed using a product kernel, and weather similarity weights are utilized. By applying a weighted average to the error kernel functions, the final one-dimensional weighted KDE probability density function is obtained. The expression is: ； in, It is the first Bandwidth of prediction error for each sample point; Step 45, Prediction Interval Construction: Substitute the one-dimensional weighted KDE into the cumulative distribution function to obtain the first... Cumulative distribution function of sample points Its expression is as follows: ； Let the cumulative distribution function take a 95% confidence interval, and we obtain the expressions for the upper and lower bounds of the prediction interval: ； ； in, This is the lower bound of the prediction error. This represents the upper limit of the prediction error; Within the error range, a set of grid cells is selected, and the cumulative distribution function is substituted to calculate its value. The two prediction errors closest to 0.025 and 0.975 are identified as [the correct values]. and , and then and Adding the predicted value, we obtain the final prediction interval, which is expressed as follows: ； ； Final prediction range : ； in: To predict the upper limit of power, This is to predict the lower limit of power.

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