Method and system for predicting the output of distributed solar power generation based on graph neural networks

Abstract

This invention provides a graph neural network-based distributed solar power output prediction method and system that improves prediction accuracy from three aspects: data, models, and parameters, and offers a practical and needs-based solution for highly accurate short-term predictions of distributed solar power plants. [Solution] The method initializes the irradiation data of distributed solar power generation for a set period prior to the current time using spatial kriging interpolation, expands the initialized irradiation data based on a graph-diffuse convolutional network to obtain expanded irradiation data, combines the graph-diffuse convolutional model and a spatial Transformer module using a residual structure to capture spatial features, and uses a trend gate recurrent unit network as input to obtain a prediction result of distributed solar power generation output for a set period after the current time.

Description

[Technical Field]

[0001] (Cross-reference of related applications) This invention claims priority to the Chinese patent application filed with the China National Intellectual Property Administration on September 6, 2024, with application number 202411244453.9, and title "Distributed Photovoltaic Power Output Prediction Method and System Based on Graph Neural Networks," the entire contents of which are incorporated by reference to this invention for any purpose and constitute part of this invention.

[0002] The present invention relates to the field of data processing, and more specifically to a distributed solar power generation output prediction method and system based on a graph neural network. [Background technology]

[0003] This section merely describes the background art related to the present invention and does not necessarily constitute prior art.

[0004] Improving the forecasting of intermittent and non-dispatchable energy output is a crucial factor in increasing the penetration rate of renewable energy in the power grid. Existing centralized photovoltaic forecasting methods can be broadly classified into two types: direct methods and data-driven methods, and research and application of these methods have already reached a fairly mature level. In contrast, distributed photovoltaic forecasting is specialized for forecasting photovoltaic output at multiple locations or regions of distributed photovoltaic power plants. In recent years, research on distributed photovoltaic forecasting has often drawn inspiration from centralized forecasting methods, but there are still significant differences in terms of data conditions, predictability of the target, and applicable forecasting models. Specifically, distributed photovoltaic forecasting faces challenges such as the lack of irradiation data and insufficient spatial correlation exploration by forecasting models, making it difficult to improve the accuracy of distributed photovoltaic forecasting.

[0005] Distributed solar power plants are characterized by their small individual capacities, dispersed locations, and large number, often resulting in localized high penetration rates and densities. Because the cost of installing weather observation equipment at each small, dispersed solar power plant is excessive, most distributed solar power plants rely on numerical weather predictions (NWP) from nearby central solar power plants. However, these NWPs often lack high-resolution, critical weather data for the entire region. Therefore, effectively obtaining high-resolution NWP data, such as solar intensity, using public data resources and statistical methods with strong nonlinear fitting capabilities, has become a crucial research challenge. In recent years, Kriging interpolation and Gaussian process regression have become prominent techniques for geographical interpolation of weather data. These methods provide fine-grained, high-resolution spatiotemporal data interpolation by considering temporal trends and spatial correlations. However, these methods have limitations in computational cost and processing large datasets, resulting in insufficient interpolation performance and making them economically unfeasible.

[0006] Deep neural networks have become the primary means of predicting short-term solar power generation. For example, convolutional neural networks and long-term short-term memory networks are used to enhance the model's fitting ability, and attention models are often integrated into various neural network units to improve the model's generalization and correlation mining capabilities. However, the above methods focus only on the temporal autocorrelation of solar power generation sequences, neglecting the spatial correlation between adjacent solar power plant sequences in the context of distributed solar power generation prediction. In recent years, researchers have shifted their focus to improving the accuracy of short-term solar power generation predictions by utilizing the spatiotemporal correlation between adjacent solar power plants, and prediction methods now take into account information from surrounding solar power plants. However, attention to spatial dimensions is mostly limited to data preprocessing and the selection of input features, resulting in universally low prediction accuracy. [Overview of the Initiative]

[0007] In order to solve the deficiencies of the prior art, the present invention provides a distributed solar power generation output prediction method and system based on a graph neural network, which improves the prediction accuracy from three aspects of data, model and parameters, and provides a practical and need-based solution for high-precision short-term prediction of distributed solar power plants.

[0008] To achieve the above object, the present invention adopts the following technical solutions.

[0009] In a first aspect, the present invention A process of initializing irradiation data using spatial kriging interpolation based on the irradiation data of distributed solar power generation in a set period before the current time, expanding the initialized irradiation data based on a graph diffusion convolutional network, and obtaining the expanded irradiation data; A process of capturing spatial features by combining a graph convolutional model and a spatial Transformer module using a residual structure based on the irradiation data of distributed solar power generation in a set period before the current time; A process of obtaining a distributed solar power generation output prediction result for a set period after the current time using a trend gate recurrent unit network with the expanded irradiation data and the spatial features as inputs, and providing a distributed solar power generation output prediction method based on a graph neural network.

[0010] As a further limitation of the first aspect of the present invention, a hyperparameter optimization feedback improvement strategy suitable for swarm intelligence algorithms is used to quantify the particle swarm density based on the information entropy function, and perturbations are added in a timely manner to improve the optimization effect of the algorithm.

[0011] In a second aspect, the present invention A data expansion unit configured to initialize irradiation data using spatial kriging interpolation based on the irradiation data of distributed solar power generation in a set period before the current time, expand the initialized irradiation data based on a graph diffusion convolutional network, and obtain the expanded irradiation data; A feature extraction unit is configured to capture spatial features by combining a graph convolution model and a spatial transformer module using a residual structure, based on irradiation data from distributed solar power generation for a set period prior to the current time. The present invention provides a distributed solar power output prediction system based on a graph neural network, comprising: an output prediction unit configured to take the expanded irradiation data and spatial features as inputs and obtain a distributed solar power output prediction result for a set period after the current time using a trend gate recursive unit network.

[0012] As a further limitation of the first aspect of the present invention, the invention further comprises a hyperparameter optimization unit configured to use a hyperparameter optimization feedback improvement strategy suitable for swarm intelligence algorithms, to quantify the particle swarm density based on an information entropy function, and to apply perturbations in a timely manner to improve the optimization effect of the algorithm.

[0013] Compared to the prior art, the present invention has the following beneficial effects. 1. The present invention provides an innovative method for augmenting meteorological data based on kriging-graph diffusion convolution, enabling the acquisition of high-resolution irradiation data at low cost and constructing a data infrastructure for improving the accuracy of subsequent distributed solar power output forecasts. 2. The present invention innovatively provides a new spatiotemporal graph transformer network model, innovatively applying spatiotemporal graph networks to distributed solar power output forecasting, using graph convolution and attention mechanisms to effectively extract spatial information between adjacent solar power plants, and realizing highly accurate short-term output forecasting for multiple solar power plants. 3. The present invention innovatively proposes a feedback improvement strategy suitable for swarm intelligence algorithms that quantifies the diversity of a group based on an information entropy function, effectively evaluating the current state of the group to guide timely perturbations and improve optimization performance and prediction accuracy.

[0014] The drawings in the specification, which constitute part of the present invention, are for the purpose of further understanding the present invention, and the exemplary embodiments and descriptions thereof are for the purpose of interpretation of the present invention and are not intended to improperly limit the present invention. [Brief explanation of the drawing]

[0015] [Figure 1] This is a schematic flowchart of the data augmentation method by kriging-graph diffusion convolution provided in Example 1 of the present invention. [Figure 2] This is a multi-module configuration diagram of the spatiotemporal graph transformer network model provided in Embodiment 1 of the present invention. [Figure 3] This is a schematic diagram of the trend gate recursive unit network provided in Embodiment 1 of the present invention. [Modes for carrying out the invention]

[0016] The present invention will be further described below with reference to drawings and embodiments. It should be noted that the following detailed description is illustrative and intended to further illustrate this application. Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art to which this invention pertains.

[0017] The embodiments and features of the present invention can be combined with each other, as long as they do not contradict each other.

[0018] Example 1 This embodiment provides a distributed solar power output prediction method based on a graph neural network. First, it designs a spatial data augmentation method using kriging-graph diffusion convolution, initializes irradiation data using a spatial kriging interpolation method, then performs data augmentation based on a graph diffusion convolution network, estimates data at unsampled locations within the graph structure, and achieves high-resolution coverage of important meteorological irradiation data. Next, it provides a novel spatiotemporal graph network model for distributed solar power output prediction. This network model captures spatial features by combining a graph convolution model and a Transformer model using a residual structure, extracts temporal autocorrelation using an improved trend gate recurrent unit network, and effectively solves the problem of prediction delay. Finally, it proposes a hyperparameter optimization feedback improvement strategy suitable for swarm intelligence algorithms, quantifies particle swarm density based on the information entropy function, and applies perturbations in a timely manner to improve the optimization effect of the algorithm.

[0019] Specifically, the distributed solar power generation output prediction method includes the following:

[0020] S1: Data augmentation using kriging-graph diffusion convolution.

[0021] Figure 1 shows a complete overview of the irradiation data augmentation method using kriging-graph diffusion convolution. First, the graph signal is initialized at the desired target resolution using kriging interpolation, i.e., the meteorological irradiation data for unsampled solar power plants is initialized. To avoid excessive smoothing effects in the graph diffusion convolution data augmentation process, at each node of the target resolution, the values ​​for unsampled locations are predicted using the distance between solar power plants, based on meteorological irradiation data for all known locations obtained from centralized solar power plants (complete solar power plants), using the kriging method.

[0022] S1.1: Kriging initialization.

[0023] In actual distributed solar power generation forecasting scenarios, the available irradiation data is usually limited, often consisting only of spatial geographic information with temporal delays and lacking complete auxiliary meteorological data. To overcome this limitation, we obtain initial irradiation values ​​for distributed solar power plants using a kriging method based on geographic location and distance information. Here, we estimate the values ​​for unsampled solar power plants using an unbiased weighted average of nearby solar power plants.

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[0024] S1.2: Data augmentation using graph diffusion convolution.

[0025] This embodiment introduces a two-layer graph diffusion convolution combined with a residual network, trains the model using a random sampling subgraph method, and its core operation is to randomly sample a subset of nodes to obtain the feature matrix X of the sampled data and construct the corresponding adjacency matrix W. The mathematical representation of the network structure of the two-layer graph diffusion convolution is as follows:

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[0026] S1.3: Construction of edge weights by the Gaussian method.

[0027] Regarding the adjacency matrix W, the irradiance of neighboring solar power plants is affected by geographical location, cloud cover, and wind speed. Considering that the edge weights of the graph are assigned using the Euclidean distance between solar power plants and the statistical correlation between auxiliary variables, and there may be a combination of observed correlation features and distance features in the information, when time-varying meteorological auxiliary data is available, the edge weights can be defined using any combination of two or more time-varying variables, static variables, and auxiliary variables. The edge weights are calculated using the Gaussian kernel and are mathematically expressed as follows:

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[0028] S2: Spatiotemporal graph transformer network distributed solar power generation prediction model.

[0029] As shown in Figure 2, which outlines the architecture of the Spatio-temporal Graph Transformer Network (STGTN) model, the STGTN model consists of a spatial network and a temporal network, which are closely coupled. The spatial network extracts spatial features using a Graph Convolution Network (GCN) and a Spatial Transformer (Transformer) model, while the temporal network handles the temporal dimension using an extended Trend Gated Recurrent Unit (TGRU) network.

[0030] S2.1: GCN model.

[0031] Unlike conventional convolutional neural networks (CNNs), which are limited to processing in Euclidean space, graph neural networks (GNNs) can process graph structures formed by distributed solar power topology more flexibly, thus capturing spatial dependencies more accurately.

[0032] Given an adjacency matrix A and a feature matrix X, the GCN model constructs a filter in the Fourier frequency domain, which manipulates the nodes of the graph, capturing spatial features between nodes through their first-order neighbors, and then constructs a two-layer GCN model by superposition, which can be mathematically expressed as follows:

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[0033] Specifically, the input is the original data, which is then input into the spatial Transformer model through graph convolution of the GCN model, a ReLU layer, and layer normalization.

[0034] S2.2: Spatial Transformer model.

[0035] To more effectively extract spatial information, drawing inspiration from the successful application of spatial transformers in long-term time series forecasting, we designed a spatial Transformer module, which can be considered a transpose of the input data of a conventional Transformer. This module treats each time sequence as an independent feature vector, captures important information within the sequence using a self-attention mechanism, and models the spatial dependencies between features. The spatial Transformer module includes two main components: a scaled-dot product attention mechanism and location encoding. Typically, location encoding is added to the input embedding to model a location index sequence, which includes the following:

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[0036] Specifically, the spatial Transformer model includes a multi-head attention layer and a feedforward network, with the output of the feedforward network being used as spatial features.

[0037] S2.3: Extended Trend Gate Recursive Unit Network.

[0038] While Gated Recurrent Units (GRUs) are a mature time-sequence prediction technique, they face inherent challenges in accurately capturing trend features of non-stationary sequences. This limitation results in a noticeable delay in predicted solar power data, impacting the accuracy of the prediction task. By introducing trend gates, TGRU models incorporate the network's sensitivity to differential data, more effectively capturing trend information and thereby more accurately modeling trend changes, thus improving their ability to predict non-stationary sequences.

[0039] The network structure is shown in Figure 3, and mathematically it can be expressed as follows:

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[0040] Specifically, as shown in Figure 2, the augmented meteorological irradiation data, along with spatial features, is input into an augmented trend gate recurrent unit network (i.e., a TGRU model), fused, and used for prediction to obtain short-term forecast results.

[0041] S3: Use improved swarm intelligence algorithm optimization hyperparameters.

[0042] Existing model parameter optimization methods primarily focus on swarm intelligence algorithms that output interpretable parameters to improve predictive performance. Swarm intelligence algorithms originate from the study of social behavior in biological groups and solve complex optimization problems by forming swarm intelligence through interaction mechanisms, but premature convergence often occurs in the optimization process. Most existing research is limited to studies of different perturbation strategies, neglecting the crucial timing of perturbation introduction. Such oversights can lead to algorithms failing to converge or perturbations failing to produce the expected effects. Therefore, this invention aims to design an improved feedback strategy based on the information entropy function, quantify swarm diversification, and timely perturbation to escape local optima. This embodiment primarily focuses on the correlation threshold (T) of the adjacency matrix of a graph neural network. s ), Hidden layer dimension (H d ), learning rate (L r ) and hyperparameters such as the dimension (T) of the input window are optimized.

[0043] The initial state of a group consisting of n individuals is the state set.

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[0044] When combined with theoretical analysis, the calculation of information entropy within a group has the characteristic of being unaffected by factors such as individual dimension, search space size, and time. Its value is related only to the size of the group and is usually positively correlated with the number of individuals in the group. In the middle of the iteration, information entropy decreases sharply, corresponding to a rapid decrease in group diversity. Such a decrease leads to early convergence of the group, causing it to fall into a local minimum. Changes in information entropy can be an effective indicator for evaluating the current state of the group and helping to determine whether the group is in a local optimum. When using information entropy to determine different states between individuals, the existing error should be taken into consideration. The distance between individuals is given by a specified error (empirically 10). -6 If the value is smaller than (set), individuals are considered to have the same state within the system. In the iterative process, the first derivative of the information entropy is calculated using differential calculus, and if the first derivative is smaller than the initial information entropy divided by the group size, the group is considered to be in a potential local optimum. After effectively recognizing the local state, adaptive dispersion perturbations are added to each position, which can be expressed mathematically as follows:

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[0045] Example 2 This embodiment is, A data augmentation unit is configured to initialize irradiation data using spatial kriging interpolation based on irradiation data from distributed solar power generation for a set period prior to the current time, expand the initialized irradiation data based on a graph-diffuse convolutional network, and obtain augmented irradiation data. A feature extraction unit is configured to capture spatial features by combining a graph convolution model and a spatial transformer module using a residual structure, based on irradiation data from distributed solar power generation for a set period prior to the current time. The present invention provides a distributed solar power output prediction system based on a graph neural network, comprising: an output prediction unit configured to take the expanded irradiation data and spatial features as inputs and obtain a distributed solar power output prediction result for a set period after the current time using a trend gate recursive unit network.

[0046] The system may further include a hyperparameter optimization unit configured to selectively use a hyperparameter optimization feedback improvement strategy suitable for swarm intelligence algorithms, quantify particle swarm density based on an information entropy function, and apply perturbations in a timely manner to improve the optimization effect of the algorithm.

[0047] It can be understood that each or all of the above units may be integrated into one or more other units, or one (or several) of these units may be divided into multiple functionally smaller units, thereby achieving the same operation without affecting the realization of the technical effects of the embodiments of this application. The above units are divided based on logical functions, and in actual application, the function of one unit may be realized by multiple units, or the function of multiple units may be realized by one unit. In other embodiments of this application, the distributed photovoltaic power output prediction system using a graph neural network may include other units, and in actual application, these functions may be realized with the help of other units, or by multiple units working together.

[0048] According to another embodiment of this application, the system described in this embodiment can be constructed by executing a computer program (including program code) capable of executing each step of the corresponding method described in Embodiment 1 on a general computing device such as a computer that includes processing elements and storage elements such as a central processing unit (CPU), a random access memory (RAM), and a read-only memory (ROM), thereby realizing the distributed solar power output prediction method using a graph neural network of the embodiment of this application. The computer program may be recorded on a computer-readable recording medium, loaded onto the computing device via the computer-readable recording medium, and executed there.

[0049] The foregoing description represents only preferred embodiments of the present invention and is not intended to limit the invention. Those skilled in the art will know that the present invention can be modified and altered in various ways. Any modifications, equivalent substitutions, improvements, etc., made without departing from the spirit and principles of the present invention shall be within the scope of protection of the present invention.

Claims

1. The process involves initializing the irradiation data using spatial kriging interpolation based on the irradiation data of distributed solar power generation for a set period prior to the current time, extending the initialized irradiation data based on a graph-diffuse convolutional network, and obtaining the extended irradiation data. Based on irradiation data from distributed solar power generation for a set period prior to the current time, a process is used to capture spatial features by combining a graph convolution model and a spatial transformer module using a residual structure. The process includes taking the extended irradiation data and spatial features as input and using a trend gate recursive unit network to obtain a prediction result for distributed photovoltaic power output for a set period after the current time, Obtaining irradiation values ​​for initial distributed solar power plants using the kriging method involves estimating values ​​for unsampled solar power plants using an unbiased weighted average of neighboring solar power plants. [Number 19] where γ(x ｉ , x ０ ) and γ(x ｉ , x ｊ ) are the semivariograms between the data point x ｉ and the unobserved point x ０ , and between the data points x ｉ and x ｊ , β ｉ and β ｊ represent the weights of the i-th and j-th data points respectively, and N represents the number of data points. The aforementioned graph-diffusion convolutional network includes the following: [Number 20] These are the forward and reverse transition matrices, respectively, K is the sum of the diffusion convolution orders, k is the diffusion convolution order, W = W / rowsum(W), W is the adjacency matrix, and the convolution process in graph diffusion convolution is approximated using Chebyshev polynomials, T ｋ (X) = 2XT ｋ－１ (X)-T ｋ－２ (X) and X is [Math 21] is the learning parameter of the first layer, which controls the transformation of each node, F(H1) represents the transformation part, and F(H １ ) + H １ represents the residual operation, W is the adjacency matrix, and H ２ This is the output of the second layer, H １ This is the output of the first layer, The aforementioned graph convolution model is, The process involves taking an adjacency matrix A and an input feature matrix X, constructing a filter in the Fourier frequency domain, manipulating the nodes of the graph with the filter, capturing spatial features between nodes using the first-order neighbors of the nodes, and constructing a graph convolution model by superimposing the spatial features of each node, with the output H of the second layer of the graph convolution model being the output H. ２ The following applies: 【Number 22】 represents an adjacency matrix with self-connection, I Ｎ This is the identity matrix, [Number 23] It is a matrix of order H ２ This is the output of the second layer of the graph convolution model, W １ and W ２ These are the weight parameters of the first and second layers, and the nonlinear activation functions are represented by relu(•) and tanh(•). The aforementioned spatial transformer module is This involves treating each time sequence as an independent feature vector, capturing important information within the sequence using a self-attention mechanism, simultaneously modeling spatial dependencies between features including a scaled-dot product attention mechanism and position encoding, and modeling a position index sequence by adding position encoding to the input embedding, wherein the position index sequence includes the following: [Number 24] In the formula, n is the position index, f is the dimension index, and d ｍｏｄｅｌ is the hidden dimension of the features, and assuming each time sequence is an independent feature vector, the scaling formula for the self-attention network is as follows: [Number 25] In the formula, query Q, key K, and value V are the three basic elements of the self-attention mechanism, obtained by a non-coordinate linear transformation of the original input, W ｑ , W ｋ , W ｖ These are the weight matrices for query Q, key K, and value V, respectively, and d ｋ is the scale factor, and d ｋ = d ｍｏｄｌｅ / h, where h represents the number of learned projections, and multi-head attention uses h sets of learned projections, with each set implementing a different attention function. The aforementioned trend gate recursive unit network includes the following: [Number 26] In the formula, x ｔ represents the feature input at time t, and h ｔ This represents the output of the hidden layer at time t, and z ｔ This is an update gate, which controls the degree to which past hidden states are retained, and r ｔ This is a reset gate, which adjusts the influence of past hidden states on the current time step, g ｔ This is a trend gate, which controls the degree to which trend information is updated, Δx ｔ This is the first-order difference of the input features, and the value is x ｔ -x ｔ－１ It represents trend information between sequences, and its initial state is 0. [Number 27] represents a new memory unit, represents a candidate update value, and σ(•) is the sigmoid activation function. [Number 28] represents the dot product, W ｚ , W ｒ , W ｇ and W ｈ Each of these represents a weight matrix, and b ｚ , b ｒ , b ｇ and b ｈ A distributed solar power output prediction method based on a graph neural network executed by a computer, characterized in that each of the vectors represents a bias vector and tanh(•) is a nonlinear activation function.

2. Edge weights of adjacency matrix W ｉｊ This includes the following: [Number 29] In the formula, d ｓ (i, j) and d ｔ (i, j) represents the difference between the static and time-varying variables of adjacent nodes i and j, respectively, and the auxiliary variable, σ ｓ and σ ｔ The distributed solar power output prediction method based on a graph neural network according to claim 1, characterized in that are weight coefficients for a static variable and a time-varying variable, respectively.

3. In a hyperparameter optimization process in a swarm intelligence algorithm, the particle swarm density is quantified based on the information entropy function, and whether the swarm is in a local optimum is evaluated based on the change in information entropy, and perturbations are applied in a timely manner to enhance the hyperparameter optimization effect of the graph convolution model, and includes the following: The initial state of a group consisting of n individuals is a state set. [Number 30] Express it in terms of x ｉ Assuming that represents the state of the i-th individual, the distribution of individual states is quantified by calculating information entropy, representing the diversity of the group, and the group's information entropy function H(X) is as follows: [Number 31] In the formula, P(x ｉ ) is particle x within the group ｉ This is the probability, and ∈ is a constant. If the distance between individuals is less than a specified error, the individuals are considered to have the same state in the system, and in the iterative process, the first derivative of the information entropy is calculated using differential calculus, and if the derivative is less than the initial information entropy divided by the group size, the group is considered to be in a potential local optimum, and adaptive perturbations are added, including the following: [Number 32] In the formula, ΔH is H ｔ and H ｔ－１ It represents the difference, H ０ represents the entropy value of the initialized group, H ｔ represents the entropy value of the group at time t, H ｔ－１ represents the entropy value of the group at time t-1, and N represents the size of the group. [Number 33] This is an algorithm-specific update rule, [Number 34] represents the state at time t+1, θ is an algorithm parameter, and p ｉ A distributed solar power output prediction method based on a graph neural network according to claim 1, characterized in that represents a perturbation acting on the i-th individual.

4. A data augmentation unit is configured to initialize irradiation data using spatial kriging interpolation based on irradiation data from distributed solar power generation for a set period prior to the current time, expand the initialized irradiation data based on a graph-diffuse convolutional network, and obtain augmented irradiation data. A feature extraction unit is configured to capture spatial features by combining a graph convolution model and a spatial transformer module using a residual structure, based on irradiation data from distributed solar power generation for a set period prior to the current time. A graph neural network-based distributed solar power output prediction system for realizing a graph neural network-based distributed solar power output prediction method according to any one of claims 1 to 3, comprising: an output prediction unit configured to take the expanded irradiation data and the spatial features as input and use a trend gate recursive unit network to obtain a distributed solar power output prediction result for a set period after the current time.

5. A hyperparameter optimization unit configured to enhance the hyperparameter optimization effect of a graph convolution model by quantifying the particle swarm density based on an information entropy function, evaluating whether the swarm is in a local optimum based on the change in information entropy, and applying perturbations in a timely manner, comprising the following: The initial state of a group consisting of n individuals is a state set. [Number 35] Express it in terms of x ｉ Assuming that represents the state of the i-th individual, the distribution of individual states is quantified by calculating information entropy, representing the diversity of the group, and the group's information entropy function H(X) is as follows: [Number 36] In the formula, P(x ｉ ) is particle x within the group ｉ This is the probability, where n is the sum of the existing states, and ∈ is a constant. If the distance between individuals is less than a specified error, the individuals are considered to have the same state in the system, and in the iterative process, the first derivative of the entropy is calculated using differential calculus, and if the derivative is less than the initial information entropy divided by the group size, the group is considered to be in a potential local optimum, and adaptive perturbations are applied to each position, including the following: [Number 37] In the formula, ΔH is H ｔ and H ｔ－１ It represents the difference, H ０ represents the entropy value of the initialized group, H ｔ represents the entropy value of the group at time t, H ｔ－１ represents the entropy value of the group at time t-1, and N represents the size of the group. [Number 38] This is an algorithm-specific update rule, [Number 39] represents the state at time t+1, θ is an algorithm parameter, and p ｉ A distributed solar power output prediction system based on a graph neural network according to claim 4, characterized in that represents a perturbation acting on the i-th individual.

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