A power system source and load multi-objective prediction method based on Laguerre polynomial theory

Abstract

This invention discloses a multi-objective prediction method for power system sources and loads based on Laguerre polynomial theory, relating to the field of power system prediction and intelligent dispatching technology. The method includes the following steps: using Spearman Rank Correlation Coefficient (SRCC) to analyze the correlation of characteristic influencing factors of wind power, photovoltaic power, and power load; and using Robust Local Mean Decomposition (RLMD) to decompose the time series of wind power, photovoltaic power, and power load into high-frequency and low-frequency components to reduce their fluctuations; using Weighted Permutation Entropy (WPE) to analyze the complexity of the subsequences after RLMD decomposition, merging subsequences with similar complexity to reduce the model's prediction complexity; and constructing a hybrid Laguerre neural network prediction model using Laguerre polynomials. This invention is the first to simultaneously consider both accuracy and stability objectives in source and load prediction, selecting a compromise solution in the Pareto front using the MORUN algorithm, making the prediction results more applicable to power system dispatching scenarios with high robustness requirements.

Description

Technical Field

[0001] This invention relates to the field of power system prediction and intelligent dispatch technology, specifically to a multi-objective prediction method for power system sources and loads based on Laguerre polynomial theory. Background Technology

[0002] Day-ahead dispatching of the power system relies on accurate forecasts of wind power, solar power, and load. Renewable energy and load forecasting are among the most commonly used methods to reduce uncertainties in optimal power system dispatching. Therefore, to ensure the safe and stable operation of the power system, it is essential to develop more accurate and stable source-load two-sided forecasting techniques. However, existing forecasting techniques still have the following shortcomings: (1) Most prediction models are single-objective optimizations that only focus on prediction accuracy and cannot take into account prediction stability, making it difficult to meet the requirements of power system dispatch for the robustness of prediction results.

[0003] (2) Traditional neural networks (such as BPNN, LSTM, etc.) are prone to overfitting, unstable training and poor generalization when dealing with complex sequences of renewable energy power fluctuations.

[0004] (3) Existing data decomposition methods (such as EMD and LMD) suffer from endpoint effects and mode mixing, which affect the decomposition effect and thus reduce the accuracy of subsequent predictions.

[0005] (4) The prediction model has a complex structure and numerous parameters, resulting in low training efficiency and difficulty in meeting the real-time requirements of online or quasi-online prediction of power systems.

[0006] Therefore, in the two-sided forecasting of power system sources and loads, it is necessary to further develop new forecasting models to meet the current needs of power system optimization and dispatch. Summary of the Invention

[0007] The purpose of this invention is to provide a multi-objective prediction method for power system sources and loads based on Laguerre polynomial theory, so as to solve the problems existing in the prior art mentioned in the background.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A multi-objective prediction method for power system sources and loads based on Laguerre polynomial theory includes the following steps: S1: Spearman's rank correlation coefficient (SRCC) is used to analyze the correlation of characteristic influencing factors of wind power, photovoltaic power and power load. Robust local mean decomposition (RLMD) is used to decompose the time series of wind power, photovoltaic power and power load into high-frequency components and low-frequency components to reduce their fluctuation and improve the accuracy of the prediction model. S2: We use weighted permutation entropy (WPE) to analyze the complexity of the subsequences after RLMD decomposition, and merge subsequences with similar complexity to reduce the model's prediction complexity. S3: A hybrid Laguerre neural network prediction model is constructed using Laguerre polynomials, and pseudo-inverse learning is used to solve the problem of insufficient generalization ability of the hybrid Laguerre neural network prediction model. S4: A novel multi-objective Runge-Kutta (MORUN) algorithm is used to optimize the weights of the hybrid pseudo-inverse Laguerre neural network, thereby improving the accuracy and stability of the model's prediction results. S5: Introducing the concept of ensemble learning, the source-load two-sided prediction model is optimized using AdaBoost.R2 to achieve self-allocation and reorganization of error weights. The effectiveness of the source-load two-sided prediction model is verified through actual data, providing an accurate and stable data foundation for day-ahead scheduling of power system source-load coordination and reducing uncertainty on both sides of the source and load.

[0009] Preferably, the specific steps of S1 are as follows: Wind power, solar power, and electricity load forecasting are influenced by numerous factors. Wind power is affected by wind speed, wind direction, temperature, humidity, and air pressure. Solar power is affected by solar irradiance, ambient temperature, air pressure, relative humidity, and cloud opacity. Electricity load is affected by rainfall, relative humidity, and ambient temperature. Although there are complex coupling relationships between these factors and wind power, solar power, and electricity load, the degree of correlation varies significantly. Furthermore, when using neural networks to find the mapping relationship between relevant influencing factors and wind power, solar power, and electricity load, excessively high-dimensional training data increases the training complexity of the neural network and reduces prediction efficiency. Therefore, it is necessary to analyze the correlation between relevant factors and wind power, solar power, and electricity load, and select highly correlated factors to construct the training sample set for the prediction model, thereby improving the model's prediction efficiency.

[0010] This invention employs Spearman's rank correlation coefficient (SRCC) to analyze the correlation between characteristic influencing factors of wind power, photovoltaic power, and electricity load. SRCC is generally used to measure the degree of nonlinear correlation between variables. Compared to Pearson correlation coefficient, SRCC does not require assumptions about data distribution, has low sensitivity to outliers, and is more consistent with correlation analysis of data in practical engineering applications. The SRCC correlation coefficient range is... The larger the absolute value of the correlation coefficient, the higher the correlation between the two variables, and vice versa.

[0011] The mathematical formula for SRCC is as follows: (2-1) In the formula, For SRCC index values, The difference between corresponding sample ranks between variables. For sample size; Robust Local Mean Decomposition (RLMD) is employed to decompose the time series of wind power, photovoltaic power, and electricity load into high-frequency and low-frequency components to reduce their volatility and improve the accuracy of the prediction model. RLMD optimizes the boundary conditions, signal envelope estimation, and stopping criteria of local mean decomposition. RLMD can adaptively decompose the number of high-frequency and low-frequency components based on the characteristics of the time series. Let the time series of wind power, photovoltaic power, and electricity load be... The RLMD decomposition process is as follows: (1) Determine the symmetrical points at both ends of the time series signal, and... Signal mirroring expansion ; (2) Searching All local extreme points The corresponding signal value is denoted as ; (3) Calculate the mean of adjacent local extreme points and local envelope estimates : (2-2) (2-3) (4) and Connect the points and process them using a moving average algorithm to generate a local mean function. and envelope estimation function ,according to and Calculate the frequency modulation signal : (2-4) (5) Complete the first round of decomposition, and... The above steps are repeated to calculate the new input signal. Next, the screening stopping criteria are reset, and the objective function for each iteration is set as follows: (2-5) in, (2-6) (2-7) (2-8) In the formula, and These are the root mean square and kurtosis of the envelope signal, respectively. For time series signal sampling points, for The arithmetic mean; (6) After the termination condition is met, extract the frequency modulation signal. and envelope signal : (2-9) (2-10) (7) and Multiplication yields the product function. , and Subtraction yields the residual signal Repeat steps (1) to (6) until the end. Decomposed into One product function and one residual signal: (2-11).

[0012] Preferably, the specific steps of S2 are as follows: RLMD adaptively decomposes wind power, photovoltaic power, and electricity load into several high-frequency and low-frequency components based on their time-series characteristics. This leads to a decrease in the model's prediction efficiency when the number of high-frequency and low-frequency components in the adaptive decomposition is large. Therefore, this invention uses Weighted Permutation Entropy (WPE) to analyze the complexity of the subsequences after RLMD decomposition, merging subsequences with similar complexities to reduce the model's prediction complexity. The WPE calculation process is as follows: (1) Decomposition of subsequences conduct Phase space reconstruction: (2-12) In the formula, and These represent the embedding bit length and latency, respectively. ; (2) For the first Sort the elements in each component in ascending order: (2-13) In the formula, For element index, when At that time, an index symbol matrix will be generated: (2-14) (3) Calculate the weights of the reconstructed components: (2-15) (2-16) In the formula, For the index symbol sequence, and They are respectively The weights and mean; (4) Using weights and arrangement Characterize the feature information of the reconstructed components and calculate each permutation. Weighted probabilities: (2-17) In the formula, for Arrangement ; (5) Calculate the subsequence WPE value: (2-18).

[0013] Preferably, the specific steps in S3 for constructing a hybrid Laguerre neural network prediction model using Laguerre polynomials are as follows: Based on Laguerre polynomials, Laguerre orthogonal basis functions and new Laguerre orthogonal basis functions are constructed according to polynomial interpolation and approximation theory. These two types of Laguerre orthogonal basis functions are used as activation functions for neural networks to predict source loads. Learning and approximation are performed to establish a basic HLNN prediction model; the detailed construction process of HLNN is as follows: (1) Laguerre orthogonal basis functions Definition: The Laguerre polynomial, proposed by Edmond Laguerre, has its domain in the interval [0, 1]. Above with power The orthogonal polynomials of the Laguerre polynomials are defined as follows: (2-19) The orthogonality of Laguerre polynomials with respect to the weight functions is as follows: (2-20) The recurrence equation for the Laguerre polynomial is as follows: (2-21) In recent years, neural networks built upon Laguerre polynomials have been widely applied. Laguerre polynomials, as orthogonal basis functions of neural networks, have the domain of their independent variables as follows: However, it cannot solve many practical engineering problems. In order to increase the domain of Laguerre orthogonal basis functions and improve their applicability in engineering applications.

[0014] (2) New Laguerre orthogonal basis functions Definition: The domain of the new Laguerre polynomial as an orthogonal basis function is... The new Laguerre polynomial is defined as follows: (2-22) The orthogonality of the new Laguerre polynomial with respect to the weight functions is described as follows: (2-23) The differential equation of the new Laguerre polynomial is as follows: (2-24) The new Laguerre polynomial recurrence equation is as follows: (2-25) The proof of the orthogonality of the new Laguerre polynomials is as follows: Proof: 1) Let Then its derivative is ,therefore: (2-26) (2-27) (2-28) Considering The following conclusions can be drawn: (2-29) Substituting formula (2-29) into formula (2-28), we get the following result: (2-30) This satisfies formula (2-22), and formula (2-24) is proven.

[0015] 2) Differentiating both sides of equation (2-22) yields: (2-31) And because, ,so: (2-32) (2-33) so: (2-34) Differentiating both sides of equation (2-34) yields: (2-35) Rearrange formula (2-35) and change the formula in formula (2-33). use The substitution yields: (2-36) (2-37) Substituting formulas (2-35), (2-36), and (2-37) into formula (2-24), we get: (2-38) In formula (2-38) use The substitution yields: (2-39) Thus, the recurrence equation (2-25) for the new Laguerre polynomial is proved.

[0016] 3) When When, both sides of formula (2-24) are multiplied by We can obtain: (2-40) Multiply both sides of formula (2-40) by We can obtain: (2-41) According to the properties of cyclic symmetry, we can obtain: (2-42) Subtracting formula (2-42) from formula (2-41) and integrating, we get: (2-43) so, .

[0017] when When multiplying both sides of formula (2-40) By integration, we can obtain: (2-44) (2-45) (2-46) Substitute formulas (2-33), (2-45), and (2-46) into formula (2-40), and multiply both sides of the formula. We can obtain: (2-47) so: (2-48) (2-49) Thus, the orthogonality of formula (2-23) is proven. According to the above proof, the new Laguerre polynomials possess orthogonality with respect to the weight functions, and the relationship between their differential equations and recursive equations is proven. Therefore, the new Laguerre orthogonal basis functions meet the theoretical requirements for constructing neural networks.

[0018] (3) Hybrid Laguerre Neural Network HLNN is constructed using Laguerre polynomials and new Laguerre polynomials, with independent variables in Laguerre polynomials within a certain range were used to construct a Laguerre neural network (LNN) prediction model to predict positive sequences, with independent variables in... The new Laguerre polynomials within the range are used to build a new Laguerre neural network (NLNN) prediction model to predict negative sequences. Both LNN and NLNN are feedforward neural networks.

[0019] Preferably, the specific steps in S3 for addressing the insufficient generalization ability of the hybrid Laguerre neural network prediction model using pseudo-inverse learning are as follows: Pseudo-inverse learning is a technique that can effectively alleviate the insufficient generalization ability of feedforward neural networks. This method utilizes the pseudo-inverse property of matrices to optimize the parameters of the feedforward neural network, improving the accuracy and robustness of prediction results. Specifically, pseudo-inverse learning constructs the outputs of hidden layer neurons using nonlinear hybrid Laguerre orthogonal basis functions, and then obtains the optimal output weights of the HLNN by calculating the pseudo-inverse solution of the output vector. Compared with gradient descent algorithms represented by error backpropagation, pseudo-inverse learning does not require iterative optimization or setting learning control parameters; it directly calculates the analytical solution of the objective function through matrix operations such as matrix inner product and pseudo-inverse. Therefore, pseudo-inverse learning is more computationally efficient and easier to use. This invention optimizes the output weights of hidden layer neurons in HLNNs through pseudo-inverse learning to solve the problem of insufficient generalization ability during prediction, thereby improving the accuracy of the prediction model.

[0020] When the input matrix of the training set is The output matrix is At that time, pseudo-inverse learning was used to train the optimal weight matrix of the HLNN. The specific process is as follows: (2-50) (2-51) In the formula, For matrix Moore-Penrose pseudo-reverse, For hidden layer output, These are mixed Laguerre orthogonal basis functions.

[0021] Preferably, the specific steps of S4 are as follows: Based on the Runge-Kutta method, state transition operators, fast non-dominated sorting, and congestion calculation theory, a MORUN algorithm is proposed. This algorithm enables wind power, photovoltaic power, and power load model predictions to simultaneously possess high prediction accuracy and strong prediction stability. The MORUN algorithm is a multi-objective version of the Runge-Kutta optimizer RUN. Its operating mechanism includes the Runge-Kutta method, solution update mechanism, solution enhancement mechanism, state transition operators, fast non-dominated sorting, and congestion distance. The detailed operating mechanism of the MORUN algorithm is described below: The core search mechanism of MORUN is the fourth-order Runge Kutta (RK4) method. Its main idea is based on the concept of slope calculation proposed in the RK4 method, using the calculated slope as the feasible solution region in the search logic exploration space. Assuming... Defined at point The optimal slope of the straight line at the point RK4 utilization point The slope at that point, obtained through the best-fit line Calculate the next point Location, among which Similarly, It can be done The calculation yields the result. This process can be repeated. This time, thus obtaining Approximate solutions within the range. Morun defines the coefficients using the first derivative. Its mathematical formula is as follows: (2-52) in, (2-53) In the formula, This represents the slope at the first position within the interval. This is the position increment, the value of which depends on the step size parameter. . and It is a random solution in the Pareto frontier (PF). This is the average of all solutions in each iteration. The scaling factor that determines the size of the solution space. This is the initial solution. yes A random number within a given range. and These are random parameters. The other three coefficients are correspondingly random. , and The mathematical formula is as follows: (2-54) (2-55) (2-56) In the formula, , and This represents the slope at the second, third, and fourth positions within the interval. and for Two random numbers within the range. Calculate... , , and Based on this, the mathematical formula for Morun's main search mechanism (SM) is as follows: (2-57) (2-58) The MORUN algorithm begins optimization by creating a set of random solutions. The position of the solution changes in each iteration according to the RK4 method, which uses the slope to determine the next generation position. .

[0022] Variable 1 and Variable 2 are respectively and , The MORUN solution update process includes an exploration phase and a development phase. These two update mechanisms are executed probabilistically, and their mathematical formulas are as follows: (2-59) in, (2-60) In the formula, An integer that is 1 or -1. It is an adaptive factor. for A random number between [a certain number of points]. It is a random number that follows a normal distribution. , and This is a random solution in PF. and It is a constant. It is a weighting coefficient that decreases as the number of iterations increases.

[0023] During the local development of Morun, Enhanced Solution Quality (ESQ) was used to improve the algorithm's ability to find solutions. ESQ uses three randomized solutions... The average value and Combining these elements, a new solution can be formed. and further generate Its mathematical formula is as follows: (2-61) (2-62) (2-63) In the formula, , and All are random numbers. and The value in Within the range, It decreases as the number of iterations increases. The value is When satisfied When the conditions are met, a new solution will be executed. Its mathematical formula is as follows: (2-64) In the formula, It is a random number with a value of The principle of combining updated solutions with enhanced solutions to update the next generation of the population is as follows: Figure 2-4 As shown: In MORUN, state transition operators are introduced.

[158] The expansion transformation (ET) and axeion transformation (AT) operators in the algorithm enhance the algorithm's exploration and development capabilities through state space transformation. The search mechanisms for the ET and AT operators are as follows: (1) Scaling transformation The ET operator can extend the search for solutions to Morun pairs to the entire space, possessing global exploration capabilities. Its mathematical formula is as follows: (2-65) In the formula, It is the scaling factor. For a random solution in PF, It is a random diagonal matrix that follows a Gaussian distribution.

[0024] (2) Coordinate transformation The AT operator directs the population's search along an axis, enhancing the one-dimensional search capability of the Morun algorithm. Its mathematical formula is as follows: (2-66) In the formula, It is a coordinate factor. It is a sparse random diagonal matrix that follows a Gaussian distribution.

[0025] Unlike single-objective RUN algorithms, multi-objective optimization algorithms have multiple optimization objectives, making it impossible to use a single metric to measure the quality of the optimization results. First, a fast non-dominated sorting method is used to divide the population into several non-dominated fronts. Second, to ensure diversity among individuals in the non-dominated fronts, crowding density calculations are needed. Finally, the non-dominated solution of the population is updated by combining the non-dominated sorting and crowding density calculations.

[0026] Preferably, the specific steps for optimizing the source-load two-sided prediction model using AdaBoost.R2 in step S5 are as follows: By learning and combining multiple MORUN-HPLNN weak predictors through the AdaBoost.R2 algorithm, the prediction error is corrected, and the error weights are self-assigned and reorganized. The resulting MORUN-HPLNN strong predictor can further improve the prediction accuracy of the model. Assuming the training sample set , For the input vector, As the output vector, the process of training the MORUN-HPLNN prediction model with AdaBoost.R2 is as follows: (1) Set initial weights and calculate the relative prediction error of the weak predictor: (2-67) (2-68) (2-69) In the formula, The initial weights of the samples, , and These are the weak predictor, maximum prediction error, and relative error, respectively. (2) Adjustment Error and update weights: (2-70) (2-71) (2-72) In the formula, This is the normalization constant; (3) Construct the final strong predictor: (2-73) In the formula, yes The weighted median. As The weight.

[0027] Preferably, the source-load two-sided prediction process in S5 is as follows: (1) SRCC, RLMD and WPE are used to analyze and process the source and load data of the power system to reduce the fluctuation of wind power, photovoltaic power and power load time series and the computational complexity of the prediction model. (2) The time series of wind power, photovoltaic power and power load are positively and negatively transformed and used as inputs to PLNN and NPLNN respectively; (3) Use MORUN to optimize PLNN weights and construct MORUN-PLNN source-load prediction model. Then use MORUN to optimize NPLNN weights and construct MORUN-NPLNN source-load prediction model. (4) Train MORUN-PLNN with AdaBoost.R2 and construct the MORUN-PLNN-AdaBoost.R2 source-load prediction model to predict the positive sequences of wind power, photovoltaic power and power load. (5) Train MORUN-NPLNN with AdaBoost.R2 and construct the MORUN-NPLNN-AdaBoost.R2 source-load prediction model to predict wind power, photovoltaic power and negative power load sequences; (6) Obtain the results of the MORUN-PLNN-AdaBoost.R2 source load prediction model and the MORUN-NPLNN-AdaBoost.R2 source load prediction model by inverse transformation; (7) Add the source load prediction results of MORUN-PLNN-AdaBoost.R2 and MORUN-NPLNN-AdaBoost.R2 and calculate the average value to obtain the final prediction result of MORUN-HPLNN-AdaBoost.R2.

[0028] Compared with the prior art, the beneficial effects of the present invention are: 1. Multi-objective collaborative optimization: This invention is the first to simultaneously consider both accuracy and stability in source-load prediction. By using the MORUN algorithm to select a compromise solution in the Pareto front, the prediction results are more applicable to power system dispatch scenarios with high robustness requirements.

[0029] 2. Strong model generalization ability: HLNN combines two Laguerre orthogonal basis functions with complementary domains. Pseudo-inverse learning avoids the local optima and overfitting problems in traditional neural network training, and significantly improves the model's adaptability to different fluctuation characteristic sequences.

[0030] 3. High prediction efficiency: RLMD-WPE preprocessing effectively reduces the complexity of the input data, pseudo-inverse learning is a one-time analytical solution, and the MORUN algorithm has a fast convergence speed. Together, they ensure that the model maintains high accuracy in training and prediction efficiency.

[0031] 4. Significantly improved prediction accuracy and stability: Experiments show that compared with traditional single-objective models, other multi-objective optimization algorithms and mainstream neural network models, the MORUN-HPLNN-AdaBoost.R2 model proposed in this invention performs better on multiple evaluation indicators (IA, MAE, RMSE, SDEX, MdAPE) for wind power, photovoltaic, and load forecasting.

[0032] 5. High engineering practicality: It provides a complete technical solution from data preprocessing, model building, parameter optimization to integrated output, which can effectively reduce the uncertainty on both the source and load sides and provide accurate and stable forward-looking data for the day-ahead optimization and dispatch of the power system. Attached Figure Description

[0033] Figure 1 This is a flowchart of the MORUN-HPLNN-AdaBoost.R2 hybrid prediction model of the present invention.

[0034] Figure 2 This is a graph showing the training and testing data of wind power, photovoltaic power, and power load of this invention.

[0035] Figure 3 This is a Spearman correlation coefficient analysis diagram of wind power, photovoltaic power, and power load in this invention.

[0036] Figure 4 This is a graph showing the relationship between wind power, photovoltaic power, and power load training and testing data.

[0037] Figure 5 This is a combined graph showing the time series components of the generated wind power, photovoltaic power, and electricity load.

[0038] Figure 6 The graph shows the positive and negative transformation results of the time series component sequences of the generated wind power.

[0039] Figure 7 The graph shows the positive and negative conversion results of the photovoltaic power time series component sequences.

[0040] Figure 8 This is a graph showing the positive and negative transformation results of the power load time series component sequences.

[0041] Figure 9 The distribution of PF solutions obtained by the four algorithms of this invention on MOP1-MOP4 is shown.

[0042] Figure 10 This is a comparison chart of the selection and prediction curves of the non-dominated solution of the PF predicted by the two sides 1 hour ahead of the originating load.

[0043] Figure 11 This is a statistical chart showing the evaluation index results for the originating load from 1 hour to 24 hours ahead of both sides.

[0044] Figure 12 This is a comparison chart of the selection and prediction curves of the non-dominated solution of the PF predicted by the two sides 24 hours ahead of the originating load. Detailed Implementation

[0045] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0046] Please see Figure 1-12 The present invention provides the following technical solutions: The overall implementation process of this invention is as follows: Figure 1 As shown, it includes the following steps: Data acquisition and preprocessing: Collect historical wind power, photovoltaic power, power load data and their related characteristics (such as wind speed, sunshine, temperature, etc.), and use Spearman's rank correlation coefficient to select strongly correlated features as model input.

[0047] Sequence decomposition and recombination: RLMD is used to adaptively decompose the three types of power sequences into multiple product function (PF) components. WPE is used to calculate the entropy value of each component, and components with similar entropy values ​​are merged to reduce the number of subsequences to be predicted.

[0048] Construct and train the HPLNN base model: Transform each subsequence into positive and negative domains, and input them into LNN and NLNN respectively. Use the pseudo-inverse learning algorithm to calculate the optimal output weights of the network to obtain the preliminary HPLNN predictor.

[0049] Multi-objective optimization of network weights: Using the proposed MORUN algorithm, the weights of HPLNN are iteratively optimized with prediction accuracy index and prediction stability index as two optimization objectives to obtain a set of Pareto optimal solutions.

[0050] Ensemble learning to form a strong predictor: The AdaBoost.R2 algorithm is used to integrate multiple MORUN-HPLNN models initialized with different Pareto solution weights as weak predictors. By adjusting the sample weights, the final strong predictor model is constructed.

[0051] Multi-step prediction and result output: A strong prediction model is used to perform rolling predictions for each subsequence, with a lead time of 1 hour to 24 hours. The positive and negative prediction results of each subsequence are inversely transformed and summed to obtain the final predicted values ​​for wind power, photovoltaic power, and load power.

[0052] 1. Source load forecast data collection and evaluation indicators 1.1 Data Collection and Preprocessing The experimental data for wind power, photovoltaic power, and electricity load in this embodiment are sourced from a region in Xinjiang, China. This embodiment collects actual data on wind power, photovoltaic power, and electricity load in this region in 2018. Historical data from July to September (sampling interval of 1 hour) were selected as the training sample set for the source-load two-sided prediction model. Therefore, each training sample set contains 2160 sampling points. The first 70% (1512 sampling points) of the training samples were used for training, and the last 30% (648 sampling points) were used for testing, performing source-load two-sided predictions with a lead time of 1 hour to 24 hours to verify the performance of the proposed MORUN-HPLNN-AdaBoost.R2 prediction model. The training and testing data for wind power, photovoltaic power, and electricity load are as follows: Figure 2 As shown in the figure, the green, orange, and blue portions represent the training datasets for wind power, photovoltaic power, and electricity load, respectively, while the red portion represents the test dataset.

[0053] (1) Selection of source and load data features To improve the prediction efficiency of the MORUN-HPLNN-AdaBoost.R2 prediction model, SRCC (Signal Response Center Correlation Analysis) was used to analyze the correlation between characteristic influencing factors of wind power, photovoltaic power, and electricity load. Feature data with high correlation were selected as the training sample set for the model. To simplify the variable names of the feature data, they were abbreviated. The abbreviation statistics of source-load feature data are shown in Table 2-1. The correspondence between the absolute value range of SRCC and the degree of feature correlation is shown in Table 2-2.

[0054] Table 2-1 Abbreviated Statistics of Source and Load Characteristic Data

[0055] Table 2-2 Correlation between SRCC Correlation Coefficient and Correlation Degree

[0056] In this embodiment, the characteristic factors affecting wind power are wind speed, wind direction, temperature, air pressure, and humidity. The characteristic factors affecting photovoltaic power are total radiation, temperature, air pressure, and humidity. The characteristic factors affecting electricity load are maximum temperature, minimum temperature, average temperature, relative humidity, and rainfall. The SRCC correlation coefficients between wind power, photovoltaic power, electricity load, and each influencing factor are as follows: Figure 3 As shown.

[0057] from Figure 3(a) It can be seen that the SRCC value between wind power and wind speed is 0.94, indicating a very strong correlation. The absolute SRCC value between wind power and wind direction is 0.77, indicating a strong correlation. The SRCC value between wind power and humidity is 0.66, indicating a relatively strong correlation. The absolute SRCC values ​​between wind power and temperature and air pressure are 0.31 and 0.14, respectively, indicating a weak correlation. Therefore, in order to improve the prediction efficiency of the MORUN-HPLNN-AdaBoost.R2 wind power prediction model, wind speed, wind direction, and humidity feature vectors, along with wind power, are selected to construct the sample training set for the wind power prediction model.

[0058] from Figure 3 (b) It can be seen that the SRCC value between photovoltaic power and total radiation is 0.83, indicating a very strong correlation. The absolute SRCC values ​​between photovoltaic power and temperature, air pressure, and humidity are 0.19, 0.024, and 0.14, respectively, indicating a weak correlation. Therefore, in order to improve the prediction efficiency of the MORUN-HPLNN-AdaBoost.R2 photovoltaic power prediction model, the total radiation feature vector and photovoltaic power are selected to construct the sample training set for the photovoltaic power prediction model.

[0059] from Figure 3 (c) It can be seen that the SRCC values ​​between electricity load and the minimum and average temperatures are 0.73 and 0.72, respectively, indicating a strong correlation. The SRCC value between electricity load and the maximum temperature is 0.68, indicating a relatively strong correlation. The SRCC values ​​between electricity load and relative humidity and rainfall are 0.12 and 0.13, respectively, indicating a weak correlation. Therefore, in order to improve the prediction efficiency of the MORUN-HPLNN-AdaBoost.R2 electricity load prediction model, the feature vectors of the maximum, minimum, and average temperatures, along with the electricity load, are selected to construct the sample training set for the electricity load prediction model.

[0060] (2) RLMD data decomposition This invention employs Restricted Range Decomposition (RLMD) to decompose the time series data of wind power, photovoltaic power, and electricity load into high-frequency and low-frequency components, thereby reducing their volatility and improving the accuracy of the prediction model. RLMD can adaptively decompose the number of high-frequency and low-frequency components based on the characteristics of the time series. The results of RLMD decomposition of the time series components (TC) of wind power, photovoltaic power, and electricity load are as follows: Figure 4 Show.

[0061] from Figure 4As can be seen, RLMD adaptively decomposes wind power, photovoltaic power, and electricity load into TC1-TC7 components based on the characteristics of source-load time series data. On this basis, MORUN-HPLNN-AdaBoost.R2 needs to predict each high-frequency and low-frequency component, summing all prediction results to obtain the final prediction. While decomposing the time series of wind power, photovoltaic power, and electricity load before prediction significantly increases the model's prediction accuracy, it also increases the prediction time cost and complexity, reducing prediction efficiency. Therefore, it is necessary to optimize and reorganize the time series components of wind power, photovoltaic power, and electricity load after RLMD decomposition to maximize the prediction efficiency of the power system source-load dual-side prediction model without reducing the model's prediction accuracy.

[0062] (3) WPE complexity calculation This invention employs WPE to qualitatively analyze the complexity of the time series subsequences of wind power, photovoltaic power, and electricity load after RLMD decomposition, and merges subsequences with similar complexity to improve the prediction efficiency of the MORUN-HPLNN-AdaBoost.R2 source-load two-sided prediction model. The entropy calculation results of the time series components of wind power, photovoltaic power, and electricity load using WPE are shown in Tables 2-3.

[0063] Table 2-3 Statistical Table of Entropy Values ​​for Time Series Components of Wind Power, Photovoltaic Power, and Electricity Load

[0064] As shown in Table 2-3, firstly, RLMD can adaptively decompose the number of time series components based on the time series characteristics of wind power, photovoltaic power, and electricity load. Secondly, the entropy value calculated by WPE represents the complexity of the time series component. A larger entropy value indicates higher complexity and more drastic fluctuations in the time series component. A smaller entropy value indicates lower complexity and smoother fluctuations in the time series component. To reduce the prediction complexity of the MORUN-HPLNN-AdaBoost.R2 source-load prediction model, this invention merges time series components with similar entropy values. The merged division results of wind power, photovoltaic power, and electricity load time series components are shown below. Figure 5 As shown.

[0065] pass Figure 5It can be seen that the entropy values ​​of the time series components of wind power, photovoltaic power, and electricity load after RLMD decomposition are similar. Therefore, this invention merges and divides the time series components with similar entropy values. The time series components TC2, TC3, TC4, and TC5 of wind power are merged; the time series components TC2, TC3, TC4, and TC5 of photovoltaic power are merged; and the time series components TC2, TC3, TC4, TC5, and TC6 of electricity load are merged. After merging, the number of time series components for wind power, photovoltaic power, and electricity load is reduced to three, significantly reducing the prediction complexity of the model.

[0066] The combined wind power, photovoltaic power, and electricity load time series components undergo positive and negative transformations, which are then used as the training sample set inputs for the MORUN-PLNN-AdaBoost.R2 and MORUN-NPLNN-AdaBoost.R2 prediction models, respectively. The mathematical formulas for the positive and negative transformations are as follows: (2-74) In the formula, and These are the positive and negative transition sequences, respectively. These are the time-series components of wind power, photovoltaic power, and electricity load. and These represent the minimum and maximum values ​​of the time series components. The positive and negative transformation results for the time series components of wind power, photovoltaic power, and electricity load are as follows: Figure 6 , Figure 7 and Figure 8 Show.

[0067] 1.1.1 Selection of Objective Function and Compromise Solution for Source Load Prediction (1) Source load prediction objective function This invention utilizes MORUN to optimize the weights of HPLNN-AdaBoost.R2, constructing a MORUN-HPLNN-AdaBoost.R2 source-load multi-objective prediction model with accuracy and stability as optimization objectives. The mathematical formula for its objective function is as follows: (2-75) (2-76) In the formula, The prediction accuracy index reflects the degree of difference between the predicted value and the actual value. The prediction stability index reflects the dispersion of the prediction error; the smaller the value, the smaller the difference in prediction error at different times. , and These represent the predicted values, actual values, and sample sizes for wind power, photovoltaic power, and electricity load, respectively.

[0068] (2) Pareto Front Compromise Solution Selection This invention employs the Morun algorithm to solve the problem of predicting wind power, photovoltaic power, and electricity load. The resulting solution is not optimal, but rather a series of Pareto non-dominated solutions. In Pareto, each solution is non-dominated. To select a "compromise solution" that balances multiple objectives in Pareto, this invention uses a fuzzy decision-making method to select the non-dominated solutions, using satisfaction as the evaluation criterion. The fuzzy membership functions of satisfaction corresponding to each objective value in Pareto are as follows: (2-77) In the formula, . Determine the target quantity. and The first The maximum and minimum values ​​of the objective function. Indicates the first The objective function value is completely unsatisfactory. Indicates the first The objective function values ​​are completely satisfactory.

[0069] Normalize the non-dominated solutions in PF to a multi-objective satisfaction space, in which there exists a virtual ideal solution that optimizes all objectives. Compare each non-dominated solution with the ideal solution. The distance between them, the distance to the ideal solution The closer the solution, the higher its satisfaction level. Therefore, it is necessary to select the solution that is closest to the ideal solution in the entire space. The most recent solution is the compromise solution, and its mathematical formula is as follows: (2-78) In the formula, , and The non-dominated solutions in the satisfaction space are respectively axis, shaft and The coordinates of the axis. The distance between the non-dominated solution and the ideal solution Spatial distance.

[0070] 1.2 Source-load Prediction Evaluation Indicators This invention uses the Stability Index (SDEX), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Index of Agreement (IA), and Median Absolute Percentage Error (MdAPE) as evaluation metrics for the source load prediction model to comprehensively evaluate the prediction performance of the MORUN-HPLNN-AdaBoost.R2 source load prediction model. SDEX reflects the stability of the model's predictions. MAE reflects the overall error level. RMSE reflects the degree of difference between predicted and actual values. IA reflects the sensitivity and proportional variation of the difference between predicted and actual values. MdAPE reflects the model's prediction accuracy. A higher IA value indicates better prediction results, while lower values ​​for MAE, RMSE, SDEX, and MdAPE also indicate better prediction results. The mathematical formulas for the prediction model evaluation metrics are as follows: (2-79) (2-80) (2-81) (2-82) (2-83) 2. Case Analysis This invention conducts a comprehensive comparative experiment on the proposed MORUN algorithm and the MORUN-HPLNN-AdaBoost.R2 source-load two-sided prediction model to verify their performance. The experiments mainly include performance testing of the MORUN algorithm, performance testing of the MORUN-HPLNN-AdaBoost.R2 model, prediction comparison of multi-objective prediction models, prediction comparison of multi-neural network prediction models, and prediction comparison of source-load two-sided 24-hour lead time. The final prediction evaluation index is the average value of 30 experimental results for comparison, and the power factor (PF) is the best value of 30 experimental results for comparison. The parameters of each compared algorithm are taken from the original literature, and the parameter settings of each compared neural network are confirmed using cross-validation.

[0071] 2.1 MORUN Test Analysis To verify the performance of the proposed MORUN algorithm, it was tested on the MOP and ZDT test suites. The test results were compared with advanced multi-objective algorithms such as Non-dominated sorting genetic algorithm III (NSGAIII), Multi-objective sparrow algorithm (MOSSA), and Multi-objective dragonfly algorithm (MODA). All MOP and ZDT test functions had a variable dimension of 10. The population size of all comparison algorithms was set to 100, and the maximum number of function evaluations (FEs) was set to 1E+04. The constants of the MORUN algorithm are also specified. and The values ​​were set to 20 and 12 respectively. The inverted generational distance (IGD) was used to evaluate the convergence and distribution performance of the algorithms. The statistical results comparing the IGD of the four algorithms are shown in Tables 2-4 and 2-5.

[0072] Table 2-4 Statistical table of IGD values ​​obtained by four algorithms on ZDT1-ZDT4 test functions.

[0073] Table 2-5 Statistical table of IGD values ​​obtained by four algorithms on the MOP1-MOP4 test functions.

[0074] Tables 2-4 and 2-5 compare and analyze the experimental results in terms of best value, average value, standard deviation, and worst value. Compared with other multi-objective algorithms, MORUN achieves the best IGD value on all MOP and ZDT test functions. This indicates that the proposed MORUN algorithm has the best convergence and distribution of solutions for solving MOP and ZDT problems. This invention uses the optimal PF comparison results of MOP1-MOP4 as an example to demonstrate the convergence and distribution of solutions on PF for the four algorithms. The optimal PF comparison of the four algorithms is shown below. Figure 9 As shown.

[0075] pass Figure 9It can be seen that the four comparative algorithms exhibit poor convergence of PF solutions on the MOP1 test function, but better convergence and distribution of solutions on the MOP2-MOP4 test functions. On the MOP1 test function, the PF solutions of all four algorithms are concentrated at one end of the actual PF front, but the MORUN algorithm shows better population distribution uniformity than the other comparative algorithms. On the MOP2-MOP4 test functions, although the Pareto solutions obtained by MOSSA and MODA converge to the true PF surface, the number of solutions obtained is small and the distribution is uneven. NSGAIII obtains a better number of Pareto solutions and better distribution uniformity than MOSSA and MODA. Compared with NSGAIII, MOSSA, and MODA, MORUN obtains the best convergence and most uniform distribution of Pareto solutions. Therefore, the MORUN algorithm proposed in this invention outperforms NSGAIII, MOSSA, and MODA, and can better solve multi-objective optimization problems.

[0076] 2.2 Analysis of Source Load Prediction Results To apply source-load forecasting results to power system optimal dispatching, it is necessary to forecast wind power, photovoltaic power, and power load 1 hour to 24 hours in advance to obtain the forecast results for wind power, photovoltaic power, and power load 24 hours before the day-ahead. This invention demonstrates the experimental results of two-sided source-load forecasting of the power system using 1-hour advance source-load forecasting as an example.

[0077] (1) Analysis of source load prediction results of MORUN-HPLNN-AdaBoost.R2 To verify the performance of the proposed MORUN-HPLNN-AdaBoost.R2 source-load two-sided prediction model, this invention designed comparative experiments on the prediction models MORUN-HLNN, MORUN-HPLNN, and MORUN-HPLNN-AdaBoost.R2. Specifically, experiments were conducted comparing MORUN-HLNN and MORUN-HPLNN to examine the prediction performance of the proposed HPLNN. Experiments were also conducted comparing MORUN-HPLNN and MORUN-HPLNN-AdaBoost.R2 to verify the effectiveness of the ensemble learning model AdaBoost.R2 in improving the model's prediction capabilities.

[0078] To ensure fairness in the comparative experiments, firstly, HLNN and HPLNN used the same initial weights, which were obtained by optimization using the MORUN algorithm. The population size of the MORUN algorithm was set to 100, the power factor (PF) was set to 100, and the number of function evaluations (FEs) was set to 1E+4. The number of weak predictors in AdaBoost.R2 was set to 20. Secondly, the MORUN-HLNN, MORUN-HPLNN, and MORUN-HPLNN-AdaBoost.R2 prediction models were used for wind power, photovoltaic power, and electricity load prediction, respectively. The average of 30 prediction results was used as the final evaluation index of the model. The statistical results of the 1-hour lead prediction of the MORUN-HLNN, MORUN-HPLNN, and MORUN-HPLNN-AdaBoost.R2 prediction models for wind power, photovoltaic power, and electricity load are shown in Table 2-6. The comparison of the PF non-dominated solution selection and prediction curves of the 1-hour lead prediction results for wind power, photovoltaic power, and electricity load is shown in Table 2-6. Figure 10 As shown.

[0079] Table 2-6 Statistical analysis of the 1-hour lead-time prediction results of the three prediction models on both the source and load sides.

[0080] Table 2-6 shows the statistical results of the three prediction models for wind power, photovoltaic power, and electricity load with a 1-hour lead time. Compared with the MORUN-HLNN prediction model, in terms of wind power prediction, the MORUN-HLNN prediction model improved the evaluation indicators IA, MAE, RMSE, SDEX, and MdAPE by 0.11%, 29.97%, 20.86%, 10.47%, and 44.81%, respectively. In terms of photovoltaic power prediction, the MORUN-HLNN prediction model improved the evaluation indicators IA, MAE, RMSE, and SDEX by 1.96%, 38.25%, 38.18%, 38.15%, and 58.75%, respectively. In terms of electricity load prediction, the MORUN-HLNN prediction model improved the evaluation indicators IA, MAE, RMSE, SDEX, and MdAPE by 0.06%, 10.75%, 11.48%, 12.69%, and 4.18%, respectively. This indicates that HPLNN can effectively improve the insufficient generalization ability of HLNN neural networks and greatly improve prediction accuracy.

[0081] Compared to the MORUN-HPLNN forecasting model, the MORUN-HPLNN-AdaBoost.R2 model improved performance in wind power forecasting by 0.29%, 35.84%, 23.16%, 5.20%, and 53.15% in terms of evaluation metrics IA, MAE, RMSE, SDEX, and MdAPE, respectively. For photovoltaic power forecasting, the MORUN-HPLNN-AdaBoost.R2 model improved performance in these metrics by 0.98%, 30.18%, 30.02%, 29.90%, and 57.33%, respectively. For load forecasting, the MORUN-HPLNN model improved performance in these metrics by 0.07%, 13.29%, 21.43%, 24.34%, and 2.99%, respectively. This indicates that ensemble learning AdaBoost.R2 can further improve the predictive power of the MORUN-HPLNN model.

[0082] Figure 10 (a), 10(c), and 10(e) represent the power PFs obtained by MORUN-HPLNN-AdaBoost.R2 for wind power, photovoltaic power, and electricity load 1 hour ahead of schedule. The "five stars" in the figures represent the compromise solutions obtained using fuzzy decision theory. The optimal weights corresponding to the compromise solutions are assigned to HPLNN for prediction, so that the prediction results can balance high prediction accuracy and strong prediction stability.

[0083] Figure 10 (b) Figure 10 (d) and Figure 10 (f) Comparison of the prediction curves obtained by MORUN-HPLNN-AdaBoost.R2 for wind power, photovoltaic power, and electricity load. As can be seen from the figures, the MORUN-HPLNN-AdaBoost.R2 prediction curve has the highest degree of fit with the actual curve. Therefore, compared with the MORUN-PLNN and MORUN-HPLNN source-load prediction models, the MORUN-HPLNN-AdaBoost.R2 wind power, photovoltaic power, and electricity load prediction model proposed in this invention has higher prediction accuracy.

[0084] (2) Comparative analysis of prediction results of different multi-objective algorithms To verify whether the proposed MORUN algorithm has advantages over other advanced multi-objective algorithms in wind power, photovoltaic power, and electricity load prediction, four source-load prediction models—NSGAIII-HLNN, MOSSA-HLNN, MODA-HLNN, and MORUN-HLNN—were established. To ensure fairness in the comparative experiments, the population size, power factor (PF), and number of function evaluations (FEs) for each algorithm were set to 1E+4, with other parameters remaining the same as in Section 2.81. The average of 30 prediction results was used as the final evaluation index for the model. The statistical results of the four prediction models in wind power, photovoltaic power, and electricity load prediction are shown in Table 2-7.

[0085] Table 2-7 Statistical analysis of the multi-objective prediction model's 1-hour lead-time prediction results on both the source and load sides.

[0086] Table 2-7 shows the statistical results of the NSGAIII-HPLNN-AdaBoost.R2, MOSSA-HPLNN-AdaBoost.R2, MODA-HPLNN-AdaBoost.R2, and MORUN-HPLNN-AdaBoost.R2 prediction models for wind power, photovoltaic power, and electricity load with a 1-hour lead time. The experimental results show that the MORUN-HPLNN-AdaBoost.R2 prediction model proposed in this invention achieves the optimal solution in the prediction error evaluation index for wind power, photovoltaic power, and electricity load. This indicates that compared to the NSGAIII, MOSSA, and MODA multi-objective algorithms, the MORUN algorithm proposed in this invention has better search capabilities in wind power, photovoltaic power, and electricity load prediction problems, and can assign better weights to the HPLNN. Furthermore, the proposed MORUN-HPLNN-AdaBoost.R2 prediction model has higher prediction accuracy and better prediction stability.

[0087] (3) Comparative analysis of prediction results from different neural networks To further evaluate the predictive performance of the proposed MORUN-HPLNN-AdaBoost.R2 wind power, photovoltaic power, and electricity load prediction model, this invention compares it with current mainstream neural network prediction models (including machine learning and deep learning models). The neural networks used for comparison include BPNN, LSTM, RBF, RELM, and HPLNN. To ensure fairness in the experimental comparison, MORUN was used to optimize the parameters of each neural network, and AdaBoost.R2 was used to construct an ensemble prediction model. The parameter settings for each neural network were determined through cross-validation. The maximum number of function evaluations (FEs) for each prediction model was set to 1E+04. All prediction models were run independently 30 times, and their average value was used as the final experimental statistical result. The prediction statistical results of the five neural network prediction models for wind power, photovoltaic power, and electricity load are shown in Tables 2-8.

[0088] Table 2-8 Statistics of the neural network prediction model's prediction results 1 hour ahead on both the source and load sides.

[0089] Table 2-8 shows the statistical results of five neural network prediction models for wind power, photovoltaic power, and electricity load prediction 1 hour ahead. In wind power prediction, each neural network prediction model achieved different advantages across various evaluation metrics. The MORUN-BPNN-AdaBoost.R2 prediction model achieved optimal values ​​for MAE and MdAPE. The MORUN-LSTM-AdaBoost.R2 model achieved optimal values ​​for IA. Compared to the comparative neural network prediction models, the MORUN-HPLNN-AdaBoost.R2 proposed in this invention achieved optimal values ​​for IA, MAE, RMSE, and SDEX. In photovoltaic power and electricity load prediction, the MORUN-HPLNN-AdaBoost.R2 prediction model proposed in this invention achieved optimal values ​​across all evaluation metrics.

[0090] In summary, compared with the MORUN-BPNN-AdaBoost.R2, MORUN-LSTM-AdaBoost.R2, MORUN-RBF-AdaBoost.R2, and MORUN-RELM-AdaBoost.R2 neural network prediction models, the MORUN-HPLNN-AdaBoost.R2 source-load prediction model proposed in this invention achieves better values ​​on the IA, MAE, RMSE, SDEX, and MdAPE evaluation metrics. This indicates that the proposed model has higher prediction accuracy and stronger prediction stability, and the HPLNN neural network has stronger prediction capabilities for wind power, photovoltaic power, and electricity load.

[0091] (4) Discussion of the results of the two-sided advance prediction of the source load In day-ahead power system dispatch optimization, relying solely on 1-hour lead-time source-load two-sided forecasts is insufficient to provide effective information for future dispatch of wind power, photovoltaic power, and electricity load. To improve the applicability of the proposed MORUN-HPLNN-AdaBoost.R2 model's forecast results in day-ahead power system dispatch optimization, it is necessary to conduct lead-time forecasts of wind power, photovoltaic power, and electricity load from 1 hour to 24 hours ahead. The statistical results of the power system source-load two-sided lead-time forecast evaluation indicators from 1 hour to 24 hours ahead are as follows: Figure 11 As shown in the figure. The comparison results of the selection of the nondominated solution of the power supply (PF) and the prediction curve of the MORUN-HPLNN-AdaBoost.R2 power system source-load two-sided prediction model with a 24-hour lead are as follows. Figure 12 As shown.

[0092] Figure 11 The left side displays the statistical results of the forecast error evaluation indicators for wind power, photovoltaic power, and electricity load from 1 hour to 24 hours in advance. The axis coordinates are MAE, RMSE, SDEX, and MdAPE index values, with the right side... The axes represent the IA index values. As the forecast time increases, the IA values ​​for wind power, photovoltaic power, and electricity load gradually decrease, while the values ​​for MAE, RMSE, SDEX, and MdAPE gradually increase. This indicates that the longer the forecast time, the worse the performance of the MORUN-HPLNN-AdaBoost.R2 source-load forecasting model.

[0093] Figure 12This paper presents a comparison of the power factor (PF) compromise solution selection and prediction curves for 24-hour advance forecasts of wind power, solar power, and electricity load using the MORUN-HPLNN-AdaBoost.R2 model. During the 24-hour advance training of the prediction model, the prediction accuracy and stability indices of the PF compromise solution obtained from wind power prediction were 0.1587 and 0.0873, respectively, representing increases of 21.7% and 28.4% compared to 0.1304 and 0.0680 for the 1-hour advance forecast. The prediction accuracy and stability indices of the PF compromise solution obtained from solar power prediction were 0.1928 and 0.0840, respectively, representing increases of 65.4% and 47.1% compared to 0.1166 and 0.0571 for the 1-hour advance forecast. The prediction accuracy and stability indices of the power load forecasting compromise solution were 0.1613 and 0.0810, respectively, representing increases of 24.3% and 25.2% compared to the 0.1298 and 0.0647 for the 1-hour lead time forecast. In the source-load dual-side forecasting process, the model's prediction performance deteriorates with increasing forecast duration, and the source-load dual-side lead time forecasting results better reflect the actual application of power system optimal dispatching.

[0094] Although the predicted wind power, solar power, and electricity load curves 24 hours in advance fit the actual curves less well than those 1 hour in advance, their predicted trends remain consistent with the actual curves. Furthermore, from... Figure 11 It can be seen that the prediction error evaluation indicators for wind power, photovoltaic power, and power load with a lead time of 1 hour to 24 hours are all within acceptable ranges. Therefore, the lead prediction results of the MORUN-HPLNN-AdaBoost.R2 source-load prediction model proposed in this invention can provide an accurate and stable data foundation for the optimal scheduling of the power system.

[0095] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-objective prediction method for power system source-load based on Laguerre polynomial theory, characterized in that, Includes the following steps: S1: The Spearman Rank Correlation Coefficient (SRCC) was used to conduct correlation analysis on the characteristic influencing factors of wind power, photovoltaic power and power load. Robust Local Mean Decomposition (RLMD) was used to decompose the time series of wind power, photovoltaic power and power load into high-frequency components and low-frequency components to reduce their fluctuation. S2: We use weighted permutation entropy (WPE) to analyze the complexity of the subsequences after RLMD decomposition, merge subsequences with similar complexity, and reduce the model's prediction complexity. S3: A hybrid Laguerre neural network prediction model is constructed using Laguerre polynomials, and pseudo-inverse learning is used to solve the problem of insufficient generalization ability of the hybrid Laguerre neural network prediction model. S4: Use the MORUN algorithm to optimize the weights of the hybrid pseudo-inverse Laguerre neural network, thereby improving the accuracy and stability of the model's prediction results. S5: Introducing the concept of ensemble learning, the source-load two-sided prediction model is optimized using AdaBoost.R2 to achieve self-allocation and reorganization of error weights. The effectiveness of the source-load two-sided prediction model is verified through actual data, providing an accurate and stable data foundation for day-ahead scheduling of power system source-load coordination and reducing uncertainty on both sides of the source and load.

2. The multi-objective prediction method for power system source-load based on Laguerre polynomial theory according to claim 1, characterized in that, The specific steps of S1 are as follows: The mathematical formula for SRCC is as follows: (2-1) In the formula, For SRCC index values, The difference between corresponding sample ranks between variables. For sample size; The RLMD optimizes the boundary conditions, signal envelope estimation, and stopping criteria for local mean decomposition. RLMD can adaptively decompose the number of high-frequency and low-frequency components based on time series characteristics. Let the time series of wind power, photovoltaic power, and electricity load be... The RLMD decomposition process is as follows: (1) Determine the symmetrical points at both ends of the time series signal, and... Signal mirroring expansion ; (2) Searching All local extreme points The corresponding signal value is denoted as ; (3) Calculate the mean of adjacent local extreme points and local envelope estimates : (2-2) (2-3) (4) and Connect the points and process them using a moving average algorithm to generate a local mean function. and envelope estimation function ,according to and Calculate the frequency modulation signal : (2-4) (5) Complete the first round of decomposition, and... The above steps are repeated to calculate the new input signal. Next, the screening stopping criteria are reset, and the objective function for each iteration is set as follows: (2-5) in, (2-6) (2-7) (2-8) In the formula, and These are the root mean square and kurtosis of the envelope signal, respectively. For time series signal sampling points, for The arithmetic mean; (6) After the termination condition is met, extract the frequency modulation signal. and envelope signal : (2-9) (2-10) (7) and Multiplication yields the product function. , and Subtraction yields the residual signal Repeat steps (1) to (6) until the end. Decomposed into One product function and one residual signal: (2-11)。 3. The multi-objective prediction method for power system source-load based on Laguerre polynomial theory according to claim 1, characterized in that, The specific steps of S2 are as follows: The WPE calculation process is as follows: (1) Decomposition of subsequences conduct Phase space reconstruction: (2-12) In the formula, and These represent the embedding bit length and latency, respectively. ; (2) For the first Sort the elements in each component in ascending order: (2-13) In the formula, For element index, when At that time, an index symbol matrix will be generated: (2-14) (3) Calculate the weights of the reconstructed components: (2-15) (2-16) In the formula, For the index symbol sequence, and They are respectively The weights and mean; (4) Using weights and arrangement Characterize the feature information of the reconstructed components and calculate each permutation. Weighted probabilities: (2-17) In the formula, for Arrangement ; (5) Calculate the subsequence WPE value: (2-18)。 4. The multi-objective prediction method for power system source-load based on Laguerre polynomial theory according to claim 1, characterized in that, The specific steps for constructing a hybrid Laguerre neural network prediction model using Laguerre polynomials in S3 are as follows: Based on Laguerre polynomials, Laguerre orthogonal basis functions and new Laguerre orthogonal basis functions are constructed according to polynomial interpolation and approximation theory. These two types of Laguerre orthogonal basis functions are used as activation functions for neural networks to predict source loads. Learning and approximation are performed to establish a basic HLNN prediction model; the detailed construction process of HLNN is as follows: (1) Laguerre orthogonal basis functions Definition: The Laguerre polynomial, proposed by Edmond Laguerre, has its domain in the interval [0, 1]. Above with power The orthogonal polynomials of the Laguerre polynomials are defined as follows: (2-19) The orthogonality of Laguerre polynomials with respect to the weight functions is as follows: (2-20) The recurrence equation for the Laguerre polynomial is as follows: (2-21) (2) New Laguerre orthogonal basis functions Definition: The domain of the new Laguerre polynomial as an orthogonal basis function is... The new Laguerre polynomial is defined as follows: (2-22) The orthogonality of the new Laguerre polynomial with respect to the weight functions is described as follows: (2-23) The differential equation of the new Laguerre polynomial is as follows: (2-24) The new Laguerre polynomial recurrence equation is as follows: (2-25) (3) Hybrid Laguerre Neural Network HLNN is constructed using Laguerre polynomials and new Laguerre polynomials, with independent variables in Laguerre polynomials within a certain range were used to construct a Laguerre neural network (LNN) prediction model to predict positive sequences, with independent variables in... The new Laguerre polynomials within the range are used to build a new Laguerre neural network (NLNN) prediction model to predict negative sequences. Both LNN and NLNN are feedforward neural networks.

5. The multi-objective prediction method for power system source-load based on Laguerre polynomial theory according to claim 4, characterized in that, The specific steps in S3 to address the insufficient generalization ability of the hybrid Laguerre neural network prediction model using pseudo-inverse learning are as follows: When the input matrix of the training set is The output matrix is At that time, pseudo-inverse learning was used to train the optimal weight matrix of the HLNN. The specific process is as follows: (2-50) (2-51) In the formula, For matrix Moore-Penrose pseudo-reverse, For hidden layer output, These are mixed Laguerre orthogonal basis functions.

6. The multi-objective prediction method for power system source-load based on Laguerre polynomial theory according to claim 1, characterized in that, The specific steps of S4 are as follows: Based on the Runge-Kutta method, state transition operator, fast non-dominated sorting, and congestion calculation theory, a MORUN algorithm is proposed, which enables the prediction results of wind power, photovoltaic power, and power load models to have both high prediction accuracy and strong prediction stability. The MORUN algorithm is a multi-objective version of the Runge-Kutta optimizer RUN, and its operation mechanism includes the Runge-Kutta method, solution update mechanism, solution enhancement mechanism, state transition operator, fast non-dominated sorting, and congestion distance.

7. The multi-objective prediction method for power system source-load based on Laguerre polynomial theory according to claim 1, characterized in that, The specific steps for optimizing the source-load two-sided prediction model using AdaBoost.R2 in S5 are as follows: By learning and combining multiple MORUN-HPLNN weak predictors through the AdaBoost.R2 algorithm, the prediction error is corrected, and the error weights are self-assigned and reorganized. The resulting MORUN-HPLNN strong predictor can further improve the prediction accuracy of the model. Assuming the training sample set , For the input vector, As the output vector, the process of training the MORUN-HPLNN prediction model with AdaBoost.R2 is as follows: (1) Set initial weights and calculate the relative prediction error of the weak predictor: (2-67) (2-68) (2-69) In the formula, The initial weights of the samples, , and These are the weak predictor, maximum prediction error, and relative error, respectively. (2) Adjustment Error and update weights: (2-70) (2-71) (2-72) In the formula, This is the normalization constant; (3) Construct the final strong predictor: (2-73) In the formula, yes The weighted median, using As The weight.

8. The multi-objective prediction method for power system source-load based on Laguerre polynomial theory according to claim 7, characterized in that, The source-load two-sided prediction process in S5 is as follows: (1) SRCC, RLMD and WPE are used to analyze and process the source and load data of the power system to reduce the fluctuation of wind power, photovoltaic power and power load time series and the computational complexity of the prediction model. (2) The time series of wind power, photovoltaic power and power load are positively and negatively transformed and used as inputs to PLNN and NPLNN respectively; (3) Use MORUN to optimize PLNN weights and construct MORUN-PLNN source-load prediction model. Then use MORUN to optimize NPLNN weights and construct MORUN-NPLNN source-load prediction model. (4) Train MORUN-PLNN with AdaBoost.R2 and construct the MORUN-PLNN-AdaBoost.R2 source-load prediction model to predict the positive sequences of wind power, photovoltaic power and power load. (5) Train MORUN-NPLNN with AdaBoost.R2 and construct the MORUN-NPLNN-AdaBoost.R2 source-load prediction model to predict wind power, photovoltaic power and negative power load sequences; (6) Obtain the results of the MORUN-PLNN-AdaBoost.R2 source load prediction model and the MORUN-NPLNN-AdaBoost.R2 source load prediction model by inverse transformation; (7) Add the source load prediction results of MORUN-PLNN-AdaBoost.R2 and MORUN-NPLNN-AdaBoost.R2 and calculate the average value to obtain the final prediction result of MORUN-HPLNN-AdaBoost.R2.

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