Power load multi-step interval prediction method based on prediction interval neural network

Abstract

The application provides a power load multi-step interval prediction method based on a prediction interval neural network, and relates to the technical field of power load prediction. The method adopts an improved LUBE method to construct an iterative BP neural network model with interval data input; then takes the coverage rate PICP of PIs and the average width PIAW of PIs as two indexes for evaluating the quality of prediction intervals PI, adopts a coverage width-based criterion CWC to construct an optimization objective function of power load prediction; finally, a particle swarm algorithm is adopted to update the parameters of the iterative neural network model, so that an optimal particle is found, and the objective function has a minimum CWC value. The method constructs an interval iterative neural network model, can overcome the defects of complex interference factors and single information of power load prediction, can better realize multi-step prediction of power load, and has good generalization ability and training effect.

Description

Technical Field

[0001] This invention relates to the field of power load forecasting technology, and in particular to a multi-step interval forecasting method for power load based on a forecast interval neural network. Background Technology

[0002] Electricity load forecasting is a crucial component of power system planning and a foundation for the economical operation of the power system, playing a vital role in both planning and operation. However, the inherent randomness and volatility of electricity load forecasting pose significant challenges to grid dispatching. Therefore, from the perspective of grid operation security and economic efficiency, electricity load forecasting is essential. Currently, however, the main method of electricity load forecasting is point-based forecasting. Interval-based electricity load forecasting, on the other hand, can describe the uncertainty of electricity load to a certain extent, providing a basis for grid decision-making and thus having greater practical significance.

[0003] Due to the volatility and uncertainty of power load, it is necessary to prevent it from posing a significant safety threat to the operation of the power supply park system and to achieve an overall balance between power supply and demand in the power grid operating area.

[0004] Traditional point-value load forecasting methods cannot properly handle the uncertainties in the operation of power load systems. Therefore, it is necessary to construct a neural network with an output range value to predict power load. This can not only reduce the computational burden of the prediction model, but also better contain uncertainties, achieve better prediction results, provide better decision-making basis for power supply parks, and have greater practical application significance. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a multi-step interval prediction method for power load based on a forecast interval neural network, which is in response to the shortcomings of the prior art, and to predict the interval of power load.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by this invention is: a multi-step interval prediction method for power load based on a prediction interval neural network, which uses an improved LUBE (Lower Upper Bound Estimation) method to construct an iterative neural network model (NN: Neural Network) with interval data input, and then predicts the power load value of the interval (PI: Prediction Interval), specifically including the following steps:

[0007] Step 1: Construct an iterative BP neural network model with interval data input using the improved LUBE (Lower Upper Bound Estimation) method;

[0008] An improvement is made to the BP neural network constructed by the existing LUBE method. Each input point value of the BP neural network is decomposed into two input points with equal lower and upper bounds, that is, one input node is transformed into two input nodes, forming a network model of interval input / interval output. The two output nodes of the BP neural network, which represent the lower and upper bounds of the prediction interval PI, are fed back to the two input nodes to form an interval iterative network structure.

[0009] Step 2: Construct the objective function for power load forecasting, transforming the multi-step interval forecasting problem of power load into an objective function optimization problem;

[0010] Using the coverage probability (PICP) and average width (PIAW) of PIs (Prediction Intervals) as two indicators to evaluate the quality of PIs in the prediction interval, the optimization objective function for power load forecasting is constructed using the coverage width-based criterion CWC.

[0011] (1) Determine the coverage of PIs (PICPs);

[0012] PICP (Portable Indexes Coverage Probability) is measured by calculating the number of target values ​​covered by the constructed PIs. It represents the probability that a target value will be covered by the upper and lower bounds of the predicted results. PICP is defined as follows:

[0013]

[0014] Where n is the total number of training samples, H is the number of prediction steps, and c h It is a Boolean variable that represents the coverage behavior of PIs; if the actual target value y h The lower bound of the predicted output covered by the BP neural network and the Upper Realm Between, then c h =1; otherwise c h =0;

[0015] (2) Determine the average width of PIs, PIAW;

[0016] The average width of PIs, PIAW, is defined as follows:

[0017]

[0018] in, and This represents the lower and upper bounds of PIs corresponding to the h-th training sample; if the width of the target value is known, then PIAW can be normalized, and the normalized PIAW is defined as follows:

[0019]

[0020] Where R is the range of the actual target value, y max and y min These represent the maximum and minimum values ​​in the actual target values, respectively.

[0021] (3) The coverage width-based criterion CWC is adopted as the optimization objective function for power load forecasting;

[0022] The Coverage Width Criterion (CWC) is used to evaluate PIs from both coverage rate and coverage width perspectives. Its expression is:

[0023] CWC=PINAW(1+γ(PICP)e -η(PICP-μ) )

[0024] Wherein, γ(PICP) is the step function, and its value is determined based on the PICP value:

[0025]

[0026] Here, constants η and μ are two hyperparameters used to determine the degree of penalty assigned to PIs with low coverage probabilities; constant μ corresponds to the nominal confidence level associated with PIs and is set to [(1-α)%], where α is the significance level;

[0027] Step 3: Use the particle swarm optimization algorithm to update the parameters of the iterative neural network model, and finally find an optimal particle that minimizes the CWC value of the objective function.

[0028] 1) Data segmentation: The entire power load sample dataset is divided into a training set and a test set, and the data in the training set and the test set are normalized.

[0029] 2) Determining the optimal neural network structure: For each candidate neural network structure, train and validate multiple times using the training set; use indicators with satisfactory coverage probability and prediction interval width to determine the optimal structure of the neural network;

[0030] 3) Initialization: Initialization of neural network weights and PSO parameters; PSO parameter initialization consists of particle position and velocity initialization; since the neural network connection weights represent the particle positions, position initialization is completed in the neural network connection weight initialization; particle velocities are randomly initialized using zero symmetric numbers;

[0031] 4) Update particle velocity and position;

[0032] 5) Construct a new PI and evaluate it using a training dataset: Use the training set as input to train the neural network parameters; after updating the neural network connection weights, apply the improved LUBE method to construct a new PI; and calculate the objective function value CWC of the PI.

[0033] 6) Update the optimal position p of the individual particles. best and the global optimal position g best :p best It is the individual optimal value for each particle, g best It is the optimal value for the entire group;

[0034] 7) Training Termination: The training termination criterion is set as follows: when the change value of the PI evaluation index CWC reaches a certain threshold within a certain number of iterations, the training is terminated; otherwise, the training process will continue and return to step 5).

[0035] 8) Testing and Evaluation: Selecting the globally optimal position g best The value is used to generate PI for the test set; the trained neural network is then applied to the test dataset for testing and evaluation.

[0036] The beneficial effects of adopting the above technical solution are as follows: The multi-step interval prediction method for power load based on a forecast interval neural network provided by this invention improves the BP neural network of the conventional LUBE method by decomposing each input point value into two input point values ​​with equal lower and upper bounds, that is, turning one input node into two input nodes, forming an interval input / interval input network model; the two nodes output by the BP neural network, representing the lower and upper bounds of the prediction interval, are fed back to the two input nodes, forming an interval iterative network structure; and multi-step interval prediction of power load is performed on this basis. In the neural network model, the number of each layer and neuron can be arbitrary. This model can overcome the shortcomings of complex interference factors and relatively simple information in power load prediction, and can better realize multi-step prediction of power load, with good generalization ability and training effect.

[0037] The PIs Coverage Probability (PICP) and PIs Average Width (PIAW) are used as two indicators to evaluate the quality of the forecast interval. A comprehensive evaluation of both indicators is provided based on the Combined Coverage Width Criterion (CWC), aiming to minimize the PIs Average Width while satisfying the PIs Coverage Probability requirement. The multi-step interval forecasting problem of power load is transformed into a single-objective optimization problem. Attached Figure Description

[0038] Figure 1 The LUBE neural network structure provided in this embodiment of the invention;

[0039] Figure 2 The correspondence between the η parameter values ​​and CWC provided in the embodiments of the present invention;

[0040] Figure 3 A flowchart of the LUBE method based on particle swarm optimization algorithm provided in an embodiment of the present invention;

[0041] Figure 4 A flowchart of the particle swarm optimization algorithm provided in an embodiment of the present invention;

[0042] Figure 5 This invention provides an embodiment of a non-disruptive multi-step load forecasting method based on the LUBE method.

[0043] Figure 6 This invention provides a perturbation-based multi-step load prediction method based on the LUBE method. Detailed Implementation

[0044] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0045] This embodiment takes the power load data of a city over 60 days as an example and uses the multi-step power load prediction method based on the forecast interval neural network of the present invention to predict the power load.

[0046] In this embodiment, the multi-step interval prediction method for power load based on the prediction interval neural network employs an improved LUBE (Lower Upper Bound Estimation) method to construct an iterative neural network model (NN) with interval data input, and then predicts the power load value of the interval (PI). Specifically, it includes the following steps:

[0047] Step 1: Construct an iterative BP neural network model with interval data input using the improved LUBE (Lower Upper Bound Estimation) method;

[0048] An improvement is made to the BP neural network constructed by the existing LUBE method. Each input point value of the BP neural network is decomposed into two input points with equal lower and upper bounds, that is, one input node is transformed into two input nodes, forming a network model of interval input / interval output. The two output nodes of the BP neural network, which represent the lower and upper bounds of the prediction interval PI, are fed back to the two input nodes to form an interval iterative network structure.

[0049] The LUBE method employs a neural network with two outputs to directly construct the PI in one step without making any assumptions about the data distribution, making it simpler and faster to implement. The two outputs of the neural network correspond to the lower and upper bounds of the PI, respectively. This design is similar to point prediction, but the PI construction process is simpler and more direct. This invention uses an improved LUBE method to construct a neural network-based PI. The improved LUBE method also uses point-value operations, but the input is constructed by using two point-value inputs to represent an interval input. Furthermore, the two outputs of the improved LUBE method (the lower and upper bounds of the PI) are iteratively substituted with the input values ​​of the next time interval as an interval input. In a real neural network model, the number of layers and neurons can be arbitrary. In this embodiment, the specific neural network structure of the improved LUBE method is as follows: Figure 1 As shown.

[0050] Assume the input x is a real vector, x∈R l x = (x1, x2, ..., x l ) T In this invention, l = 20, and x2= x t-1 , x4 = x t-2 ,..., x l = x t-n The output y is a real vector, y∈R n y = (y1, y2, ..., y n ) T Where n = 2, and y2= y t The hidden layer has m nodes, and its output u is a real vector, u∈R. m u = (u1, u2, ..., u m ) T The weights from the input layer to the hidden layer are Threshold is The weights from the hidden layer to the output layer are Threshold is Where i = 20, j = m, k = 2, and all are real numbers.

[0051] Then the hidden layer neurons output u j The output of the output layer neuron is y k They are respectively:

[0052]

[0053]

[0054] Its activation function f(·) can be selected according to different functions depending on the actual situation.

[0055] Iterative Strategy: In the recursive strategy for predicting load demand 1, 2, ..., K hours in advance (K is generally less than 10), only one model, M, is needed. In this strategy, the prediction interval for the load 1 hour in advance is used as an input variable to predict the load interval for 2, 3, ..., K hours in advance, as shown in the following formula. For example, to use the recursive strategy to predict the load K hours in advance, first find the load for the prediction interval of 1, 2, 3, ..., (K-1) hours, i.e. y (t+1) , y (t+2) ,..., y (t+k-1) These predicted loads are then used as input variables in the same input model M to predict load demand K hours in advance. In this strategy, the number of input variables is the same in each model.

[0056]

[0057]

[0058] in, y (t+1) , y (t+2) ,..., y (t+k) These are the interval values ​​for load forecasting in hours 1, 2, 3, ..., k, respectively. x (t) , x (t-1) ,..., x (t-9) Let be the interval values ​​of the actual load at times t, t-1, ..., t-9, and M be the prediction models for hours 1, 2, 3, ..., k, respectively. There is only one prediction model.

[0059] This model can overcome the shortcomings of complex causes and limited information in power load forecasting, and can better predict the nonlinear performance of power load. It has good generalization ability and training effect.

[0060] Step 2: Construct the objective function for power load forecasting, transforming the multi-step interval forecasting problem of power load into an objective function optimization problem;

[0061] PI is a statistical estimator consisting of an upper and lower bound. To evaluate the quality of PI, this invention uses the coverage probability (PICP) and average width (PIAW) of Prediction Intervals as two indicators to assess the quality of the PI. The latter measures the width of the interval as the difference (minimization) between the estimated upper and lower bounds. The optimization objective function for power load forecasting is constructed using the Coverage Width Criterion (CWC). Generally, these two indicators are conflicting; for example, achieving a higher coverage probability may also result in a wider forecast width. If the forecast width is made infinitely large simply to achieve a better coverage probability, the resulting forecast is meaningless. Therefore, in practice, both high coverage probability and narrow width are equally important in the forecasting process.

[0062] (1) Determine the coverage of PIs (PICPs);

[0063] Typically, coverage is considered a key characteristic of Power Attached Storage (PIs). PI Coverage Probability (PICP) is measured by calculating the number of target values ​​(electricity load data) covered by the constructed PIs. It represents the probability that a target value will be covered by the upper and lower bounds of the predicted results; a larger PICP means more targets are located in the constructed PIs, and vice versa. PICP is defined as follows:

[0064]

[0065] Where n is the total number of training samples, H is the number of prediction steps, and c h It is a Boolean variable that represents the coverage behavior of PIs; if the actual target value y h The lower bound of the predicted output covered by the BP neural network and the Upper Realm Between, then c h =1; otherwise c h =0; c h The definition is as follows:

[0066]

[0067] The prediction interval coverage probability (PICP) is a spontaneously generated performance metric closely related to the quality of the constructed interval. It represents the predicted estimated points that will contain the true output value y(x) (maximizing). Prediction quality is measured by the number of actual target values ​​included; a higher coverage probability indicates higher prediction accuracy, and vice versa. Ideally, PICP = 100%, meaning that PIs cover all targets.

[0068] (2) Determine the average width of PIs, PIAW;

[0069] If we take the extreme values ​​of the target as the upper and lower bounds of the entire prediction interval, then the resulting PICP will achieve 100% coverage. In reality, such a wide prediction interval is worthless because it doesn't convey any information about changes in the target. According to c... h As can be seen from the definition formula, the PICP value directly depends on the width of the PIs, and the width of the PIs determines their informativeness. Expanding the PIs from either side will yield a 100% PICP value. However, in practical engineering, PIs that are too wide are worthless because the prediction interval does not convey information about the target variable. Therefore, another measure is needed to quantify the width of the prediction interval, namely the average width of the PIs. The average width of PIs, PIAW (PIs Average Width), is defined as follows:

[0070]

[0071] in, and This represents the lower and upper bounds of PIs corresponding to the h-th training sample. If the width of the target value is known, PIAW can be normalized to allow for an objective comparison of the prediction intervals developed by different methods, and to improve computational speed and prediction accuracy. The normalized PIAW (PINAW, PIs Normalized Average Width) is defined as follows:

[0072]

[0073] Where R is the range of actual target values ​​(maximum minus minimum), normalizing PIAW using the target range allows for an objective comparison of PIs without considering the size of the technology or actual target used for estimation. max and y min These represent the maximum and minimum values ​​in the actual target value, respectively, i.e., y. max=max(y1,y2,…,y n ), y min =min(y1,y2,…,y n ).

[0074] PINAW is a standardized PIAW, a dimensionless measurement that uses the average width of the prediction interval as a percentage of the base target range, regardless of the actual estimation technique and the size of the target value.

[0075] (3) The coverage width-based criterion CWC is adopted as the optimization objective function for power load forecasting;

[0076] From a practical engineering perspective, high coverage and narrow width PIs are needed to meet engineering requirements, i.e., a large PICP value and a small PINAW value. Theoretically, these two goals are conflicting; reducing the width of PIs usually leads to a reduction in PICP.

[0077] Both PICP and PINAW evaluate the quality of PIs from one aspect, so a comprehensive index is needed to comprehensively evaluate performance indicators from both coverage and breadth perspectives; the new metric should give PICP higher priority because it is a key feature that determines whether the constructed PIs are theoretically correct.

[0078] The Combined Coverage Width (CWC) standard provides a comprehensive evaluation of both metrics. It attempts to find a trade-off between the informativeness (PINAW) and validity (PICP) of the prediction interval. CWC effectively addresses these issues in evaluating prediction intervals.

[0079] The Coverage Width-Based Criterion (CWC) is used to evaluate PIs from both coverage rate and coverage width perspectives. Its expression is:

[0080] CWC=PINAW(1+γ(PICP)e -η(PICP-μ) )

[0081] Training is performed using γ(PICP) = 1. μ and η are two control parameters. When selecting parameter μ, the nominal confidence level [(1-α)%] can be used as a reference. It represents the pre-assigned value that PICP must satisfy. η is a hyperparameter that amplifies the difference between PICP and μ, and should generally be chosen as a large value. The specific correspondence between η parameter values ​​and CWC is as follows: Figure 2As shown. If the pre-allocated PICP is not satisfied, CWC will apply an exponential penalty to that term. When PICP reaches around μ, there is a balance between PINAW and PICP. As the gap between PICP and μ increases, the exponential term gradually flattens out, causing the PINAW factor to become increasingly dominant in CWC. Therefore, the algorithm will eventually stop at a PICP slightly above μ. For example, suppose μ is 90%. If the PICP of the training set is exactly equal to 90% during the training process of this invention, then the PICP of the test set is likely to be below 90%, thus violating the constraint. Violating the PI constraint (PICP should be greater than 90%) may produce results with large biases, while a PICP slightly above 90% means that this invention is only somewhat conservative.

[0082] If the pre-assigned PICP is satisfied, then the comparison between the two CWC metrics will more reasonably focus on the narrower PICP. Therefore, for the test sample, γ(PICP) is a step function whose value is determined by the satisfaction of PICP, as shown in the following formula:

[0083]

[0084] When evaluating the test PI, if PICP is not less than the specified μ, and γ(PICP) = 0, only one metric needs to be considered, namely PINAW. Otherwise, if γ(PICP) = 1, it needs to be calculated according to the corresponding CWC formula.

[0085] Generally, a smaller CWC value indicates better PI quality. However, when PIs have low coverage, they will always have a large CWC value regardless of their width. As shown in the CWC expression, when PICP is greater than or equal to the nominal confidence level [(1-α)%], γ(PICP) = 0, meaning that the exponential term will be eliminated. Therefore, CWC = PINAW. In this case, the optimization algorithm only needs to process PINAW to reduce the width of PIs to obtain higher quality PIs. When PICP is less than its corresponding confidence level, the CWC value will become very large due to its exponential increase, regardless of the width of the PIs.

[0086] In traditional algorithms, neural networks are trained by minimizing error-based cost functions, such as the sum of squared errors, weight decay cost functions, Akaike information criterion, and Bayesian information criterion. This approach is theoretically and practically acceptable if the goal of modeling and analysis is point prediction. However, if the neural network is to be used for PI (Pi) construction, it is more reasonable to train it by minimizing PI-based cost functions. This allows the neural network to construct a set of optimal PIs with better quality in terms of width and coverage probability. To achieve this, the neural network training process can be based on minimizing a newly proposed cost function, namely the CWC (Concentrated Wage Conversion) function.

[0087] The objective function described above guarantees the reliability of the established LUBE model. However, since the validation process mainly involves comparing the test dataset and the network output prediction dataset, and to provide a more intuitive comparison with point value prediction output methods, this invention uses error-based evaluation metrics to assess the model's prediction accuracy. The following Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) metrics are used to express the prediction accuracy, and their expressions are as follows:

[0088]

[0089]

[0090]

[0091] Where K is the number of samples in the test set, e t a t and Let a represent the t-th error, the actual load value, and the predicted load value, respectively. Since the network forecast output is an interval value with upper and lower bounds, while the actual data is a point value... t If this happens, data inconsistency issues will arise when applying the formula. Here, we take the mean of the prediction interval, i.e. midpoint value Therefore, the above formula can be modified as follows:

[0092]

[0093]

[0094]

[0095] Step 3: Update the parameters of the iterative neural network model using the particle swarm optimization algorithm, such as... Figure 3 As shown, an optimal particle is eventually found that minimizes the CWC value of the objective function;

[0096] In Particle Swarm Optimization (PSO), each individual (a named particle) possesses its own position, velocity, and memory, and acts as a point in the search space. After initializing the particle population, the fitness value of each particle is calculated. In each iteration, particles update their own historical best positions and the information about the best positions found in the entire population. Each particle's goal is to search the space of feasible solutions to find the optimal solution. Initially, the initial particles may be far from the optimal solution and scattered throughout the search space. Then, by communicating with each other, particles can track the population's optimal position and their own historical best positions, thereby continuously changing their velocity and position, gradually moving towards the optimal solution. Finally, with continuous iterations, the scattered particles will converge around the optimal solution.

[0097] The key to the point-value PSO algorithm lies in the update formulas for individual velocity and position, which use real numbers for calculation. During the algorithm's iteration process, the particles in the population continuously adjust their velocity and position based on their historical best position and the global best position of the population, thereby enabling the particles to continuously move towards the optimal solution.

[0098] The flowchart of the particle swarm optimization algorithm is as follows: Figure 4 As shown. The main steps of the particle swarm optimization algorithm are as follows:

[0099] Step 1: Initialize the population

[0100] Set the relevant parameters of the algorithm: maximum number of iterations K, learning factors c1 and c2, inertia weight ω, population size m, and the initial position and velocity of each particle randomly generated, where the initial individual best position of a particle is itself.

[0101] Step 2: Calculate the fitness value for each particle.

[0102] Calculate the fitness value for each particle based on the fitness function. For each particle, compare its current fitness value with its historical best position. and the global optimal position The corresponding fitness values ​​are compared respectively. If the current position is better than the previous one, then the fitness value is determined by the previous one. If the current position is closer to the optimal solution, then assign the current value to... Similarly, if the current position is better Then assign the current position to

[0103] Step 3: Update particle velocity and position

[0104] The velocity and position of each particle are updated according to the formula.

[0105] Step 4: Determine if the algorithm has ended

[0106] The algorithm checks whether the current iteration count has reached the maximum iteration count or whether the optimization result has reached the preset optimal accuracy. If either condition is met, the algorithm stops and outputs the optimal solution, i.e., the global optimal position; otherwise, it proceeds to Step 2 to continue iterating.

[0107] 1) Data Partitioning: The entire power load sample dataset is divided into a training set and a test set, and the data in both sets are normalized. The training set is used to adjust the connection weights of the BP neural network, while the test set will evaluate the final performance of the algorithm. After the dataset is partitioned, the training set data is normalized to [-1, 1], which improves both the speed and accuracy of computation. The same settings are then applied to the test set for data normalization.

[0108] 2) Determining the optimal neural network structure: For each candidate neural network structure, train and validate multiple times using the training set; use indicators with satisfactory coverage probability and prediction interval width to determine the optimal structure of the neural network; that is, determine the number of hidden layers and the number of hidden layers in the neural network.

[0109] 3) Initialization: Initialization of neural network weights and PSO parameters; the initialization process directly affects the quality of PI and the repeatability of the algorithm. PSO parameter initialization consists of particle position and velocity initialization; since the neural network connection weights represent the particle positions, position initialization is completed in the neural network connection weight initialization; particle velocities are randomly initialized using zero symmetric numbers, which means that the input dataset is normalized to [-1, 1] here;

[0110] 4) Updating Particle Velocity and Position: Velocity and position updates are the core of the PSO algorithm. During the update process, these particles exchange information they discover. This allows for efficient information exchange throughout the particle swarm. The formulas for updating velocity and position are shown below:

[0111]

[0112]

[0113] Where ξ and η are random numbers in the range [0,1]. and These are the velocity and position of the i-th particle in the k-th iteration, respectively. and c1 and c2 are the historical optimal position and the global optimal position of the i-th particle in the k-th iteration, respectively. c1 and c2 are learning factors, non-negative real numbers. When c1 is large, most particles in the population will oscillate in the local space; when c2 is large, it will cause premature convergence. Generally, c1 = c2 and its range is [0, 4]. ω is the inertia weight, which represents the influence of the particle's previous velocity on its current velocity. If ω is large, the global optimization performance of the particle is enhanced, reducing the risk of the algorithm getting trapped in local optima; if ω is small, the local optimization performance of the particle is enhanced, and accurate optimization can be achieved. Generally, ω = 0.8 is more appropriate.

[0114] In the speed update formula, the first term This reflects the tendency of particles to fly in their original direction, playing a role in balancing global and local optimization. (Second term) This describes the particle moving towards its previously best possible position, thus giving it global optimization capabilities. (The third term...) This reflects the impact of information exchange within the population, the movement of particles towards the optimal position in the search space, and demonstrates the cooperative ability among particles in the population. The position update formula expresses the information about particles moving towards the optimal position.

[0115] In the particle swarm optimization algorithm, each individual particle, through continuous iterative search and information exchange within the swarm, eventually leads all particles to reach the optimal value in the search space.

[0116] 5) Construct a new PI and evaluate it using a training dataset: Use the training set as input to train the neural network parameters; after updating the neural network connection weights, apply the improved LUBE method to construct a new PI; and calculate the objective function value CWC of the PI.

[0117] 6) Update the optimal position p of the individual particles. best and the global optimal position g best :p best It is the individual optimal value for each particle, g best It is the optimal value for the entire group;

[0118] 7) Training Termination: The training termination criterion is set as follows: when the change value of the PI evaluation index CWC reaches a certain threshold (small change) within a certain number of iterations, the training is terminated; otherwise, the training process will continue and return to step 5).

[0119] 8) Testing and Evaluation: Once the training process is complete, the globally optimal position g will be selected. best The value is used to generate PI for the test set; the trained neural network is then applied to the test dataset for testing and evaluation.

[0120] This embodiment uses 60 days of load data from a city as a sample. Data is collected every hour each day, resulting in 24 data points per day and a total of 1440 historical load data points over 60 days for analysis. This embodiment tests these 1440 power load data points, evaluating both disturbed and undisturbed data using the LUBE method. The results are compared with simulation results from a point-value iterative BP neural network to demonstrate the advantages of the network proposed in this invention.

[0121] During the training of a neural network model, different parameters will have different effects on the training results, as will the training speed, and consequently, the results of power load prediction will also vary.

[0122] The neural network structure used in this embodiment is a single-hidden-layer neural network, specifically a three-layer neural network with a structure of 20-m-2, where m is 10, 11, 12, ..., 20. Based on experimental results, the number of hidden layers is determined to be 16. Since the original power load data consists of point values ​​without upper and lower bounds for the prediction interval, the point values ​​of the initial input data are treated as intervals with equal upper and lower bounds. In the process of parameter optimization using the particle swarm optimization algorithm, this invention selects CWC as the optimization index. The selection of parameters in the PSO algorithm is shown in Table 1 below.

[0123] Table 1. Parameter values ​​in the PSO algorithm

[0124]

[0125]

[0126] The LUBE neural network proposed in this invention was fully trained on the selected dataset, with H=8 steps for multi-step prediction. The simulation results are as follows. Figure 5 and Figure 6 As shown, where, Figure 5 This indicates the fitting effect of the undisturbed power load forecast. Figure 6 The figure shows the fitting effect of the power load forecast with disturbances; in the figure, the solid line represents the target output range, and the dashed line represents the actual output of the load data.

[0127] Table 2 shows the experimental results. According to the evaluation indicators proposed above, it can be found that the improved LUBE method proposed in this invention can achieve the following: when predicting data without disturbance, PI can fit the data well; when predicting data with large disturbance, the network can still obtain good simulation results, the predicted values ​​can completely contain the actual output values, and the prediction width can meet the accuracy requirements, thus obtaining a good fitting effect.

[0128] Table 2 Experimental Results

[0129] objective function Undisturbed Disturbance PICP 1 0.9792 PINAW 0.2135 0.4787 CWC 0.2135 1.4501

[0130] To better evaluate the superiority of the proposed iterative LUBE method over the point-value method, this embodiment uses performance indicators such as MAE and RMSE to demonstrate the predictive performance of the proposed network from different perspectives. Table 3 compares the mean absolute error and root mean square error of the point-value neural network and the LUBE neural network for undisturbed data. Table 4 compares the mean absolute error and root mean square error of the point-value neural network and the LUBE neural network for perturbed data. Comprehensive analysis of the above parameters shows that, regardless of the degree of data perturbation, the PIs constructed in this invention have a smaller error than the point-value neural network, and the predicted output load value can include more uncertainty. It also possesses the advantages of the simple structure and small error of the direct multi-step prediction of the point-value iterative neural network, exhibiting better convergence performance and accuracy.

[0131] Table 3. Experimental Results with Unperturbed Data

[0132] MAE RMSE Point value iterative multi-step prediction 103.0833 152.9251 LUBE Iterative Multistep Prediction 49.1979 61.0636

[0133] Table 4 shows the experimental results with perturbation data.

[0134]

[0135]

[0136] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A multi-step interval forecasting method for power load based on a forecast interval neural network, characterized in that: An improved LUBE method is used to construct an iterative neural network model NN with interval data input, which is then used to predict the power load value of multi-step intervals. The method specifically includes the following steps: Step 1: Construct an iterative BP neural network model with interval data input using the improved LUBE method; An improvement is made to the BP neural network constructed by the existing LUBE method. Each input point value of the BP neural network is decomposed into two input points with equal lower and upper bounds, that is, one input node is transformed into two input nodes, forming a network model of interval input / interval output. The two output nodes of the BP neural network, which represent the lower and upper bounds of the prediction interval PI, are fed back to the two input nodes to form an interval iterative network structure. Step 2: Construct the objective function for power load forecasting, transforming the multi-step interval forecasting problem of power load into an objective function optimization problem; The multi-step coverage ratio (PICP) and the multi-step average width (PIAW) of PIs are used as two indicators to evaluate the quality of PIs in the forecast interval. The optimization objective function for power load forecasting is constructed using the multi-step coverage width criterion (CWC). The multi-step coverage ratio (PICP) of the PIs is measured by calculating the number of target values ​​covered by the constructed PIs. It represents the probability that the target value will be covered by the upper and lower bounds of the predicted results. PICP is defined as follows: ； in, H represents the total number of training samples, and H represents the number of prediction steps. It is a Boolean variable that represents the coverage behavior of PIs; if the actual target value The lower bound of the predicted output covered by the BP neural network and the Upper Realm Between, ;otherwise ; The multi-step average width PIAW of PIs is defined as follows: ； in, and This represents the lower and upper bounds of PIs corresponding to the h-th training sample; if the width of the target value is known, then PIAW can be normalized, and the normalized PIAW is defined as follows: ； Where R is the range of the actual target value, and These represent the maximum and minimum values ​​in the actual target values, respectively. Step 3: Use the particle swarm optimization algorithm to update the parameters of the iterative neural network model, and finally find an optimal particle that minimizes the CWC value of the objective function.

2. The method for multi-step interval prediction of power load based on a forecast interval neural network according to claim 1, characterized in that: Step 2 uses the CWC (Criterion for Multi-Step Coverage) criterion to evaluate PIs from two perspectives: multi-step coverage rate and multi-step coverage width. Its expression is: ； in, It is a step function, and its value is determined based on the PICP value: ； Among them, constants and These are two hyperparameters used to determine the degree of penalty assigned to PIs with low coverage probabilities; constants. Corresponding to the nominal confidence level associated with PIs, and set to [(1- )%], It is the significance level.

3. The method for multi-step interval prediction of power load based on a forecast interval neural network according to claim 1, characterized in that: The specific method for step 3 is as follows: 1) Data segmentation: The entire power load sample dataset is divided into a training set and a test set, and the data in the training set and the test set are normalized. 2) Determining the optimal neural network structure: For each candidate neural network structure, train and validate multiple times using the training set; use indicators with satisfactory coverage probability and prediction interval width to determine the optimal structure of the neural network; 3) Initialization: Initialization of neural network weights and PSO parameters; PSO parameter initialization consists of particle position and velocity initialization; since the neural network connection weights represent the particle positions, position initialization is completed in the neural network connection weight initialization; particle velocities are randomly initialized using zero symmetric numbers; 4) Update particle velocity and position; 5) Construct a new PI and evaluate it using a training dataset: Use the training set as input to train the neural network parameters; after updating the neural network connection weights, apply the improved LUBE method to construct a new PI; and calculate the objective function value CWC of the PI. 6) Update the optimal position of individual particles and the global optimal position : It is the individual optimal value for each particle. It is the optimal value for the entire group; 7) Training Termination: The training termination criterion is set as follows: training terminates when the change value of the PI evaluation index CWC reaches a certain threshold within a certain number of iterations. Otherwise, the training process will continue and return to step 5). 8) Testing and Evaluation: Selecting the Globally Optimal Position The value is used to generate PI for the test set; the trained neural network is then applied to the test dataset for testing and evaluation.

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