Improved Whale Algorithm for Short-Term Load Forecasting of Deep Extreme Learning Machines

Abstract

An improved method for short-term load forecasting using the whale algorithm and optimized deep extreme learning machine (IWOA-DELM) is proposed. This method introduces Tent chaotic mapping to initialize the initial whale population and employs IWOA as the base load forecasting model to mine deep hidden information in the data. The improved whale algorithm is then used for parameter optimization. Finally, considering the significant impact of factors such as temperature and humidity on load changes, a multi-dimensional IWOA-DELM load forecasting model is established. This method addresses the problem of insufficient initial population distribution in the whale algorithm and enriches the model input by considering the influence of climate factors on load values, thereby improving the accuracy of short-term load forecasting.

Description

[Technical Field]

[0001] This invention relates to the application of deep extreme learning machines in short-term load forecasting, and in particular to an improved whale algorithm-optimized method for short-term load forecasting using deep extreme learning machines. [Background Technology]

[0002] The power system permeates all industries, serving as the backbone of industrial development. Every development and innovation in the power system brings progress to the industrial sector. With the introduction of the "dual carbon" target and the large-scale integration of clean energy into the grid, the power industry is transforming towards a "low-carbon" and "green" direction. Simultaneously, under the pressure of resource scarcity and environmental issues, the power system needs to seek a balance between supply and demand—that is, between power generation and electricity consumption—to ensure its stability, security, and energy efficiency. Therefore, when power companies formulate power generation plans, load forecasting is crucial for predicting future user load.

[0003] Broadly speaking, load forecasting can be categorized by time frame into ultra-short-term load forecasting, short-term load forecasting, medium-term load forecasting, and long-term load forecasting. Regardless of the type, load forecasting is fundamentally based on historical load data, with some consideration given to factors such as day type and climate, to predict future load levels. Accurate load forecasting is the foundation for power companies' load management and demand-side responses, and it is of great significance for improving power quality, reducing generation costs, and ensuring the economical and safe operation of the power grid.

[0004] Short-term load forecasting refers to predicting load at fixed points in time (mostly on the hour) over the next few hours or days, and it is a crucial part of power system load forecasting. Traditional short-term load forecasting methods mainly rely on conventional mathematical methods, and their prediction accuracy is generally unsatisfactory. Some AI-based forecasting methods cannot be widely used in short-term load forecasting due to their large fluctuations in prediction accuracy. Therefore, it is necessary to propose a load forecasting method with high prediction accuracy. [Summary of the Invention]

[0005] The purpose of this invention is to provide an improved short-term load forecasting method for deep extreme learning machines using the whale algorithm, in order to solve the problem of low load forecasting accuracy in existing methods. This method is simple and easy to implement.

[0006] The technical solution of this invention: A short-term load forecasting method for optimizing deep extreme learning machines using the improved whale algorithm, characterized by comprising the following steps:

[0007] Step 1: Divide the load data into a training set and a test set according to the time scale. The training set serves as the training sample for the load prediction model, and the test set serves as the test sample for the prediction accuracy of the load prediction model trained based on the training sample. Normalize the data in the training set and the test set.

[0008] The data in the training and testing sets in step one include load data, humidity, daily maximum temperature, daily minimum temperature, and daily average temperature.

[0009] In step one, the training set consists of the first 90% of the load data after being divided by time scale, and the test set consists of the last 10% of the data.

[0010] The normalization method in step one is shown in formula (1):

[0011]

[0012] In the formula: Y i Y is any value in the dataset that needs to be normalized. i The normalized value of Y min It is the minimum value within the selected sample range, Y max It is the maximum value within the selected sample range.

[0013] Step 2: Set the parameters of the whale algorithm, namely: whale population size, number of iterations, variable dimension, upper and lower limits of variables; use the Tent chaotic mapping method shown in formula (2) to initialize the parameters, randomly initialize the position values ​​of all whale individuals, and the position value of each whale individual represents the initial input weight of the deep extreme learning machine model;

[0014]

[0015] Among them, X n Let X be the initial position of the nth whale. n+1 Let X be the initial position of the (n+1)th whale, and a be a constant in the range [0,1]. n+1 >1, then X n+1 The return value is 1; if X n+1 <0, then X n+1 The return value is 0;

[0016] Step 3: Construct a deep extreme learning machine model, pre-train the deep extreme learning machine using the training set, and select the root mean square error of the model training set as the objective function to calculate the fitness value of each whale individual;

[0017] The deep extreme learning machine model in step three is a multi-layered neural network structure composed of extreme learning machine autoencoders, with each layer being an extreme learning machine (ELM) structure.

[0018] Suppose there are N different input and output samples (x) i ,t i ), where the input sample x i =[x i1 ,…,x in ] T ∈R n Output sample t i =[t i1 ,…,t im ] T ∈R m Then, an ELM with L hidden nodes and activation function G(x) can be represented by equation (3):

[0019]

[0020] Where, β i =[β i1 ,β i2 ,…,β im ] T It is the output weight connecting the i-th hidden layer node, a i =[a i1 ,a i2 ,…,a in ] T b is the input weight connecting the input layer and the i-th hidden layer. i It is the bias of the i-th hidden layer node, G(a i ,b i ,x j ) is the output of the i-th hidden layer;

[0021] The matrix form of equation (3) is shown in formula (4):

[0022]

[0023] Among them, a i and b i If the value is randomly set, then the β that makes the ELM algorithm output the optimal solution... i It can be calculated from H and T, as shown in formula (5):

[0024] β=H + T (5)

[0025] Among them, H + Let H be the generalized inverse matrix;

[0026] The solution obtained using the orthogonal mapping method is as follows:

[0027] β=(H T H) -1 HT (6)

[0028] Introducing the regularization coefficient C, the solution is shown in equation (7):

[0029]

[0030] Where I is the identity matrix;

[0031] Since the extreme learning machine autoencoder is characterized by input equal to output and both weights and biases being orthogonal, the weight β can be transformed from equation (7) into equation (8):

[0032]

[0033] Where X is the input matrix of each autoencoder layer.

[0034] The first layer of the model uses the original data to obtain the output weight matrix β1. During the extraction process, the input weight matrix W of each layer... i Both are β i The transpose of H. Thereafter, for each hidden layer of DELM, the H of the previous layer is used. i-1 It serves as the input matrix for the next layer until the last layer.

[0035] In step three, the root mean squared error (RMSE) of the model training set is selected as the objective function to calculate the fitness value of each whale individual as shown in formula (9):

[0036]

[0037] Where n is the number of samples, y i This is the load forecast value. This represents the actual load value.

[0038] Step 4: Sort the fitness values ​​of each whale individual obtained in Step 3, and take the position of the whale individual with the smallest fitness value as the optimal position for this iteration. Then drive other whale individuals to change their positions and move towards the optimal position to surround the prey and attack the prey according to the working principle of the subsequent whale algorithm. Then randomly search for the next prey.

[0039] Step 5: Repeat steps 3 and 4 until the maximum number of iterations set in step 2 is reached. Use the result of the last iteration as the optimal initial input weights and feed them into the deep extreme learning machine model established in step 3 to obtain the load prediction result.

[0040] The working principle of this invention: The whale algorithm is a global optimization algorithm that simulates the predation process of whale populations in nature. It has three core parts: surrounding the prey, attacking the prey, and then searching for more prey.

[0041] (1) Surround the prey

[0042] In the first iteration, the current optimal individual position must be determined and used as the target prey position for all whale individuals. Positions are then updated based on this position. That is:

[0043] D = |C·X * (t)-X(t)|

[0044] X(t+1)=X * (t)-A·D

[0045] In the formula: X is the current position vector of the whale; t is the number of iterations; A and C are coefficient vectors; X * This is the position vector of the whale at its current optimal position.

[0046] The calculation methods for A and C are as follows:

[0047] A = 2ar - a

[0048] C = 2r

[0049] In the formula: a has a linear decreasing relationship with the number of iterations, decreasing from 2 to 0; r is any vector between 0 and 1.

[0050] (2) Attacking prey

[0051] The WOA algorithm simulates the spiral bubble web attack behavior of humpback whales, gradually approaching their prey in a spiral pattern based on the distance between the whale and the prey to launch an attack.

[0052] D′=|X * (t)-X(t)|

[0053] X(t+1)=D′·e bl ·cos(2πl)+X * (t)

[0054] In the formula: b is a constant used to define the shape of the spiral attack route, and l is a random number in the interval [-1,1].

[0055] (3) Search for prey again

[0056] In actual search operations, when the absolute value of A exceeds 1, it is easy to get trapped in local optima. Therefore, it is necessary to randomly select another whale position globally and use it as the optimal position to update the positions of other whales for re-hunting. That is:

[0057] D = |C·X rand -X|

[0058] X(t+1)=X rand -A·D

[0059] In the formula: X rand The position vector randomly selected for the current whale pod.

[0060] The advantages of this invention are as follows: First, it introduces Tent chaotic mapping to initialize the initial whale population, solving the problem that the initial population distribution of the whale algorithm is not broad enough and easily gets trapped in local optima. Second, it introduces an improved whale algorithm to optimize the deep extreme learning machine model and considers the influence of climate factors on load values ​​to enrich the model input, improving the accuracy of short-term load forecasting. Third, it effectively overcomes the shortcomings of the extreme learning machine model in effectively mining deep information and can comprehensively consider meteorological information such as temperature to accurately predict short-term load. This invention can predict short-term load for the next few hours or days based on historical load data and meteorological information such as temperature and humidity, providing reliable data for power companies to conduct demand-side response or virtual power plant planning. [Attached Image Description]

[0061] Figure 1 This is a schematic diagram illustrating the specific process of a short-term load prediction method for an improved whale algorithm optimized for deep extreme learning machines, as described in this invention.

[0062] Figure 2 is a training structure diagram of the deep extreme learning machine in the short-term load prediction method of the improved whale algorithm for optimizing deep extreme learning machine according to the present invention (wherein, Figure 2-a This refers to the input / output structure of the i-th hidden layer. Figure 2-b (This refers to the hidden layer structure for the output of the last layer).

[0063] Figure 3 This refers to the training set error in one specific embodiment of the present invention.

[0064] Figure 4 shows the test results and errors of the test set in a specific embodiment of the present invention (wherein, Figure 4-a For the test results, Figure 4-b (This refers to the error between the test result and the actual value).

Detailed Implementation Methods

[0065] Example: To enable those skilled in the art to better understand the present application, the present application will be further described in detail below with reference to the accompanying drawings.

[0066] like Figure 1 As shown, this is a basic embodiment of the present invention. It includes the following steps:

[0067] Step 1: Divide the load data into a training set and a test set according to the time scale. The training set serves as the training sample for the load prediction model, selecting the first 90% of the load data after the time scale division. The test set serves as the test sample for the prediction accuracy of the load prediction model trained based on the training sample, selecting the last 10% of the load data after the time scale division. Normalize all relevant data (including load data, humidity, daily maximum temperature, daily minimum temperature, and daily average temperature) in both the training and test sets. The normalization method is shown in formula (1):

[0068]

[0069] In the formula: Y i Y is any value in the dataset that needs to be normalized. i The normalized value of Y min It is the minimum value within the selected sample range, Y max It is the maximum value within the selected sample range.

[0070] Step 2: Set the parameters of the whale algorithm, namely: whale population size, number of iterations, variable dimension, upper and lower limits of variables; use the Tent chaotic mapping method shown in formula (2) to initialize the parameters, randomly initialize the position values ​​of all whale individuals, and the position value of each whale individual represents the initial input weight of the deep extreme learning machine model;

[0071]

[0072] Among them, X n Let X be the initial position of the nth whale. n+1 Let X be the initial position of the (n+1)th whale, and a be a constant in the range [0,1]. n+1 >1, then X n+1 The return value is 1; if X n+1 <0, then X n+1 The return value is 0;

[0073] Step 3: Construct a deep extreme learning machine model, pre-train the deep extreme learning machine using the training set, and select the root mean square error of the model training set as the objective function to calculate the fitness value of each whale individual.

[0074] The deep extreme learning machine model in step three is a multi-layered neural network composed of extreme learning machine autoencoders. As shown in Figure 2, the first layer of ELM-AE uses the original data to obtain the output weight matrix β1. During the extraction process, the input weight matrix W of each layer... i Both are β iThe transpose of H. Thereafter, for each hidden layer of DELM, the H of the previous layer is used. i-1 It serves as the input matrix for the next layer until the last layer.

[0075] The deep extreme learning machine model is a multi-layered neural network structure composed of extreme learning machine autoencoders, with each layer being an extreme learning machine ELM structure:

[0076] Suppose there are N different input and output samples (x) i ,t i ), where the input sample x i =[x i1 ,…,x in ] T ∈R n Output sample t i =[t i1 ,…,t im ] T ∈R m Then, an ELM with L hidden nodes and activation function G(x) can be represented by equation (3):

[0077]

[0078] Where, β i =[β i1 ,β i2 ,…,β im ] T It is the output weight connecting the i-th hidden layer node, a i =[a i1 ,a i2 ,…,a in ] T b is the input weight connecting the input layer and the i-th hidden layer. i It is the bias of the i-th hidden layer node, G(a i ,b i ,x j ) is the output of the i-th hidden layer;

[0079] The matrix form of equation (3) is shown in formula (4):

[0080]

[0081] Among them, a i and b i If the value is randomly set, then the β that makes the ELM algorithm output the optimal solution... i It can be calculated from H and T, as shown in formula (5):

[0082] β=H + T (5)

[0083] Among them, H + Let H be the generalized inverse matrix;

[0084] The solution obtained using the orthogonal mapping method is as follows:

[0085] β=(H T H) -1 HT (6)

[0086] Introducing the regularization coefficient C, the solution is shown in equation (7):

[0087]

[0088] Where I is the identity matrix;

[0089] Since the extreme learning machine autoencoder is characterized by input equal to output and both weights and biases being orthogonal, the weight β can be transformed from equation (7) into equation (8):

[0090]

[0091] Where X is the input matrix of each autoencoder layer.

[0092] As shown in Figure 2, the first layer of the model uses the original data to obtain the output weight matrix β1. During the extraction process, the input weight matrix W of each layer... i Both are β i The transpose of H. Thereafter, for each hidden layer of DELM, the H of the previous layer is used. i-1 It serves as the input matrix for the next layer until the last layer.

[0093] The root mean square error (RMSE) of the model training set is selected as the objective function to calculate the fitness value of each individual whale, as shown in formula (9):

[0094]

[0095] Where n is the number of samples, y i This is the load forecast value. This represents the actual load value.

[0096] Step 4: Sort the fitness values ​​of individual whales, find the position of the individual with the smallest fitness value as the optimal position for this iteration, then drive the individual whale to change position and search for the next prey.

[0097] Step 5: Repeat steps 3 and 4 until the maximum number of iterations is reached to obtain the optimal initial input weights, which are then fed into the deep extreme learning machine model to obtain the prediction results.

[0098] Using daily maximum temperature, minimum temperature, average temperature, relative humidity, and hourly load data from January 1st to January 30th, 2012, a total of 720 load data points were collected. The first 28 days (672 load data points) were selected as the training set to train the model, and the last two days (48 load data points) were selected as the test set. The test results are as follows. Figure 3 Figure 4 shows the results. WOA stands for Whale Optimization Algorithm (WOA), IWOA for Improved Whale Optimization Algorithm (IWOA), and DELM for Deep Extreme Learning Machine (DELM).

[0099] Depend on Figure 3 It can be intuitively seen that, in the training set prediction error, the IWOA-DELM model has a smaller prediction error than the WOA-DELM model; Figure 4-a and Figure 4-b It can be seen that in the test set prediction results, the IWOA-DELM model is closer to the true value than the WOA-DELM model, and its prediction error is smaller.

[0100] In summary, the present invention can effectively improve the accuracy of short-term load forecasting and can play an important role in situations where high-precision short-term load forecasting results are required.

Claims

1. An improved whale algorithm-optimized short-term load forecasting method for deep extreme learning machines, characterized in that... It includes the following steps: Step 1: Divide the load data into a training set and a test set according to the time scale. The training set serves as the training sample for the load prediction model, and the test set serves as the test sample for the prediction accuracy of the load prediction model trained based on the training sample. Normalize the data in the training set and the test set. Step 2: Set the parameters of the whale algorithm, namely: whale population size, number of iterations, variable dimension, upper and lower limits of variables; use the Tent chaotic mapping method shown in formula (2) to initialize the parameters, randomly initialize the position values ​​of all whale individuals, and the position value of each whale individual represents the initial input weight of the deep extreme learning machine model; Among them, X n Let X be the initial position of the nth whale. n+1 Let X be the initial position of the (n+1)th whale, and a be a constant in the range [0,1]. n+1 >1, then X n+1 The return value is 1; if X n+1 <0, then X n+1 The return value is 0; Step 3: Construct a deep extreme learning machine model, pre-train the deep extreme learning machine using the training set, and select the root mean square error of the model training set as the objective function to calculate the fitness value of each whale individual; Step 4: Sort the fitness values ​​of each whale individual obtained in Step 3, and take the position of the whale individual with the smallest fitness value as the optimal position for this iteration. Then drive other whale individuals to change their positions and move towards the optimal position to surround the prey and attack the prey according to the working principle of the subsequent whale algorithm. Then randomly search for the next prey. Step 5: Repeat steps 3 and 4 until the maximum number of iterations set in step 2 is reached. Use the result of the last iteration as the optimal initial input weights and feed them into the deep extreme learning machine model established in step 3 to obtain the load prediction result.

2. The short-term load prediction method for optimizing deep extreme learning machines using the improved whale algorithm as described in claim 1, characterized in that... The data in the training and testing sets in step one include load data, humidity, daily maximum temperature, daily minimum temperature, and daily average temperature.

3. The short-term load prediction method for optimizing deep extreme learning machines using the improved whale algorithm as described in claim 1, characterized in that... In step one, the training set consists of the first 90% of the load data after being divided by time scale, and the test set consists of the last 10% of the data.

4. The short-term load forecasting method for optimizing deep extreme learning machines using the improved whale algorithm as described in claim 1, characterized in that... The normalization method in step one is shown in formula (1): In the formula: Y i Y is any value in the dataset that needs to be normalized. i The normalized value of Y min It is the minimum value within the selected sample range, Y max It is the maximum value within the selected sample range.

5. The short-term load prediction method for optimizing deep extreme learning machines using the improved whale algorithm according to claim 1, characterized in that... The deep extreme learning machine model in step three is a multi-layered neural network structure composed of extreme learning machine autoencoders, with each layer being an extreme learning machine ELM structure: Suppose there are N different input and output samples (x) i ,t i ), where the input sample x i =[x i1 ,…,x in ] T ∈R n Output sample t i =[t i1 ,…,t im ] T ∈R m Then, an ELM with L hidden nodes and activation function G(x) is represented by equation (3): Where, β i =[β i1 ,β i2 ,…,β im ] T It is the output weight connecting the i-th hidden layer node, a i =[a i1 ,a i2 ,…,a in ] T b is the input weight connecting the input layer and the i-th hidden layer. i It is the bias of the i-th hidden layer node, G(a i ,b i ,x j ) is the output of the i-th hidden layer; The matrix form of equation (3) is shown in formula (4): Among them, a i and b i If the value is randomly set, then the β that makes the ELM algorithm output the optimal solution... i It can be calculated from H and T, as shown in formula (5): β=H + T (5) Among them, H + Let H be the generalized inverse matrix; The solution obtained using the orthogonal mapping method is as follows: β=(H T H) -1 HT (6) Introducing the regularization coefficient C, the solution is shown in equation (7): Where I is the identity matrix; Since the extreme learning machine autoencoder is characterized by input equal to output and both weights and biases being orthogonal, the weight β can be transformed from equation (7) into equation (8): Where X is the input matrix of each autoencoder layer; In the first layer of the model, the output weight matrix β1 is obtained by solving the original data. During the extraction process, the input weight matrix W of each layer is... i Both are β i The transpose of the matrix; thereafter, for each hidden layer of DELM, the H of the previous layer is used. i-1 It serves as the input matrix for the next layer until the last layer.

6. The short-term load forecasting method for optimizing deep extreme learning machines using the improved whale algorithm as described in claim 1, characterized in that... In step three, the root mean square error (RMSE) of the model training set is selected as the objective function to calculate the fitness value of each individual whale, as shown in formula (9): Where n is the number of samples, y i This is the load forecast value. This represents the actual load value.

Images