3.1 Preprocessing of Power Load Data

Power load calculation is a fundamental link in achieving power dispatch. Accurate power load data can help the power grid achieve a balanced distribution of supply and demand, ensuring reasonable power dispatch. The electrical load data was first preprocessed to improve the accuracy of power dispatch ^[16]. The wavelet decomposition method is a method for analyzing and processing non-stationary signals. The charge data was analyzed by introducing the wavelet decomposition method to decompose the original signal into high-frequency (HFS) and low-frequency (LFS) signals. Among them, HFS and LFS underwent drastic and stable changes in a short period, respectively. Therefore, the power data processed using the wavelet decomposition method can be applied effectively to analyze the impact factors of power load changes. Fig. 1 presents the electrical load data processing method based on wavelet decomposition.

Fig. 1. Power load data processing process based on wavelet decomposition.

The initial power data signal $A_{1}$ is decomposed to HFS $A_{1}$ and LFS $D_{1}$. The HFS continues to decompose to generate new HFS $A_{2}$ and LFS $D_{2}$. The HFS is decomposed until a noise interference signal is obtained, as expressed in (1).

where $D$ represents a LFS. $A$ represents a HFS. $H'$ is a high-pass filter. $G'$ is a low-pass filter. $A_{m}$ represents the HFS component when the resolution is $2m$. $D_{m}$ represents the LFS component. The impact of different influencing factors on electrical load varies in magnitude. Therefore, after processing the charge data using the wavelet decomposition method, the Pearson correlation coefficient is used to calculate the correlation $fit_{i}$ of each influencing factor on the electrical load data. (2) illustrates the calculation method.

where $X$ and $Y$ are two random variables. $E$ is the expected value. $\sigma X$ and $\sigma Y$ are the standard deviations. $\mathrm{cov}$ is the covariance. The correlation was determined using (2). Table 1 lists the corresponding relationship between the correlation coefficient $r$ and the correlation.

Table 1. Correlation Coefficient and Correlation Degree.

When decomposing electric load data, the main process includes feature analysis, feature decomposition, and feature selection of electric load data. In the feature decomposition process, errors will occur as decomposition times increase. Residual sequences were calculated to reduce the errors and the impact of decomposition errors on the decomposition times ^[17]. Fig. 2 presents the overall decomposition process of electrical load data features.

In the process shown in Fig. 2, the power load data was first subjected to feature analysis ( ). The wavelet transform was used for feature decomposition to obtain corresponding high-frequency and low-frequency signal data. The Pearson correlation coefficient was used to calculate various electrical load data correlations. Based on the Pearson correlation coefficient degree, the calculation results were judged. The appropriate weights were retained. Finally, the process was concluded.

Fig. 2. Process of feature decomposition.

DED is meaningful for the operation of power systems. The objective function of DED is the total production cost of $N$ generator units in $T$. The production cost can be approximated as the quadratic function of the active power output of the generator set, as shown in (3).

where $T$ represents the total scheduling time. $i=1,2,3,\ldots ,N$. $N$ denote the online generator units to be dispatched. v represents the energy consumption coefficient. $P_{ih}$ represents the actual output power of the generator (MW).

3.2 Construction of Power Dispatching Model based on ABC Algorithm

The power dispatch model in the power grid system belongs to a non-deterministic polynomial problem. Their difficulty and computational complexity are increasing rapidly with the increasing complexity of planning problems. Determining the optimal solution in complex situations is meaningful for solving the scheduling problems. ABC is a Swarm intelligence optimization algorithm with fewer control parameters, strong robustness, and a simple structure. The ABC algorithm consists of three stages: leading bees to find food sources (FSs) and calculating fitness values, following bees to find the new FS and updating them based on fitness values, and detecting bees to find the new FS ^[18]. In the ABC, the FS is located where the optimal solution is located. A point in the space corresponding to the location of the FS is represented as $\left\{x_{id}\left| i=1,2,3,\ldots ,M\right.\right\}$. The fitness $fit_{i}$ stands for the quality of the FS. $M$ is for the FS. When solving optimization problems, every point in space may become the optimal solution. The location initialization of the FS is expressed as (4).

where $d$ stands for the dimension of the individual vector. In the search space, $U_{d}$ represents the upper limit, and $L_{d}$ denotes the lower limit. $rand(0,1)$ is a random number between $fit_{i}$. Guide bees search randomly for a new FS around the FS, as shown in (5).

where $\varphi $ represents a random number in $\left[-1,1\right]$. $i$ and $j$ are random integers between $\left[1,N\right]$. If the fitness value of the new FS found by the leading bee is higher than $x_{id}$, it follows the new FS. On the other hand, the initial FS will still be used. The probability of selecting a new FS during this process is expressed as (6).

According to the roulette strategy, $r$ is generated randomly in $\left[0,1\right]$. This value is compared with $P_{i}$. If $P_{i}>r$, the FS is updated; otherwise, the existing FSs continue to be used. According to roulette, FSs with better fitness values are selected. The parameter $trial$ in the FS represents the number of times the FS has not been updated. If the FS has not been updated, then $trial$ = 0. If the FS is updated, then $trial$ = 1. During the search process, the FS undergoes $trial$ iterations. Before reaching the threshold $\lim it$, it is determined if there are FSs with better fitness values. If there is a better FS, it will be updated according to (2); otherwise, the existing FSs are abandoned. Through self-feedback, leading bees become reconnaissance bees, searching for new FSs, according to (7).

Fig. 3 shows the basic process of the ABC.

Fig. 3. Artificial bee colony algorithm process.

3.3 Construction of Power Dispatching Model based on the Improved ABC

In the human bee colony algorithm, the leading and following bees are half the total number of bees. This situation can easily lead to insufficient global search ability and low efficiency ^[19]. At the same time, there are also shortcomings when using (7) to develop FSs. When the threshold reaches its limit, the mutation ability of the ABC is insufficient, resulting in low local search accuracy. Therefore, an improved bee colony optimization algorithm (IBCOA) is proposed to overcome the shortcomings of the ABC optimization algorithm in practical use. The adaptive factor $\varphi $ of traditional artificial bee colony algorithms is a random number distributed between $\left[-1,1\right]$. The search range is not controlled, resulting in low convergence efficiency. Therefore, the study introduces the search factor $u$ without affecting the randomness of $\varphi $. The adjustment formula for the search factor $u$ is expressed as (8).

where $fit_{i}$ is the fitness of the FS after the previous iteration of the leading bee. $k$ represents a random number that can be adjusted. The index function ensures that the search scope can be effectively expanded in the early stage. After introducing the search factor $u$, the leading bee updates the FS using (9).

where the fitness value of the FS determines the search range of the ABC. In the early stage, if the fitness value of the FS is relatively small and the objective function value is large, the search range will be expanded to increase the probability of obtaining the optimal solution. During the following bee search, if the fitness value is high and the distance from the local optimal solution is small, the search range is reduced to improve the speed of the following bee to find the global optimal solution. Introducing search factors can balance global development and local search capabilities. The ABC is completed mainly by the leading and following bees when searching for the optimal solution ^[20]. Therefore, a selection strategy for local optimal solutions is introduced, which is expressed as (10).

where $X_{P(i),d}$ is the local optimal solution used when updating the FS. The FS updated by the leader bee is the local optimal solution if the fitness value searched by the leader bee is greater than the local optimal solution during the iteration process. The initial FS is considered the local optimal solution if the fitness value is less than the local optimal value in the existing iteration. The formula for updating FSs that can reduce the search time by following bees during the exploration phase is expressed as (11).

where the leader bee provides the location $x_{id}$ of the FS after the information exchange. This location is updated to the local optimal solution location $X_{P(i),d}$ found by the leader bee. Each update was completed around the local optimal solution. A search factor $u$ was also added to the adaptive factor $\varphi $. When approaching the global optimal solution, the fitness increases, the search factor $u$ decreases, and the change amplitude decreased. As it gradually approached the optimal target value, the following bee searches continuously to improve the probability of the algorithm obtaining the optimal value. At the same time, the speed is also more ideal. Fig. 4 presents the specific implementation process of the IBCOA algorithm.

Fig. 4. Implementation of the IBCOA algorithm.

4.1 Electrical Load Data Preprocessing Analysis based on Wavelet Decomposition Method

Experiments are designed to validate the power dispatch model and prove the availability of the model. First, the performance of the preprocessing method for electrical load data based on wavelet decomposition was verified. The experiment used the electricity load data of a certain power company in A city in 2019 as a sample. The data were the electricity load for 2019, recorded hourly with 24 pieces of data per day. Eight thousand seven hundred and sixty pieces of data were collected throughout the year, measured in kW·h, which is the electricity consumption per hour. Table 2 lists the specific power load data.

The power load data obtained in actual use generally contains much noise. Therefore, the proposed wavelet decomposition method was used to analyze the power load data. After decomposition, three component sequences were obtained: one low-frequency component and two high-frequency components. These three component sequences can exhibit different patterns of power load data variations. Fig. 5 presents the decomposition results. Fig. 5(a) depicts the time series diagram of the original signal data. Fig. 5(b) shows the low-frequency time series obtained from the wavelet decomposition. Fig. 5(c) represents the first high-frequency time series diagram from the wavelet decomposition. Fig. 5(d) presents the second high-frequency time series diagram of the wavelet decomposition. The relevant power load data was divided accurately into high-frequency and low-frequency sequences. The subsequent power dispatch models can effectively support the scheduling analysis of power load data.

Fig. 5. Original data and wavelet decomposition time sequence diagram.

The accuracy of the wavelet transform algorithm used was tested. The model parameters of the final wavelet transform algorithm obtained through model training and parameter adjustment were as follows. The learning rate of the low-frequency time series was 0.0005. The learning rate of the high-frequency detail sequence was 0.001. The time steps were all one. The number of neurons was 250. The batch sizes were all 256. The dropout was 0.25, which means randomly removing 25\% of neurons. The training duration epochs were all 300. Fig. 6 shows the error change in training and verification of each subsequence. In Fig. 6, the low-frequency sequence converged from 0.03 and 0.015 in the training and validation sets, respectively. Both eventually converge to 0.0015, with small fluctuations throughout the entire process. The first high-frequency sequence converged from 0.035 and 0.004 in the training and validation sets, respectively. Ultimately, they all converged to 0.001, with small fluctuations occurring after 210 iterations. The second high-frequency training converged from 0.005 and 0.0005 in the training and validation sets, respectively. The final convergence value of both was 0.0001. There were no significant fluctuations throughout the entire iteration process. Overall, the training errors under the three conditions stabilized and approached zero in the validation and testing sets. Hence, the fitting ability of the three sequence models was good, and the training effect was ideal. The obtained training data can be used for testing the power dispatch model.

Fig. 6. Error of Subsequence in the training and verification sets.

4.2 Application Analysis of Improved ABC Algorithm in Power Dispatch Model

After preprocessing the data using the above methods, the performance of the power dispatch model based on the improved ABC was verified. The test environment was set as follows. The simulation environment was that the processor was Inter(R) Core (TM)i5-4590S3.00G Hz, and the operating system was Windows 7. The programming software was MATLAB R2014a. In the experiment, IBCOA was compared with the ABC and the improved algorithm based on hierarchical optimization (HABC) to verify the competitiveness of the algorithm. First, six benchmark functions were used to analyze the accuracy of the proposed algorithm. The six benchmark functions were the Sphere function (f$_{1}$), Rosenbrock function (f$_{2}$), Quartic function (f$_{3}$), Griewink function (f$_{4}$), Shifted and Rotated Rastigins Function (f$_{5}$), and Shifted and Rotated Levy Function (f$_{6}$). Table 3 lists the test results in six benchmark functions. From Table 3, the IBCOA was superior to the other optimization methods. In particular, in the f$_{1}$ and f$_{6}$ functions, the accuracy reached 10$^{-16}$ and 10$^{-15}$, respectively. Hence, the IBCOA algorithm can achieve high optimization accuracy.

The proposed power dispatching methods were compared using common methods, including the Whale Optimization Algorithm (WOA), Fruit Fly Optimization Algorithm (FOA), and Particle Swarm Optimization (PSO). Fig. 7 shows the convergence rate of this method in the six different reference functions. In the f$_{1}$ function, the loss values of the four types of power dispatch models decreased gradually as the iterations increased. Among them, the loss values of FOA and PSO models were relatively close. The trend of the change was consistent. The loss value of the IBCOA algorithm proposed in this study was significantly lower than other methods. In the f$_{2}$ function, the PSO algorithm remained at 10$^{10}$. The WOA algorithm converged from 10$^{10}$. The FOA and IBCOA algorithms converged from 10$^{8}$. The IBCOA algorithm had the best convergence effect when the function iteration value was 10$^{3}$. The minimum loss value was 10$^{4}$. In the f$_{3}$ function, both PSO and FOA algorithms converged from 10$^{11}$. The WOA algorithm converged from 10$^{10}$. The IBCOA algorithm converged from 10$^{5}$. The loss value was significantly lower than the other three methods. In the f$_{\mathrm{4－}}$f$_{6}$ functions, the IBCOA algorithm exhibited the best convergence performance. This suggests the proposed IBCOA power dispatch model exhibits good convergence performance under different benchmark function conditions.

Fig. 7. Convergence rate of the different algorithms.

The proposed algorithm was then applied to power dispatch. In this experiment, each algorithm ran independently 50 times under 1000 iterations. The population size was 30, 50, 100, and 500 respectively. Fig. 8 shows the fitting effect of the obtained power dispatch model. When the population size was 30, the convergence changes in the FOA and WOA models were consistent, without significant differences. The IBCOA algorithm showed the best performance. At this point, all four methods changed smoothly, and the convergence effect was not significant. When the population size was 50, after 10 iterations, except for the PSO algorithm, all three other methods began to converge. The convergence rate was fast. The convergence performance of IBCOA was superior to the other methods. The loss value was 10$^{4}$ when the iterations reached 10$^{3}$. All four methods began to converge when the population size was 100. After 10$^{3}$ iterations, however, the final loss of the IBCOA was 10$^{2}$, which is significantly below the other methods. The initial loss value of the IBCOA algorithm was the smallest when the population size was 500. On the other hand, the convergence rate was slow. Overall, when the population size was 100, the IBCOA algorithm showed the best performance. In addition, the IBCOA algorithm achieved significantly better quality and computational efficiency than other methods when the objective function became complex. Therefore, the IBCOA algorithm is an important tool for solving more complex optimization problems in power systems.

Fig. 8. Convergence of different scales in power dispatch.

The IBCOA algorithm is used for power dispatch experiments. Table 4 lists the experimental results under different population sizes. For the DED, a lower cost of electricity was obtained. In actual power dispatch, the variance value was the smallest when the population was 100, indicating that the data was relatively more stable and less volatile at this time. In terms of the DED problem, the improved algorithm was more suitable for power dispatch to achieve cost reduction. These results confirmed that the IBCOA method has robustness, higher solution quality, and higher computational efficiency than the original ABC algorithm.

Five units were selected to participate in the simulation test. Fig. 9 shows the convergence and optimization results of the proposed IBCOA algorithm. The convergence iteration of the PSO algorithm was 46 times (Fig. 9(a)). During the iteration process, there was always a local optimal situation. The convergence iteration of the WOA algorithm was the same as that of the FOA algorithm. The IBCOA algorithm proposed in this study had the smallest convergence iteration, which was 15 times, avoiding local optima. The IBCOA algorithm proposed in this study had the lowest cost, 853.4903 million yuan (Fig. 11(b)). The IBCOA algorithm proposed in the study took the least time, 9.33ms (Fig. 11(c)), indicating the best performance of the algorithm.

Fig. 9. Convergence and optimization results of the IBCOA.

Fig. 10. Thermal power plant output and system cost under different scale base station energy storage.

The IBCOA algorithm proposed in the study was applied to power dispatch. Fig. 10 shows the output and system cost of thermal power plants under different scale base station energy storage. Significant differences in the output energy of thermal power plants were observed under different units (Fig. 10(a)). A larger base station scale in the same unit meant less energy from the thermal power plant outputs. Under the energy storage of 200000 base stations, Unit 5 had the lowest energy output of 111.00 MW. The maximum output of Unit 1 thermal power plant was 117.00 MW. The minimum cost without base station energy storage was 1159.8362 million yuan (Fig. 10(b)). The total optimization cost of the system with 200000 base station energy storage was at least 853.61278 million yuan, which was 306.22342 million yuan less than that without base station energy storage.