An improved whale algorithm for power load forecasting based on adaptive weight adjustment

With the progress of the times, people have higher and higher expectations for the electric power system in the new era. To meet the new requirements, improving load forecasting capabilities has become an important part of the process. In this article, an improved whale algorithm based on adaptive weight adjustment is presented to predict user load, using a Cubic-map strategy to achieve better population effect, combining the whale algorithm and the BP algorithm so as to improve the rate of convergence and prediction accuracy of the algorithm. Simulation software is used to conduct simulation experiments on multiple algorithms. From the experimental data, it can be concluded that compared with a single algorithm, the algorithm proposed in this paper has a stronger ability to find the optimal value within the effective boundary. Both the rate of convergence is faster, and it has higher accuracy.


INTRODUCTION
Power load forecasting is mainly based on historical power data to comprehensively forecast and calculate the power load and power consumption in the future period.In the course of the gradual prosperity of the power industry now, the expectations for load forecasting in the new era are getting higher and higher, and economic operation has become a hot topic [1][2] [3] .The power sector in some developing countries still employs traditional statistical methods such as regression analysis method for load forecasting to make generation planning and power dispatching.However, in some developed countries, the prediction method of artificial intelligence is widely adopted in the field of short-term power load prediction.
At present, a single model is used for load prediction in many fields in China, including time series and BP neural networks [4][5][6] [7] .Even though the prediction results obtained by these methods are referrable to a certain extent, every single prediction model has its own emphasis and limitations, so using a single prediction model will inevitably lose some useful information.Whale optimization algorithms have the advantages of simple heuristic mechanisms and few constraints, and are often combined with other algorithms to achieve improved performance [8] .
Because of this, it is considered to propose an improved whale algorithm in this paper.In order to have better traversal uniformity, the Cubic map strategy is used in this paper to make the initial individual distribution more uniform, and then adjusted by using a new weight adjustment formula to improve the ability of the algorithm to search within the effective boundary and prevent the prediction results from falling into a very small range for the optimal solution derived from the comparison, and finally the optimal value is obtained, and after simulation experiments, it can be seen that the prediction ability of the algorithm is relatively considerable and can better predict short-term change trend of electric load in the future.

The BP neural network
The BP neural network algorithm is a known relationship between the corresponding input and output patterns and it continuously adjusts the weights and thresholds in the network, with the ultimate goal of minimizing the sum of squared errors in the output layer [9][10] [11] .

The whale algorithm
In WOA, the whale closes its circle as it spirals toward its prey.Therefore, in this model of synchronous behavior, a probabilistic selection contraction enveloping mechanism of π and a probabilistic selection spiral model of 1-π are assumed to update the whale's position, and its mathematical model is as follows.

Chaotic mapping strategy
A chaotic mapping is a sequence of randomness generated by a simple deterministic system.It is experimentally proven that chaotic sequences can influence the whole process of the algorithm and often achieve better results than pseudo-random numbers.In this paper, the Cubic map strategy is used, and its expression is: where ρ is the control coefficient, which is 1 in this paper.

Adaptive weight adjustment strategy
In this paper, we improve the adaptive weight formula by using a slightly larger weight value in the humpback whale feeding phase to improve the ability to search within the effective boundaries, and as the algorithm progresses, the weight value decreases exponentially in the later stages of the algorithm, making the algorithm less likely to find the optimal value in a very small range.The adaptive weights are given by   * exp / where maxgen stands for evolutionary algebra and mm for adjustment coefficient, taking 1 here.
where p i is taken as 0.5.

ALGORITHM STEPS
In summary, The algorithm in this paper proceeds as follows： Step 1: We initialize the parameters.
Step 2: We initialize the whale location using the Cubic map policy.
Step 3: We solve the objective function, and calculate the value of the criterion for each individual's feature combination.In this method, the best-fit value can be obtained.
Step 4: If A judges whether p is less than 0.5, p < 0.5 and | A | < 1, we update it according to Formula (3).
Step 5: If p < 0.5 and | A | ≥ 1, then the WOA corresponding formula is updated.
Step 6: If p > 0.5, we perform a global search according to Formula (1) Step 7: We complete the location update, and find the optimal location.
Step 8: If the final condition is reached, we output the optimal solution, and vice versa, we return to Step 3.

SIMULATION RESULT
In this paper, we use the daily user demand load data of a location from January 1, 2014, to December 31, 2014, as sample data.Therefore, it was determined to construct a neural network with 5 inputs and 1 output, and the number of nodes in the implicit layer appeared by consulting the literature, and the number of nodes with the smallest error was tested before the simulation, and its value was 7.
Common intelligent algorithms are used for simulation comparison.A comparison of the real value and predicted value of each algorithm is shown in Figure 1.The error comparison of each algorithm is shown in Figure 2.After bringing the data into each model, we can learn and train independently, and finally get the prediction accuracy of each model, as is shown in Table 1 From the experimental data above, it can be seen that the C-I-WOA-BP algorithm has the smallest error and the C-I-WOA-BP algorithm has the highest prediction accuracy of 90.8181% when compared with the BP, the SSA-BP, and the C-WOA-BP models, respectively.It shows that the improved whale algorithm can better characterize the prediction data, which is more reasonable for the power sector in arranging the work and improving the economic benefits.

CONCLUSION
To enhance customer load forecasting capability, an improved whale algorithm model based on adaptive weight adjustment is proposed in this paper to verify the load data of a certain place.In this paper, the BP model, the C-WOA model, the SSA-BP model and the C-I-WOA model are respectively used for testing and comparison, and the conclusion is drawn: 1) The C-I-WOA model has less prediction error and is more able to find the optimal value within the effective bound compared to the traditional model, and the experimentally derived output layer values are closer to the expected values.
2) Although the simulation results in this paper have shown an improvement, there is still room for further improvement and further research is still needed.

Figure 1 .Figure 2 .
Figure 1.Comparison of the real value and predicted value of each algorithm

Table 1 .
. Comparison of accuracy of each model