## 5 Photovoltaic Power Prediction Based on Objective Optimization IHO-ELM
### Results and Discussion  
Before making a prediction, first normalize the sample data, as shown in Equation (31):  
\[x^{\prime}=\frac{x_{i}-x_{\mathrm{min}}}{x_{\mathrm{max}}-x_{\mathrm{min}}} \tag{31}\]  
wherein \(x^{\prime}\) is the normalized value, \(x_{i}\) is the normalized raw data required, \(x_{\mathrm{max}}\) and \(x_{\mathrm{min}}\) is the maximum and minimum of the raw value, respectively.  
The IHO-ELM can be used to predict the power flow chart, as shown in Figure 6.  
The computational efficiency of optimization algorithms can usually be evaluated for their performance. So, this article first analyzes the efficiency of algorithms. When optimizing the connection weights and thresholds of the ELM model, set the value of the optimization algorithm population to 20 and set the maximum number of iterations to 150. The fitness values of the IHO algorithm proposed in this paper were compared with those of the HO algorithm and CSO algorithm; the results are shown in Figure 7.  
According to Figure 7, the CSO algorithm converges at 94 iterations with a fitness of approximately 0.013988; The HO algorithm converges after approximately 68 iterations with a fitness of approximately 0.0044711; The IHO algorithm proposed in this article converges with a fitness of approximately 0.003473 after approximately 26 iterations. The IHO algorithm has a faster convergence speed and stronger optimization ability, which can increase the probability of jumping out of local optimal solutions, finding better solutions, and improving computational efficiency.  
Secondly, to assess the performance of the model presented in this paper, we compared it with the three models from the two perspectives of optimization algorithm and single model. In terms of a single model, an ELM single model is selected for comparison. In terms of optimization algorithms, a comparison was made between the CSO-optimized ELM and the unimproved HO algorithm-optimized ELM. The comparison results are presented in Tables 3 and 4.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Prediction Model** & **MAE** & **MAPE** & **MSE** & **RMSE** & **R2** \\ \hline IHO-ELM & 0.04760 & 0.11662 & 0.00376 & 0.06129 & 0.99998 \\ HO-ELM & 0.06164 & 0.14158 & 0.00611 & 0.07819 & 0.99996 \\ CSO-ELM & 0.11791 & 0.12216 & 0.03314 & 0.18203 & 0.99979 \\ ELM & 0.23916 & 0.31099 & 0.10427 & 0.32291 & 0.99934 \\ LSTM & 0.43945 & 0.33520 & 0.39491 & 0.62842 & 0.99750 \\ TCN & 0.27854 & 0.66627 & 0.39963 & 0.63216 & 0.99747 \\ BP & 0.9067 & 0.86687 & 1.83062 & 1.35310 & 0.98843 \\ SVM & 1 & 1.30972 & 1.89581 & 1.37690 & 0.98801 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Prediction error results of 8 models.  
Figure 6: Flowchart of IHO-ELM prediction.  
Figure 7: Iteration curves of three models.  
Table 3 shows the performance of different comparison models, and the results are analyzed as follows:  
1. Compared with the ELM, CSO-ELM, and HO-ELM, the IHO-ELM prediction model achieved the best accuracy, with MAPE, RMSE, MAE, and MSE values being 11.6626%, 0.06129, 0.047593, and 0.0037564.
2. From Figures 8-11, the accuracy of the ELM model using optimization methods is significantly higher than that of a single optimized ELM model without using optimization methods, indicating the necessity of connecting the weights and thresholds of the optimized ELM model.
3. The optimized model has better accuracy than the unoptimized model and the traditional CSO-optimized model. The MAPE, RMSE, MAE, and MSE indicators of the IHO-ELM were reduced by 17.62%, 21.61%, 22.78%, and 38.5%, respectively, compared to the HO-ELM from Table 4, significantly better than the unimproved HO optimization model.