## 4 Simulations
### Performance of Proposed Model with Inputs Containing Errors  
In this section, we assess the robustness of the proposed ensemble model in predicting solar power generation. This was achieved by deliberately adding errors at fixed proportions to select weather variables and then inputting all of the fields at time t into the target ensemble model. Finally, we measure the difference between the power generation forecast results at time t and the actual data  
We use Figures 17-20 to explain how the proposed model achieves robust prediction. In particular, considering that when selecting five factors to combine, both lightweight models can obtain relatively good results, the experiment in this section will be conducted with a combination of five factors. Among them, for lightweight NC-RBF-DNN, its five factors are [_total column ice water_, _10-m V wind component_, _surface solar rad down_, _total precipitation_, _month_] and for random forest, its factors are [_Hour_, _Month_, _two-meter temperature_, _surface solar rad down_, _zone ID_]. All three of these figures present the results of two models, including the combination with the minimum error found by the heap method and the average of the five combinations with the smallest errors as determined using the heap method. Furthermore, the \(-10\%\), \(-5\%\), \(0\%\), \(5\%\), and \(10\%\) on the \(x\) axes in each graph represent the percentage of error added to or subtracted from certain factors, and the \(y\) axes indicate the final output error resulting from the input error. Note that where x equals \(0\%\), there is no error in the input, so naturally the final output error is also \(0\). Figures 17 and 18 only consider situations where errors only exist in a single factor, which is necessarily used in the optimal model, and errors may occur. Finally, Figures 19 and 20 consider situations where errors exist in two factors, which is necessarily used in the optimal model or ensemble models. In the sub-graphs of these figures, we can clearly see that with either the lightweight NC-RBF-DNN or the random forest, the output errors caused by errors in the input factors of the ensemble model are all less than those of the optimal model, thereby demonstrating that the proposed ensemble model can perform better than a single model. After completing the comparison with the single best model, we compared the target ensemble model against an existing ensemble model [19]. The comparison model employed a gradient boosting machine, a support vector machine, the random forest algorithm, and the k-nearest neighbor algorithm to train models on the target data set. An ensemble model was then used for model integration. The comparison results in Figures 21-24 show that their muti-faceted approach outperformed our simple method in terms of resistance to input error. Nonetheless, the NRMSE of their model was more than ten times higher than that of the proposed method, regardless of the input error combination. Despite the effects of input error, the proposed model achieved output predictions that are closer to the actual results, making it a highly robust solution. Figure 16: Factors chosen in near-optimal solution with different number of factors in a combination, where the darker the color, the more factors are selected. (**a**) modeling with lightweight NC-RBF-DNN; (**b**) modeling with random forest. Figure 17: When using lightweight NC-RBF-DNN to model, the impact of one input error on the model output error. (**a**) Total column ice water, (**b**) 10-m V wind component, (**c**) surface solar rad down, (**d**) total precipitation. Figure 18: When using the random forest to model, the impact of one input error on the model output error. (**a**) Two-meter temperature, (**b**) surface solar rad down. Figure 19: When using lightweight NC-RBF-DNN to model, the impact of two input errors on the model output error.