## 5 Conclusions  
Due to the strong randomness and volatility of the load, accurate value prediction is difficult. After analyzing the problems existing in the current load prediction method, this paper proposed a multi-objective interval prediction method based on the conditional copula function in discrete form, which helps power system staff to make more reasonable, safe, and economical scheduling decisions. Specifically, we did the following research:  
1. At present, some load interval prediction methods need to rely on point prediction or require appropriate kernel functions to be selected in advance, which reduces the prediction accuracy. With the excellent characteristics of the copula function, we could take full advantage of the correlation relationship between load sequences in adjacent time periods by establishing the discrete condition copula function of the point to be predicted, to obtain the prediction interval of a point to be predicted, and then, the rolling prediction method is adopted to obtain the prediction result of the whole prediction period, which improves the interval prediction accuracy; the method has the advantages of being simple and quick, and easy to expand. 2. Based on the problem of contradiction between multiple evaluation indicators, when the values of the conditional copula prediction model parameters (\(K\), \(t\)) change, we use the NSGA-II multi-objective algorithm to seek the optimal model parameter within its value range such that the non-inferior solution set of the conditional copula prediction model parameters is obtained. Then we use the average weight method to get a group of the optimal set of conditional copula prediction model parameters. 3. To validate the effectiveness and applicability of the load interval prediction method proposed in this paper, the method was applied to three regions in China. We compared the prediction results obtained using the proposed method with those of three more mature methods (ELM [26], GPR algorithm [28], and ANN [29]). The comparative analysis showed that the method proposed in this paper has the smallest PIAW, the largest PICP, and the best effect. 4. As is mentioned in the discussion, we believe that when PICP and PIAW are endowed with their weights, we must combine the actual requirements of scheduling. The prediction results obtained using this method are not exactly the same in different practical situations. At the same time, the method proposed in this paper can provide a new idea for dispatching departments, because it can be more effective and safer to conduct power system dispatching after combining with point value prediction. Meanwhile, the construction process of a conditional copula function can also be extended to other fields such as wind speed, PV, and so on. However, there are still some shortcomings in our work, in that if the correlation relationship between load sequences is weak, the prediction results using this method are usually bad. On the other hand, since the ultra-short-term load prediction resolution is relatively high (within 15 min), the influence of weather factors on the prediction results is small, and the numerical weather prediction model is very complicated, so we did not consider the weather factors and prediction day types features in the study. In future work, if this method could be applied to medium- and long-term load prediction, we could further study how to better combine meteorological factors, day type features, and copula interval prediction methods. [PERSON] and [PERSON] conceived and designed the experiments; [PERSON], [PERSON] and [PERSON] performed the experiments; [PERSON], [PERSON] and [PERSON] analyzed the data; [PERSON] and [PERSON] contributed reagents/materials/analysis tools; [PERSON], [PERSON] and [PERSON] wrote the paper.