## 3 Results  
### Example Data Source  
To verify the effectiveness of the proposed method in this paper, we apply the multi-objective ultra-short-term prediction method of the conditional copula function to three regions in Shaanxi Province, China, which are recorded as region 1, region 2, and region 3. The load data of each region are derived from the local power grid. According to China's power industry standard (DL/T 1711-2017) and the actual application requirements of ultra-short-term load prediction, the resolution of the load data is determined to be 15 min.  
We divide the historical load data collected in one area into three parts, which is called respectively training data, validation data and test data, while the NSGA-II algorithm is only used during the validation data.  
(1) training data: We use most of the historical load data of a region as training data, and use these data to construct the conditional copula function. At this time, the prediction model parameters (\(K\), \(t\)) are not fixed, if the selected parameters are not suitable, the prediction effect will be poor.  
(2) validation data: In the ultra-short-term load prediction, due to the full consideration of the principle of \"near load with large correlation and far load with small correlation,\" namely, the future change trend of load is more dependent on the development law of recent load in the historical period, and the correlation with the development trend of long-term loads is weak. Therefore, we use the load data of the day before the test period to find the optimal parameters of the prediction model, and use  
Figure 2: The specific process of the NSGA-II (Non-dominated Sorting Genetic Algorithm-II) algorithm.  
the NSGA-II multi-objective optimization algorithm to obtain the optimal solution set of the prediction model parameter values (\(K\), \(t\)), finally we obtain a group of optimal parameters (\(K\), \(t\)) by evaluating the solution set.  
(3) test data: In order to verify the actual accuracy of the optimal parameter prediction model, we use the test data to test to ensure the unbiasedness of the prediction model, and compare the results with the three commonly used load interval prediction methods.  
Region 1 is located in Yan'an City, Shaanxi Province, China. We use the load data from the Yan'an Power Grid Corporation from 1 January 2016 to 31 January 2017 as the training data, and we take the load data of 1 February 2017 as the validation data. Finally, the test is performed using the (96 points) load data of 2 February 2017 to verify the actual accuracy of the prediction model with the optimal parameters.  
Region 2 is located in Hanzhong City, Shaanxi Province, China. We use the load data from the Hanzhong Power Grid Corporation from 1 March 2016 to 31 March 2017 as the training data, and we take the load data of 1 May 2017 as the validation data. Finally, a test is performed using the load data (96 points) of 2 May 2017 to verify the actual accuracy of the prediction model.  
Region 3 is located in Shangluo City, Shaanxi Province, China. We use the load data from the Shangluo Power Grid Corporation from April 2016 to August 2016 as the training data, and we take the load data of 1 September 2016 as the validation data. Finally, the test is performed using the load data (96 points) of 2 September 2016 to verify the actual accuracy of the prediction model.  
The computer CPU model we use is Core i7-7700K with 4 core 8 thread, clock speed is 4.2-4.5 GHz; computer memory is 16 GB, solid state disk is SAMSUNG 960 EVO 500G; the operating system is Windows 10 64-bit; the proposed load ultra-short-term prediction model was built on MATLAB R2016b. In the validation period, the execution time is 17.815 s; while in the testing period, conduct the load prediction of a point (15 min), the execution time is 0.841 s.