## 2 Knowledge and Tools of Model Preparation
Therefore, as an advanced swarm intelligence algorithm, MOEA/D is used to improve BP parameters to improve forecasting performance. In particular, the _predict\({}_{1}\)_, _predict\({}_{2}\)_, _predict\({}_{3}\)_ and _predict\({}_{4}\)_, which contains 336 power load prediction values obtained from the RBF, ELM, ENN and ARIMA models mentioned in **Step 2**, are the basic data of the BP model, where the first 240 values are considered as the training set and the remaining 96 values are taken as the testing set. Then the 96 prediction values obtained by BP are the forecasting results of our proposed model. It is worth noting that it is difficult to find the weights and thresholds of neurons in each layer of BP network, so MOEA/D is introduced to search for the best weights and thresholds of neural network, which solves this problem to a certain extent. The input and output structure of BP network training is shown in Equations (17) and (18). \[input_{2}=\left[ \begin{array}{cccc}predict_{1}&predict_{2}&predict_{3}& predict_{4}\\ \hat{x}_{1}(1)&\hat{x}_{2}(1)&\hat{x}_{3}(1)&\hat{x}_{4}(1)\\ \hat{x}_{1}(2)&\hat{x}_{2}(2)&\hat{x}_{3}(2)&\hat{x}_{4}(2)\\ \vdots&\vdots&\vdots&\vdots\\ \hat{x}_{1}(N)&\hat{x}_{2}(N)&\hat{x}_{3}(N)&\hat{x}_{4}(N)\\ \end{array} \right] \tag{17}\]

\[output_{2}=\left[ \begin{array}{cccc}x(1)&x(2)&\cdots&x(N)\\ \end{array} \right]^{T} \tag{18}\]

In which \(N\) is 336, and \(\hat{x}_{1}(k),\hat{x}_{2}(k),\hat{x}_{3}(k),\hat{x}_{4}(k)\) is the \(k\)-th load value predicted by RBF, ELM, ENN and ARIMA, respectively. By _input_ and _output_, the optimized BP neural network can be trained. **Step 4:** Power load point prediction. According to the established nonlinear prediction model, the rolling forecasting technique is applied for multi-step forecasting, and the final prediction results are obtained. The evaluation index is calculated by using the prediction result and _test_, and then the performance of the model is effectively evaluated. ### Interval Forecasting Module

Interval forecasting is obtaining the value interval of future load by certain forecasting methods, which shows the possible fluctuation range of future load. If accurate load point prediction can guarantee the daily operation of power grid, then effective interval prediction can further quantify the uncertainty of power load and provide reliable and accurate load information. The interval forecasting method of this system is developed according to point prediction, which is an interval prediction method based on fuzzy system. The principle of the interval forecasting method proposed in this study is to classify the point forecasting results according to different kinds of load data and construct different but adaptive intervals. The classification is based on the real load data, and judge which category the prediction results belong to, and then construct a specific confidence interval for this category, so as to get the predicted load interval. The three steps of interval forecasting module are shown as:

**Step 1:** Data classification. The training set _train_ of load data is clustered into several classes by FCM clustering method. Assume that the data in each category follows the same normal distribution. Therefore, we can get some interval classes \(F_{1},F_{2},\cdots,F_{k}\). The mean value and variance of each category are calculated respectively to prepare for the interval construction next. **Step 2:** Load interval estimation. The confidence degree of each category interval is 95%. According to the mean and variance of each category data, the corresponding confidence interval is constructed. Different categories have different width of unified prediction interval. This process of constructing different adaptive intervals according to different data characteristics is also one of the innovations of this model. According to the testing set _test_ point prediction results in the point prediction module, identify the category F that each prediction value falls into.