## 1 Introduction
As a new feedforward neural network, extreme learning machine (ELM), which overcome the defects of traditional BPNN and SVM, has been applied in a number of prediction areas and has obtained more accurate prediction results [16; 17; 18] for reducing the risk of falling into the local optimality. Since ELM has poor predict stability because of the characteristics of random initialization of inputting weight and hidden layer offset, [PERSON] et al. [19] introduced a kernel extreme learning machine (KELM) algorithm, which overcomes the weakness of poor stability of ELM and improves the learning accuracy of the algorithm. However, the performance of KELM is easily affected by the penalty coefficient \(C\) and the kernel parameter \(\sigma\), therefore KELM needs to be solved by intelligent algorithms for parameter optimization with regard to the problems of difficult selection for these two parameters. The inspiration of fireworks algorithm comes from the explosion of air fireworks, which is a new type of swarm intelligence algorithm with global optimization solution of explosive search mechanism, shows great accuracy and high efficiency when solving complex optimization problems [20]. Thus, FWA to be selected for optimizing the parameters of KELM in this paper. It is worth noting that the load forecasting of DES has a number of influence factors if all load factors are employed as the input characteristics of the prediction method, there will be a great number of factors due to the strong coupling, non-linearity, and information redundancy among factors [21]. Therefore, it is also important to reduce the dimension of input features. Principal component analysis (PCA) has a preferable treatment effect as a multivariate statistical method to synthesize multiple variables into a few variables, when it is dealing with various indicators with strong linear relationships [22]. On the other hand, factors that affect load changes in distributed energy systems, such as humidity, cloudiness, barometric pressure, and temperature, are non-linear in most cases [23]. However, as a linear method, PCA, which cannot obtain the high-order characteristics of the data and ignores the nonlinear information of the data while reducing the dimension. As a result, this paper uses kernel principal component analysis (KPCA) [24] to map the initial input variables to the high-dimensional feature space through nonlinear transformation and reduce the dimensionality of the input variables while preserving nonlinear information between the input variables. In summary, this study preliminarily established the feature set of candidate influence factors of distributed energy system load and builds a distributed energy system load prediction model based on KPCA and FWA algorithm to optimize KELM. The other parts of this article are arranged as follows. The next part introduces the algorithm of this article, including kernel principal component analysis, FWA algorithm and KELM model, and constructs a complete prediction framework. The third part selects the practical cases to verify the effectiveness and stability of the proposed method. The fourth part is the conclusion.