Solar irradiance forecasting based on direct explainable neural network

[Display omitted] •Direct explainable neural network is proposed for solar irradiance forecasting.•Ridge activation function is designed to extract the nonlinear features of DXNN.•A new training process, including pretraining for error estimation, is developed.•The input-output relationship of DXNN is actually a quadratic function.•DXNN has many advantages such as small model size and short training time. As the penetration of solar energy into electrical power and energy system expands in recent years over the world, accurate solar irradiance forecasting is becoming highly important. However, the existing solar irradiance forecasting methods based on soft-computing techniques are modeled as black-boxes, which are generally expressed by typical unreadable functions such as sigmoid. These functions are difficult to interpret the prediction results. Therefore, a new direct explainable neural network consisting of one input layer, two linear layers and one nonlinear layer, is innovatively proposed for solar irradiance forecasting. The proposed explainable neural network is basically a feed-forward neural network, using ridge function as the activation function to interpret the solar feature mapping. The training process of direct explainable neural network is designed based on back-propagation algorithm. It consists of data preprocessing, error-estimation pretraining and parameter fine-tuning. The main advantage of the proposed explainable neural network is that it can theoretically extract the nonlinear mapping features in solar irradiance, thereby providing a clear explanation of the relationship between the input and the output of the forecasting model. Solar irradiance samples from Lyon in France are used to simultaneously assess the forecasting accuracy and interpretability of the proposed explainable neural network. The experimental results demonstrate that direct explainable neural network not only exhibits a better prediction performance than traditional neural networks such as support vector regression, but also mathematically interprets how the input of the forecasting model affects the final prediction results, showing that the proposed explainable neural network has a high application potential in the real world.