Machine Learning-Based Approach to Nonlinear Functional Data Analysis for Photovoltaic Power Forecasting

Despite high-resolution data being available and providing more comprehensive information, existing forecast models fail to utilize the available high-resolution data due to the lack of methods for processing such type of data and thus use the average values over a specific time interval instead as input, resulting in a loss of information. Functional Data Analysis (FDA) offers a pathway to modelling such data by fitting discrete data into functional curves. However, the existing statistics-based FDA methods lack nonlinear functional modelling capabilities as the explicit expression of the mapping between predictor and response in infinite function space is unknown. Further, there is little research using FDA for photovoltaic power forecasting. For these reasons, this paper proposes a novel machine learning-based approach to nonlinear FDA and introduces this approach as a new method for Day Ahead Photovoltaic Power Forecasting (PVPF). The proposed method utilizes machine learning techniques to reveal the nonlinear relationship between input and output without searching for the explicit expression. Moreover, the difficulty of traditional machine learning when dealing with infinite-dimensional data is avoided by mapping the prediction task from infinite functional space into finite parameter space and learning the prediction model in the parameter space. Based on a publicly available data set from NREL Solar Radiation Research Laboratory, the effectiveness and improved accuracy of the proposed method are evaluated and illustrated compared to currently used machine learning approaches, including the state-of-the-art Long-Short-Term Memory approach.