Very short-term probabilistic and scenario-based forecasting of solar irradiance using Markov-chain mixture distribution modeling

Abstract

This study investigates probabilistic and scenario-based forecasting of solar irradiance with Markov-chain mixture (MCM) distribution modeling, Persistence Ensemble (PeEn) and Climatology. Forecasts from MCM models with uniform and empirical emission distribution settings, respectively, are compared with PeEn and Climatology in terms of probabilistic forecasting performance. The MCM model is also extended with scenario generation capabilities and compared to scenario generation of the Climatology by means of Monte Carlo sampling. Forecasts were made on minute resolution normalized solar irradiance, i.e. the clear-sky index, from National Renewable Energy Laboratory and Swedish Meteorological and Hydrological Institute for two climatic regions: Oahu, Hawaii, USA and Norrköping, Sweden, respectively. Results show that the MCM models are neither necessarily the most reliable, nor the sharpest in terms of Prediction Normalized Average Width (PINAW), but they are the most accurate in terms of Continuous Ranked Probability Score (CRPS). MCM models with uniform and empirical emission distribution settings perform similar in the tested probabilistic forecasting metrics. In terms of scenario forecasting, MCM models with $N=30$ perform similar in probability distribution goodness-of-fit and autocorrelation Mean Absolute Error (MAE) and superior to $N=2$ and $N=10$ number of states. Mathematically, forecasts from the MCM model with empirical distribution setting are shown to correspond to PeEn and Climatology forecasts given special settings of the MCM model. Based on the conclusions, the suggestion is to use the MCM scenario forecast generator with uniform emission distribution setting as benchmark for scenario forecasts of very short-term solar irradiance.