A novel combination of Mycielski–Markov, regime switching and jump diffusion models for solar energy. (1st November 2021) - Song, Xiaodong; Johnson, Paul; Duck, Peter
Abstract: With renewable energy sources growing, solar power generation is becoming ever more popular around the world, so forecasting and scenario analysis of Solar Photovoltaic production is beneficial for grid operators and investors. In this paper, we introduce a novel combination of a Mycielski–Markov model, standard regime switching, and jump diffusion models to generate 1-minute Global Horizontal Irradiance time series over any time scale. It can simulate different scenarios of solar irradiance in the future after being trained on empirical data. We verify our model using statistical tests to compare our simulations with those from an observed time-series in Mauritius. The resulting model is able to generate simulations retaining the statistical properties of the data. Further, we find the proposed calibration process to be robust, and identified that splitting the day into 16 periods to be perfect balance to counter overfitting. The proposed model has the potential to better understand the effects of including large scale Solar Photovoltaic generation into an energy network, value future investments, or even allow for a cost–benefit analysis of subsidies. Highlights: Novel combination of regime switching with jump diffusion equation. Calibrates stochastic regime switching models using real data with clustering. Uses Mycielski algorithm with regime switching model for detailed scenarios. Can simulate minute by minute solar irradiance over days, months or even years. Simulations are shown to retain statistical properties of original data.