Analysis and Impact of Data-Driven Hourly Probability Distribution Functions in Microgrids Day-Ahead Energy Management under Uncertainties: A Case Study in New South Wales, Australia

Microgrids are critical for achieving smart grid objectives, enhancing reliability, resilience, and supplying under-served areas. However, day-ahead scheduling of generating resources remains challenging due to uncertainties inherent in renewable energy systems. Although stochastic optimization addresses uncertainties, conventional probability distribution functions (PDFs) used in scenario generation methods may yield sub-optimal outcomes. This study proposes an improved stochastic optimization method that selects hourly unique PDFs via best-fit criteria derived from forecasting errors. Forecasts for solar irradiance, load demand, and electricity prices were generated using an XGBoost model trained on data from the Australian Electricity Market Operator (2013–2020). Forecast errors were evaluated annually and hourly, testing various PDFs using Kolmogorov-Smirnov (KS) and Cramer Von-Mises (CvM) goodness-of-fit tests. Unit commitment (UC) and economic dispatch (ED) were then performed using Monte Carlo simulation, with 1000 scenarios reduced to 10 using the backward reduction method (BRM). To benchmark the proposed method, a robust optimization model with an ellipsoidal uncertainty set was implemented. Results showed that the proposed stochastic approach reduced total costs by 9%–39% compared to conventional fixed PDF selections. Compared to the optimal stochastic case, the robust approach incurred a moderate 13% cost overhead but outperformed some other traditional PDF cases. This confirms that while robust optimization offers conservative protection against uncertainty, the proposed data-driven unique PDF selection method delivers better economic performance, making it a valuable tool for microgrid operators and policymakers.