Forecasting the Power Generation of a Solar Power Plant Taking into Account the Statistical Characteristics of Meteorological Conditions

The integration of solar generation into national energy balances is associated with a wide range of technical, economic, and organizational challenges, the solution of which requires the adoption of innovative strategies for energy system management. The inherent variability of electricity production, driven by fluctuating climatic conditions, complicates system balancing processes and necessitates the reservation of capacities from conventional energy sources to ensure reliability. Under modern market conditions, the pricing of generated electricity is commonly based on day-ahead forecasts of day energy yield, which significantly affects the economic performance of solar power plants. Consequently, achieving high accuracy in day-ahead electricity production forecasting is a critical and highly relevant task. To address this challenge, a physico-statistical model has been developed, in which the analytical approximation of daily electricity generation is represented as a function of a random variable—cloud cover—modeled by a β-distribution. Analytical expressions were derived for calculating the mathematical expectation and variance of daily electricity generation as functions of the β-distribution parameters of cloudiness. The analytical approximation of daily generation deviates from the exact value, obtained through hourly integration, by an average of 3.9%. The relative forecasting error of electricity production, when using the mathematical expectation of cloudiness compared to the analytical approximation of daily generation, reaches 15.2%. The proposed forecasting method, based on a β-parametric cloudiness model, enhances the accuracy of day-ahead production forecasts, improves the economic efficiency of solar power plants, and contributes to strengthening the stability and reliability of power systems with a substantial share of solar generation.