Simplified Implementation for Stochastic Production Simulation in Power Systems (Featuring Convolution, Cumulant, and Equivalent Energy Function Methods)

This is a streamlined program designed for stochastic production simulation in power systems, incorporating three fundamental methodologies: conventional convolution method, cumulant method, and equivalent energy function method. These approaches are essential for estimating uncertainties in power system operations and play critical roles in reliability analysis. The conventional convolution method serves as a foundational probability calculation technique, where code implementations typically involve discretizing probability density functions and performing sequential convolution operations to derive new probability distributions. The cumulant method employs statistical techniques based on probability characteristics of stochastic processes; algorithm implementations often leverage Fast Fourier Transform (FFT) to efficiently compute cumulant properties and reconstruct distributions. The equivalent energy function method transforms power system states into equivalent energy values, requiring state enumeration algorithms and load duration curve processing in practical coding. While these methods differ in mathematical foundations and computational approaches, they collectively enhance our capacity to model and analyze stochastic production challenges in modern power systems through distinct algorithmic implementations.