Analysis of a Stochastic Energy Supply and Demand Model with Renewable Integration

Abstract

In this work, a stochastic energy supply-demand model with renewable integration is developed and analyzed. The basic nonlinear deterministic model describing the relationship among regional demand, external supply, energy imports, and renewable resource integration is extended to an Ito-type stochastic system that captures the uncertainties due to market volatility, climatic variation, policy interventions, and technical changes. Also, the noise structure is multiplicative, ensuring proportional fluctuations and preservation of nonnegativity of the state variables. Global existence, uniqueness of positive solutions, moment boundedness, and stochastic persistence are established rigorously. Furthermore, the deterministic system is analyzed, and stochastic stability is examined using matrix inequality criteria to guarantee almost sure exponential stability of the system in the stochastic setting. Among other results, stochastic perturbations significantly alter the effective system capacity compared to the deterministic case; however, under suitable parameter conditions, boundedness and stability cases are preserved. The Euler-Maruyama scheme is employed to perform numerical simulations to illustrate various dynamical behaviors and highlight the effects of uncertainty on system dynamics.The numerical reliability of the proposed model is further confirmed by additional numerical experiments via the Milstein scheme and parameter sensitivity analysis. Moreover, the results indicate that stochastic effects should be considered for capturing complex energy systems' behavior under uncertainty and its implications for renewable integration.