Probabilistic multi objective planning of battery storage and mixed distributed generation for reliable and efficient grid connected distribution systems

This study addresses the challenge of optimally planning distributed energy resources in grid-connected distribution systems under significant uncertainty in renewable generation and load demand. As high penetration of wind, solar PV, and battery energy storage systems (BESS) increases variability and operational risks, developing a robust long-term planning framework is essential for ensuring economic efficiency, technical reliability, and environmental sustainability. To tackle this, a stochastic mixed-integer nonlinear programming (MINLP) model is proposed, incorporating probabilistic representations of wind speed, solar irradiance, load profiles, and market energy prices using Weibull, lognormal, and normal distributions. Monte Carlo Simulation combined with a Backward Reduction Algorithm is used to generate representative scenarios. A hybrid evolutionary optimisation approach—integrating Genetic Algorithm (GA), Particle Swarm Optimisation (PSO), and Differential Evolution (DE)—is developed to solve the multi-objective problem. The framework simultaneously minimises cost, emissions, power losses, voltage deviation, and enhances reliability and voltage stability. Application to the IEEE 33-bus and 118-bus systems demonstrates substantial improvements: cost reductions up to 19.3%, emission reduction up to 80.9%, and significant improvements in network losses, voltage profiles, and reliability indices. The results confirm that coordinated planning of dispatchable DGs, renewable DGs, and BESS yields a resilient, economical, and sustainable solution for future smart distribution networks.