Stochastic Load Modeling and Chance-Constrained Optimization of DG Placement and Sizing with Emission Incentives

This study proposes an optimization model for determining the placement and sizing of photovoltaic distributed generation (PV-DG) units in electrical distribution systems, accounting for load uncertainty and PV output variability. The model is formulated as a Mixed Integer Linear Programming (MILP) problem that incorporates stochastic load modeling based on normal distribution, and applies a chance-constrained programming approach to ensure supply reliability with a specified confidence level. Additionally, a clean energy-based incentive scheme is integrated into the objective function to enhance the economic feasibility of PV investments. Simulation results under various stochastic scenarios demonstrate that the system can reliably meet all load demands without supply deficits. PV contributions are particularly significant during daytime hours, leading to a noticeable reduction in overall system costs and carbon emissions. The proposed approach is proven effective in delivering adaptive, economical, and reliable solutions under distribution system uncertainty, while also highlighting the role of output-based incentives as a policy tool to accelerate the transition toward clean energy.