Enhancing optimization accuracy in power systems: Investigating correlation effects on objective function values

This study addresses the critical yet often overlooked aspect of incorporating correlations among input stochastic variables in power system planning and scheduling optimization. While existing literature has extensively focused on uncertainty modelling, there remains a gap in fully assessing the consequences of disregarding correlations on objective function values across different power network sizes. To bridge this gap, we utilize Monte Carlo simulation with Cholesky decomposition, alongside Quasi-Monte Carlo sampling and Latin Hypercube Sampling, to effectively model uncertainty and capture correlation coefficients among input variables, including wind, solar photovoltaic, and load power. The most efficient technique is then integrated into our optimization model, which is applied to small, medium, and large power network models. Our proposed optimization model addresses conflicting objectives using a hybrid NSGAII-MOPSO, aiming to simultaneously minimize total operational cost, power loss, and voltage deviation. By implementing this model on selected power networks and comparing outcomes between cases with independent and correlated variables, we rigorously assess discrepancies in objective function values. We visualize and analyze these errors across systems of varying sizes, shedding light on the impact of neglecting variable correlations. Notably, the maximum discrepancies are observed at $3.26/h, $40.66/h, and $2754.04/h for the IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus systems, respectively. Crucially, as the system size increases, so does the magnitude of these differences, underlining the escalating impact of neglecting variable correlations on optimization outcomes. We stress the importance of integrating such considerations into future planning and operational strategies to mitigate errors and enhance decision-making processes.