Analyzing the Performance of Linear and Nonlinear Multi -Period Optimal Power Flow Models for Active Distribution Networks

With the rapid integration of grid edge devices (GEDs) such as batteries and solar photovoltaics, multi-period optimal power flow (MPOPF) frameworks have become essential for managing modern electricity distribution networks (EDNs). Traditional MPOPF formulations based on nonlinear branch flow models yield non-convex programming (NCP) problems that suffer from slow convergence and high computational demands. Linear programming (LP)-based approaches, while computation-ally efficient, introduce an optimality gap. Despite their promise, the impact of EDN size and GED penetration on this gap remains underexplored. In this paper, we develop and compare MPOPF models using both NCP (via a nonlinear branch flow model) and LP (using the LinDistFlow approximation) formulations. Our evaluation on a small (10-bus) and a medium (IEEE-123-bus) system under varying GED deployments-validated through OpenDSS simulations-reveals that although the LP-based methods incur an increasing optimality gap with larger system sizes and higher battery penetration, they achieve near-optimal performance in terms of the primary cost objective. However, significant discrepancies in other decision variables, such as reactive power dispatch and substation power predictions, warrant greater caution when employing the LinDistFlow model in practice.