The global proliferation of plug-in electric vehicles (PEVs) poses a major challenge for current and future distribution systems. If uncoordinated, their charging process may cause congestion on both network transformers and feeders, resulting in overheating, deterioration, protection triggering and eventual risk of failure, seriously compromising the stability and reliability of the grid. To mitigate such impacts and increase their hosting capacity in radial distribution systems, the present study compares the levels of effectiveness and performances of three alternative centralized thermal management formulations for a real-time agent-based charge control algorithm that aims to minimize the total impact upon car owners. A linear formulation and a convex formulation of the optimization problem are presented and solved respectively by means of integer linear programming and a genetic algorithm. The obtained results are then compared, in terms of their total impact on the end-users and overall performance, with those of the current heuristic implementation of the algorithm. All implementations were tested using a simulation environment considering multiple vehicle penetration and base load levels, and equipment modeled after commercially available charging stations and vehicles. Results show how faster resolution times are achieved by the heuristic implementation, but no significant differences between formulations exist in terms of network management and end-user impact. Every vehicle reached its maximum charge level while all thermal impacts were mitigated for all considered scenarios. The most demanding scenario showcased over a 30% reduction in the peak load for all thermal variants.
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