This paper presents a mathematical optimization framework for the strategic placement of quasi-dynamic wireless charging (QWC) stations within road networks to address the charging needs of battery electric buses (BEBs). This study evaluates two scenarios for powering the buses. In the first scenario, a grid-connected system is considered. The optimization aims to minimize annual costs related to capital, operation, and energy losses of the electric bus fleet. This involves determining the optimal locations for QWC stations, the length of power transmitters, and the corresponding battery capacities for the BEBs. Using MATLAB-based optimization tools Casadi and Yalmip, with solvers Bonmin and Fmincon, the optimal configuration includes a 13 kWh battery capacity and a 300 m power transmitter distributed across five bus stop areas. The second scenario employs a chance-constrained optimization approach for an isolated solar photovoltaic (PV) and battery energy storage system (BESS). This system is designed to reliably meet the BEBs' energy requirements throughout the day, considering different seasonal data (winter, summer, all seasons/year-round). The optimization results for the PV and BESS capacities vary with the seasons: 394.247 kW and 2012.6 kWh using summer data, 1762.1 kW and 2738.2 kWh using winter data, and 1610.8 kW and 2741.9 kWh using year-round data. Additionally, the paper examines the impact of varying bus fleet sizes on the optimal battery size and power transmitter combination using a real-world example of the bus route between Khalifa City and Abu Dhabi Downtown in the UAE. The findings suggest that larger batteries with fewer or no charging stations are more economical for smaller fleets. Conversely, as the fleet size increases, a combination of smaller battery sizes and a greater number (and length) of QWC (power transmitters) becomes more cost-effective. This research offers significant insights into the efficient deployment of QWC stations and the integration of renewable energy and energy storage for sustainable urban electric bus networks. The proposed optimization models provide a systematic approach to designing and operating charging infrastructure, contributing to sustainable urban transportation systems. Moreover, the study highlights the influence of seasonal data on PV system sizing and costs.
Keywords: Chance-constrained optimization; Electric vehicles; Optimal siting; Quasi-dynamic wireless charging.
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