The adoption of electric aircraft (EA) offers notable environmental advantages by mitigating greenhouse gas emissions and enhancing regional accessibility through reduced operational costs. Despite these benefits, EA faces significant challenges, partly in achieving practical operational ranges and developing robust airport charging infrastructures. The infrastructure challenge is compounded by the need for rapid turnaround times (TAT) in regional aviation, requiring high-power charging solutions above 1 MW. This paper explores various topologies for EA power supply systems and discusses pros and cons with those. Furthermore, an optimization model is developed using quadratic programming (QP) to allocate charging power among multiple aircraft, ensuring efficient and reliable operations under different system configurations. Simulations evaluate the performance of these configurations, highlighting the impact of grid power capacity, dimensioning of battery energy storage systems (BESS), and number of charging stands on system feasibility. The findings in this paper provide a foundational framework for designing airport infrastructures capable of supporting a growing demand for electric aviation, ensuring efficient power management and minimal operational disruptions.