Optimal Placement of Distinct Size EV Charging Stations Using Exhaustive Search and BFS Load Flow
Uncoordinated electric vehicle (EV) charging can cause voltage violations and feeder overloading in radial distribution networks. To address this issue, this paper presents a four-stage exhaustive Backward-Forward Sweep (BFS) framework for the simultaneous optimal placement of three heterogeneous EV charging stations (50, 35, and 20 EVs) in the IEEE 33-bus system. A single-station screening first identifies voltage as the dominant constraint and selects Bus 2 as the strongest candidate location. Subsequently, all ${ }^{32} C_{3} \times 3!=29,760$ bus-triplet and charger-size combinations are evaluated under three simultaneity levels $(f=1.0,0.5,0.3)$, guaranteeing the true global optimum placement. The hosting-capacity analysis further determines the maximum EV penetration each bus can accommodate before exceeding voltage or thermal limits. The globally optimal configuration is obtained at Buses 2, 19, and 20, where the largest, medium, and smallest stations are assigned, respectively, to minimize $I^{2} R$ losses under all operating conditions. Results also show that smart charging significantly reduces feeder losses and increases feasible EV charging locations.