The intensity of sunlight becomes lower when weather conditions change, which affects whether a solar-electric vehicle can be driven on a shady road. The power delivered by solar cells can be vary depending on the amount of shade. As a result, the battery system is often used to compensate for variations in the power delivered by solar cells. Therefore, studies of power control systems for solar-electric vehicles are required. In this paper, mathematical models for such a power control system are studied and important variables are considered. Simulation and test results show that the mathematical model and actual designs developed here would be effective when used with solar-electric vehicles.