A promising design of a Space-Based Solar Power (SBSP) system for a lunar demonstration mission has been developed. SBSP technology can offer a continuous power supply using solar energy and wireless power transmission, addressing challenges like the 15-day lunar night. The proposed concept employs Laser Power Transmission (LPT) due to its compact design and high power density, delivering 3 kW from a Frozen Polar Low Lunar Orbit to a surface receiver. The satellite integrates deployable MegaFlex solar arrays, a custom LPT subsystem, and robust power management, thermal control, and communication systems. A system sizing model estimates a total mass of 4057.43 kg and a solar array output of 15.8 kW. The scalable and redundant architecture could support future operations up to 45 kW.