Several space organizations have been planning to establish a permanent, manned base on the Moon in recent years. Such an installation demands a highly reliable electrical power system (EPS) to supply life support systems and scientific equipment and operate autonomously in a fully self-sufficient manner. This paper explores various technologies available for power generation, storage, and distribution for space microgrids on the Moon. Several factors affecting the cost and mass of the space missions are introduced and analysed to provide a comprehensive comparison among the available solutions. Besides, given the effect of base location on the design of a lunar electrical power system and the mission cost, various lunar sites are introduced and discussed. Finally, the control system requirements for the reliable and autonomous operation of space microgrids on the Moon are presented. The study is complemented by discussing promising future technological solutions that could be applied upon a lunar microgrid.