The space-based solar power transmission from satellites has been a long-term project and is finally planned to be realized in a few decades. Space-terrestrial heterogeneous networks can feed solar power from the space to large rectennas (rectifying antennas) located in unpopulated areas, and then distribute to each user through terrestrial power line or wireless links. In this paper, as a step stone for implementing economically feasible end-to-end solar power transmission from satellites to end-users, we focus on the modeling of solar power relays from satellites to terrestrial power grids via ground rectennas for space-terrestrial heterogeneous networks. We survey the mathematical model of the terrestrial smart grid power system, apply it to the satellite for space-based solar power transmission, and model solar power relays for ultimate integration of space power satellite and Earth smart grid. Compared to the terrestrial power delivery system, we identify distinct features for space power transmission, and formulate a joint problem of making decisions on solar power generation and resource allocation for rectenna feed.