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As for lunar, solar seems to be perfect – there is no atmosphere, no wind, no rain, no clouds, thus constant perfect sunshine. It would be possible to utilise arrays of photovoltaic cells and transmit the energy as microwaves. The paper provides a fun figure – the lunar surface receives 12 trillion kW solar energy in 1 year, which is 25,000 times energy produced on Earth. Nuclear fusion is also an option, but utilising Helium-3 as a viable future energy source (with deuterium).
In conclusion, space energy can supplement both earth energy and also power space missions. Research poses possibilities for synergies for the different power directions. Breakthrough technologies are useful not only for that specific power direction, but for all space missions.
Source:
Zhang, T., Li, Y., Chen, Y., Feng, X., Zhu, X., Chen, Z., Yao, J., Zheng, Y., Cai, J., Song, H., & Sun, S. (2021). Review on space energy. Applied Energy, 292, 116896. https://doi.org/10.1016/j.apenergy.2021.116896