TIL, thanks! I am not really involved in powerplay / BGS. Thought every system controlled by a Fed faction would have a powerplay attached to it, etc.
The BGS and Powerplay are mostly independent of each other with the interactions being indirect. (As a result, Sirius and Yuri Grom, two of the three Powers with identifiable BGS factions as well, have their Power space nowhere near their BGS space)
- Powerplay spheres extend 15 LY out from each control system, except where they intersect with another power's sphere where they cancel out. A Powerplay control system doesn't have to have a matching BGS control faction and the much greater number of exploited systems in the 15LY bubble certainly don't.
- there is some interaction in that the Powerplay spheres are easier for the Power to maintain if the government types of the controlling factions are compatible with the power. This is based on the government type - Democracy, Dictatorship, etc. - rather than the superpower allegiance, and for Aisling Duval and Zachary Hudson this leads to the rather silly situation that their control spheres are strongest when they
don't contain any factions of their superpower! This is where most of the real interaction between the two systems comes from as most Powers have BGS teams trying to keep the BGS environment favourable to them, and large enough to win fights against the average player-backed faction.
- there was a proposal as part of Sandro's "Powerplay suggestions" thread to make "same superpower" factions automatically count as positive for a Power. This would be sensible but like the rest of that suggestions thread nothing has been heard for several years about if or when it might be implemented.
- in theory some of the Power effects that they apply to exploited or controlled systems can make it easier or harder for particular BGS factions to achieve or retain control ... the effect is pretty marginal and certainly not cleanly aligned with same-superpower relationships.