<FactionPowerProductionPointMultiplier>0.3</FactionPowerProductionPointMultiplier>
<FactionPowerBattleRatingMultiplier>0.002</FactionPowerBattleRatingMultiplier>
<FactionPowerTreasuryMultiplier>0.001</FactionPowerTreasuryMultiplier>
<FactionPowerInfluenceMultiplier>0.1</FactionPowerInfluenceMultiplier>
<FactionPowerUnlockedTechsMultiplier>0.25</FactionPowerUnlockedTechsMultiplier>
<FactionPowerUnlockedCultureMultiplier>0.1</FactionPowerUnlockedCultureMultiplier>
For determining power scores, this is the relevant bits of code in globaldefs.xml. In each case, it's a flat multiplier for score - every 1 point of production gives 0.3 power score; every 1 point of battle rating gives 0.002 power etc.
Production appears largely broken, since it uses the final output score. This means it varies wildly depending on your slider settings. Late-game, you can increase your power score by several thousand points simply by fiddling with the output circle; and I've often noticed my score going up by anything upto 50% when I go bankrupt and the game throws everything into cash generation, which implies that treasury multiplier is too low - every point of income is worth 30 times as much as cash you already have. Battle Rating multiplier is quite good; I think it uses some code from AIdefs to determine initial battle rating. Influence and ideology likewise appear to do a decent job. Tech might be a little undervalued (I think it grants 25% of base tech cost, which is too high early on and too low later).
I think ultimately, there needs to be some kind of measure of social development added separately from production, and production should simply use raw prod rather than eventual output. We have to get away from a situation where just shifting your slider settings can cause such wild swings in total power rating. Presently, if I have a planet with 1000% research bonus currently set to manufacturing (say, to finish some upgrades), it's power rating sinks down to (basically population+5)*0.3. When I switch it to produce research, it suddenly becomes ((population+5)*11)*0.3. Let's illustrate that with a real game example:
25 pop planet with 1000% research bonus set to manufacturing power score = 9.
25 pop planet with 1000% research bonus set to research power score = 99.
90% of the planet's potential is completely ignored while it's set to non-optimal settings. If, instead, we used raw production for score and then gave, say, 0.1 per 1% bonus to manu, research etc, then the score becomes pretty much fixed - you get 9 from the raw production and 100 from the bonus, even if you're not making use of it. The score loss from maintaining 'bad' slider settings comes from not getting the score from techs as quickly.