Assuming:
AC 18
To hit +13
Base Damage+6 (+9 two handed)
7th level
Full attack action.
Great Axe d12+9 avg 15.5 per hit
first swing 80% hit x 15.5
Second swing 55% x 15.5
Expected damage per round = 20.95 or ~21
Your power Attack example with TWF
First swing 50%x13.5
Off hand swing 50% x9.5
Second swing 25%x13.5
Expected damage per round = ~16 hp
If you ignore to-hit chance, or in your case make an assumption that PA is used to reach a certain to hit chance, then you skew the data. You have started from a bad analysis method.
PA is only usefull when the odds of hitting (sides on d20 that make a hit, in this case 16 for the greataxe or 14 for the swords and 5 less for each iterative attack) is GREATER THAN the expected damage per hit. With the greataxe, with 15.5 damage and 16 sides hitting, there is NO BENEFIT to using PA and using anything like 5 PA shift actually lowers your expected damage.
First swing on the longsword makes it beneficial to use no power attack either, as 14 sides vs 13.5 damage is no real difference. The second swing makes use of power attack actually hurt the damage.
As for magic, buffs and all those things you want to leave out, its very simple... they affect both the to hit and the per hit damage. If they raise to-hit more than per hit damage, they encourage power attack. That is of course rare. If they raise per hit damage more than to-hit, they make PA a worse idea. So in most cases, they will either make noe difference in how much PA you should use OR they will likely make it less beneficial.
Power attack will be most beneficial for characters with lower damage per hit and good attack bonuses. Probably the optimum case would be a fighter type who uses expertise (say with a 22 dex instead of a 22 strength) but it wont in most cases catch him up to the guy who just goes normal bash 'em with the greataxe.
FYI, for determining best PA allocation for a given swing...
Best Shift = (H-D)/2
Best shift is the amount to shift from hit to damage to produce the best results in expected damage.
H = chance of hitting expressed as sides on a d20 that are successful.
D = average damage per hit assuming NO use of PA.
So if you hit 16 times in 20 and do 10 damage average your best result would be to PA 3 making it 13 to hit and 13 damage. (Yes, for best results equalize the damage and chances to hit.)
If you have multiple swings, then you have to run the calculation for both and then make an estimate... whats good for one wont be good for the other. You might want to split the difference and run PA at 2 below the optimal first swing.
Again, while it is more likely that PA can be used by a TWF than a THW, since strength bonus per hit is lowered, its rather unlikely that the TWf will be able to use PA to do more than catch up, if he can do that.
Simplicity said:
Now, suppose I'm a seventh level fighter with a STR of 22, and a non-magical greataxe (I'm leaving magic out of it to make the
numbers easier). And let's say you want a 50% chance of hitting an AC of 18.
My Strength gives me a +6 to hit, my BAB gives me a +7.
Thus, I add +13 to whatever I roll, so I need to roll a 5 to get
an 18. If I want a 50% chance to hit 18, I can afford to use +5 on my power attack with a single weapon.
With a greataxe then I've got
1d12(axe) + 9(str) + 5 (powerattack) = 20.5.
If I want the same chances with each of two wielded weapons (say a long sword and a short sword). Then I get
1d8(longsword) + 6(Str) + 3(powerattack) = 13.5 dmg
1d6(shortsword) + 3(str) + 3(powerattack) = 9.5 dmg