Here is a reason
1 Some equipment require a 3 phase supply ie motors
2 some use only one ie windscreen heaters
if you had single phase generators you would need 3 for 3 phase and then you would require a very complicated timing circuit to make sure the phases were the correct angle apart.You would also need to duplicate this system or triplicate it to get an airframe certified -the weight would be large .
So why not put a 3 phase genny on two engines and the apu that can supply all the power required and attach them to a constant speed drive that rotates the gen at a speed that gives you 400Hz depending on how many poles your choice of gen has because Freq= RPM x pairs of Poles
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60
So know we know how to gear the constant speed drive to get 400 Hz whilst varying engine RPM ( still not said why 400Hz stay with me)
Now that we have gone to the effort of making 400Hz we can do a couple of things .
We tell everyone that's the standard so all equip is made to operate at 400 Hz and when they ask Why? we can say it's so we can use 3 phase generators to save weight and simplify power production because 400 Hz means a complete cycle occur's every 1/400 th of a second therefore a pole passes a coil of the gennny and generates max voltage every 1/1200 second (remeber 3 phase so 3 coils.The less the coils again the greater the weight saving but three is the minimum ) we therefore get the 3 phases 120 degrees apart because the same pole passes the next coil another 1/1200 of a sec later and then the third and all our electrical need's right down to Coffee is done on each 360 degree cycle of the genny or 400 times a second.