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Assuming you are referring to the electrical power system:
Weight
Light weight inductor cores on alternators, solenoids, Transformers etc. The compromise is 400c/s AC 3phase.
Low weight conductors, minimal volts drop over distance, compromise 115volts
Stability
115v 400c/s within mechanical feasibility of reliable constant speed drives for alternators. 12pole/6000rpm.
Versatility
For DC systems 24v is the minimum for acceptable volts drop over wiring distances encountered. Batteries can be small and light. Some compatibility and backup capability with the 26v 400c/s instrument systems.
Safety
Voltages within safety capability of insulation exposed to a wide environmental range of temperature, humidity, vibration, and aircraft fluids. All safety systems able to detect and trip 'out of range' voltage, current, frequency, and earth faults.
Terminations, plugs and sockets have to be selected for the aircraft environment and to consider security and corrosion.
It is a system that has evolved from years of learning from experience.

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Why is 400 Hz used as an aircraft power supply?

Although most all utility power in the world use either 50 Hz or 60 Hz, 400 Hz power systems are typically used in large aircraft. The reason for the higher frequency is that most of the power system parts, especially the 400 Hz alternator and 400 Hz motors are much smaller compared with similar 60 Hz equipment of the same power rating. In aircraft, every pound saved in equipment weight, equates to about a five pound savings in gross weight during flight. When equipment weight is reduced, both airframe structure and fuel load can also be reduced. As flux is inversely proportional to speed and speed is proportional to frequency Higher the frequency lesser the flux required.Lesser the flux,lesser the core size.Lesser the size means less weight.Hence the pay load can be increased. Also frequency above 400 hz not taken because the radiation takes place beyond this.

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