I'm an electrical apprentice, just studying electrotechnology. I know this doesn't really have anything to do with my trade and that I don't need to understand, but I'm curious as to how a change in frequency will affect power, or if it affects power at all, or if I'm on the wrong track completely. What does a change in frequency do to current, etc.?
To keep it very simple, if you have a 1000 watt heater intended to operate on 120 V 60 Hz power, it will produce the same heat at 50 Hz or 400 Hz, provided the voltage remains at 120 V. When you get into motors, transformers, and other non-resistive loads, the power may vary with frequency.
It can certainly affect power. Reactive elements will take more or less (reactive) power with changes in frequency. Many lossy components will have losses that increase with frequency (hysteresis losses, skin and proximity effects). It really depends on the load, and the frequency range you are considering. If you have specific examples we can comment further.
In terms of power frequency, the core excitation current reduces for increasing f so turns are adjusted to yield capacity whatever core steel is chosen, typically 1.5T to 2T. Slightly less core mass in kW/kg with rising f for power transmission.
In terms of eddy current losses , they increase with f for same power density slightly.
Partial Discharge seems to be more affected by dv/dt excitation which is derived from V and f and insulation quality and contamination from voids or particles in solids and liquids.
For long haul DC is best.
There is no advantage to use 50 or 60Hz power systems in general but specific components may have preference.
But Aircraft prefer much higher f, for lower mass generators.