Caution is needed applying the MPT to generators! Imagine the electricity supply network was simplified to a single alternator capable of supplying 57GW at 230V and a single load. The generator “impedance” would be a small fraction of an ohm. If you “matched” that with the load a huge current would flow, the voltage on the load would be 115V, half the power would be dissipated in the load – i.e. 28.5GW – and half in the internal impedance of the generator. Only 50% efficient! In reality for power supply systems one aims for a very small internal impedance and minimum voltage drop on load. In the case of the dynamo the power limit shouldn’t come from the internal resistance but the capacity of the prime mover.
Ah, but isn’t the joy of AC that impedances can be matched with transformers?
John is right except there’s no need for a big generator to match at 230V. It can be manufactured to produce the highest voltage that doesn’t zap its internal insulation, say 20kV, and then immediately transformed up to 200kV, 500kV, or more for distribution. The impedance of the source can be almost anything. At the other end, the voltage can be transformed down to match the load. 230Vac 100A in my home (2.3ohms), or 1.2V 10000A in an industrial electrolyser (0.00012ohms).
Do Electrical Engineers calculate impedance? At 50Hz I’d guess the power network can almost be considered entirely resistive. If so, then transformers simply apply voltage ratios, and provided they don’t overheat, all is well. Guessing though, because I’ve no idea how much capacitance and inductance are in a power system. And there are lots of wires in the air, bundled in cables, and wound in iron-cored coils.
Radio Engineers can’t avoid calculating impedance because otherwise nothing works properly. One thing that surprised me about Model Engineering is how little maths is needed compared with amateur radio, or horology.
Dave