Regarding the number of valves/tubes in the power network computer: that's a good question! I don't know anything about what was inside the machine; whether there were any active components, or if it was all resistors, capacitors, and inductors.
Certainly some analog computers did have a lot of tubes. A Western Electric booklet notes that the Electrical Gun Director (which the company built to control Army artillery) contained more than 100 tubes. It's pretty impressive that so many tubes could perform reliably in a combat environment!
One of the specs for a power network analyzer was the number of simulated power sources, or "generators". Presumably the sources were three-phase for AC analyzers, but I don't know if they were actual rotating machines (probably motor-alternators), or if they were transformers or electronic oscillators.
