Power cable hot and neutral conductors are carrying the same current in opposite directions being, in a sense, "balanced". Twisting them will make them exposed to external fields evenly causing cancellation. Same goes for radiated field from the cable. This works perfect as long as pitch of the twist is shorter than wavelength of the offending signal (4.9" for 2.4GHz). This makes practically no noise induction in ground wire. Twisting also increases capacitance (not important) and reduces inductance (important).
As for balanced circuitry - it does not reduce normal mode powerline harmonics the same way as balanced audio amplifier does not remove harmonics of the music - it only reduces harmonics produced by amplifier itself and only even harmonics (does nothing to odd harmonics). Balanced input supposed to reduce common mode noise. Power supply transformer does that already. Shield, in instrumentation/measurement amps cables, is usually driven with common mode input signal. This scheme eliminates capacitance between shield and signal wires for common mode noise reducing greatly capacitive pick-up. It works quite well, but I’m not sure if it makes any audible difference with power cables.
As for balanced circuitry - it does not reduce normal mode powerline harmonics the same way as balanced audio amplifier does not remove harmonics of the music - it only reduces harmonics produced by amplifier itself and only even harmonics (does nothing to odd harmonics). Balanced input supposed to reduce common mode noise. Power supply transformer does that already. Shield, in instrumentation/measurement amps cables, is usually driven with common mode input signal. This scheme eliminates capacitance between shield and signal wires for common mode noise reducing greatly capacitive pick-up. It works quite well, but I’m not sure if it makes any audible difference with power cables.