Fast Fourier Transform (FFT) of power consumption signals
If you take two raw signals and subtract, you will get a value that could be used to indicate the difference between the signals.

However, if you do the FFT you will lots of signal information, perhaps the power line is very noisy on one signal line. This would affect power consumption but may not be the component you wish to measure.

You could do multiple plots, say at 50Hz, 40Hz, etc. and compare.

FFT gives more signal detail than Euclidean distance.