In something like a regular household, how much energy consumed is transient power vs steady state and what kind of frequency distribution does it have, roughly? I imagine the vast bulk of the energy being in the lower frequencies but have been unable to find any information backing that up. Aside from curiosity, the reason I ask is I am currently working on an Amp hour monitoring project for off-grid systems using coulomb counting (measuring voltage drop across a current shunt) and filtering that with a low pass filter before ADC, just wondering if this would cause an inaccuracy worth worrying about. Thanks.
Transients, by definition, are very short period. And (in the context of the vague scenario you describe) they're the effect of either infrequent load switching, or highly periodic 'switch-mode' noise that may result from use of a DC-to-AC inverter, for example, or an actual load drawing non-DC or non-sinusoidal current. The former can probably be ignored without a second thought, due to the comparative rarity of them.
As for highly periodic 'switching noise', well, "it depends" on the specifics of the equipment (inverter?) & load in use. If it were me, I'd want to see at least a voltage waveform, & ideally a current waveform, with the system under various loads, to "see if you have a problem" that needs to be accounted for in your measurements, or not. But my gut feeling is that the energy in any such 'noise' is probably going to at least 2, probably more like 3- orders of magnitude less (one hundredth or one thousandth) energy than the actual steady-state (DC or sinusoidal) load - if that guess is actually the case, then you can make a call as to whether that matters to your desired measurement accuracy. In a "regular household", I'd expect not :)