Gene from Audioholics has a video on the effect of low voltages on power amplifiers. If the voltage gets low enough it will affect the output of your amplifier if you play it loud. IIRC he was talking about voltages of around 100 volts or even lower.
Amir from ASR has also discussed the effect of low voltages in a video of a power conditioner (I believe it was the review of the PSA P12). He stated that audio gear is designed to operate on a wide voltage range and that it is very unlikely that you could damage your gear from operating it at low voltages. If the voltage gets too low the unit will malfunction or shut down but it would be rare for any damage to occur.