RE "...All of the peak demand supplied from batteries...." This is a very good start. My question is how do the batteries go , if there is 1 - N days of cloudy

RE "...All of the peak demand supplied from batteries...." This is a very good start. My question is how do the batteries go , if there is 1 - N days of cloudy weather? Can the batteries supply the peak for more than one day? Is there ( or where would they go ) transmission lines to bring in the needed peak supply from other storage (battery / pumped hydro ) areas? Another step would be to include days of peak electricity demand, which in my country occurs in cold weather ( heaters) and very hot weather ( air conditioner's ) OR is there demand limits like in Spain demand limit for some houses is around 3KW (YUKS)