[tzs]

That makes no sense whatsoever. Thought experiment:

Household #1 uses 7 kWh of electricity per day. They install a solar + battery system that produces 7 kWh per day, covering 100% of their use. This costs them $C, and the reduction in the amount of electricity they use from the grid will save them enough to break even in 5 years.

Household #2 uses 14 kWh of electricity per day. They also install a solar + battery system that produces 7 kWh per day, which covers 50% of their use. This costs them $C, and reduces the amount of electricity they use from the grid by 7 kWh per day, just like household #1. Therefore it should take them 5 years to break even, just like household #1.

Breakeven time is a function of cost and the amount your grid usage goes down. How much electricity from the grid you use if your solar system cannot supply 100% of your usage should be irrelevant to the payback time.