How to size a home battery
A question that frequently arises is home much energy storage does one need?
Motivation
The main motivation for battery storage is that the utility companies are increasingly changing the way they meter your electricity. Originally they used to meter it 1:1, that is they charged you the same amount that they paid you. That is if you paid them $0.50 for a kwh of power, then they paid you $0.50 when your solar system put a kwh of electricity back onto the grid.
But the utilities quickly realized that was a losing game for them for several reasons. Firstly, a utility can buy power from large provoders at a much cheaper "whole sale" rate and sell it at the "retail rate" for individuals. Secondly, the demand for power fluctuates over the course of the day, and a utility is primarily concerned with matching supply to demand in order to avoide brown or in the worst case scenario, black outs when demand far exceeds supply.
The problem is that power from solar is only generated during the day, starting in the morning, building to a peak at mid-day and then gradually decreating to nothing in the evening. This leads to the infamous "duck curve" where peak demand happens in the evening precisely when generation from solar is decreasing. As a result the utilities decided to add "demand" charges for Time of Use (TOU) rates.
Arbitration
As a result, when utility TOU charges increasingly become more wide spread, consumers can use batteries for arbitrage. Basically meaning that they store electricity during the day when its cheap, and then use the power from those batteries in the evening when getting it from the utlity would be very expensive.