Peak demand reduction means using stored power during the expensive early-evening window instead of drawing from the grid. This lowers your bill and eases pressure on the network.
Energy arbitrage means charging the battery when electricity is cheap or free, such as midday solar or off-peak periods, and discharging when prices are high. The benefit depends on your tariff, so compare retailers before you size a system.
A battery earns its keep only in the hours your solar isn’t generating. Your real energy use should decide the battery size, and the battery size should decide how much you finance, not the other way around.