The best way to look at how a solar system saves money is to look at the price of grid connected electricity and the ‘Levelised cost of Energy’ from your solar system.
Levelised cost of Energy is a measure that basically looks at the cost of each unit of energy your solar system produces. This is done by taking the price of your solar system divided by the amount of energy that system is expected to produce in its lifetime. For this the life of the inverter is used because it has the shorter expected lifespan (15 versus solar panels (20-25 years).
The precise figure for each system is dependent on the price of the system, the location it is installed, if there is any shading on the panels etc. However, typically, a well placed residential solar system will have a levelised cost of energy of approximately $0.11/kWh.
That means that you are effectively paying $0.11 for every unit that solar system produces, though obviously that cost is all bundled up into one up front payment.
So how does this save you money?
Every time you use a unit of energy from your solar system, that’s one unit of energy you didn’t need to buy from the grid.
That one unit of energy cost you $0.11 versus the $0.22 it would have cost you to buy from the grid (WA Residential Tariff).
So every unit of energy that you get from your solar saves you fully half the cost it would otherwise be from the grid. Over 15 years this saving will increase since that $0.11/kWh is fixed for the life of the system whilst electricity prices will only increase over that period.