Do I Need Energy-Efficient Appliances?
The short answer is: no, you don't need energy-efficient appliances when installing solar, but it can help reduce costs.
Energy-Efficiency and Your Solar System
So, what's the link between energy-efficiency and your solar system?
The less power consumed by your appliances (predominantly air conditioners in this climate) means that you need fewer solar panels or less electricity from the grid in order to meet your needs. This can result in a lower expenditure on the solar system or your ongoing electricity bill.
Should I Buy Energy-Efficient Appliances?
If you have existing appliances that work well, the cost of buying a new appliance (such as an inverter air conditioner) is probably more than what you would save by accordingly reducing the size of your solar installation.
However, if a particular appliance is nearing the end of its usable life, then it's a much easier decision to upgrade.