Batteries are definitely hard to justify on cost alone. However a smaller battery is generally what you want, if you pay for a larger battery and never use the capacity, then it’s a waste of money. The only time this is not the case is when you use it for a battery backup due to regular grid outages.
At $4k, one complete discharge of 4.79kWh per day for 10 years will end up effectively costing around 22.8c/kWh. This is overly simplistic as the battery won’t have its full capacity after that many cycles. Take into account the cost of charging the system via solar by not getting feed in rates, say 5c/kWh, you need to be paying more than 27.8c/kWh currently for electricity to justify on cost alone.
Further to that, you may still import power due to the 3kW inverter, put the kettle and microwave on at the same time and you will be importing power.
If I were to get a battery, I would be on time of use electricity plan and aim to discharge the battery each evening when electricity prices were over 50c/kWh. I would not get a huge battery as we have not lost mains in 2 years.
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