I find it difficult to visualise batteries as cost effective in any grid connected system. As beeutey comments, there are some aspects of battery use you may not be taking into account.
1. Charge/discharge efficiency. While the batteries used mostly give back the same current as used to charge them, they do not give back the same power. To use the numbers for a lead acid system (other batteries will be similar or worse), a twelve volt battery charges at about 14v, but discharges at about 12.5v. This gives a charge/discharge power efficiency of about 89%. There are likely to be further losses from other mechanisms, so this is about the best case.
2. As a general rule, depending on the battery type, the nominal battery capacity needs to twice (or more) the capacity you plan to use. And the deeper you discharge the batteries, the shorter their life. And battery replacement needs to be factored in as a running cost.
John
John
JDNSW
1986 110 County 3.9 diesel
1970 2a 109 2.25 petrol
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