Correction of my sums in bold below-Pc1996 #13 has told you that the provision of 3kW at 240V from a 12V battery is not impossible but to be avoided because of the very high current drawn from the battery which will rapidly discharge it and the need for very short very thick cables to carry this large current at 12V. You would need a special battery to cope regularly with such prolonged high current otherwise its life will be rapidly consumed . My suggestion should have been clearer but I did give my car’s inverter and the knife grinder as an examples. Using you car battery perhaps supplemented by the engine generator is workable for up to about 500W for very short periods - the knife grinder example I gave or as in my car up to 150W for phones, lap top power supplies, tv, small fridge cool box maybe for a few hours but longer with engine running.
If one discharged the battery at a higher rate than the charging rate by the engine then over time it will become flatter and maybe then unable to start the engine nor run the car electrics satisfactorily.
As davesparks said gas is the answer for high power heating. Time to bite the bullet methinks.
Storing electricity at low voltages in batteries is demanding chemistry. And expensive per kWh stored. I did a solar off grid with gennie back up which had a 24V battery ( 4 x 12 V) each of 200Ah. Total Ah is 2 x 200 = 400Ah which is theoretically 400 x 24 = 4.8kWh.
They were agm batteries. To maximise their life they are never completely discharged over a 24 hour period. On demanding days they are 50% discharged. Thus they only reslly are used to store and then deliver 2.4kWh
We get this performance by supplying an equivalent low average power over a 24 hour period of 2.4/24 = 0.1kWh every hour or 100 Watts. This is a discharge current of 100/25/2 = 2 A through each of the 4 batteries - trivial for a 200Ah battery.
We this set up the batteries are never flat , quickly recharged by solar or gennie and their life is maximised ( 1800 cycles of charge discharge). Total cost of 4 batteries £1800 if I remember correctly with about £300 of cabling and sundries including a locked safe enclosure for them.
Storing electricity at low voltages in batteries is demanding chemistry. And expensive per kWh stored. I did a solar off grid with gennie back up which had a 24V battery ( 4 x 12 V) each of 200Ah. Total Ah is 2 x 200 = 400Ah which is theoretically 400 x 24 = 9.6kWh of stored electricity.
They were agm batteries. To maximise their life they are never completely discharged over a 24 hour period. On demanding days they are 50% discharged. Thus they only really are used to store and then deliver 4.8kWh.
We get this performance by supplying an equivalent low average power over a 24 hour period of 4.8/24 = 0.2kWh every hour or 200 Watts. This is a discharge current of 200/25/2 = 4 A through each of the 4 batteries - trivial for a 200Ah battery.