A home using 30 kWh/day needs ~37–47 kWh battery capacity for 1 day of backup at 80% DoD.
Tesla Powerwall 3: 13.5 kWh usable at ~$11,500 installed. LFP batteries last 4,000–6,000 cycles.
Divide daily usage by DoD efficiency. 30 kWh/day ÷ 0.80 ÷ 0.95 ≈ 39 kWh raw capacity needed.