Off-Grid Solar Cabin in Rural Montana

Scenario

A remote off-grid cabin near Bozeman, Montana serves as a seasonal retreat for a family of four. The site has no utility grid access, extreme winter temperatures (−25°C), and limited roof space for PV. Key constraints include: strict weight limits on battery transport (no >100 kg units), requirement for 3-day autonomy due to snowbound access, and need for reliable operation during sub-zero conditions—necessitating conservative DoD and derated inverter capacity.

Given Data

• Daily Energy Consumption: 2,850 Wh
• Autonomy Days: 3
• Battery Voltage: 24 V
• Depth of Discharge (DoD): 0.7 (conservative due to cold-temperature derating)
• Peak Load Power: 4,200 W (well pump + induction cooktop + refrigerator startup)
• Inverter Efficiency: 0.92
• Power Factor: 0.85

Calculation

Battery Capacity (Ah): Required usable energy = 2,850 Wh × 3 days = 8,550 Wh Usable capacity = Total battery capacity × 24 V × 0.7 → Total capacity (Wh) = 8,550 Wh ÷ 0.7 = 12,214.3 Wh → Battery capacity (Ah) = 12,214.3 Wh ÷ 24 V = 509.0 Ah

Inverter Size (VA): Peak apparent power = Peak load power ÷ (Inverter efficiency × Power factor) = 4,200 W ÷ (0.92 × 0.85) = 4,200 ÷ 0.782 ≈ 5,371 VA

Result and Decision

Selected: Two parallel strings of 24 V, 270 Ah LiFePO₄ batteries (total 540 Ah @ 24 V, 12.96 kWh nominal), providing 9.07 kWh usable (≥8.55 kWh required) with 15% headroom for cold-temperature derating. Paired with a 6,000 VA hybrid inverter (e.g., Victron MultiPlus 24/6000) — chosen for built-in BMS communication, low-temp charging support, and scalable AC coupling.

Lesson

Cold ambient temperatures reduce battery capacity and increase internal resistance — always apply DoD conservatism and verify inverter low-temp derating curves; a 6 kVA inverter rated at −20°C delivers only ~85% of its nameplate VA, so oversizing by ≥15% is non-negotiable in alpine climates.