Battery Bank and Inverter Sizing Tool

Battery capacity (Ah) is calculated as: $\text{Ah} = \frac{\text{Energy Consumption (Wh)} \times \text{Autonomy Days}}{\text{Battery Voltage (V)} \times \text{Depth of Discharge (DoD)}}$. For example, with 2,000 Wh/day, 3 days autonomy, 24 V nominal voltage, and 80% DoD: $\frac{2000 \times 3}{24 \times 0.8} = 312.5\,\text{Ah}$. This aligns with IEEE 1547-2018 guidance on energy storage sizing and accounts for usable capacity—not total rated Ah. Always round up to the next standard battery module size (e.g., 320 Ah or 350 Ah) and verify against manufacturer datasheets, which specify DoD limits at rated temperature (typically 25°C per IEC 61427-2). Avoid undersizing: exceeding DoD reduces cycle life—e.g., cycling a LiFePO₄ battery at 90% DoD may cut lifespan by >40% vs. 80% DoD.

Inverter size must be rated in volt-amperes (VA) because AC loads draw apparent power ($S = P / \text{PF}$), not just real power (W). With a 5,000 W peak load, 0.8 power factor, and 90% inverter efficiency, required VA = $\frac{5000}{0.8 \times 0.9} \approx 6944\,\text{VA}$. Per UL 1741 and NEC Article 705.12(B)(2), inverters must support 125% of continuous load and 100% of non-continuous peak—including motor startup surges. A 7,000 VA inverter is therefore recommended. Low PF increases current draw, stressing wiring and thermal management; undersized inverters risk overload tripping or derating. Always validate against manufacturer surge ratings (e.g., 2× rated VA for 3–5 sec) and confirm compliance with IEEE 1547-2018 grid-support requirements—even for off-grid use, as many inverters share firmware stacks.

For a 5 kW off-grid system, 48 V is strongly preferred over 12 V or 24 V. Higher voltage reduces DC current: at 48 V, 5,000 W draws ~104 A (ignoring losses); at 24 V, it’s ~208 A; at 12 V, ~417 A. Per NEC Article 310.15(B)(16) and IEEE 1547 Annex D, higher current demands larger conductors (e.g., 2/0 AWG vs. 4 AWG for 48 V), increasing cost, voltage drop, and fire risk. Voltage drop must stay ≤3% per NEC 215.2(A)(1)—achievable only with 48 V for >10 m runs. Also, 48 V systems better match modern LiFePO₄ modules (16S nominal) and enable higher-efficiency MPPT charge controllers (e.g., Victron SmartSolar 150/100). Industrial best practice (IEC 62109-1) mandates ≥48 V for systems >3 kW to limit fault current and simplify arc-flash mitigation.

Depth of discharge directly governs lithium and lead-acid battery cycle life. Per IEC 62620 and manufacturer datasheets (e.g., CATL LFP spec sheets), cycling a LiFePO₄ battery at 100% DoD yields ~2,000 cycles; at 80% DoD, it extends to ~3,500–4,500 cycles—a 75–125% gain. For flooded lead-acid, 50% DoD delivers ~1,200 cycles vs. ~500 at 80% DoD (IEEE 1625-2014). Using 80% DoD balances usable energy with longevity and safety: deeper discharges accelerate cathode degradation and increase internal resistance. BMS enforcement of DoD limits is mandatory per UL 1973 and UN 38.3. Note: '80% DoD' means 20% state-of-charge (SoC) remaining—not 80% SoC. Real-world DoD must account for temperature derating (e.g., -20% capacity at 0°C per IEC 62620).

Automotive-grade Li-ion (e.g., NMC cells from EV packs) are unsuitable for off-grid storage due to fundamental design differences. Automotive cells prioritize high C-rate discharge (>3C) and crash safety—not calendar life or partial-state-of-charge (PSOC) tolerance. Stationary storage cells (e.g., LiFePO₄ prismatic cells per UL 1973 Annex A) are engineered for 1C max continuous discharge, >6,000 cycles at 80% DoD, and stable PSOC operation—critical for solar self-consumption. Automotive BMS lacks low-voltage disconnect logic for deep-cycling duty. UL 1973 and IEC 62619 explicitly prohibit repurposed EV batteries for stationary ESS without full requalification—most fail thermal runaway propagation tests (UL 9540A). Use only UL 1973-listed, ETL-verified, and IEEE 1625-compliant stationary cells with integrated cell-level fusing and thermal monitoring.

Temperature and altitude significantly impact component derating. Per UL 1741 Supp 1 and NEC 110.40, inverters lose ~0.5% output per °C above 40°C ambient; at 50°C, derate by 5%. Above 1,000 m, air cooling efficiency drops—NEC requires 3% derating per 300 m elevation. Batteries suffer similarly: LiFePO₄ capacity drops ~0.3%/°C below 25°C (IEC 62620), while charge acceptance falls sharply below 0°C—requiring heater integration. At -20°C, usable capacity may be only 70% of rated. Always apply combined derating: e.g., a 7,000 VA inverter at 50°C and 1,500 m needs $7000 \times 1.05 \times 1.03 \approx 7530\,\text{VA}$. Battery Ah must be increased by ≥15% for sites averaging <5°C. Validate with manufacturer derating curves—not generic tables.

Oversizing the inverter relative to the PV array (e.g., 7 kW inverter for 5 kW PV) is not only acceptable but recommended for off-grid systems—unlike grid-tied designs where clipping is avoided. Off-grid inverters must handle peak AC loads *and* battery charging simultaneously; UL 1741 mandates inverters support 125% of nameplate AC output continuously. Undersizing risks catastrophic failure: a 5 kW inverter fed 5.5 kW load will trip, brown out, or overheat—violating NEC 705.12(B)(2) and voiding UL listing. Oversizing improves surge handling (e.g., well pump startup) and enables future load growth. However, avoid extreme oversizing (>2× PV rating): idle losses rise, and low-load efficiency drops below 15%—wasting battery energy. Target 1.2–1.5× peak load, verified via 15-min demand interval analysis per IEEE 1547-2018 Annex H.

Inverter efficiency is non-linear: typically 85–88% at 10% load, peaking at 92–95% near 30–70% of rated VA, then dropping to ~89% at full load (per UL 1741 test protocol). The default 90% reflects a realistic weighted average across typical off-grid load profiles (e.g., lighting, refrigeration, intermittent tools). Using 90% instead of 95% avoids optimistic yield overestimation—critical for autonomy calculations. A 2,000 Wh/day load with 90% inverter efficiency consumes $2000 / 0.9 = 2222\,\text{Wh}$ from batteries; at 95%, it’s only 2105 Wh—a 5.3% difference that compounds over 3 autonomy days. Per IEC 61850-10 and NREL’s SAM model, using manufacturer-measured weighted efficiency (not peak) is required for accurate LCOE and ROI analysis. Always request the full efficiency curve—not just peak value.