How to size a battery bank for off-grid PV

Size battery bank for off-grid PV system or UPS backup. Compute Ah capacity from Wh load, autonomy, depth of discharge DoD, efficiency. LiFePO4 vs AGM lead comparison.

Calculation parameters
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How to size a battery bank: required capacity C (Ah) = (E_daily * N_autonomy) / (V_system * DoD * eta * f_T), where E_daily is daily consumption (Wh), N_autonomy days without recharge, V_system bus voltage (12/24/48 V common), DoD maximum depth of discharge (LiFePO4 0.90; AGM 0.50), eta round-trip efficiency (LiFePO4 0.97; AGM 0.85), f_T temperature correction factor (0.95 at 0°C). For off-grid PV systems IEC 61427: minimum 3-day autonomy for temperate zones, 5+ for mountain. For data center UPS: 5-15 minutes runtime IEEE 1188. Essential tool for stand-alone PV design, telecom backup, EV charging station, residential energy storage Powerwall/Sonnen/LG, marine boating, RV camper.

Sizing formula and parameters

Fundamental equation: C_Ah = (E_daily_Wh * N_autonomy) / (V_system * DoD * eta * f_T). Example: off-grid home Arizona 5 kWh/day, 3-day autonomy, 48V system, LiFePO4 (DoD=0.85, eta=0.95), mild temperature (f_T=1.0): C_Ah = (5000 * 3) / (48 * 0.85 * 0.95 * 1.0) = 15000/38.76 = 387 Ah. Battery bank 48V, 387 Ah = 18.6 kWh nominal. Standard 200 Ah module: 2 parallel strings, 4 12V modules series per string = 8 total batteries.

Depth of discharge DoD: ratio used charge / nominal capacity. Lithium (LFP/NMC) 80-95% without premature degradation; lead AGM/Gel 30-50% for acceptable life (1000-2000 cycles at 50%, 5000+ cycles at 30% Peukert). DoD 100% drastically reduces cycles: lead at 100% DoD only 200-300 cycles. NEC 2023 PV recommends DoD 50% lead, 80% lithium.

Round-trip efficiency eta: discharge energy recovered / charge energy. LiFePO4 95-97%, NMC lithium 92-95%, lead AGM 85-88%, flooded lead 80-85%, gel 85-87%. Heat losses transformer inverter, BMS battery management. When sizing, divide capacity by eta to compensate. Tier 1 systems (Tesla Powerwall, Sonnen) total efficiency (incl inverter) 90-93%, tier 2 (Chinese vendors) 85-90%.

Temperature factor f_T: lithium battery capacity decreases with cold: at 0°C 80%, -10°C 60%, -20°C 40%. Lead: at -20°C only 50%, at +25°C 100%, beyond +40°C accelerates aging. For Alpine zones f_T = 0.80-0.90. For tropical zones HVAC cooling mandatory. ISO 12405 EV battery temperature testing, IEC 60068 environmental testing.

Series/parallel configuration: V_system = N_series * V_module (e.g., 4*12V = 48V). C_total = N_parallel * C_module (e.g., 2*200Ah = 400Ah). Parallel strings require synchronized BMS (Tesla, Victron, BYD) to prevent circulating currents between modules with different SoC. Maximum recommended: 4 parallel strings for 48V (lithium), 8 for AGM lead. Beyond requires busbar system with CT-meter for balancing.

History and context

First practical battery was Volta's pile (1800), followed by Plante (1859) who invented rechargeable lead-acid, still dominant in automotive starter. Edison invented nickel-iron (1901). Sony commercialized first lithium-ion (1991), Yoshino-Whittingham-Goodenough Nobel Chemistry 2019. Phadke et al. (1996) CSIRO Australia commercialized LiFePO4 (LFP) with superior thermal stability and cycle life. Modern Battery Management System BMS (Texas Instruments, NXP, Analog Devices) handles SoC, temperature, cell balancing. Tesla Gigafactory Nevada (2016+) scales production 100 GWh/year. CATL and BYD China dominate automotive LFP (BYD Blade Battery 2020). US: Duke Energy, NextEra, Sunrun invest storage IEEE 1547 grid integration. EU Battery Regulation 2023/1542 mandates 50% materials recycle, end-of-life management. Global storage industry > $600 billion/year (2024). NEC USA NFPA 855 fire safety, IEC 62619 industrial safety, UL 9540 ESS systems. NEC 706 ESS installation. MIT, NREL National Renewable Energy Lab, Argonne research US.

Battery types and parameters table

  • LiFePO4 (LFP): 200 Wh/kg, DoD 90-95%, eta 97%, 5000-6000 cycles, life 12-18 years
  • Li-Ion NMC: 230 Wh/kg, DoD 80-90%, eta 95%, 3000-5000 cycles, life 10-15 years
  • Lead AGM: 35 Wh/kg, DoD 30-50%, eta 85%, 1000-2000 cycles, life 5-8 years
  • Flooded lead: 30 Wh/kg, DoD 30-50%, eta 80%, 800-1500 cycles, maintenance
  • Gel lead: 33 Wh/kg, DoD 30-50%, eta 85%, 1000-2000 cycles, maintenance-free
  • Nickel-Iron Edison: 30 Wh/kg, DoD 80%, eta 70%, 50,000+ cycles, life 30+ years
  • Sodium-ion (CATL 2025): 160 Wh/kg, DoD 95%, eta 92%, 3000-4000 cycles, LFP alternative
  • Solid-state Toyota 2026: 400 Wh/kg, DoD 95%, eta 96%, 2000-3000 cycles (research)
  • Tesla Powerwall 3: 13.5 kWh, 48V, NMC, integrated MPPT inverter
  • BYD Blade: 100-200 Ah modules LFP, automotive grade safety
  • Sonnen ecoLinx: 12-20 kWh modular, 10-year warranty
  • LG Resu Prime: 9.6/16 kWh LFP, UL 9540 compliance

Worked numerical examples

Example 1 - off-grid home Arizona 5 kWh/day. 48V LiFePO4 system, 3-day autonomy, DoD 85%, eta 95%, f_T 1.0 (mild climate). C_Ah = (5000*3)/(48*0.85*0.95) = 15000/38.76 = 387 Ah. Solution: 4x BYD B-Box LFP 12.8 kWh = 51.2 kWh total, 1000 Ah equivalent 48V. Cost $35,000 + inverter $8,000. NEC 706 ESS, ASHRAE energy storage compliance.

Example 2 - mountain refuge 8000 ft elevation. 3 kWh/day, 5-day autonomy, V=24V, AGM (DoD 0.50, eta 0.85), f_T 0.80 (cold mountain). C_Ah = (3000*5)/(24*0.50*0.85*0.80) = 15000/8.16 = 1838 Ah at 24V = 44 kWh. Replacement 2x parallel strings 12 batteries 200 Ah AGM total 24x200=4800 Ah. NEC 690 PV system, REA mountain reference.

Example 3 - data center server room UPS. Critical load 50 kW, 15-min autonomy = 50000*0.25 = 12500 Wh. 480V system (data center standard IEEE 1188). LiFePO4 DoD 90%, eta 96%. C_Ah = 12500/(480*0.90*0.96) = 12500/414.7 = 30.1 Ah. Vertiv Liebert APM 30 Ah 480V complete module. ANSI/TIA-942 Tier IV datacenter, IEEE 1188 maintenance.

Example 4 - electric vehicle EV city car. Range 200 km, consumption 15 kWh/100km = 30 kWh capacity. Battery pack voltage 400V Tesla, useful DoD 90%, eta 95%, f_T 0.90 (climate test). C_Ah = (30000)/(400*0.90*0.95*0.90) = 30000/308 = 97.4 Ah. Typical Tesla 4680 cell 26 Ah, 4P configuration (4 parallel) 96 series cells = 384 total cells. UN ECE R100, R136 EV battery compliance.

Example 5 - 30ft cabin cruiser pleasure boat. Onboard consumption 100 Ah/day @ 12V = 1,200 Wh, 2-day autonomy without generator, dual-purpose AGM battery (DoD 0.50, eta 0.85), f_T 1.0 (summer Caribbean). C_Ah = (1200*2)/(12*0.50*0.85*1) = 2400/5.1 = 470 Ah. 2x AGM 250 Ah batteries parallel = 500 Ah. ABS classification, US Coast Guard regulations, ABYC E-11 boat DC protection.

Limits and considerations

  1. Nominal Ah capacity at 20h discharge rate (C/20); fast discharge (C/5, C/2) effective capacity 70-80% (Peukert for lead).
  2. Calendar aging: even unused batteries degrade 1-3%/year (lithium slower).
  3. Cycle aging: SoH (state of health) drops with cycles; LFP 80% SoH after 3000 cycles, NMC after 1500-2000.
  4. Critical temperatures: optimal 15-25°C; above 40°C ages 2x; below 0°C lithium charging forbidden (lithium plating).
  5. BMS mandatory for lithium: overcharge, overdischarge, overheating, cell balancing protection.
  6. Cable sizing critical: max voltage drop 3% (NEC, IEC 60364), AWG/mm^2 for DC current.
  7. Fusing mandatory: class T (lithium), class ANL (lead), value = 1.25x max discharge current.
  8. Lead venting room: H2 escapes during charge, explosive > 4% (NFPA 70 art. 480).
  9. EU Battery Regulation 2023 end-of-life recycling: 50% materials recovered 2027, 75% 2031.
  10. Costs: LFP $400-600/kWh installed (2025), ROI 8-12 years with state incentives.

Common errors

  1. Undersizing DoD: actual cycles drastically reduced, premature replacement.
  2. Ignoring temperature: winter capacity 50% for lead at high latitude.
  3. Mixing new and old batteries in parallel: unequal SoH rapid degradation.
  4. Mixing lithium and lead same system: incompatible charge voltages.
  5. Asymmetric parallel connections: unbalanced currents (Tesla rule: same-length cables).
  6. BMS not installed for lithium: thermal runaway, fire risk (NFPA 855 fire safety).
  7. Neglecting electronics IP rating: IP65+ outdoor, IP54 indoor.
  8. Computing DC energy on AC side: inverter conversion eta 92-96% loss.
  9. Not considering inverter standby consumption (10-50W 24/7 = 100-500 Wh/day).
  10. Excessive oversizing: beyond 5-day autonomy not economically advantageous.

Practical applications

  1. Off-grid residential PV: isolated houses, refuges, cabins, ITC tax credit.
  2. Grid-tied residential storage: Tesla Powerwall, Sonnen, LG, BYD B-Box, Sungrow.
  3. Telecom backup: BTS cellular towers AT&T, Verizon, T-Mobile 24x7.
  4. Data center UPS: Vertiv Liebert, Schneider APC, Eaton, Tier III/IV TIA-942.
  5. EV charging station: Tesla Supercharger, Electrify America, EVgo fast charge 350 kW.
  6. Electric vehicles: Tesla Model S/X, Ford Mustang Mach-E, GM Ultium platform.
  7. Marine: cabins Beneteau, Bavaria, DC onboard systems, ABYC E-11.
  8. RV/camper: Winnebago, Airstream, off-grid 12V/24V systems.
  9. Industrial: AGV automated guided vehicles, robotics, Plug-and-play.
  10. Aerospace satellites: NASA Mars rovers Curiosity/Perseverance, ESA Sentinel.

Support

Questions: info@calcoi.com. Educational tool for storage sizing. For professional applications consult IEC 61427 PV batteries, IEEE 1188 maintenance, NFPA 855 ESS fire safety, UL 9540, EU Battery Regulation 2023/1542, NEC 706 ESS, software Victron VRM, Tesla Solar Designer, Jinko/REC sizing software.

Updated July 2026

Frequently Asked Questions

Difference between nominal and useful capacity?

Nominal capacity (Ah or kWh) is label value measured at 20h discharge rate (C/20) at 25°C. Useful capacity = nominal * effective DoD. Example: 100 Ah LFP battery DoD 90% = 90 Ah useful; AGM 100 Ah DoD 50% = 50 Ah useful. For equivalent useful kWh, LFP 100 Ah 12V = 1.08 kWh useful (1.2 nominal); AGM 100 Ah 12V = 0.6 kWh useful (1.2 nominal). Always size on useful, not nominal.

Which system voltage to choose?

Higher V reduces current for same power, reduces cable size (P=VI). 12V: small systems 3000W (residential, off-grid). For residential storage 48V dominant: standard BMS, common 48V module (Tesla Powerwall, BYD). Above 48V requires different certification (DC > 60V low voltage threshold IEC 60038). EVs use 400-800V for fast charge reduced I^2*R losses.

How many autonomy days for off-grid?

IEC 61427 recommends 3-5 day autonomy for temperate zones, 5-7 for low winter radiation zones (northern climates, Alaska). 1-2 days economically convenient only if diesel backup generator available. 7+ days excessive: beyond threshold battery aging exceeds PV power autonomy benefit. For seasonal homes 6 months/year: size for worst case (January +/- 30%). Professional software (PVSyst, HOMER) computes loss-of-load probability LOL <5%.

LFP lithium vs AGM lead: which is better?

Initial cost: lead $130-200/kWh, LFP $400-650/kWh (3x). But 10-year total cost of ownership: LFP wins. AGM 1500 cycles @ 50% DoD = 750 effective cycles; LFP 5000 cycles @ 90% DoD = 4500 cycles. Cost per kWh-cycle: AGM $0.25, LFP $0.13 (-45%). LFP no maintenance, no venting, reduced weight. For new installations LFP dominant choice. AGM still valid for low-budget startup if replacement planned.

What happens if you overcharge a battery?

Lithium: above V_max (LFP 3.65V/cell, NMC 4.2V/cell) is lithium plating + dendrites, thermal runaway risk > 60°C, fire NFPA 855. BMS interrupts charging. If BMS broken -> fire (Boeing 787 grounding 2013, hoverboard 2015 ban). Lead: overcharge generates explosive H2, mandatory ventilation. Water decomposes, lowers electrolyte. Sulfation irreversible crystals. Always use correct charger (lithium CC-CV vs lead float, equalize). IEC 62619 industrial safety.

How to handle SoC mismatch between parallel modules?

BMS synchronizes exchanging CAN bus data between modules (Tesla, Victron, BYD). Passive cell balancing (shunt resistor) or active (capacitive charge-discharge). For new modules same brand same batch OK. Never parallel different lithium (LFP+NMC different cell voltage). For lead: all same brand, age, SoH. Asymmetry generates circulating currents, overheating, BMS fault. Tesla rule: all same-length cables between parallel modules to minimize differential resistance.

Battery temperature management?

Lithium: optimal zone 15-25°C; charging forbidden below 0°C (lithium plating); above 40°C accelerates aging Arrhenius (Q10=2). Residential systems: conditioned garage HVAC, insulation. Tesla Powerwall has integrated active cooling (hydronic). For Alpine off-grid: tech room heated 5-15°C minimum. EV battery thermal management is top engineering challenge: Tesla TMS, BYD CTP cell-to-pack design. ISO 12405-4 EV thermal performance test. Heat pump COP 3-4 efficient for battery rooms.

Formula

C_Ah = (E_giornaliera * N_autonomia) / (V_sistema * DoD * eta * f_T)
12V (small), 24V (medium), 48V (residential), 400-800V (EV)
LFP 80-95%, AGM 30-50%, Gel 30-50%
LFP 97%, NMC 95%, AGM 85%, flooded 80%
f_T = 0.80-1.0 a seconda zona climatica
V_sistema = N_serie * V_modulo
C_totale = N_parallelo * C_modulo
IEC 61427 PV batteries; IEEE 1188 maintenance; NFPA 855 fire safety; UE Battery Reg 2023/1542

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