Battery Life Calculator

Battery runtime calculation is essential for sizing backup power systems, portable devices, renewable energy storage, and mission-critical equipment. The fundamental relationship derives from energy storage capacity: $\text{Runtime (hours)} = \text{Capacity (Ah)} \div \text{Load Current (A)}$. However, real-world performance deviates from this ideal due to rate-dependent capacity reduction (Peukert effect), temperature sensitivity, depth of discharge limitations, and aging degradation. Engineers must account for these factors through derating calculations to ensure reliability. IEEE 485 recommends 1.25 design margin (80% end-of-life capacity) for UPS and stationary battery systems.

Battery Chemistry Characteristics: Lead-acid batteries (flooded and VRLA sealed types) offer mature, economical technology with 5-8 year flooded and 3-5 year VRLA service life at 50% depth of discharge (DOD). Both suffer Peukert effect where capacity decreases at higher discharge rates—a $100\,\text{Ah}$ battery at $C/10$ rate may deliver only $70\,\text{Ah}$ at $1C$ rate. Lithium-ion chemistries, particularly LiFePO4 and NMC, dominate modern applications with LiFePO4 delivering 3,000-5,000 cycles at 80% DOD, 10-15 year life, and minimal Peukert effect. NMC provides higher energy density but shorter cycle life (1,000-2,000 cycles). Both require battery management systems (BMS) for cell balancing and protection.

Peukert Effect and Discharge Rate: The Peukert equation quantifies capacity reduction at high discharge rates: $C_p = C \times (C\text{-rate})^{k-1}$, where $k$ is the Peukert coefficient (1.0 ideal, 1.1-1.15 deep-cycle lead-acid, 1.2-1.3 automotive batteries, ~1.0 lithium). A $100\,\text{Ah}$ battery with $k=1.25$ discharged at $C/2$ delivers only $84\,\text{Ah}$ effective capacity, reducing runtime from $2.0\,\text{hours}$ theoretical to $1.68\,\text{hours}$ actual. High-rate applications like UPS and engine starting require significant oversizing to compensate for Peukert losses.

Temperature Effects: Lead-acid capacity decreases ~1% per $°\text{C}$ below $25°\text{C}$ reference (50% loss at $-20°\text{C}$). Every $10°\text{C}$ above $25°\text{C}$ halves VRLA battery life through electrolyte decomposition and grid corrosion. Lithium batteries maintain better low-temperature performance (70% capacity at $-20°\text{C}$) but suffer permanent damage if charged below $0°\text{C}$ due to lithium plating. Cold weather applications require heated enclosures maintaining $15\text{--}25°\text{C}$ for optimal performance and longevity.

Depth of Discharge and Cycle Life: Lead-acid batteries achieve 1,500-2,000 cycles at 30-50% DOD but only 300-500 cycles at 80% DOD. Off-grid solar applications typically design for 50% DOD maximum, requiring 2× capacity versus load. Lithium LiFePO4 tolerates 80% DOD at full cycle life, providing 1.6× usable capacity versus lead-acid. This partially offsets lithium's 3-4× higher initial cost through reduced bank size and longer replacement intervals.

State of Charge (SOC) Estimation: Voltage-based SOC uses open-circuit voltage but requires 4-hour rest period. Coulomb counting integrates current over time: $\text{SOC}(t) = \text{SOC}(0) + \int (I_{\text{charge}} - I_{\text{discharge}}) \, dt / C$, but accumulates measurement errors. Advanced BMS combines voltage, current, temperature, and impedance with Kalman filtering for ±5% SOC accuracy. Battery aging reduces capacity through calendric degradation (VRLA 3-5% annually, lithium 2-3%) and cyclic aging from DOD and temperature extremes.

Series/Parallel Configuration and Applications: Series connection adds voltages (four 12V 100Ah = 48V 100Ah); parallel adds capacities (four = 12V 400Ah). Large installations use series-parallel (16S5P of 3.2V 280Ah = 51.2V 1,400Ah / 71.7kWh). Data centers size UPS for 5-15 minute runtime to generator, telecommunications target 8-24 hour autonomy, solar systems balance 2-5 autonomy days against cost.

Standards Reference: IEEE 485 (Lead-Acid Batteries for Stationary Applications), IEC 60896 (Stationary Lead-Acid Batteries), IEEE 1188 (Maintenance and Testing).