The Core Math: Translating Charge (Ah) to Current (A) in Storage Systems
To properly size a battery bank, you must map the entire system block from source to load. A standard DC-coupled storage system flows like this: Solar Array (Source) $\rightarrow$ MPPT Charge Controller $\rightarrow$ Battery Bank (Storage) $\rightarrow$ Inverter $\rightarrow$ AC Main Panel (Load). When sizing the storage block, we work backward from the AC load. Let's assume a continuous load of 2000W. At a nominal 48V DC bus, the baseline DC current is $I = P / V$, which equals $2000W / 48V = 41.6A$. However, inverters are not 100% efficient. Assuming a 93% inverter efficiency, the actual current pulled from the battery is $41.6A / 0.93 = 44.7A$. If you are using Flooded Lead-Acid (FLA) batteries, you must also apply Peukert's Law, which accounts for the fact that batteries deliver less total charge when discharged at higher currents. Peukert's equation is $t = C / I^k$, where $C$ is the rated capacity at a 1-amp discharge, $I$ is the actual current, and $k$ is the Peukert exponent (typically 1.2 to 1.3 for lead-acid). Pulling 44.7A from a 200Ah FLA bank will yield significantly less than 4.5 hours of runtime; it will likely drop to under 3 hours due to the $k$ exponent. Lithium chemistries, by contrast, have a Peukert exponent very close to 1.05, meaning their usable charge remains relatively stable regardless of the discharge current.| Chemistry | Nominal V (per cell) | Usable DoD | Max Discharge C-Rate | Peukert Exponent ($k$) | Round-Trip Efficiency |
|---|---|---|---|---|---|
| Flooded Lead-Acid (FLA) | 2.0V | 50% | 0.2C (C/5) | 1.25 - 1.30 | 75% - 80% |
| AGM / Gel (Sealed) | 2.0V | 50% | 0.25C (C/4) | 1.15 - 1.20 | 80% - 85% |
| LiFePO4 (LFP) | 3.2V | 80% - 90% | 1.0C (Standard) | 1.02 - 1.05 | 95% - 98% |
| NMC (Lithium-Ion) | 3.7V | 80% - 90% | 1.0C - 3.0C | 1.05 - 1.08 | 92% - 95% |
Series vs. Parallel: How Wiring Alters the Charge-Current Equation
The physical wiring topology of your battery bank fundamentally changes the relationship between charge and current at the system terminals. Understanding the series vs parallel consequence for Voltage (V) and Amp-hours (Ah) is critical for matching your battery bank to your inverter's DC input requirements.Series Wiring: When you wire batteries in series, the voltages add together, but the total charge (Ah) remains identical to a single battery. For example, wiring four 12V 100Ah batteries in series yields a 48V 100Ah bank. The total energy capacity is 4800Wh. The maximum continuous current the bank can safely deliver is limited by the C-rate of a single 100Ah battery. Series wiring is preferred for high-power systems because the higher voltage keeps the DC current low, allowing you to use smaller, cheaper AWG wire and reducing $I^2R$ heat losses in the cables.
Parallel Wiring: When you wire batteries in parallel, the voltage remains the same, but the total charge (Ah) adds together. Wiring four 12V 100Ah batteries in parallel yields a 12V 400Ah bank. Total energy is still 4800Wh, but to pull 4000W from a 12V system, you would need to push over 350A of DC current, requiring massive 4/0 AWG or parallel busbar runs.
CRITICAL SAFETY WARNING: Mismatched Parallel Cells
Never wire batteries of different capacities, ages, or chemistries in parallel. If you parallel a 100Ah battery with a 50Ah battery, or mix a new battery with an old one with higher internal resistance, the stronger battery will continuously push current into the weaker one to equalize voltage. This parasitic cross-current causes severe overheating, venting, and in lithium cells, thermal runaway. If you must parallel strings, ensure they are identical models, purchased in the same batch, and use symmetrical wiring (equal-length cables from a central busbar) to balance the resistance path.
Never wire batteries of different capacities, ages, or chemistries in parallel. If you parallel a 100Ah battery with a 50Ah battery, or mix a new battery with an old one with higher internal resistance, the stronger battery will continuously push current into the weaker one to equalize voltage. This parasitic cross-current causes severe overheating, venting, and in lithium cells, thermal runaway. If you must parallel strings, ensure they are identical models, purchased in the same batch, and use symmetrical wiring (equal-length cables from a central busbar) to balance the resistance path.
Charge/Discharge Limits and Sizing the Inverter/Charger
Once you understand your total charge capacity, you must enforce the charge and discharge limits dictated by the battery's C-rate. The C-rate is a measure of the rate at which a battery is discharged relative to its maximum capacity. A 1C discharge rate for a 100Ah battery means drawing 100A. A 0.5C rate means drawing 50A. Let's size an inverter/charger for a stated load of 4000W continuous on a 48V LiFePO4 system.- Calculate Max DC Discharge Current: $4000W / (48V \times 0.93 \text{ inverter efficiency}) = 89.6A$.
- Apply C-Rate Limits: Most quality LiFePO4 cells (like EVE LF105 or CATL prismatic cells) are rated for a 1C continuous discharge. Therefore, the absolute minimum battery capacity required is 90Ah. However, running a battery constantly at 1C degrades cycle life and causes voltage sag. For optimal longevity, target a 0.5C continuous draw, which means you should install a 200Ah 48V battery bank (yielding a comfortable 100A max continuous draw).
- Size the Inverter/Charger: A 4000W load requires at least a 5000VA inverter (like the Victron MultiPlus II 48/5000) to handle surge loads from inductive motors (fridges, well pumps).
- Size the Charge Current: To recharge a 200Ah bank from 20% State of Charge (SoC) to 100% in 4 hours, you need to replace 160Ah. $160Ah / 4h = 40A$ of charge current. The Victron MultiPlus II 48/5000 has a built-in 70A charger, which is more than sufficient, but you must ensure your MPPT charge controllers and generator can supply the AC/DC input required to sustain that 40A+ charge rate.
LITHIUM FIRE-SAFETY CALLOUT: Low-Temperature Charging
While LiFePO4 is inherently more stable than NMC, charging any lithium cell below 0°C (32°F) forces lithium ions to plate as solid metal on the anode rather than intercalating. This lithium plating creates dendrites that pierce the separator, causing internal short circuits and catastrophic fire. Your Battery Management System (BMS) MUST have a low-temperature charge cutoff. Never rely solely on the inverter's temperature-compensated charging profile; the BMS must physically open the charge MOSFETs when cell temperatures drop below freezing.
While LiFePO4 is inherently more stable than NMC, charging any lithium cell below 0°C (32°F) forces lithium ions to plate as solid metal on the anode rather than intercalating. This lithium plating creates dendrites that pierce the separator, causing internal short circuits and catastrophic fire. Your Battery Management System (BMS) MUST have a low-temperature charge cutoff. Never rely solely on the inverter's temperature-compensated charging profile; the BMS must physically open the charge MOSFETs when cell temperatures drop below freezing.
Finally, wire sizing must match the calculated current. For our 89.6A continuous draw (which the NEC considers a continuous load if it lasts 3 hours or more, requiring a 125% multiplier: $89.6 \times 1.25 = 112A$), you must use a minimum of 1/0 AWG THHN copper wire in conduit, or 1/0 AWG welding cable for flexible battery interconnects, paired with a 125A Class T fuse or DC breaker placed within 18 inches of the battery positive terminal. Always consult manufacturer wiring guidelines and local AHJ requirements before finalizing your DC bus topology.
