Reading the Discharge Curve of Lead Acid Battery Banks
The discharge curve of a lead acid battery is fundamentally non-linear. Unlike lithium chemistries that hold a flat voltage plateau until nearly empty, a flooded lead-acid (FLA) or AGM battery experiences a gradual voltage sag that accelerates sharply once you cross the 50% State of Charge (SoC) threshold. If you size your off-grid battery bank based solely on the 20-hour (C/20) amp-hour rating printed on the sticker, your system will brownout under real-world loads. You must size based on the actual C-rate you intend to draw.
The C-rate defines how fast you are emptying the battery relative to its total capacity. A 200Ah battery discharged at 10A is at a C/20 rate (taking 20 hours to empty). Discharge that same battery at 40A, and you are at a C/5 rate. Due to internal resistance and the sluggish chemistry of lead dioxide converting to lead sulfate, higher discharge rates yield significantly less total usable energy. This penalty is quantified by Peukert's Law, but you can see the practical reality in the voltage sag data below.
| State of Charge (SoC) | Resting Voltage (No Load) | Voltage at C/20 (10A draw) | Voltage at C/5 (40A draw) | Usable Capacity Delivered |
|---|---|---|---|---|
| 100% | 12.70V | 12.45V | 12.10V | N/A (Starting point) |
| 75% | 12.45V | 12.25V | 11.85V | 50Ah (C/20) / 42Ah (C/5) |
| 50% | 12.20V | 12.00V | 11.55V | 100Ah (C/20) / 78Ah (C/5) |
| 25% | 11.95V | 11.75V | 11.20V (Inverter LVD Trip) | 150Ah (C/20) / 95Ah (C/5) |
| 0% (Dead) | 11.70V | 10.50V | 9.80V (Severe Plate Damage) | 200Ah (C/20) / 115Ah (C/5) |
Notice the critical takeaway from the table: if your inverter's Low Voltage Disconnect (LVD) is set to 46V (11.5V per 12V block), a C/5 discharge will trigger a shutdown at roughly 25% SoC, leaving you with only 95Ah of usable capacity out of a 200Ah battery. According to Battery University, pushing lead-acid cells below 11.8V under load causes rapid sulfation, permanently reducing future capacity.
System Architecture, Peukert Math, and Inverter Sizing
To apply this data, we need a complete system block description. A standard robust off-grid architecture flows as follows: 48V FLA Battery Bank → 150A DC Disconnect/Breaker → 4000W 48V Hybrid Inverter/Charger → AC Subpanel (Critical Loads). Sizing the components in this chain requires accounting for both inverter efficiency and the Peukert effect.
The Sizing Math
Assume a continuous AC load of 1500W. We need to run this load for 4 hours.
- Calculate DC Current: Inverters are not 100% efficient. Assume 90% efficiency. DC Current = AC Load / (Nominal Voltage × Efficiency).
1500W / (48V × 0.90) = 34.7A continuous DC draw. - Calculate Ideal Amp-Hours: 34.7A × 4 hours = 138.8Ah required.
- Apply Peukert's Law: Lead-acid batteries suffer from the Peukert effect, modeled by the formula $t = C_p / I^k$, where $k$ is the Peukert exponent (typically 1.25 for FLA). If we use a 200Ah battery (rated at 10A for 20 hours), its Peukert capacity $C_p = 10^{1.25} × 20 = 355.6$.
At our 34.7A draw, the actual time to empty is $355.6 / (34.7^{1.25}) = 4.15$ hours. The usable capacity at this C-rate drops to roughly 144Ah. - Apply Depth of Discharge (DoD) Limit: To get a 5-year lifespan from FLA, you must limit DoD to 50%. Therefore, required bank capacity = 138.8Ah / 0.50 = 277.6Ah at the operating C-rate.
Because a single 200Ah battery only yields ~144Ah at this draw rate (and we can only use half of that without damaging the plates), a single string is insufficient. We must parallel two strings to double the capacity and halve the current per string, moving us to a more favorable C/10 discharge rate per battery.
Inverter and Charger Sizing
For a 1500W continuous load with potential surge loads (like a well pump starting), a 4000W inverter provides the necessary 2.5x surge headroom. For the charger, the National Renewable Energy Laboratory (NREL) guidelines and battery manufacturers recommend a charge current between 10% and 13% of the C/20 capacity. For a 400Ah (C/20) parallel bank, your inverter/charger must be configured to output exactly 40A to 50A of DC charge current. Undersizing the charger leads to chronic undercharging and stratification; oversizing it boils the electrolyte and warps the plates.
Series vs. Parallel Consequences and Operational Limits
Building a 48V bank from 12V monoblocks requires strict adherence to series and parallel wiring rules. The physical consequences of these configurations dictate your system's voltage and amp-hour totals.
- Series Wiring (Voltage Adds, Ah Stays Constant): Wiring four 12V 200Ah batteries in series yields a 48V 200Ah string. The current flows through each battery sequentially. If one cell in one battery develops high internal resistance, the entire string's voltage sags, and the charger will overcharge the healthy batteries trying to reach the target voltage.
- Parallel Wiring (Ah Adds, Voltage Stays Constant): Wiring two 48V 200Ah strings in parallel yields a 48V 400Ah bank. Current divides between the strings. Crucial rule: Never parallel mismatched batteries, different ages, or different chemistries. The string with lower internal resistance will hog the discharge current and take the bulk of the charging current, leading to premature failure.
Charge and Discharge Limits
Operating outside the manufacturer's C-rate and voltage limits is the fastest way to destroy a lead-acid bank.
- Maximum Discharge Rate: Limit continuous discharge to C/5 (e.g., 40A per 200Ah battery). Brief surge loads (up to 3 seconds) can hit C/2, but sustained C/5 draws will overheat the internal busbars and cause massive voltage sag.
- Charge Voltage Limits (at 25°C): Bulk phase charges at maximum current until reaching 14.4V (per 12V block). Absorption holds at 14.4V until current tapers to 2% of capacity. Float maintains at 13.5V. Temperature compensation is mandatory: drop voltage by 0.03V per °C above 25°C.
Verification, Equalization, and Maintenance Protocol
You cannot manage what you do not measure. Relying solely on the inverter's built-in battery monitor is a mistake, as cheap shunts drift over time and fail to account for the non-linear discharge curve accurately. To verify your battery health and true State of Charge, implement this bench-and-jobsite protocol:
- Specific Gravity Testing (FLA Only): Voltage is a lagging indicator. A fully charged FLA battery should read a specific gravity of 1.265 to 1.275 on a hydrometer. If one cell reads 1.220 while others read 1.265, that cell is sulfated or shorted. No amount of standard charging will fix it.
- Controlled Load Testing: Once a month, disconnect the solar array and apply a known, steady DC load (like a 12V/48V resistive heater) that draws exactly your C/10 rate. Log the voltage drop every 30 minutes. Plot this against the manufacturer's discharge curve. If your voltage drops faster than the spec sheet dictates, your bank has lost capacity to sulfation.
- Equalization (EQ) Charge: For flooded lead-acid batteries, perform an EQ charge (a controlled overcharge to 15.5V per 12V block) every 30 to 60 days. This boils the electrolyte intentionally to mix the stratified acid and blast sulfate crystals off the plates. Never equalize AGM, Gel, or Lithium batteries. Ensure the battery room is heavily ventilated during EQ, as it off-gasses highly explosive hydrogen gas.
By respecting the non-linear discharge curve, applying Peukert's math to your load calculations, and strictly enforcing C-rate limits, a well-maintained flooded lead-acid bank will reliably deliver off-grid power for 5 to 7 years. Ignore the curve, size for the C/20 sticker rating, and you will be shopping for replacement batteries by year two.
