The fundamental battery charging formula dictates that charge current (I) equals the usable Amp-hours (Ah) divided by the desired charge time (T), adjusted for system efficiency. However, translating this into a working off-grid or backup power system requires adjusting for inverter overhead, chemistry-specific C-rates, and Peukert losses. If you size your charge controller or inverter-charger based on naive math, you will either trip breakers during bulk charging or starve your loads during high-draw events.
The Core System Block and Charging Math
Before running numbers, map your system block. Power flows in a strict sequence: Source (PV array/Grid/Generator) → Charge Controller or Inverter-Charger → Battery Bank (with BMS) → DC/AC Load. The charging path is constrained by the narrowest bottleneck in this chain.
The baseline battery charging formula for determining required charge current is:
I_charge = (Battery_Ah × Depth_of_Discharge) / (Charge_Time × η)
Where η (eta) is the charging efficiency factor (typically 0.90 to 0.95 for lithium, 0.80 to 0.85 for lead-acid due to gassing and heat losses).
To size your inverter-charger or MPPT, you must calculate the DC current required to both run the continuous AC load and charge the battery simultaneously. If your AC load draws 1500W and you want to push 40A into a 48V battery bank, your total DC power requirement is:
P_total = (1500W / 0.85 inverter_eff) + (48V × 40A / 0.95 charge_eff) = 1764W + 2021W = 3785W
At 48V nominal, this requires a DC bus capable of handling ~79A continuous, meaning your busbars, fuses, and inverter-charger internal relays must be rated for at least 100A.
Series vs. Parallel: Voltage, Ah, and C-Rate Consequences
How you wire your cells fundamentally changes the math in the battery charging formula.
- Series Wiring: Voltage adds, Amp-hours remain identical. Four 12V 100Ah batteries in series yield 48V at 100Ah. This is the preferred architecture for 3kW+ systems because higher voltage halves the current, reducing I²R heat losses and allowing smaller AWG wire.
- Parallel Wiring: Amp-hours add, voltage remains identical. Four 12V 100Ah batteries in parallel yield 12V at 400Ah. This creates massive current bottlenecks and requires 2/0 AWG or 4/0 AWG copper for main feeders.
Your wiring configuration directly impacts the C-rate (Charge/Discharge rate relative to capacity). A 1C rate on a 100Ah battery is 100A. A 0.5C rate is 50A. Pushing a 1C charge rate into a lead-acid battery will boil the electrolyte; pushing it into a standard LiFePO4 cell without active thermal management will degrade the anode and trip the BMS high-temperature cutoff.
Sizing Math: Factoring in Peukert and Depth of Discharge
The battery charging formula assumes linear capacity, which is true for lithium but false for lead-acid. Electronics Tutorials details how Peukert's Law penalizes lead-acid batteries under high loads.
Peukert's formula: t = H × (C / (I × H))^k
Where k is the Peukert exponent (1.05 to 1.3 for lead-acid, ~1.0 for LiFePO4). If you draw 50A from a 200Ah Flooded Lead-Acid (FLA) battery (k=1.25), your effective capacity drops to roughly 135Ah. You aren't just losing runtime; you are altering the state-of-charge (SoC) baseline your charge controller uses to transition from Bulk to Absorption.
| Chemistry | Max Charge C-Rate | Recommended DoD | Charge Efficiency (η) | Typical Cycle Life |
|---|---|---|---|---|
| Flooded Lead-Acid (FLA) | 0.2C (20A per 100Ah) | 50% | 75% - 80% | 500 - 800 |
| AGM / Gel (VRLA) | 0.25C to 0.3C | 50% - 60% | 80% - 85% | 800 - 1200 |
| LiFePO4 (LFP) | 0.5C (Standard) to 1C | 80% - 90% | 92% - 98% | 3000 - 6000 |
Notice the DoD (Depth of Discharge) column. If you design a system using 200Ah of FLA, you only have 100Ah usable. To get 100Ah usable from LiFePO4, you only need a 125Ah battery (using 80% DoD). This drastically changes the numerator in your battery charging formula, reducing the required solar array and charge controller size.
Inverter-Charger Sizing for the Stated Load
When selecting an inverter-charger, you must size for the combined peak of the AC load and the battery charging current. According to the Victron Energy Wiring Unlimited Guide, the AC input breaker and internal transfer switch must handle the sum of the pass-through load and the charger draw.
Let's size an inverter-charger for a remote cabin with a 2000W continuous load (fridge, well pump, lights) and a 48V 280Ah LiFePO4 bank that we want to recharge from 20% to 100% in 4 hours using a generator.
- Usable Ah to replace: 280Ah × 0.80 (DoD swing) = 224Ah.
- Required Charge Current: 224Ah / 4 hours = 56A. (This is ~0.2C, well within the 0.5C safe limit for LFP).
- AC Load Draw: 2000W continuous. Inverter efficiency is ~90%. DC draw = 2222W. At 48V, that's 46.3A.
- Total DC Bus Current: 56A (charge) + 46.3A (load) = 102.3A.
- AC Input Requirement: To supply 2000W load + 2688W (56A × 48V) charging = 4688W total AC input. At 240V AC, this requires a 20A to 30A AC input breaker.
You need an inverter-charger capable of passing 3000W+ continuously and outputting at least 60A of DC charge current. A 3000W inverter with a 35A charger will bottleneck your generator's recharge speed; a 5000W inverter with a 70A charger is the correct mathematical fit.
Decision Path: Selecting Your Charge Controller and Inverter
Use this decision tree to terminate your component selection. Do not mix MPPT and inverter-charger charging on the same battery bank without configuring them for identical temperature compensation and absorption voltages, or they will fight each other and trigger BMS over-voltage faults.
| System Scenario | If Load & Bank Size Is... | Then Pick This Architecture | Concrete Part Number |
|---|---|---|---|
| Small Cabin / Van (12V) | < 1000W load, < 200Ah 12V LFP | All-in-one MPPT + Inverter | Victron EasySolar-II GX 12/1600/70 |
| Medium Off-Grid (24V) | 1500W load, 200Ah 24V LFP | Split MPPT + Inverter-Charger | MultiPlus-II 24/3000/70 + SmartSolar 150/45 |
| Full Home Backup (48V) | > 3000W load, 280Ah+ 48V LFP | High-Power Inverter-Charger + External MPPTs | MultiPlus-II 48/5000/70 + 2x SmartSolar 250/100 |
Final Default Recommendation for a 48V Off-Grid Build
If you are building a standard 48V off-grid or backup system with a 280Ah server-rack style LiFePO4 battery (like an EG4 or SOK 48V100) and a 4kW solar array, stop debating edge cases and use this exact bill of materials. This setup respects all C-rate limits, handles Peukert/efficiency losses inherently via the MPPT algorithm, and provides a hard default that works for 90% of residential DIY builds.
- Inverter-Charger: Victron MultiPlus-II 48/3000/35-50 (Part # PMP482301100). The 35A DC charger is perfectly matched to a 0.12C trickle/maintenance charge on a 280Ah bank, while the 3000W inverter handles standard household loads.
- Solar Charge Controller: Victron SmartSolar MPPT 150/35 (Part # SCC9004). Handles up to 2000W of solar at 48V, outputting ~35A max, keeping you safely under the 0.5C charge limit for standard BMS configurations.
- Battery Bank: 48V 280Ah LiFePO4 with a 100A continuous BMS. (Ensure the BMS supports CAN-bus communication to the Victron GX device so the inverter automatically derates charge current when a cell hits 3.55V).
For a deeper understanding of lithium charge profiles and why constant-current/constant-voltage (CC/CV) algorithms are mandatory for LFP, refer to the Battery University guide on prolonging lithium-ion batteries. By anchoring your build to the math above rather than forum guesswork, your system will balance charge times, component lifespan, and wire sizing without requiring a second trip to the electrical supplier.
