Off-Grid Solar and Battery Sizing: A 3 kWh/day Worked Example
Size a first-pass battery bank and solar array from daily energy, autonomy, usable depth of discharge, peak-sun-hours, and system derating.
Why this calculation matters
A solar system is an energy-balance problem before it becomes an equipment-selection problem. Daily consumption sets the energy target; autonomy and usable depth of discharge set storage; solar resource and system losses set array size.
This example intentionally uses average planning values. A production design should use location-specific time-series solar data, seasonal loads, temperature, battery limits, and inverter/charge-controller specifications.
What you will calculate
- Convert daily load and autonomy into required usable battery energy.
- Convert battery energy into approximate amp-hour capacity at a chosen bus voltage.
- Estimate PV array size from peak-sun-hours and a derating factor.
- Understand why seasonal/time-series simulation is stronger than a single average-day calculation.
Given values
- Daily AC energy demand = 3.0 kWh/day
- Desired autonomy = 2 days
- Usable battery depth of discharge = 80%
- Nominal battery bus = 48 V
- Average solar resource = 4.5 peak-sun-hours/day
- Aggregate PV/system derating factor = 0.75
Governing equations
Battery energy target
First-pass stored-energy target before chemistry/temperature corrections.
Approximate battery amp-hours
Nominal-voltage conversion only.
PV array power
Average-day energy-balance estimate.
Worked solution
1. Size the nominal battery energy
Two days of 3 kWh/day load requires 6 kWh of usable energy. If the planning limit allows 80% of nominal battery energy to be used, the nominal bank target is 7.5 kWh.
2. Convert to a 48 V capacity estimate
At a nominal 48 V bus, 7.5 kWh corresponds to about 156 Ah. Real module series/parallel combinations must use actual nominal voltage and usable energy from the product datasheet.
3. Estimate average-day PV size
With 4.5 peak-sun-hours and a 0.75 aggregate derate, the mathematical minimum for replacing 3 kWh on the average design day is about 0.889 kW of PV.
4. Add design margin and seasonal context
A practical preliminary design might round the array upward—for example toward 1.1–1.2 kW—after checking the actual module/string limits and seasonal resource. The correct margin depends on winter production, weather autonomy, generator backup, load criticality, temperature, soiling, and recovery requirements after a low-state-of-charge event.
Engineering interpretation
The simple average-day screen produces a 7.5 kWh nominal battery target, about 156 Ah at 48 V, and approximately 0.89 kW of PV before design margin.
Those are starting points. The full power-system model should test seasonal solar availability, battery state of charge, inverter surge, MPPT voltage/current limits, cable loss, generator support, and lifecycle behavior.
Sanity checks
- More autonomy days must increase required battery energy.
- A lower allowed depth of discharge must increase required nominal storage.
- Lower peak-sun-hours or higher system losses must increase PV array size.
- PV string voltage must remain inside controller limits across temperature extremes; energy sizing alone cannot verify that.
Common mistakes
- Sizing from panel wattage without starting from daily energy demand.
- Using yearly-average sun hours for a system that must survive the worst season.
- Ignoring inverter surge and battery/BMS current limits.
- Treating nominal battery kWh as fully usable kWh.
References and model boundaries
- Use location-specific solar-resource data and actual component datasheets for final sizing.
- Battery usable energy and PV production are temperature-, age-, operating-point-, and system-dependent.
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