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Environmental & Energy Engineering · Worked example

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.

By 9 minute readPublished 2026-08-11Reviewed 2026-08-11

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

Ebatt = Edaily × days / DoDusable

First-pass stored-energy target before chemistry/temperature corrections.

Approximate battery amp-hours

Ah ≈ 1000 Ebatt(kWh) / Vnom

Nominal-voltage conversion only.

PV array power

Ppv ≈ Edaily / (PSH × derate)

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.

Ebatt = 3×2/0.80 = 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.

Ah ≈ 7500/48 = 156.25 Ah

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.

Ppv ≈ 3/(4.5×0.75) = 0.889 kW

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.

Result

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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