Methodology
Usable Battery Energy
The two multiplications that separate a battery's nameplate from what it will actually run — commonly a factor of two and a half.
Nameplate is not usable
A battery's rated capacity is reduced twice before it reaches a load. First by depth of discharge: the fraction of the rated capacity you may actually draw without destroying cycle life. Second by round-trip efficiency: the energy lost as heat on the way in and again on the way out.
For lithium iron phosphate the product is around eighty-five percent. For flooded lead-acid it is around forty. That is why a ten kilowatt-hour daily load needs an eleven point eight kilowatt-hour lithium bank or a twenty-five kilowatt-hour lead-acid one — and why comparing the two on price per nameplate kilowatt-hour is the wrong comparison entirely.
- D
- depth of discharge (0.5 for lead-acid, 0.9 for LiFePO₄)
- η
- round-trip efficiency (0.80 to 0.95 by chemistry)
Energy and power are different questions
A bank with ample energy can still be unable to start a motor. Energy in kilowatt-hours determines how long something runs; power in kilowatts determines whether it can run at all, and surge capacity determines whether it can start.
Sizing on energy alone is a common omission. A battery adequate for a day's consumption may still trip on the inrush of a well pump or a compressor, and that is a continuous and peak kilowatt question the energy figure does not touch.
Both figures decay
Capacity falls with age and with temperature. Most warranties guarantee seventy to eighty percent of nameplate at end of term, so a bank sized exactly for today's load is undersized by year eight. Cold reduces available capacity substantially in the moment, and lithium cannot be charged below freezing at all without a heater.
None of this is modelled by the equation. It is why an off-grid system sized to exactly meet its load is a system that will not meet it for long.
Calculators that use this method
- Battery Bank Sizing CalculatorSize a battery for a daily load and days of autonomy — with the usable capacity, not the nameplate.
- Off-Grid Autonomy CalculatorWork out how long a battery bank runs a given load, and how much array is needed to replace it each day.
- Battery Backup Runtime CalculatorEstimate how long a battery backup system will power a load before depleting.
Basis
- Depth of discharge and round-trip efficiency figures from manufacturer datasheets; LiFePO₄ 90%/95%, flooded lead-acid 50%/80%.