The Cold Battery Bound: What Low Temperature Takes from a Lead–Acid Store, and Oversizing versus Insulating Priced in Usable Winter Capacity

Lead–acid batteries lose capacity as they cool, and they lose it exactly when an off-grid store is needed most. This paper puts a bound on the loss for a stated system — a 48 V, 200 Ah bank of 9.6 kWh nominal capacity, discharged to a 50 percent limit, serving a daily load of 1.2 kWh — using two stated empirical relations: capacity falls by 0.9 percent of its 25 °C value for each degree below 25 °C, and internal resistance grows exponentially with cooling. At −20 °C the capacity fraction is 0.595 and the internal resistance has multiplied by 2.25, and the usable energy falls from 4.702 kWh at 25 °C to 2.728 kWh, a loss of 42 percent, cutting autonomy from 3.92 days to 2.27 days. Two remedies are then priced in a single account, as capital cost per kilowatt-hour of usable capacity at the winter condition. Restoring the full warm-weather usable capacity at −20 °C by oversizing alone requires a bank 1.723 times as large — 16.55 kWh nominal, at a total cost of $2,978, or $633 per usable winter kilowatt-hour. An insulated enclosure costing $350 that holds the same bank at 10 °C recovers usable capacity to 4.042 kWh at $514 per usable winter kilowatt-hour, but leaves a shortfall of 0.660 kWh and burns 0.36 kWh per day in its own heater, 23.1 percent of total daily demand. Combining the enclosure with a modest oversizing factor of 1.163 restores the full 4.702 kWh for $2,360 in total, $502 per usable winter kilowatt-hour — cheaper than either remedy used alone at full restoration. The remedies cross in capital cost at an ambient temperature of about 7 °C: above it, the extra battery needed is cheaper than the enclosure; below it, the enclosure is the cheaper first purchase. Cold, in short, is not a footnote to sizing an off-grid store; at −20 °C it is nearly half the store.