Ask how long a battery takes to charge and the naive answer is capacity divided by current: 150 Ah on a 15 A charger, ten hours from empty, five from half. The real answer is longer at the start, because not every amp-hour delivered is stored, and slower at the end, because a battery near full will not take the current however hard the charger pushes. The two effects explain most of what goes wrong with batteries in Pakistani homes, where the utility rarely stays on long enough for the second half of the charge to happen.
Amp-hours in, amp-hours out: the efficiency loss
Charging a lead-acid battery reverses the discharge reaction: the lead sulphate on both plates is converted back into lead, lead dioxide and sulphuric acid. Not all of the current does that. Some of it, especially near the top of charge, splits water into hydrogen and oxygen instead, which is the gassing you can hear in a flooded battery, and some is lost as heat. The ratio of amp-hours stored to amp-hours delivered is the coulombic, or charge, efficiency: about 80–90 % for flooded lead-acid, 90–95 % for AGM and gel, where the oxygen recombines inside the cell, and 97–99 % for lithium iron phosphate, which has no side reaction to feed.
The consequence is that a 50 % discharge of a 150 Ah battery takes 75 Ah out and needs 75 ÷ 0.85 = 88 Ah put back. The energy efficiency is lower again, because the battery charges at 14 V or more and discharges at 12 V or less: round trip, a flooded battery returns roughly 70–80 % of the energy it was given, and LiFePO4 over 90 %.
The three stages: bulk, absorption, float
A modern charger, whether a bench unit, the charger inside a UPS or hybrid inverter, or a solar charge controller, works in three stages.
- Bulk: constant current at the charger's rating. The battery voltage rises steadily as it charges. The stage ends when the voltage reaches the absorption set point, 14.4–14.8 V for a 12 V flooded battery, which for a healthy battery at a sensible current happens at about 80 % state of charge.
- Absorption: constant voltage. The charger holds the set point and the current falls as the battery approaches full, because the current is driven by the difference between the charger voltage and the battery's own rising voltage, and that difference is shrinking. The remaining 20 % goes in during this taper, which takes two to four hours regardless of how large the charger is: a lead-acid battery can only absorb charge as fast as acid diffuses into the pores of the plates. The stage ends when the current has fallen to about 1–2 % of the capacity, or after a set time.
- Float: a lower constant voltage, 13.5–13.8 V per 12 V, that replaces self-discharge and keeps the battery full without gassing it. A standby battery spends its life here.
Lithium iron phosphate follows the same shape with different proportions: constant current to about 95 %, a short constant-voltage tail of a few minutes to half an hour, and then no float at all; the battery management system disconnects the charge path or the charger backs off.
C-rate: how hard you can push a battery
The C-rate expresses current as a fraction of capacity: 15 A into a 150 Ah battery is 0.1 C, and would fill it in ten hours if the efficiency were perfect and there were no absorption stage. The rate a battery accepts without damage is set by its construction.
- Flooded lead-acid: about 0.1 C, the classic ten-hour rate. Tubular-plate batteries, the standard type under Pakistani UPS inverters, are often rated for a little more than flat-plate ones, but not much. Above the limit the plates heat, water splits faster than the gas can escape, the active material on the positive plate loosens and sheds, and the water level falls; each of these shortens life.
- AGM and gel: about 0.2 C, because the immobilised electrolyte and the recombination of oxygen inside the cell cope with a higher rate. They must not be overcharged, though: there is no water to top up and no vent to release sustained gassing.
- LiFePO4: 0.5 C routinely and 1 C for many cells, limited by the battery management system and by heat. A 100 Ah lithium battery on a 50 A charger is full in a little over two hours, a different world from lead-acid.
A larger charger than the battery accepts is not a faster charge; it is a hotter battery and, for lead-acid, an earlier arrival at the absorption voltage, so the bulk stage ends at 60 % instead of 80 % and the slow stage is longer. The battery charging time calculator flags any current above the recommended rate for the chemistry.
Why the last 20 % takes as long as the first 50 %
The bulk stage scales with the charger: double the current and it halves. The absorption stage does not: it is set by how fast the chemistry can finish, and the charger simply waits. So for a 150 Ah AGM battery on a 30 A charger (0.2 C) the arithmetic runs: 30 % to 80 %, 150 × 0.5 ÷ 0.92 ÷ 30 = 2.7 h; 80 % to 100 %, 2.5 to 4 hours of absorption. The last twenty points take as long as the fifty before them, and on a bigger charger, longer. That is the origin of the "80 % in an hour" figures quoted for phones and electric cars: the fast part is the bulk stage, and the slow part is left out of the headline.
The physics is diffusion. As the plates convert, the sulphate that is left sits in the deepest pores, where fresh acid arrives slowly; the reaction can only go as fast as the acid gets there, and forcing more current only splits water. Holding the voltage and waiting is the only way to finish, and a charger that gives up early, or a supply that goes away, leaves that sulphate in place. Old batteries take longer still, because their internal resistance is higher, so they reach the absorption voltage sooner in the bulk stage and hand more of the job to the slow stage.
Charging from solar: current is what the array gives, not what the battery wants
A mains charger delivers its rated current for as long as it is asked to. A solar charge controller delivers whatever the array is producing at that moment: nothing at dawn, a ramp through the morning, a plateau around midday, a fall in the afternoon, and less than half of all that under cloud. The battery sees a bulk stage stretched over the morning and an absorption stage that must fit into the afternoon before the sun goes, and on a poor day it may never reach the absorption voltage at all.
The sizing consequence is that the array must be able to deliver something like 0.1 C into the bank in full sun to complete a daily cycle. For a 12 V 150 Ah battery that is 15 A at about 14.4 V, or 216 W at the battery terminals; allowing for controller, temperature and wiring losses, roughly 270–300 W of panel through an MPPT controller. With a PWM controller the panel voltage must match the battery, and a high-voltage panel through a PWM controller on a 12 V battery delivers only its rated current at battery voltage, about a third of its wattage.
The solar sizing calculator sizes the array from the daily energy; check the result against this charge-rate requirement too, and size the bank so that the daily discharge is within what the array can put back before the afternoon ends. The solar sizing guide covers the losses.
The load-shedding trap: chronic undercharging
Put the numbers together for the battery under a typical Pakistani UPS: a 12 V 150 Ah tubular, an inverter that charges it at 15 A, and a summer schedule of outages every few hours.
Suppose an outage takes the battery to 50 %. Refilling it takes about 6 hours, 3.5 in bulk and 2.5 in absorption. If the utility returns for 4 hours, the charger completes the bulk stage and half an hour of absorption, and the battery is a little over 80 % when the next outage begins. That outage takes out the same 75 Ah, so it ends near 30 %; the next 4-hour window puts back at most 4 × 15 × 0.85 = 51 Ah, or 34 %, and the battery does not even reach the absorption voltage. Each cycle starts about 16 percentage points lower than the last, until the inverter's low-voltage cut-off ends an outage early and the household blames the battery.
What this does to lead-acid is sulphation. Lead sulphate is the normal discharge product and converts back on charge, but only if the battery is brought to full charge regularly; sulphate that sits for days recrystallises into a coarse, hard form that will not convert, and the capacity it represented is gone. A battery that never sees the end of an absorption stage loses capacity month by month, shows a full voltage on the inverter display, which measures voltage rather than capacity, and collapses under load. It is replaced in a year or two and the replacement meets the same schedule.
Three things break the cycle. A charger current near 0.1 C rather than whatever the inverter was set to when it was installed; an absorption stage allowed to finish, which needs a long enough utility window or a solar array every few days; and, where the outages are long and frequent, LiFePO4, which charges at 0.5 C so that a four-hour window refills it completely, and which does not sulphate: it is content to live at partial charge indefinitely. That, more than the cycle life on the brochure, is the practical case for lithium in a load-shedding backup system.
The example in numbers
The calculator's default: 12 V 150 Ah flooded, at 50 %, 15 A charger, 85 % charge efficiency, 2.5 h absorption.
- Ah to replace: 150 × 0.5 ÷ 0.85 = 88.2 Ah.
- C-rate: 15 ÷ 150 = 0.10 C, at the recommended limit for flooded lead-acid.
- Bulk, 50 % to 80 %: 150 × 0.3 ÷ 0.85 = 52.9 Ah, 3.53 h at 15 A.
- Absorption, 80 % to 100 %: 35.3 Ah, 2.35 h at full current, so the 2.5 h set time governs.
- Total about 6.0 h. Energy into the battery ≈ 88.2 × 12 = 1 059 Wh, roughly 1.4 units from the mains after the charge voltage and the charger's losses.
- To refill in an 8-hour night, 11.0 A (0.07 C) is enough: at that current the absorption stage stretches to 3.2 h and bulk plus absorption come to exactly 8.
The same 150 Ah as LiFePO4, at 98 % efficiency on a 75 A (0.5 C) charger with a half-hour tail: 76.5 Ah to replace, 0.92 h of constant current to 95 %, the half-hour tail, and full in about 1.4 hours. That is the difference a four-hour utility window turns into a full battery instead of a slowly dying one.
Reading the charger: when it is done
Any three-stage charger or inverter shows its stage, and the stage tells you more than the percentage on the display, which is usually a guess from voltage. In bulk, the current is at the rating and the voltage is climbing. In absorption, the voltage is pinned at the set point and the current is falling; for lead-acid the battery is full when the current has dropped to about 1–2 % of its capacity, 1.5–3 A for a 150 Ah battery, and stays there. When the charger drops to float and the current settles at a fraction of an amp, the job is done. If the charger reaches float within an hour of a deep discharge, the battery has lost capacity; if it never reaches absorption, the charger is too small for the load or the utility windows are too short.
Off charge, a flooded battery rested for a few hours reads about 12.6–12.8 V per 12 V when full, 12.2 V at half and 12.0 V at a quarter; a hydrometer reading of the specific gravity in each cell is the direct measure for flooded types, and a cell reading well below its neighbours is the failed one. Temperature matters to all of this. Charge voltages should be compensated by about −3 to −5 mV per °C per cell above 25 °C, which in a 40 °C summer takes a 14.6 V setting down by 0.3–0.45 V; a charger without compensation gasses the battery all summer.
References
- IEC 61427-1:2013, Secondary cells and batteries for renewable energy storage — General requirements and methods of test — Part 1: Photovoltaic off-grid application
- IEEE Std 450-2010, Recommended Practice for Maintenance, Testing, and Replacement of Vented Lead-Acid Batteries for Stationary Applications — charging, float and equalisation of flooded batteries
- IEEE Std 1188-2005, Recommended Practice for Maintenance, Testing, and Replacement of Valve-Regulated Lead-Acid (VRLA) Batteries for Stationary Applications — AGM and gel
- IEC 62619:2022, Secondary cells and batteries containing alkaline or other non-acid electrolytes — Safety requirements for secondary lithium cells and batteries, for use in industrial applications — charge limits and battery management for lithium