# LiFePO₄ Efficiency

## An Eccentric Anomaly: Ed Davies's Blog

Having just carefully charged some LiFePO₄ cells and also just read a thread on the Green Building Forum about battery efficiency I decided to do a little science and measure the efficiency of these cells.

The Green Building Forum discussion particularly mentioned the efficiency at the top end of the charge cycle so that's what I tried to deal with. I took the first four of my cells which had had a proper logged charge cycle and formed them into a nominally 12 V (actually a bit over 13 V) battery. I connected a 12 V, 25 W soldering iron taking a bit under 2 A for just over an hour with the aim of discharging the cells by about 10% of their capacity.

I then recharged the cells individually to about the same state of charge as before: constant current/constant voltage to 3.62 V stopping when the charge current dropped to around 50 mA.

I used the same meters for the discharge and charge cycles - this gave slightly lower voltages and currents than those indicated by the bench power supply. I've no idea which, if either, is right.

As I went along I logged the currents and voltages into a text file: lifepo4-efficiency-expt.txt. Three digit numbers are the tail ends of cell serial numbers, four digits are time of day in hours and minutes, pairs of reals are voltages (V) and currents (A) respectively.

Some rather quick-and-dirty Python in lifepo4-recharge.py reports on the amount of charge (in coulombs and amp·hours) and the amount of energy transferred (in joules and watt·hours) for each run. It linearly interpolates the voltages and currents between readings. In many cases only one of the voltage or current is changing but when they're both changing the power changes quadratically. That'd be easy enough to integrate analytically but that would mean thinking (which is dangerous and needs testing) so the code just does the integration by adding up in one second steps.

The discharge via the soldering iron extracted 7594 C (2.11 A·h) in charge and 99903 J (27.751 W·h) in energy.

The totals for the charge cycles for each of the cells were:

Cell Charge Energy
C A.h % J W·h %
132 7457 2.071 101.8 25704 7.140 97.2
133 8011 2.225 94.8 27575 7.660 90.6
134 8251 2.292 92.0 28949 8.042 86.27
136 7926 2.202 95.8 27402 7.612 91.1

Charge efficiencies are calculated simply by dividing the charge extracted during discharge (which should be the same for all of the cells) by the amount required to recharge each. Energy efficiencies are done in the same way but for one quarter of the extracted energy. A better scheme would have logged the individual cell voltages during discharge to note the energy provided by each cell.

The efficiencies calculated for the first cell are implausibly high. I think the problem was that I was not logging the recharge sufficiently often to accurately follow the point at which the power supply went from constant current to constant voltage. There's a sharp drop in current at that point which is not reflected properly by linear interpolation of currents and voltages giving a large underestimate of the currents and voltages. For the second cell I got lucky and happened to log just before and just after the cut over point so I think the results happen to be reasonable. For the last two cells I (tediously) logged at much higher time resolution giving, I think, much more accurate results.

Obviously, these are approximate efficiency figures for the cells themselves. Chargers and inverters on the input and output will introduce losses as well.