SmartGauge Electronics - The "charge efficieny" anomoly

Charge efficiency of lead acid batteries.

Charge efficiency is usually expressed as a percentage representing the amount of power got out of a battery when compared to the amount put into it during charging.

A common figure for wet cell deep cycle batteries is 85%. Gells and AGMs are usually quoted as being slightly higher at around 90 to 95%

Some amp hours counters claim to show the charge efficiency as a result of the meter calculating how many amp hours were returned to the battery compared to how many were removed during discharging.

Only when one tries to think rationally about what these figures actually mean, and try to use them as the basis of some form of calculation does one realise just how misleading the whole idea really is.

Let's tackle it in the usual way with some examples.

We'll take a 100 amp hour (20 hour rate) battery with a quoted charge efficiency of 90%. This means that whatever we take out of the battery, we will have to put more back in during recharging in the ratio of 10/9^ths

So assume we remove 9 amp hours from the battery. We will have to put back in 10 amp hours to reach the same level of charge. This is what the 90% charge efficiency means.

Let's start by making the assumption that the amp hours removed must be Peukert corrected otherwise the calculations will be wildlly out. If this makes no sense to you, then go back and read the section on Peukert's Equation.

So let's try this. We discharge the battery, at a certain rate, so that the Peukert corrected amp hours removed is exactly 9 amp hours.

Use the Peukert Calculator again. Enter the capacity of 100 Amp hours, 20 hour discharge rate and a Peukert's exponent of 1.3

Enter (in the bottom box) a discharge rate of 7.86 amps. Now look at the Peukert corrected amps. You will see it is 9.00 amps. So if we maintain this discharge rate for one hour we will remove 9 amp hours from the battery. Assuming the battery was fully charged when we started, the battery will now be at 91% charge state.

According to the quoted charge efficiency of 90% we now have to return 10 amp hours to the battery in order to reach 100% charge state again. This seems perfectly fair and rational. Nothing is 100% efficient.

So we removed 9 amps hours and put back in 10 amp hours. This is (as we started from this figure) a charge efficiency of 90%. However, due to Peukert's effect we only actually got out of the battery 7.86 amp hours to power our loads. So if we use this figure (i.e. the useful power we actually got) then the charge efficiency becomes 78.6%. Somewhat lower than the quoted 90%.

So which is correct? One (or perhaps both) must be incorrect.

If we say that the useful power we got out of the battery to power our loads is the correct figure to use, then this means that at higher discharge rates the charge efficiency becomes lower. For instance let's try this again at double the discharge rate, i.e. 15.72 amps. Use the Peukert calculator again. This gives a Peukert corrected amps figure of 22.17 amps. So if we run this load for 0.46 (decimal) hours this adds up to 9 amp hours. But to power our loads we got useful power of 15.72 amps for 0.46 hours = 7.23 amp hours. So now the charge efficiency comes out at 72.3%. This is even lower than last time.

So if we try to use the actual power we used, the charge efficiency seems to get lower as the loads become heavier. Clearly this cannot be correct. The whole point of charge efficiency is that it shows how much power we have to put back in, when expressed against how much power we got out. How we took the power out is not supposed to have any effect on the charge efficiency. But in this example it clearly does have a very large effect. (how we took the power should not affect the result, if it is supposed to affect the result, then it should be called the discharge/recharge efficiency, which it isn't).

So now let's try it with the Peukert corrected amps.

We know from the first calculation that 7.86 amps removed 9 amp hours (Peukert corrected) in 1 hour. We also know that according to the charge efficiency of 90% we would have to put back in 10 amps hours to get back to the same state of charge.

Let's double this figure again to 15.72 amps. This gives a Peukert corrected amps figure of 22.17 amps. So this load for 0.46 hours removes 9 amp hours. 10 amps to get back to fully charged. Now we can't actually test this idea without actually running the test on a battery. But this seems to be the figure that is implied. Let's assume this to be correct.

And then let's try something different.

Let's discharge the battery at a very low rate. Let's discharge it with a 1 amp load for 9 hours. Thus we get out of the battery 9 amp hours of useful power to run the load. 1 amp gives a Peukert corrected amps figure of 0.62 amps. We ran the load for 9 hours, 9 hours * 0.62 amps = 5.58 Peukert corrected amp hours. So according to the charge efficiency of 90% we will have to replace 10/9^ths of this which is 6.2 amp hours.

With me so far?

Good, then you'll realise how ridiculous this is. According to this "charge efficiency" number we now have a situation where we got out of the battery a useful 9 amp hours to power the load, but only had to return 6.2 amp hours to get back to the same state of charge.

Even worse..... A quoted charge efficiency of 90%, seems to imply that, with our 100 amp hour battery, discharged to 91% charge state, we have to return 10 amps to get back to 100% charge state. Assume that the battery discharged to 91% by self discharge, i.e. with no load connected, with a wet cell this would take around 2 to 3 weeks. We now have to return 10 amp hours to get back to a fully charged state. But we got no power from the battery. So in this case the charge efficiency is zero.

A simpler way to look at this anomoly is as follows........

A quoted charge efficiency of 90% is supposed to mean that we have to return 10 amps to a battery in order to take the charge status of that battery from 91% back up to 100%. But to discharge the battery from 100% to 91% depends upon how we discharged it. A very heavy discharge would reach 91% after having actually used very little total amp hours, a very light discharge would reach 91% after having used a lot of total amp hours. This is due to Peukert's effect.

So if we perform the calculation using Peukert corrected amps, we find that the charge efficiency varies depending upon the rate of discharge.

If we perform the calculation using non Peukert corrected amps we find that the charge efficiency can exceed 100% which is an impossibility.

Clearly something is very wrong.

I can assure you it isn't Peukert's equation or effect that is wrong. Peukert's equation has been used and tested for well over 100 years and found to operate reliably every time (assuming the correct formula is used).

The problem is the "Charge Efficiency". It is something that can only be measured for a certain discharge and recharge cycle. It cannot be calculated. It cannot predict anything. The effect of it can be measured. But change the discharge loads, or their duty cycles, or the charge rate, and the "charge efficiency" will come out different every time.

It is perfectly possible to run 2 consecutive discharge/recharge cycles on the same set of batteries and get results of 20% in one cycle and 90% in the other.

It is possible to run tests, and give demonstrations, showing just about any "charge efficiency" figure for a certain battery. Obviously to quote a higher figure gives a better impression. But as I have shown here, that figure is actually quite useless.

In tests during the devlopment of SmartGauge we found the charge efficiency as displayed by some amp hours counters to be around 80% to 90% for most batteries. Yet when we actually measured the effect manually we found the true figures to be anywhere between 30% and 70% depending upon how the battery had been discharged and how fast it was recharged with a true average figure of around 55%

"Charge efficiency" is almost completely unrelated to the battery it supposedly applies to. True, the battery can affect the results of a certain test, but nowhere near as much as how the power is removed and returned to the battery.

"Charge efficiency" is more or less meaningless. It cannot be used to make any predictions of how long it will take to recharge batteries. It can be used an as estimate, but that is all it will ever be. It most certainly cannot be used to calculate how many amp hours will have to be replaced in order to reach a fully charged state as some amp hours counters attempt to do.

For those who are intersted there is a further discusion here of a very closely related subject.

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