# What is the charge-discharge watt hour (Wh) efficiency for lead acid batteries at different SoC and charge current 10-35A/100Ah C10?

There is a 1996 Sandia study with the title "A study of lead-acid battery efficiency near top-of-charge and the impact on PV system design" for charge and discharge lead-acid battery amp hour [Ah] efficiency at different states of charge (SoC) for a Trojan 30XHS low-antimony flood lead acid battery.

## Current variation

However these results are measured using a charge current of only 3.3 amps per 100Ah of rated battery capacity. Real world PV/solar charge current are much more varying and at least have high peaks. That is one of the reasons why AGM is chosen, the ability to charge with up to 40 amps per 100Ah of rated capacity. Manufacturers for solar OPzS (flooded lead acid batteries) do allow charge current of 35 amps per 100Ah of rated C10 capacity.

## Watt hour efficiency

Due to the fact that charging voltage is higher then discharging voltage, the nett effective Wh power efficiency is always lower then the Ah efficiency. And that Wh-efficiency is the only (real world) efficiency statistic I am interested in.

The only numbers I could find are in this "Electrolyte mixing for VLA cells" document from Hoppecke at page 10, with 10 amps per 100Ah charge current and from 50 to 106% SoC resulting in a watt hour [Wh] efficiency of 71.6%.

Is there any study know for flooded lead acid charge/discharge watt hour efficiencies at higher then 0.033C charge currents?

• Talk to the battery manufacturer. They'll know their batteries better than anyone else. – Michael Karas Feb 10 '15 at 15:08
• 70% or so sounds about right. A first-order clue is the ratio between the average charge voltage and the average discharge voltage, which is about 75-85% for a lead-acid battery. That just accounts for the I^2R losses inside the battery, and there are other inefficiencies as well. – Dave Tweed Feb 10 '15 at 15:24
• It is VITAL to note the difference between Wh and Ah efficincy. LA Ah efficiencies can be in the 90%+ area. Wh efficincies will be lowered by the voltage differences. You head your question AND the paragraph related to figs 21 & 22 with WH BUT it is stated in the cited manual that they are Ah. The Wh %ages will be 'somewhat lower'. – Russell McMahon Dec 28 '15 at 22:55

# 90.5% @0–100% SoC

for electrolyte type A

# 89.1% @0–100% SoC

for electrolyte type B

I read reverse calculated this from graphs in a non-public measurement report where 2 different types of battery electrolyte (solid/gel) technologies were compared for a 0 to 100% SoC (state-of-charge).

Battery measurements were taken by a technical university, at 21ºC room temperature during 1 month, the year 2013, comparing the results from 150-180 discharge/charge cycles. Batteries under test were all in the range between 5 and 10Ah.

• charging curve: CC-CV
• charge to discharge point: V = 14.375V and I < 0.30A
• discharge to charge point: 0% SoC
• resting period: not specified
• 0% SoC was defined as discharge voltage reached 10.8V (1.8V per cell)
• 100 SoC was defined as charge voltage reached 14.375V (2.396V per cell)
• charge was done at a rate of 0.3C (+/- 0.05C)
• discharge was done at a rate of approximately 0.1C (fixed resistor was used)

The result between charging and discharge power was (remarkably) about 1.6Wh for both battery types, where one battery had a remaining capacity of approximately 40Wh and the other 20Wh.

Some data read back from the graph (resulting in lower accuracy) for electrolyte technology A:

Cycle   Charge [Wh]   Discharge [Wh]
1       100           91
2       100           88
3       100           86
4        97           81
5        92           76
6        86           73
7        81           69
8        78           67
9        74           64
10       73           63
11       70           61
12       69           59
13       65           56
14       63           55
15       61           52

136      44           40
137      44           40
138      44           40
139      45           40
140      45           40
141      43           40
142      44           40
143      45           40
144      44           40
145      44           40


According to my opinion the last measurements are more significant than the first measurements due to the initial formation process. Average last 10 cycles power charged into the battery is 44.2Wh. Average last 10 cycles power discharged from the battery is 40.0Wh.

Some data read back from the graph (human graph point via line to value translation) for electrolyte technology B:

Cycle   Charge [Wh]   Discharge [Wh]
1        85           75
2        83           72
3        80           70
4        78           69
5        76           67
6        76           67
7        75           67
8        75           67
9        74           66
10       74           66
11       73           65
12       73           66
13       72           66
14       72           65
15       73           64

136      25           22
137      25           22
138      25           22
139      24           22
140      25           22
141      24           22
142      25           22
143      25           22
144      25           22
145      24           22


Average power charged into the battery during last 10 cycles is 24.7Wh. Average power discharged from the battery is 22.0Wh.