The article below was written by Christopher LaForge, NABCEP Certified PV Installation Professional and IREC Certified Master Trainer. Christopher LaForge teaches Batteries in Solar PV Systems, a 6week course that provides indepth analysis of the issues surrounding the use of batteries for PV applications. The course covers battery design, specification, use, maintenance and concludes with a capstone project where students create the design for a batterybased solar PV system. Christopher has created a free lecture, Battery Capacity – The Basis of Storage, that is available to view any time. It also includes a 1hour MP3 recording of a Q+A call in which Christopher answers participant questions.
BATTERY CAPACITY
Battery capacity is the amount of energy that a battery is rated to provide. This amount of energy is indicated by metrics that include current (amperage) or power (wattage) over a given period of time (usually hours).
Therefore, battery capacity is usually given in amphours or watthours. Battery manufacturers of true deepcycle batteries almost exclusively rate their products in terms of amphours.
While this may seem simple, unfortunately battery capacity is affected by many factors and conditions that make straightforward understanding challenging.
The capacity of any battery is created by a combination of the type and amount of active materials in the battery, the size of the surface area of the battery plates, the plate density, and the makeup and quantity of the electrolyte.
Typical leadacid batteries come in two primary types: those used for motor starting and those used in deepcycle applications such as traction batteries used in vehicles, fork trucks, and storage as in PV systems. Motor starting batteries have less dense plates (often referred to as ‘spongelead’) that give great contact surfaces to the electrolyte and allow for greater amperages for motor starting. True deepcycle batteries use denser plates and can store more energy for greater periods of time.
The capacity of each battery is measured by discharging the battery at constant amperage until it goes below its useful (or terminal) voltage. Under standard test conditions the measurement is conducted at a constant temperature – usually 77°F (25°C). The battery’s capacity is calculated by multiplying the discharge amperage by the time it took to reach its terminal voltage.
So one amperehour or amphour (Ah) is the unit of electrical charge represented by the amount of electric charge transferred by a current of one ampere for one hour.
Many parameters affect the measurement achieved in the testing process.
CharlesAugustin de Coulomb proposed that a battery that receives a charge current of one ampere (1A) passes one coulomb (1C) of charge every second. This has led the battery industry to use Crate to scale the charge and discharge current of a battery. Small portable batteries are most often rated at the 1C rate. Therefore if a battery is considered a 1000 mAh battery it is expected to provide enough energy to achieve 1000mA current for one hour.
It was the German scientist W. Peukert who mathematically represented the fact that the capacity of a battery changes based on the rate at which it is discharged, showing that as the rate increases, the battery’s available capacity decreases. His “law” can be expressed as:
With ‘It’ being equal to the capacity in amphours at the discharge rate “I”
H – is the rated discharge time (in hours)
C – is the rated capacity at that discharge rate (in amperehours)
I – is the actual discharge current (in amperes)
K – is the Peukert constant (dimensionless)
T – is the actual time to discharge the battery (in hours)
To make this all a bit more interesting, Peukert’s constant is not a single constant but rather is a constant based on the makeup of the components of the battery and its age. This “constant” therefore changes with battery type and age.
For our purposes this is as deep as we will go with this article. However, if you are interested in the deep vagaries of Peukert’s law – the equations that represent it and how you calculate changes in Peukert’s “constant” you can delve deeper in this article from BatteryStuff.com.
The most critical fact here is that the amount of energy a battery will provide is influenced by the rate at which the power is removed. If power is removed in large quantities (high amperage rates) the capacity of the battery is reduced. If power is removed more slowly the capacity is increased. This has led manufacturers to provide battery capacity data in different rates based on the amount of time the capacity is consumed by a given amperage load. Hence the capacity of a given battery is represented in its “6hour rate” (0.166C) or “20hour rate” (0.05C) or “100hour rate”(0.01C).
So the Ah capacity of a given battery depends both on the rate at which it is being discharged and the amount of time it takes to discharge it (for industrial deepcycle use usually to 80% state of discharge). Large industrial batteries like the forktruck type are often rated at the “6hour” rate, indicating a large ampere discharge rate bringing the battery to a terminal voltage (often 20% state of charge) in 6 hours. For renewable energy systems we usually employ the “20hour” rate indicating a modest discharge rate that brings the battery to a terminal voltage (again often 20% state of charge) over 20 hours.
The most common rates used to represent capacity are found to be the “6hour” rate and the “20hour” rate. Heavy industry works with high amperage discharge and therefore most often employs the “6hour” rate. In the renewable energy industry we tend to design our systems to cycle the batteries more “lightly” and for this reason we most often use the “20hour” rate. Because of this it is handy to be able to convert the two common rates. This can be accomplished using a general rule of thumb:
CONVERT 20HR TO 6HR CAPACITY
To convert a 20hour rate to a 6hour rate, multiply 20hour amperehour capacity by 0.84. Divide the result by 6 hours to determine the approximate discharge current rate.
To convert a 6hour rate to a 20hour rate multiply it by 1.5764705.
By this rough method we can convert rates and adjust the discharge rate employed.
Here is an example for converting 6hour rates to other longer rates:
GB Industrial Battery’s Battery Capacity Calculator
In this example we can see that a typical L16 (350Ah/6VDC at the 20 hour rate) has a 225 Ah capacity at the 6hour rate.
Hours 
AH 
KWH 
Continuous Amps 
1000 

6 
225 
1.31 
37.50 
1.350 

7 
232 
1.35 
33.20 
1.395 

8 
240 
1.43 
30.01 
1.441 

9 
248 
1.48 
27.56 
1.488 

10 
256 
1.53 
25.62 
1.537 

11 
265 
1.58 
24.06 
1.588 

12 
273 
1.63 
22.78 
1.64 

13 
282 
1.68 
21.72 
1.694 

14 
292 
1.74 
20.84 
1.75 

15 
301 
1.80 
20.09 
1.808 

16 
311 
1.85 
19.46 
1.868 

17 
322 
1.92 
18.92 
1.929 

18 
332 
1.98 
18.45 
1.993 

19 
343 
2.04 
18.06 
2.059 

20 
354 
2.11 
17.72 
2.127 

21 
366 
2.18 
17.44 
2.197 

22 
378 
2.25 
17.19 
2.27 

23 
391 
2.33 
16.99 
2.344 

24 
404 
2.41 
16.82 
2.422 

Accuracy = +/ 2% depending on model. 
BATTERY TEMPERATURE
Batteries are specified with the assumption of operation at 77°F (°C). When we move out of the 60°F to 80°F range, the battery performance changes. At somewhat higher temperatures batteries may perform better, but at high temperatures (125°F+) batteries can be severely damaged.
Batteries at temperatures below the 60°F range begin to show reduced capacity. Below 32°F batteries will show significantly lower capacity, and, while the battery has not actually lost the energy it is storing, the cold temperatures restrain the battery’s chemical activity resulting in lower availability of its capacity. Remember, a discharged battery’s electrolyte is no longer highly acid, and, being more like water, it can easily freeze. Freezing a battery can destroy the cells. Some final considerations to examine are battery age and the effect depth of cycling has on aging.
Battery Age
As batteries age there is depletion of the active material and sulfation occurs on the plates. Both actions reduce the plate conductivity and thereby reduces the battery’s capacity. While careful maintenance— including regular equalizing charges—can slow battery aging, all batteries will age and eventually become useless. How aging affects the capacity of a battery depends on how the battery is operated.
Depth of Cycling
Aging is not a matter of months and years, but rather number of cycles and the depth of each cycle. Therefore if each cycle is shallow—less than 50% depth of discharge (DOD)—the number of cycles (cyclelife) is increased and the battery ages more slowly. Conversely, if each cycle is deep (80% DOD or greater) the battery ages more quickly and its cyclelife is reduced.
One manufacturer’s cyclelife vs. depth of discharge graph:
This set of issues is expanded on and illuminated in my 6week intensive course: Batteries In Solar PV Systems.
Please send feedback, comments, and your thoughts to me through the HeatSpring website or by commenting below. Thank you for your interest in batteries and their capacity!
Energetically, Christopher LaForge, NPIP & IREQMT
Additional information can be found on these websites:
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