Christopher LaForge: Battery Capacity – The Basis of Storage

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 6-week course that provides in-depth 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 battery-based 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 1-hour 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 amp-hours or watt-hours. Battery manufacturers of true deep-cycle batteries almost exclusively rate their products in terms of amp-hours.

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 make-up and quantity of the electrolyte.

 

Typical lead-acid batteries come in two primary types: those used for motor starting and those used in deep-cycle 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 ‘sponge-lead’) that give great contact surfaces to the electrolyte and allow for greater amperages for motor starting. True deep-cycle 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 ampere-hour or amp-hour (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.

Charles-Augustin 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 C-rate 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 amp-hours at the discharge rate “I”
H – is the rated discharge time (in hours)
C – is the rated capacity at that discharge rate (in ampere-hours)
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 make-up 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 “6-hour rate” (0.166C) or “20-hour rate” (0.05C) or “100-hour 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 deep-cycle use usually to 80% state of discharge). Large industrial batteries like the fork-truck type are often rated at the “6-hour” 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 “20-hour” 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 “6-hour” rate and the “20-hour” rate. Heavy industry works with high amperage discharge and therefore most often employs the “6-hour” 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 “20-hour” 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 20-HR TO 6-HR CAPACITY

To convert a 20-hour rate to a 6-hour rate, multiply 20-hour ampere-hour capacity by 0.84. Divide the result by 6 hours to determine the approximate discharge current rate.
To convert a 6-hour rate to a 20-hour 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 6-hour 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 6-hour 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 (cycle-life) 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 cycle-life is reduced.

One manufacturer’s cycle-life vs. depth of discharge graph:

 

This set of issues is expanded on and illuminated in my 6-week 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:

Battery University

The Gizmologist’s Lair

Electropaedia

BatteryStuff.com