## Introduction

A battery is a device that converts chemical energy into electrical energy. The amount of energy that can be stored in a battery is expressed through the battery’s capacity.

Capacity is the total Ampere hours available when the battery is discharged at a specific discharge current from a fully charged state to the end voltage. End voltage or cut-off voltage varies depending on battery type:

- Lead acid – 1.75 V per cell
- NiCd –1.0 V per cell
- Li-ion – 3.0 V per cell

Capacity is calculated by multiplying the discharge current (in Amperes) by the discharge time (in hours) and decreases with increasing discharge current.

For secondary batteries, nominal capacity is usually given as capacity for a specific discharge rate, typically for stationary batteries a 10-hour or a 20-hour rate.

Discharge current, as well as charging current, is usually expressed as a C-rate. A current required for a 1-hour discharge is described as 1C, a 2-hour discharge is C/2 or 0.5C and a 10-hour discharge is C/10 or 0.1C.

The table below shows the discharge times for different C-rates.

C-Rate | Time |

0.05C or C/20 | 20 h |

0.1C or C/10 | 10 h |

0.2C or C/5 | 5 h |

1C | 1 h |

2C | 30 min |

Discharging batteries with different C-rates will yield different capacity measurements. A higher discharge current than the C-rate at which the nominal capacity was determined will result in lower capacity removed from the battery before it is fully discharged.

For example, a battery with a nominal capacity of 100 Ah (C_{10} capacity for a 10hour discharge), when discharged with a 10 A current (C/10 rate) will take 10 hours to discharge the battery fully. However, if the same battery is discharged with double the current (20 A), due to the internal losses, the discharge time would not be the expected 5 hours, but a shorter time. The same is true and vice versa. When discharging with lower C-rates than the one based on which the nominal capacity is determined, the capacity will be increased.

As shown in the table above, the current for a 10h discharge down to 1.75V per cell is 16.4 A. If the capacity did not depend on the discharge current, we would expect the test current for a 5h test to be twice as high (32.8 A). However, in this case, the C/5 test current is slightly lower at 30.9 A.

The nominal capacity of a battery is usually shown in Ampere hours for a certain C-rate, for example, 100 Ah/ C10. In order to compare batteries, we need to know the rate at which the nominal capacity is determined.

The table below is an example of two batteries with 120 Ah nominal capacity:

- Battery 1 – nominal capacity (C/10): 120 Ah
- Battery 2 – nominal capacity (C/20): 120 Ah

If our application requires the battery to provide a current of 12A for 10 hours (which is 120 Ah), Battery 2 would not be able to comply with the requirement. As can be seen from the table, despite this battery having a nominal capacity of 120 Ah, that capacity is for a 20-hour discharge rate. The C/10 rate for Battery 2 is 11.17 A which is lower than the required 12 A. In this example, only Battery 1 can comply with the requirement.

## Determining the C-Rate for a Performance Capacity Test

The discharge rate for a capacity test should be a constant current or constant power load based on the manufacturer’s rating of the battery for the selected test length

Typically, the C-rate that will be used for a performance capacity test of a certain battery depends on the following:

- Battery’s duty cycle
- Previous performance tests
- Available test equipment

### Battery duty cycle

According to IEEE and IEC standards which define recommended practices for maintenance, testing, and replacement of secondary batteries (VLA, VRLA, and NiCd) for stationary applications, the discharge rate should be selected so that it is approximately the same as the duty cycle of the battery.

### Previous performance tests

It is recommended to use the same C-rate used in previous performance tests. This way the results can be compared and capacity degradation over time can be tracked more easily.

### Available test equipment

Performance tests are constant current discharge tests. The equipment used for testing does not only need to be able to regulate itself to keep the current constant as the voltage is falling throughout the test; it also needs to have a high enough discharge current to discharge at a specific C-rate.

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November 3, 2022