Battery Capacity & Peukert Exponent with the Victron SmartShunt [UPDATED 2024]

Battery capacity is quantified in Ampere-hours (Ah), representing the amount of current a battery can supply over a specific time period. For example, a 100Ah battery, when discharged at a consistent 5A, will be entirely depleted in 20 hours.

Table of Contents

What is the C Rating?

The C rating is a way to describe how quickly a battery will discharge its energy. It’s a measure of the rate at which a battery is either charged or discharged.

How to Understand C Rating Numbers

1C Rate:
- This means the battery will be discharged in 1 hour.
- For a 100Ah battery, the discharge current at 1C would be 100A.
5C Rate:
- This means the battery will be discharged in 1/5 of an hour (discharging quickly only 12 minutes).
- For a 100Ah battery, the discharge current at 5C would be 500A (high current).
C5 Rate:
- This means the battery will be discharged in 5 hours (discharging slowly, lasting 5 hours).
- For a 100Ah battery, the discharge current at C5 would be 20A (low current).

The Two Ways to Write C Ratings

The C rating can be expressed in two ways: either with a number BEFORE the C rating, or AFTER the C rating:

Number Before ‘C’: When the number is before the ‘C’ (like 5C or 1C), it tells you how many times faster than one hour the battery will discharge. If you have a 100Ah battery and you discharge it at 5C, you’re pulling 500A from it. So, 5C means 5 times faster than an hour, or 12 minutes.
Number After ‘C’: When the number is after the ‘C’ (like C5 or C1), it tells you how many hours it will take to fully discharge the battery. For a 100Ah battery, this means you’re pulling 20A from it (because 100Ah/5h = 20A). So, C5 means it will take 5 hours to discharge.

Converting Between the two Notation Formats

With the above in mind, we can therefore say that:

5C = C0.2
0.2C = C5

This is because:

5C is the same as C0.2 because 1/5 = 0.2. So, 5C and C0.2 both mean the battery will discharge in 12 minutes.
1C is the same as C1 because 1/1 = 1. Both mean the battery will discharge in 1 hour.

As you can see, there is one exception to note is which is 1C = C1.

The 1C and C1 notation both refer to the baseline discharge rate over 1 hour. All other “C” ratings are derived or compared based on this 1-hour standard.

In other words:

“1C” Rating:

The number before the “C” indicates how many times the battery’s capacity it will discharge in one hour the battery will discharge. As this is 1, it means the battery will be discharged at its full capacity in 1 hour.
For example, for a 100Ah battery, a 1C discharge rate would mean drawing 100A from the battery, depleting it entirely in 1 hour.

“C1” Rating:

The number after the “C” indicates the number of hours over which the battery will be discharged.
In the case of C1, it means the battery will be discharged over a 1-hour period, which is essentially the same as the 1C rate.

In Summary

5C = C0.2:
- 5C represents a discharge rate where the battery is depleted 5 times faster than its 1-hour rate.
- When you see 5C, think of it as the battery giving out its full capacity in just 1/5 of an hour (12 minutes).
- C0.2 is another way of expressing this same rate, emphasizing the time (0.2 hours or 12 minutes) it takes to deplete the battery.
- C0.2 signifies that the battery is discharged entirely over a duration of 0.2 hours.
C5 = C(5/1):
- C5 represents a discharge rate where the battery is depleted over 5 hours.
- This means if you draw power from the battery at a rate defined by its capacity divided by 5, it will last for 5 hours before being fully depleted.
Relationship: (5/1)C = C(1/5):
- This equation emphasizes the relationship between the two notations.
- While (5/1)C focuses on how many times the battery’s capacity is discharged in an hour, C(1/5) focuses on the fraction of an hour it takes to discharge the battery.

Therefore:

5C ≠ C5:
- 5C represents a discharge rate where the battery is depleted 5 times faster than its 1-hour rate, meaning that the battery gives out its full capacity in just 1/5 of an hour (12 minutes).
- C5 signifies that the battery is discharged entirely over a duration of 5 hours, meaning that the battery will last for 5 hours before being fully depleted if power is drawn at a rate defined by its capacity divided by 5.
0.2C ≠ C0.2:
- 0.2C represents a discharge rate where the battery is depleted at 0.2 times its capacity over 1 hour, meaning that you’re drawing power at 20% of the battery’s full capacity every hour. For a 100Ah battery, this would be 20A every hour.
- C0.2 signifies that the battery is discharged entirely over a duration of 0.2 hours, meaning that the battery is fully depleted in 1/5 of an hour (12 minutes). For a 100Ah battery, this means drawing 500A to empty it in 12 minutes.
Relationship: (1/5)C ≠ C(1/5):
- Both notations involve the fraction 1/5 or 0.2, but they refer to different aspects of battery discharge.
- (1/5)C focuses on the battery’s capacity, indicating you’re using 20% of its total capacity every hour.
- C(1/5) emphasizes the time, indicating the battery is fully discharged in 1/5 of an hour (12 minutes).

While:

1C (1/1) = C1 (1/1) (baseline exception)
- Both “1C” and “C1” refer to discharging the battery over a 1-hour baseline period, thus both refer to the fraction 1/1.

The Peukert Exponent and Battery Chemistry

Battery capacity is not a constant; it diminishes with faster discharge rates.

This relationship is mathematically defined by Peukert’s Law, which uses a variable known as the Peukert exponent. Different types of batteries, such as lead-acid and lithium, are affected differently by the discharge rate.

Battery monitors usually have a setting for the Peukert exponent to account for this.

Discharge Rate Example

A lead-acid battery with a 100Ah capacity at a C20 rate can deliver 100A over 20 hours, or 5A per hour. However, if the same battery is discharged in just 2 hours, its effective capacity may drop to around 56Ah due to the higher C2 discharge rate.

A lead-acid battery rated at 100Ah at C20 can deliver a total of 100A over 20 hours, at a rate of 5A per hour (C20 = 100Ah, because 5 x 20 = 100).

If the same 100Ah battery is fully discharged in two hours, its capacity significantly decreases, possibly providing only C2 = 56Ah due to the higher discharge rate.

Peukert’s Formula

The adjustable value in Peukert’s formula is the exponent ‘n’. In the battery monitor, this exponent can be set between 1.00 and 1.50. A higher Peukert exponent means the effective capacity decreases more rapidly with an increasing discharge rate.

An ideal battery, theoretically, has a Peukert exponent of 1.00, meaning its capacity remains constant regardless of the discharge rate. The default setting for the Peukert exponent in the battery monitor is 1.25, which is a reasonable average for most lead-acid batteries.

The Peukert Formula is:

Cp = I^n * t

Where:

C is the rated capacity of the battery (usually in amp-hours, Ah).
l is the discharge current (in amperes, A).
t is the time of discharge (in hours).
n is Peukert’s exponent, a constant that is specific to each battery type.

Here, n is the Peukert Exponent, which can be adjusted in the battery monitor between 1.00 and 1.50. A higher exponent means the effective capacity decreases more quickly as the discharge rate increases.

An ideal battery would have a Peukert exponent of 1.00, indicating a constant capacity regardless of discharge rate.

To calculate n (Peukert Exponent), we use the following formula:

n = (log(t2) – log(t1)) / (log(I1) – log(I2))

Here, t1and t2 are the discharge times at currents I1 and I2, respectively.

How to Determine the Peukert Exponent

To find the Peukert exponent, you need two different rated capacities for the battery, usually the 20-hour and 5-hour discharge rates.

To determine the Peukert exponent, you’ll need two different rated battery capacities. These are typically the 20-hour and 5-hour discharge rates, although you could also use the 10-hour and 5-hour rates, or the 20-hour and 10-hour rates.

The idea is to use one low discharge rating in conjunction with a significantly higher one.

These capacity ratings are usually available in the battery’s datasheet. If you’re uncertain, it’s advisable to consult your battery supplier for this information.

Example Calculation

Let’s go through a calculation example to find the Peukert exponent using the 5-hour and 20-hour ratings.

Given the following:

C5 Rating: 75Ah (This means the battery can deliver 75A over 5 hours)
C20 Rating: 100Ah (This means the battery can deliver 100A over 20 hours)

Calculating Currents I1 and I2

For the C5 Rating:

t1 = 5h
I1 = 75Ah / 5h = 15A

For the C20 Rating:

t2 = 20h
I2 = 100Ah / 20h = 5A

Calculating the Peukert Exponent (n)

The formula for n is:

n = (log(t2) – log(t1)) / (log(I1) – log(I2))

Plug in the values:

n = (log(20) – log(5)) / (log(15) – log(5))
n = (log(4)) / (log(3))
n = 0.6021 / 0.4771
n = approximately 1.26

So, the Peukert exponent (n) is approximately 1.26.

Note on Peukert Exponent

The Peukert exponent is a rough approximation and may not be entirely accurate, especially at very high currents where the battery may deliver even less capacity than predicted. It’s generally not recommended to change the default value in the battery monitor, except for lithium batteries.

Peukert Exponent Calculator

For those who prefer a more straightforward approach, here is a Peukert Exponent calculator.

Simply enter your custom t1 (discharge time 1), t2 (discharge time 2), I1 (current 1) and I2 (current 2) values to get the accurate Peukert Exponent for your system.

Conclusion

Battery capacity and the Peukert exponent are crucial concepts in understanding the performance and longevity of batteries. The capacity, measured in Ampere-hours (Ah), indicates the amount of current a battery can supply over a specific duration. The C rating, on the other hand, provides insight into how swiftly a battery can discharge its energy. This rating can be expressed in two distinct notations, each conveying either the speed of discharge or the duration of discharge.

The Peukert exponent, derived from Peukert’s Law, is a testament to the fact that a battery’s capacity isn’t static; it varies based on the discharge rate. Different battery chemistries, like lead-acid or lithium, respond differently to varying discharge rates. This exponent, which can be adjusted in battery monitors, offers a mathematical representation of this relationship. The higher the Peukert exponent, the faster the effective capacity of a battery diminishes with an increasing discharge rate.

In practical terms, understanding these concepts is vital for anyone dealing with batteries, whether for personal or professional use. It aids in making informed decisions about battery usage, ensuring optimal performance, and prolonging battery life. Furthermore, it underscores the importance of referring to battery datasheets and consulting with suppliers to obtain accurate and specific information about a battery’s characteristics.