Super capacitors derating

Question

I want to use supercaps in a system for minimal power interruption backup (1-2 seconds). My systems works at - 40 to 85°C.

I have seen that supercaps are usually rated for 1000 - 2000 hours at max temp (say 85°C) and max voltage (say 5.5V).

And from my understanding this rating is the point where the capacitor will loose 30% of its capacitance and its resistance will double.

Now say my system works at average of 45°C (but will peak to 85°C during hottest days for few hours) and instead of using 5.5V I run it from 3V and instead of needing the whole capacitance I am OK with even 50%

How do I calculate the actual lifespan? I don't see charts in the datasheet but only the number of 1000 hrs @85°C with 5.5V.

Answer 1

Generally the estimate that manufacturers recommend is that life doubles for every 10°C below rated. This is the Arrhenius equation with some assumptions.

Some also have a correction factor for slight voltage derating of Vop/Vrated for up to 2x. The factor used is Vop/Vrated.

So at 45°C the life would be 2^4 times the 85°C rating approximately, or 16x the 85°C rating, so 16,000-32,000 hours ignoring any improvement from voltage derating.

n.b. The relevant temperature is the core temperature of the capacitor, not the ambient. There can be a significant difference between the two for power supply capacitors where self-heating is significant. Probably not so much for a supercapacitor in a typical application.

The excursions above 45°C and the time below 45°C will affect the life, so there will be a shelf life (sometimes specified separately).

If you have a known temperature-time curve you could probably write an equation for instantaneous 'wear out' as a function of time and integrate to get an estimate of the life (when wear out passes 1.0, say) for your arbitrary time-temperature curve.

Or, in a simplified form, consider the time spent at 85° as a = 10% and the rest spent at 45°C. We can then write:

Life \$\approx \frac{1}{\frac{a}{2000}+\frac{1-a}{16000}}\approx\$ 9400 hours

Answer 2

Check the application notes. For example, KEMET provides this paper:

Choosing the Right Supercapacitor for your Application

Wurth's ANP012 | How does a Supercapacitor age? Lifetime Model of Electric Double Layer Capacitors also gives curves for temperature, though not a calculation method.

The materials used should be fairly common between manufacturers, but to be sure, check with your manufacturer.