# How Long will my Supercapacitor Last?

The thorn in the side of the supercapacitor is its limited lifetime.

Supercapacitors can do many things in the field of energy storage and have be touted as being the future batteries.

However any supercapacitor if not lifetime-engineered properly can fail prematurely.  This leaves your company with potentially large warranty costs.

Supercapacitor lifetime stems from chemical reactions in the capacitor causing the capacitance to decrease.  These reactions happen more often when it is hotter and thus lifetime can vary significantally with temperature.  These reactions are governed by the Arhennius equation and appear on the datasheet as a lifetime.  A typical lifetime for a supercapacitor is 1000 hours at 70C.  This means that if your supercapacitor is at 70C it burns through a lifetime in 42 days!  At only 83C some electrolytes can even boil causing your supercapacitor to rupture!  However, if the temperature is decreased a supercapacitor’s lifetime can be increased greatly.  It is all governed by this equation:

where t is lifetime, Tn is the nominal temperature, tn is the lifetime at the nominal temperature, Ea is the activation energy, T is temperature and kB is Boltzmann’s constant.  In most cases this can be approximated by “halving the temperature doubles the lifetime”. If you are not using this equation in designing your supercapacitor systems then you better start using it fast!  Note that this equation is for any electrolytic capacitor not just supercapacitors.

## Lowering voltage

From the prior equation it can be seen that managing the temperature of supercapacitors can do wonders in increasing their lifetime.  It is a lesser known fact that running them at voltages below the rated voltage also increases their lifetime.

## Verify!

Once you have your product in the field, re-engineering can become costly, so verification of your design and predicting failure rates becomes very important.  This is done by measurement of the capacitors and then statistically analysing the results.

## Measurement is important

Measurement of supercapacitors relies on the use of a simple capacitor model with just capacitance and ESR.  This allows measurement by using the fact that the voltage response to a constant current source is a straight line.  From this straight line you can thus measure the capacitance.  When a constant current is applied there is also a small offset due to the ESR, which can be used to measure the ESR.

## After measurement

Once you made the measurements of a random group of supercapacitors you can begin to analyse the results.  First of all you calculate the lifetimes that the supercapacitors have experienced up to the measurements based on their capacitance.  Then these lifetime results typically fit a Weibull distribution. Using this fact, you can curve-fit your sampled data to a distribution with certain parameters and calculate the confidence of your fit.  You now have a range of distributions that fit your data.  From this range you simply find the worst case and use it to predict worst-case future failure rates.  This information can be passed on to the accountant in the form of warranty liability.

## How can we help?

ELMG Ltd have designed a system which can use this measurement technique to measure supercapacitor’s capacitance during both charging and discharging.  This is done using a controlled constant current source.  This system is highly scalable meaning that it can be used on capacitors ranging from a few farads to hundreds of farads.  Once the measurements are made ELMG can then perform the statistical analysis and come up the results to tell your finance people what you warranty liability is.