This is a general response open to corrections.

1.Drawing on semiconductor design methods, the rating of devices would be dependent on thermal considerations viz the maximum temperature in the device based on  losses in the device /thermal impedance. If such an approach is used it should be possible to equate steady state loss+ switching loss for different waveforms if internal rs/ls value is

available.

2. Sometimes each switching operation may reduce the effective capacitance

 by a certain amount .e.g. self healing capacitors in snubber circuits so end of life

would be reached by specifying the minimum acceptable capacitance value.

3.A practical method would be to actually incorporate in  circuit and check

 when tech specs begin to deviate. I think there would be Standards that

use probability methods to accelerate the test at higher values to shorten

testing time.

Cheers

Thank you. But for example, if supercapacitor is used in Antarctica (-40 degrees) than operating current can be increased or it leads to fast damage however.

Generally the preferred operating temperature for electronics in Industry is 20deg  celsius.Personal experience of supplying power electronic control cubicles to steel/ cement/paper industry validates this. So in a limited range the cooler the better from life/ rating point of view. Again from semiconductor experience e.g. there will always be  a peak current limit irrespective of s.s thermal considerations(for junction temp design ) perhaps due to local thermal stresses or other phenomena. Your question would best be answered by a practical test of storing the capacitor at this temp and testing. Will it still work as a super capacitor at this temp is a question? Obviously there are many factors such as condensation at terminals etc which would come into the picture. again personal experience says it is best to test unless the supplier provides reliable data.

 Cheers

The lifetime of supercapacitors is reduced due to side reactions occurring in the electrode electrolyte interface, so the most lifetime reducing phenomena are those accelerating this side reactions. Therefore, you should avoid working at high temperatures and voltages as long as it is possible for your application.

Usually a supercapacitor is supposed to have reached the end of life when one or both of the following conditions are reached: (i) capacitance decreases 20% or, (ii) ESR is 200% of the rated value. Nevertheless, you could have some other constraints.

Some authors use as rule of thumb that increasing 10°C (above 20°C), or increasing 0.1V above the rated voltage will double the speed of capacitance degradation.

For the lower temperatures you mentioned, an organic electrolyte supercapacitor presents more or less the same performance above 0°C, but the ESR is increased below 0°C even though it still could work properly in your application (depending on the proper sizing of the system). This happens due to increasing ionic resistance of the electrolyte below that temperature.

What do you think about this publication:https://www.researchgate.net/publication/261028996_Study_of_Supercapacitor_Aging_and_Lifetime_Estimation_According_to_Voltage_Temperature_and_RMS_Current

it shows that supercapacitor can be killed much faster regardless of ambient temperature. It is true?

Article Study of Supercapacitor Aging and Lifetime Estimation Accord...

Yes of course: it is true! This publication is based on experimental results!

We have realized several accelerated aging tests with 3000F, 2.7V components. We found that lifetime was not only related to the temperature and voltage but also to current amplitude.

A current in the component generates an increase in the temperature but we showed that the decrease of lifetime is not just related to this heating.

For example, for an ambient temperature of 25°C, if a current of 300A leads of a heating of 15°C, the temperature component is 40°C. We showed that a component at a temperature of 40°C (current =0) ages more slowly than a component at 25°C, I=300A.

Why you are testing 4 ultracapacitors in series connection?

We tested components in series connection in order to have the same  solicitation (current) in 4 elements

 Dear Pascal I read your publication and I acknowledge the quality of your work.

However I have the same question: Can we derive a kind of rule of thumb also for the current. Example: the manufacturer declare X cycles with a current having a specific value Y. How we can predict the reduction X associated to a value of current of 2Y?

thank you in advance