Capacitor Self-Discharge:

(Continued from previous page that discussed reducing leakage in old aluminum electrolytic capacitors)

Ultracapacitors are also known as supercapacitors or EDLC (electric double-layer capacitors). These capacitors are available with capacitances in the farad range. There are two classes of ultracapacitors that are widely available.

The older class has an ESR (equivalent series resistance) greater than 1 ohm and a maximum voltage between 3.3 V and 5.5 V. This means they charge and discharge slowly. They are commonly used for retaining power in portable devices during a battery swap, or to run clock chips when power is disconnected.

The newer class of ultracapacitors has an ESR less than 1 ohm and a maximum voltage of 2.7 V or less. They charge and discharge rapidly. They are available in much larger capacities, such as over 10 farad. They are commonly used to supply massive surge current to get a large electric motor started or for regenerative braking in electric cars.

If you want to make a solar robot that drives a motor, you need to use the newer types of ultracapacitors. (Look for an ESR of 100 milliohms or less.) The relatively high resistance of the older type means that the capacitor will be unable to supply enough current to get the motor to spin.

Ultracapacitors are lightweight and can store more energy in a given volume than aluminum electrolytic capacitors. In the image below, it would take 400,000,000 of the 1 µF capacitors to provide the same capacitance as the 400 F EDLC ultracapacitor. Obviously, the 400 F capacitor is much smaller in volume than that.

Left to right and to approximate scale: 1 microfarad aluminum electrolytic, 1 farad EDLC capacitor, 400 farad EDLC ultracapacitor.

To be fair, the pictured 1 µF capacitor has a maximum voltage of 50 V, which is 18 times as much as the 2.7 V 400 F capacitor. The low maximum voltage reduces the power density and the types of circuits that ultracapacitors can be used in, without resorting to series capacitors with voltage balancing circuitry.

Unlike rechargeable batteries, ultracapacitors can be recharged hundreds of thousands of times. Unfortunately, ultracapacitors tend to have significant higher self-discharge rates. That is, they cannot store energy for as long as a battery.

Self-discharge rate of ultracapacitors.

Notice the discharge is not a straight line, but tends to flatten out?
The manufacturers noticed this also.
So, they cheat a little bit and quote the insulation resistance or self-discharge current *after* a certain number of hours.
That is, they’ll say “1.5 mA after 72 hours”.

This makes it difficult for you to calculate how much energy will remain after a particular amount of time. And, because there is no standard for testing self-discharge (how long to charge, when to start measuring current), it is difficult to compare different capacitors to determine which really has the lowest leakage for your project.

A 1 farad capacitor is large enough that my test circuit drain has no measurable effect on it for a period of 10000 seconds. A drain of 4 megohm would be required for the voltage to go from 2.5 V down to 2.49 V, but my test circuit is somewhere in the 1 trillion ohm range. Therefore, I can be reasonably sure the loss of power in the above graph is due to self-discharge.

I suspect the reason why the 1 F capacitor performs poorly in comparison to the 400 F capacitor is that the 1 F capacitor is fairly old, but the 400 F capacitor is newly purchased. Ultracapacitor technology has improved greatly over the years.

Finally, let’s took a look at a peculiar effect in capacitors where voltage magically appears on a drained capacitor.