# How to calculate hybrid lithium-ion supercapacitor (LiC) requirements for my application?

## What is a hybrid lithium-ion supercapacitor?

The supercapacitor is a relatively recent development. These devices have high capacitance measured in tens or even hundreds of Farads. By definition, the hybrid lithium-ion capacitor (LiC) is a member of the supercapacitor family that incorporates a lithium-ion doped material into its structure. It’s a hybrid with a cathode of a traditional supercapacitor and the anode of a lithium-ion battery. The resulting device offers superior performance in terms of power density and higher cell operating voltage.

This article presents a representative application and explores the run-time math to see if the capacitor is a viable solution for your project.

Tech Tip: The hybrid lithium-ion supercapacitors such as this Eaton brand LiC are shipped in a charged state. Precautions must be taken to prevent the terminals from shorting causing subsequent damage to the capacitor. To mitigate this situation, the capacitors are shipped in the plastic carrier as shown in this picture.

## Explore a capacitor based back up power supply

One useful application of the supercapacitor is a backup of ride-through for industrial equipment. In this application the capacitor, or series-connected bank of capacitors, can power your application for a few minutes. If primary power is not restored in a set amount of time the system can perform an orderly system shutdown.

As an example, let’s assume a system that requires a continuous nominal 24 VDC for 1.0 A for 2 minutes. We will allow the voltage to fluctuate about this setpoint +2 to -1 VDC. The total nominal energy requirement is:

Energy = Power x time = 24 VDC x 1.0 A x 120 seconds = 2,900 Watt seconds = 2,900 W \cdot s

### Capacitor Requirements

Now that we know our system requirements, we can search for an appropriate capacitor. There are a few constraints including:

#### Voltage

A typical LiC has a working voltage of 3.8 VDC. This voltage is reduced as capacitor discharges. For the 24 VDC system we will select a series string of 7 cells (7s). Depending on the application and component availability plus cost, it may be beneficial to use series parallel configuration such as two parallel strings of 7 series cells (7s2p).

#### Current

Each LiC has a design max continuous current as well as a peak surge current. For our application, the 7s1p connection would require capacitors with a 1 A continuous current, while a 7s2p would require 0.5 A.

#### Temperature

The LiC technology is sensitive to elevated temperatures. If properly cared for they have a lifetime of several decades. If operated at temperature extremes the lifetime is measured in months.

#### Cell Balancing

Like their lithium-ion battery cousins, the LiC must include a method of cell balancing. We could say that the 7s1p is only as strong as its weakest link. We therefore want the voltage to be equally distributed across all cells. This also accounts for the natural tendency of a single cell burdened and then damaged by excessive voltage. This topic is beyond the scope of this short post. However, there are a host of cell balancing integrated circuits. Here are a few demo boards. Do study the designs to see how these systems may be assembled.

### Math calculations for the backup power supply

With that said, let’s look at the math for a 7s1p system. We will assume a conservative approach where the cell voltage is allowed to vary from 3.8 to 3.3 VDC. This equates to a total system voltage of 26.6 to 23.1 VDC.

For the 7s1p system we need to locate a capacitor that will give up 2900 W \cdot s as the voltage drops from 3.8 and 3.3 VDC.

Let’s rephrase this important distinction.

We are not calculating the energy stored in the fuel tank!

Instead, we are calculating the fuel consumed as the voltage drops from 3.8 to 3.3 VDC. The remaining fuel below 3.3 VDC is unusable as we are below the required system voltage.

Let’s start by selecting the 220 F capacitor shown in the opening picture.

Energy = \dfrac{1}{2}CV^2

Energy_{26.6 VDC} = 7 * \dfrac{1}{2}220\ C\ 3.8^2 = 11,100\ W \cdot s

Energy_{23.1 VDC} = 7 * \dfrac{1}{2}220\ C\ 3.3^2 = 8,390\ W \cdot s

The 2,700 W \cdot s difference between the 26.6 and the 23.1 VDC capacitor storage is the available energy. We will stop here as the 2700 W \cdot s value is close to our nominal 2900 W \cdot s value. A quick glance at the capacitor’s datasheet shows that it will indeed handle the 1 A nominal current with the ability to surge to 15 A.

Tech Tip: The energy goes as voltage squared. Consequently, a small change in voltage can have a large impact on energy. The 0.5 VDC voltage reduction in this example has reduced the stored energy by about 25%.

At today’s price, assuming a 1000-unit production run, this equates to an estimated cost of \$47.55 (U.S.) for 7 ea of the 220 F to be installed into each unit. Understand that this is only an estimate. Contact DigiKey sales for a proper quote.

## Parting Thoughts

We welcome your feedback to this post. For example, do you agree with the assumption about 3.3 being the limit for working voltage? Have I properly applied the energy storage equation to the LiC?

How have you used supercapacitors in your project(s).

Best Wishes,

APDahlen

Aaron Dahlen, LCDR USCG (Ret.), serves as an application engineer at DigiKey. He has a unique electronics and automation foundation built over a 27-year military career as a technician and engineer which was further enhanced by 12 years of teaching (interwoven). With an MSEE degree from Minnesota State University, Mankato, Dahlen has taught in an ABET accredited EE program, served as the program coordinator for an EET program, and taught component-level repair to military electronics technicians. Dahlen has returned to his Northern Minnesota home and thoroughly enjoys researching and writing articles such as this. LinkedIn | Aaron Dahlen - Application Engineer - DigiKey

2 Likes

Hi,
What are the requirements for charging a VMF/VPF Series Hybrid LIC Supercapacitors ?
I cannot find this information in the data sheets.
Could you please also recommend some devices capable of handling those capacitors safely?
Best regards,
Gustavo

Hello gzarba - welcome to the Tech Forum. Here is the link to the full handling guidelines for these capacitors. There is also a Technical Guide to Supercapacitors and the FAQs on Supercapacitors from CDE’s website which may help you.

1 Like

Hello gzarba,

That’s a good question. I’m working on an article to explore this concept.

In many respects the LiC is like its lithium-ion battery cousin.

• There are specific limitations on the charging and discharging current.

• Be careful not to exceed the design maximum voltage.

• Be careful not to discharge the capacitor below minimum recommended voltage.

• Cell balancing is required for series connected capacitors.

The situation is complicated when the cells are series connected. Like a chain, the series string is only as strong as its weakest link. Also, slight differences in individual cells can result in voltage hogging and quick destruction of one or more cells. As a consequence, it is necessary to monitor and balance the cells.

As for technology, there are many different methods ranging from a simple resistor to op amp steering. To get you started, please consider the ap note at the end of this article. You will notice that many of the techniques are similar to battery balancing.

Best Wishes,

APDahlen

1 Like

hi,
many thanks for the prompt answers.
Thanks, Jenny for the links. Those docs I had already seen, but, I could not really see specific information on how to safely charge the parts.
For instance, if one would use a BQ25173 from Ti, which can charge supercaps, te charging profile would eventually not fit with the profile needed by a LiIon Batt. So my doubts were about handling the LiC s like a LiIon battery or like a supercap.
Best regards,
Gustavo

Hello again gzarba: I sent your inquiries to my Product Specialist for the VMF Supercaps and he has contacted the manufacturer for additional information. As soon as I have that reply, I will post it here. Thank you for your patience!

Hello gzarba,

You mentioned TI’s BQ25173EVM evaluation board.

The data sheet tells us that:

Charging current can be set from 10 mA to 800 mA with external resistor on ISET.

If we look at the 220 F Eaton LiC as found at the top of this note, we find the continuous current is 1.1 A with a stipulation of a 15 °C temperature rise. Note that small capacitors in the Eaton series have reduced current capabilities. For example, the 50 F device has a design max of 250 mA.

• Profile: The BQ25173 IC featured on the demo board has two profile “settings.” The first is a constant current to bulk charge the LiC. The second is a constant voltage. We could interpret this as charge the capacitor as quickly as possible with a constant current. Then maintain the capacitor at the desired working voltage forever. Both voltage and current limitation are essential for long life.

• Balance: The BQ25173 does not address capacitor balance. Instead, the 4S (4 series connected cells) are shown with equalization resistors. Ref: Figure 8-13 of the datasheet. While the resistor is the simplest balancing method, it is parasitic. It’s also a bad idea with LiC technology the LiC should never be fully discharged. In fact, as shown in my original article (above), this is the reason the LiC are shipped in a charged state. You will need an alternative equalization method or a way to electrically disconnect the LIC to prevent this damaging discharge.

• Temperature: The LiC can have a decades long lifespan but not at elevated temperatures. It may be beneficial to add temperature monitoring circuitry and control algorithm to the LiC monitoring system. For example, an alarm may sound when the system is overtemperature. The system may also refuse to charge the LiC if the temperature is elevated.

You mentioned other considerations. Please let me know if I have missed them in this note.

Sincerely,

Aaron

4 Likes

Hi Aaron,
thanks for the explanation, you pointed me into the good direction.
Now I have enough to start experimenting with different options.
Need to harvest energy from a piezo generating a non periodic voltage between 0.4V and 16V. Limiting the 16V with a zener is not an option, and loosing the low voltage impulses is also not an option, since both are the energy I want to harvest. I cannot find a device capable of handling this, but I hope I will.

I wish you a pleasant day!
Kind regards,
Gustavo

1 Like

Understood, Gustavo.

Harvesting at intermittent energy source such as piezo is indeed a difficult task.

In some ways, it’s like harvesting a bolt of lightning. There is certainly a considerable amount of energy available for the taking. Yet, the system must be overbuilt to handle the high impulse (your Zener diode) with being destroyed. At the same time such an overbuilt system will have difficulty extracting low level signals.

Hopefully your chosen mechanical system has a predictable frequency with consistent amplitude to simplify the electronics.

Best Wishes,

APDahlen

1 Like

Hi APDahlen,
yes, it is a challenge.
But I am seeing light at the end.
If I have a “predictable frequency with consistent amplitude” is difficult to say. There are no regular vibrations in the system.
By now, I first have to build a stable prototype of the real mechanic, to see how much I really get in a real life situation.
Thanks for the help!
Best regards,
Gustavo

1 Like