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

The supercapacitor is a relatively recent development. These devices have high capacitance measured in tens or even hundreds of Farads. There are even lithium-ion hybrid capacitors (LiC) that offer superior performance in terms of power density.

In this article we will present a representative application and explore the run-time math to see if the capacitor is a viable solution.

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.

Representative example

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 temperature. 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 the 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.

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 rephase this important distinction.

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

Instead, we are looking for 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 show 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 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.

image

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 you 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).

Please share your comments and suggestion below.

Best Wishes,

APDahlen

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