## Energy (Wh): A forgotten parameter for State of Health (SoH) estimation

Witnessing current climate change, now more than ever we need to protect our environment regardless of cost. As society is becoming more aware of protecting the environment, the technology for the electrification of transportation facilities (i.e., electric vehicles) has been improved tremendously in recent years and is still being improved by scientists and engineers. One of the key technologies used in today ‘s electric vehicles is the Lithium Ion Battery (LIB). Even with all the technological developments in battery technology, it is still challenging to know the exact remaining useful life of a battery, because it is a very complex electrochemical system.

It is very important to know the remaining useful life of a battery as accurately as possible so that we are able to achieve safe, durable and high performance of the battery for its relevant application. The remaining useful life of a battery is determined by its state of health (SoH) estimation. The accurate SoH estimation is also especially important because the accuracy of State of Charge (SoC), State of Energy (SoE) and State of Power (SoP) are also highly dependent on the precise estimation of SoH.

At LION Smart, Scientists and Engineers tackle the challenge of knowing the exact remaining useful life of a battery by developing advanced algorithms for SoH estimation together with algorithms for State of Charge (SoC), State of Power (SoP), and State of Energy (SoE). These algorithms are implemented with the data provided by the **L**ION **S**ingle **C**ell **M**onitor (LSCM). The LSCM can monitor voltage and temperature. It is also capable of measuring an internal resistance by means of the electrochemical impedance spectroscopy as well as has also an integrated cell balancing function. This LSCM is meant to be used for the applications related to electromobility and also for stationary energy storage systems.

As stated earlier that the SoH estimation tells the remaining useful life of a battery, this SoH estimation is mostly done by considering either the change in the charge capacity (Ah) or the change in the internal resistance of a battery as it ages. But one parameter, which is still not common to be considered for the SoH estimation, is the change in the energy capacity (Wh) of a battery.

In this article, we will not only explore the charge capacity (Ah) and the internal resistance as the parameters for the SoH estimation, but also dive into the energy capacity (Wh), the forgotten parameter for the SoH estimation. We will see which parameter gives a close to accurate estimation of the remaining useful life of a battery and why.

## 1. What is actually the state of health (SoH) of a battery?

State of Health (SoH) of a battery (i.e., a cell or a battery pack or a battery module) indicates the ongoing general condition and the performance abilities of the battery compared to when it is new.

The unit of SoH is in percentage (%). 100% SoH = BoL- Beginning of Life

- It means that the condition of a battery meets the manufacturer’s specifications.

0% SoH = EoL- End of Life

- It means that the battery is no longer suitable to use for a given application

Over time, SoH of the battery decreases linearly from 100% to 0% because the performance abilities of the battery decrease. Normally, the battery uses up to 70% or 80% SoH for applications related to electromobility. This is considered as the first life of the battery. After that, the battery enters into its second life. In that, it can be used further for the applications related to stationary energy storage systems.

The purpose of knowing SoH is to provide an indication of the expected performance of the battery in its current condition and to know how much the battery has consumed and how much is remaining before the battery must be replaced.

The SoH cannot be measured directly by any sensor. It has to be derived and estimated by monitoring other parameters of a battery, which change as the battery is used over a period of time.

These parameters are as follows and can be considered to determine SoH.

- Charge Capacity (Ah)
- Internal Resistance (Ω)
- Energy Capacity (Wh)

### Quote from CEO

*“At LION Smart, we believe in a sustainable future. We are passionate about making technologies smarter, contributing to decarbonization and driving electrification.”*

*Winfried Buss, CEO, LION Smart*

## 2. How is the SoH estimated?

From the charge capacity of a battery, the SoH is estimated by comparing the actual charge capacity (𝐶𝑎𝑐𝑡𝑢𝑎𝑙 ) of the battery with its initial charge capacity (𝐶𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ) when the battery is new. The charge capacity decreases as the battery gets older.

From the internal resistance of a battery, the SoH is estimated by comparing the actual internal resistance (𝑅𝑎𝑐𝑡𝑢𝑎𝑙) with the internal resistance (𝑅𝑖𝑛𝑖𝑡𝑖𝑎𝑙) when the battery is new, and with the cut-off internal resistance (𝑅_{𝑐𝑢𝑡−𝑜𝑓𝑓}), when the battery is needed to be changed. The internal resistance increases as the battery gets older.

From the energy capacity of a battery, the SoH is estimated by comparing the actual energy capacity (𝐸𝑎𝑐𝑡𝑢𝑎𝑙 ) of the battery with its initial energy capacity (𝐸𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ) when the battery is new. The energy capacity decreases as the battery gets older.

## 3. Comparison of *SoH Energy*, *SoH Charge *and *SoH Internal Resistance*

To compare the above mentioned three different ways of estimating 𝑆𝑜𝐻, the Li-ion battery aging dataset collected by NASA Ames Prognostics Center of Excellence (PCoE) is analyzed. For this purpose, commercially available 2Ah Li-ion 18650 batteries were run through three operational profiles, i.e., Charge, Discharge and Electrochemical Impedance Spectroscopy at room temperature. Charging was carried out in a constant current (CC) mode at 1.5A until the battery voltage reached 4.2V and then continued in a constant voltage (CV) mode until the charge current dropped to 20mA. Discharge was carried out at a constant current (CC) level of 2A until the battery voltage fell to 2.7V. Impedance measurement was carried out through an electrochemical impedance spectroscopy (EIS) frequency sweep from 0.1Hz to 5kHz.

Repeated charge and discharge cycles result in accelerated aging of the batteries while impedance measurements provide insight into the internal battery parameters that change as aging progresses. The experiment was stopped when the charge capacity of the battery reached to 70% of its initial charge capacity.

The following figures A, B and C show changes in the charge capacity, the energy capacity and the internal resistance of the battery respectively. The charge capacity and the energy capacity decrease and the internal resistance increases as the battery ages. Figure A and B look similar visually but one should consider that the scale on the y-axis is different. The line of fit is used to simplify the noisy experimental data and to see the trend clearly.

The 𝑆𝑜𝐻 estimated from the energy capacity (Wh), the charge capacity (Ah) and the internal resistance (Ohm) are shown in the figure D and denoted as 𝑆𝑜𝐻𝐸𝑛𝑒𝑟𝑔𝑦, 𝑆𝑜𝐻𝐶ℎ𝑎𝑟𝑔𝑒, and

𝑆𝑜𝐻𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 respectively. From the figure D, it is clear that all three ways of estimating

𝑆𝑜𝐻 of the battery lead us to three different conclusions about the remaining useful life of the battery.

Now, the question is which parameter i.e., the energy capacity or the charge capacity or the internal resistance gives a more accurate estimation of 𝑆𝑜𝐻, so that the remaining useful life of the battery can be determined.

*4. SoH Energy *is more accurate than *SoH Charge *and *SoH Internal Resistance*. But why?

As it is already stated that 𝑆𝑜𝐻𝐶ℎ𝑎𝑟𝑔𝑒 is estimated by considering 𝐶𝑎𝑐𝑡𝑢𝑎𝑙 and 𝐶𝑖𝑛𝑖𝑡𝑖𝑎𝑙 and

𝑆𝑜𝐻𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 is estimated by considering 𝑅𝑎𝑐𝑡𝑢𝑎𝑙, 𝑅𝑖𝑛𝑖𝑡𝑖𝑎𝑙 and 𝑅𝑐𝑢𝑡−𝑜𝑓𝑓, these two 𝑆𝑜𝐻 estimations lead to two different conclusions for the remaining useful life of a battery. As a reference, there is on an average 3% difference between 𝑆𝑜𝐻𝐶ℎ𝑎𝑟𝑔𝑒 and 𝑆𝑜𝐻𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 for the aging data given in this article. It is because the charge capacity and the internal resistance influence the life of a battery independently. That is why the influence of the internal resistance is missing in the estimation of 𝑆𝑜𝐻𝐶ℎ𝑎𝑟𝑔𝑒 and the influence of the charge capacity is missing in the estimation of 𝑆𝑜𝐻𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒.

The more accurate 𝑆𝑜𝐻 can be achieved, if the influence of both, the charge capacity and the internal resistance, is considered in the estimation of 𝑆𝑜𝐻. It can be accomplished by considering the energy capacity for the estimation of 𝑆𝑜𝐻. The energy (𝐸) of a battery can be calculated by the following equation.

Where, 𝑉 = Voltage, 𝐼 = Current, 𝑡 = time, 𝑅 = Internal Resistance

In the above energy equation, the term 𝐼 ∙ ∫ 𝑡𝑑𝑡 is nothing but the charge capacity and the term

𝐼^{2} ∙ 𝑅 is the loss of energy (also called Joule heating) due to the internal resistance (𝑅) of a battery. In this way, the energy capacity includes the influence of both, the change in the charge capacity and the change in the internal resistance. That is why the estimation of

𝑆𝑜𝐻𝐸𝑛𝑒𝑟𝑔𝑦 is more accurate than the estimation of 𝑆𝑜𝐻𝐶ℎ𝑎𝑟𝑔𝑒 and 𝑆𝑜𝐻𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒.

## 5. Conclusion

𝑆𝑜𝐻𝐸𝑛𝑒𝑟𝑔𝑦, 𝑆𝑜𝐻𝐶ℎ𝑎𝑟𝑔𝑒 and 𝑆𝑜𝐻𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 give three different conclusions about the remaining useful life of a battery. Among these, 𝑆𝑜𝐻𝐸𝑛𝑒𝑟𝑔𝑦 should be considered closer to the exact remaining useful life a battery because 𝑆𝑜𝐻𝐸𝑛𝑒𝑟𝑔𝑦 includes the influence of the changes in the charge capacity, the internal resistance and the energy capacity. In practical applications

i.e., in electric vehicles, the best strategy for knowing the remaining useful life of a battery is to have a BMS which is able to monitor all these three SoH estimations. LION Smart has already achieved this state of art technology with the help of its LSCM by incorporating online electrochemical impedance spectroscopy for monitoring the change in the internal resistance together with monitoring the change in the energy capacity and the charge capacity.

**Kapil Faliya ***Battery Algorithm Engineer* LION Smart