How To Calculate SOH Of Battery

When designing a BMS, if you want to accurately estimate SOH (State of Health), relying solely on basic arithmetic operations will not suffice; you need dynamic multi-parameter estimation. The industry-standard approach is to focus on two key metrics: capacity fade and increased internal resistance (IR). The basic capacity-based SOH formula is straightforward:

$SOH_{capacity}=\left(\frac{C_{actual}}{C_{nominal}}\right)\times100\%$

The SOH formula based on internal resistance is:

$SOH_{resistance}=\left(\frac{R_{EOL}-R_{current}}{R_{EOL}-R_{BOL}}\right)\times100\%$

(where EOL stands for end of life and BOL for beginning of life). You can’t measure these directly when the equipment is running. The current reliable BMS algorithm basically has to use the equivalent circuit model (ECM) with the extended Kalman filter (EKF). EKF can integrate real-time voltage and current data, ampere-time integral (coulomb meter) and open circuit voltage (OCV) look-up tables. This architecture can correct the accumulated error, dynamically calculate the current capacity and AC impedance, no matter how the depth of discharge (DOD) jumps, or how the ambient temperature changes, and finally predict the remaining useful life (RUL) is quite accurate.

The Two Core Dimensions Of SOH Calculation

Recognizing the fact that battery aging is never a single dimension. Evaluating SOH is to look at two interrelated indicators:

• Capacity Attenuation ($SOH_{capacity}$): The battery has been used for a long time, and the amount of electricity that can be stored is definitely not as good as before. This is the capacity fade. The SOH calculated by capacity is defined as the ratio of actual capacity to nominal capacity.. The formula is:$SOH_{capacity} = \left(\frac{C_{actual}}{C_{nominal}}\right) \times 100\%$
• Increased Internal Resistance ($SOH_{resistance}$): The aging of the battery is often accompanied by a larger internal resistance, which not only limits the power output, but also generates heat. For those applications that require high power output, keeping an eye on the internal resistance is too critical. The problem of heating is often the first place to expose the bottleneck of the system. The formula is written as follows:$SOH_{resistance} = \left(\frac{R_{EOL}-R_{current}}{R_{EOL}-R_{BOL}}\right) \times 100\%$
  • $R_{current}$: The current measured internal resistance value.
  • $R_{BOL}$ (Beginning of Life): Initial reference internal resistance of the new battery.
  • $R_{EOL}$(End of Life): The internal resistance scrap threshold set in advance. After this line, the battery cannot be used in the current application.

The Formula Mentioned Above Works Perfectly?

In real-world operating conditions, direct measurement is impractical. Just because of this limitation, it is not enough to calculate the basic math problems. Modern BMS must throw away static calculation and turn to dynamic multi-parameter estimation, so as to cut out the healthy state abruptly under the harsh working conditions of battery load charging and discharging.

How To Put The Theoretical Formula Into Practice?

The robust BMS architecture basically depends on the advanced algorithm model to build bridges.

• Equivalent Circuit Model (ECM): BMS uses ECM composed of resistors and capacitors networks to run mathematical simulations to understand the physical and chemical temper of the battery. This is equivalent to building a digital twin to the physical battery in the system.
• Extended Kalman Filter (EKF): EKF is the mathematical engine for real hard work. The characteristics of the battery are very nonlinear. EKF takes the data simulated by ECM and corrects the results over and over again against the actual readings captured by the sensor.

Data Fusion: Squeeze Out The Real-time Sensor Data

It depends on whether the data fusion process is rough or not. The EKF algorithm is like a data hub inside, constantly processing several channels of information:

• Real-time voltage and current: This is the lowest electrical parameter sampled at the highest frequency.
• Amper hour integral: Calculate the total power in and out of the battery. This trick is easy to use, but it is easy to drift after using it for a long time, and the integral error is accumulated more and more.
• Open circuit voltage look-up table: BMS will look up the pre-calibrated table and compare the static voltage of the battery with SOC (state of charge) and health.

By combining Ampere-hour integral and OCV look-up table and throwing it to EKF for processing, this framework can completely correct the accumulated error saved by pure Ampere-hour integral.

Dynamic Estimation And RUL Prediction

When the equivalent circuit model and EKF are well matched, BMS can achieve extremely high fidelity dynamic estimation. The system can calculate the current capacity and AC impedance without interrupting the normal work of the battery. This hard-core algorithm architecture is designed to allow us to accurately grasp the remaining service life (RUL) of the battery pack. Because EKF can adapt to various variables at any time, even when encountering wide temperature fluctuations, the calculation results of SOH can firmly grasp the real state.

Author: Kevin

I am a Senior Engineer at Gerchamp’s BMS R&D Department with over 12 years of industry experience. I specialize in leading the architecture design and core algorithm development for our advanced Battery Management Systems.