The **State of charge (SOC)** has an important role in determining the remaining capacity of the battery pack. Accurate estimation of the SOC is very complex and is difficult to implement, because of limited battery model. Battery **State of Health (SOH)** is an important indicator of battery’s life. SOH reflects the ability of a battery to deliver and receive of energy and power.

Table of Contents

## Definition of SOC

The SOC of a battery is defined as the ratio of its current capacity (*Q(t)*) to the nominal capacity (*Q _{n}*). Nominal Capacity, Qn is the maximum amount of charge that can be stored in the battery. This rating is given by the manufacturer.

In other words, State of charge means the ratio of the remaining charge of the battery and the total charge while the battery is fully charged at the same specific standard condition.

During charges and discharges, battery internal parameters like resistance, temperature, etc. vary with SOC, so these parameters are shown useful for SOC estimation. SOC is expressed in percentage.

SOC = 100% → battery fully charged

SOC = 0% → battery fully discharged

## Classification of SOC estimating methods

**1. Direct Methods**

- Open circuit voltage (OCV) method
- Terminal voltage method
- Impedance method
- Impedance spectroscopy method

**2. Indirect Methods or Book-keeping Methods**

- Coulomb counting method
- Modified Coulomb counting method

**3. Adaptive systems**

- BP (Back Propagation) neural network
- RBF (Radial Basis Function) neural network
- Support vector machine (SVM)
- Fuzzy neural network
- Kalman filter

**4. Hybrid methods**

- Coulomb counting and EMF combination
- Coulomb counting and Kalman filter combination
- Per-unit system and EKF combination

### 1. Open circuit voltage (OCV) method

The Open circuit voltage (OCV) method is based on the Open circuit voltage of the battery that is proportional to the SOC when the battery is disconnected from the loads for a period longer than two hours. For lead-acid batteries, there is an approximately linear relationship between SOC and its open circuit voltage.

V_{oc}(t) = b_{1} × SOC(t) + b_{o}

where b_{o }= terminal voltage of the battery when SOC = 0%.

By measuring open circuit voltage, the SOC can be estimated.

**Note:** Li-ion battery does not have a linear relationship between SOC and OCV as the lead-acid battery have.

**Advantage of OCV method**

- It is simple.

**Disadvantage of OCV method**

- It is an open loop method.
- This method is sensitive to the voltage sensor precision.
- It is unsuitable for cells having flat SOC-OCV characteristics like Li-ion battery.

## Definition of SOH

The SOH of a battery is defined as the ratio of its maximal instantaneous releasable capacity, (*Q _{max}(t)*) to the capacity of the new battery (

*Q*).

_{new}

- State of health(SOH) is a figure of merit of the present condition of a battery cell (or a battery module, or a battery system), compared to its ideal conditions.
- The SOH is represented in percentage form. A SOH equal to 100% means it is a fresh/new battery.
- The SOH could be derived by capacity and the internal resistance, and it could also be derived from other battery parameters like AC impendence, self-discharge rate, and power density.
- Take the capacity as an example, SOH could be defined as the ratio of the current capacity and the rated capacity given by the manufacture. Generally, if the battery capacity is 80% less than the initial value, which means the SOH is less than 80%, then the BMS would warn the user to change the batteries.
- The SOH decrement of a battery cell is mostly caused by the battery aging and degradation, namely, durability problems. That means with the using or storing of the battery cells, the battery capacity would decrease and the internal resistance would increase. Thus the SOH of the battery cells worsen.
- For the battery in the PHEV (Plug-in Hybrid Electric Vehicle) which requires both enough energy and sufficient power, both the capacity and internal resistance should be considered for SOH estimation.

**Excercise**

**Q. What are the Closed loop methods for SOC measurement?**

**Answer.** The Closed loop methods for SOC measurement are

- Kalman Filter (KF)
- Extended Kalman Filter (EKF)
- Adaptive Extended Kalman Filter (AEKF)
- Unscented Kalman Filter (UKF)
- Adaptive Unscented Kalman Filter (AUKF)
- Artificial Neural Networks (ANN)
- Support Vector Machine (SVM)
- Fuzzy Adaptive Kalman Filter (FAKF)