**1. Introduction**

Automobiles powered by gasoline engines account for nearly 25% of the global energy consumption [1]. Rechargeable batteries promise a way to replace them by electric vehicles (EVs) in the near future. In addition to EVs, rechargeable batteries have been widely adopted in portable electronic equipment, household appliances, power tools, aerospace equipment and renewable energy storage systems. A battery management system (BMS) ensures the safety, efficiency and reliability of a battery powered system. Research on BMS has been very intense in the last two decades and significant improvements were achieved in the safety, efficiency and reliability of battery systems [2,3]. However, there are challenges remaining and in this paper we describe a list of challenges and outline possible solutions.

Two schools of approaches for battery management systems have emerged over time; one models the battery through *electrical equivalent circuit model (ECMs)* [2,3] and the other seeks to model it through *electrochemical models* [4]. However, most practical systems adopt the electrical ECM based approaches due to their simplicity. The research challenges faced by the present day BMS are three pronged: *safety, efficiency* and *reliability*. Lithium ion batteries are susceptible to *thermal runaway* which is an irreversible chemical process triggered by several conditions including over-voltage and high temperature. The need

to fast-charge the battery, which is important in electric vehicle applications, increases the possibility of thermal runaway and safety issues [5,6]. There are wide ranging issues affecting the efficiency of energy storage in batteries; particularly, electric vehicle applications strive to improve efficiency in every possible way. For example, charging efficiency is the percentage of the total energy needed during charing [7]; fast charging requirements results in significant energy waste in the form of heat. BMS algorithms attempt to enhance efficiency of batteries in multiple ways; optimal charging algorithms aim to reduce the amount of heat waste and the degradation of state of health; precise SOC estimation algorithms will help to improve the efficiency by helping to design minimal battery-pack configurations based on specific needs. Individual cells in a battery-pack are known to become imbalanced over time causing safety and reliability issues; short circuited cells are another common cause of safety and reliability issues in Li-ion batteries [8–10].

An emerging challenge for battery management systems comes in the form of battery reuse [11,12]. It is predicted that the electric vehicle sales are about to grow by nearly 500% in the next 10 years [13]. The state of the art BMS algorithms heavily depend on prior characterization carried out in laboratories [2,3]; Consequently, they are only effective for first time use of batteries. Considering the fact that the first use of the battery alters its electrochemical characteristics in unique ways, traditional BMS approaches that rely on empirical modeling, under the assumption that batteries of the same chemistry and size have similar characteristics, will be inadequate to manage used batteries.

The present manuscript is written in the form of an *expository paper* detailing the many solutions developed by the authors in the recent past in order to address specific challenges in battery management systems. Section 2 describes in more details about the specific goals of a state of the art battery management systems and the challenges it needs to overcome. Section 3 describes some specific solutions developed by the authors in order to address the challenges faced by the present day battery management system. Finally, the paper is concluded in Section 4.

### **2. Battery Management System: Goals and Challenges**

In this section, some of the challenges faced in designing battery BMS are briefly described.

## *2.1. State of Charge Estimation*

Coulomb counting is the easiest approach to estimate the state of charge (SOC) of a battery [2,3]. Figure 1a gives the approximate Coulomb counting equation that is used to compute SOC in a recursive manner. However, Coulomb counting method suffers from the following sources of errors:


Alternatively, the open circuit voltage (OCV) can be modeled as a function of the SOC of the battery. This OCV-SOC model [17] can be exploited to estimate the SOC based on voltage measurements. However, measuring the OCV in real-time during battery operation is not feasible because the battery needs to be rested for several hours before the OCV can be measured. While the battery is operational a measure of OCV can be obtained by estimating the voltage across the battery ECM; this requires the estimation of the ECM parameters as well. Once the OCV is estimated, the SOC can be looked-up [17] using the OCV-SOC characterization parameters. Figure 1b summarizes the voltage based approach to SOC estimation. The following errors are encountered by the OCV-SOC based state of charge estimation approach:


Most of the advanced BFG's use a *fusion based approach* where both the Coulomb counting method and the OCV-lookup method a combined in an efficient manner.

$$\begin{aligned} s(k) &= s(k-1) + \frac{1}{3600 \text{C}\_{\text{batt}}} \int\_{t(k-1)}^{t(k)} i(\tau) d\tau \\ s(k) &\approx s(k-1) + \frac{\Delta\_k i(k)}{3600 \text{C}\_{\text{batt}}} \end{aligned}$$

(**a**) Current based approach

**Figure 1. State of charge estimation.** The fusion based approach is one of the most robust approaches to accurate battery SOC estimation.

Th fusion approach to SOC estimation (more appropriately, SOC tracking) is modelled as a recursive Bayesian estimation problem and by employing a nonlinear filtering approach (such as an extended Kalman filter) for online SOC tracking [2,3]. A complete SOC tracking solution involves the following:


Figure 1c illustrates the fusion based approach to SOC estimation. The fusion based approach needs to have the knowledge of OCV parameters, battery capacity, ECM parameters as well as the sensitivity of the voltage and current measurement sensors. Section 3 briefly describes the approaches to estimate them.
