Battery Management Systems – Part 1: Battery Modeling
Edis Osmanbasic posted on January 21, 2020 |
A look at what the BMS does for EVs and the many ways batteries are modeled.

2017 Chevrolet Bolt EV 350.4V Li-Ion battery pack with a control module. (Image courtesy of Weber State University.)

One of the most important components of electric vehicles (EVs) is the Battery Management System (BMS). In this first part of a three-part series on BMS technology, we’ll look at one of the main aspects of a BMS: battery modelling. 

The Need for Management

EVs have many advantages over internal combustion engine vehicles: superior efficiency, a high energy density, good acceleration, less pollution, and more. But EVs aren’t perfect; one big drawback is the need for an expensive battery system with specific maintenance requirements and a long charging time. 

To meet high power and voltage requirements, EVs use battery packs with hundreds of battery cells connected in a series or parallel configuration—this creates a complex battery system. Improper battery conditions such as over-current, over-voltage, over-charging, and over-discharging cause battery damage and rapid aging, and above all, can lead to safety risks such as fire and explosion. For these reasons a battery management system, or BMS, is needed to provide safety as well as proper battery performance. 

"The intelligence of the battery does not lie in the cell but in the complex battery system,” commented Dieter Zetsche, CEO of Mercedes. 

What Does a BMS Do?

The main tasks of a BMS are:

  • ensuring safety and long life (mandatory for Li-ion batteries)

  • indicating state-of-function in the form of state-of-charge (SoC) and state-of-health (SoH)

  • safety controls, alarms, and services (high temperature, cell imbalance, etc.)

  • indicating the battery end-of-life

The BMS includes sensors to measure battery parameters (voltage, current, temperature) and the proper battery modeling and estimation methods to define internal battery states. After defining the electric and thermal behaviors of the battery, the charging and discharging algorithms need to be optimized to provide optimal EV efficiency and battery lifespan. Another important part of BMS is the alarm and safety control module, which has to record or eliminate any abnormalities in battery operation and condition.

An efficient BMS includes four main technologies:

  • Battery modeling 

  • Internal state estimation

  • Battery charging

  • Alarm and safety control

Battery Modeling

Designing the proper battery model is the starting point of a BMS. BMS parameters, such as voltage and current during the charging and discharging processes, are dependent on the battery operation conditions (the load, age, temperature, etc). It is necessary to collect reliable data of the battery behavior during charging/discharging processes, but it is not practical to do so for real battery operation in all operation conditions throughout the battery’s lifespan. Thus, battery modeling uses a mathematical model of a virtual battery to verify that the BMS will work properly for the corresponding battery pack. Battery modeling defines battery behavior analysis, battery state monitoring, design of the real-time controller, fault diagnosis, and thermal management. 

Battery models can be classified into three main types: electric, thermal, and coupled models (other models, such as kinetic models, are used less in BMS design). The three classifications of battery modeling are presented in Diagram 1.

Diagram 1 – Classification of different battery models.

Battery Electric Model

The battery-electric model includes the electrochemical model, reduced-order model, equivalent circuit model, and the data-driven model.

The electrochemical model provides information about battery electrochemical behaviors. This model can be very accurate but requires a complex simulation and computation effort. Because of this, it is difficult to implement this model in a real-time application.

Consequently, the reduced-order electric model is developed as a simplified physics-based electrochemical model to estimate Li-ion battery state of charge (SoC). Simplified reduced-order electric models provide less information, but are still convenient for real-time battery applications.

The equivalent circuit model is the most commonly used battery model in a BMS. This model estimates battery-electric behaviors based on the battery equivalent circuit which contains a combination of circuit components, such as resistors, capacitors, and voltage sources. This model has been widely adopted in real-time battery applications mostly because of its simple structure and small number of parameters.

The typical battery equivalent circuit is shown in Figure 1. The resistor-capacitor networks simulate transient responses of the battery during charging and discharging transients. The number of R-C networks represents the model order, which has to be carefully determined. In real applications, the first and second-order models are usually used. The R-C network models have a better dynamic performance for SoC and power predictions. 

Figure 1 – Battery equivalent circuit model.

Data-driven models measure the difference between input and output signals of batteries. These models require the test data collected during battery operation. Since the test data improves with battery operation, these models require sufficient battery operation to be reliable and generalizable. The training parameters must be efficiently tuned as well.

Battery Thermal Model

Regulating battery temperature is an important task of the BMS. A battery’s performance can decrease if operated in higher or lower temperatures. Different cooling systems are usually used to maintain proper battery temperature. For example, Tesla uses a patented battery pack design with a plate-based cooling system to dissipate the heat and regulate battery temperature. 

Figure 2 – Cold plates that remove heat generated by the battery pack. (Drawings from Tesla patent.)

In order to capture accurate battery thermal behaviors, the battery thermal model contains different models such as heat generation, heat transfer, reduced-order thermal, and data-driven models. The heat generation is described by three equations:




where R is battery internal resistance, I is battery current, V is battery voltage, and OCV is battery open-circuit voltage. Heat marked with Q1 represents the battery heat caused by the large current crossing the battery internal resistance. Q2 is the battery heat open-circuit by the over-potentials across the R-C network. Finally, Q3 is the battery heat generation caused by both the entropy change and Joule heating.

The three main forms of the battery heat transfer model are heat convection, heat conduction, and heat radiation. For the Li-ion battery, a 3D distributed-parameter heat transfer model is developed that analyzes the distribution of the geometrical current and heat inside the battery. The 3D heat transfer models calculate temperature distribution inside the battery, which is important for applications that require high heating of the battery. The model can be used to detect possible temperature hot spots inside the battery. One dimensional heat transfer model calculates the temperature gradient along one direction. These models require too large computational overheads which are not convenient for real-time applications, so they are mainly used in offline simulations.

The reduced-order thermal model needs to provide the control purpose for battery thermal management. This model reduces the order of a Li-ion battery model by converting the one-dimensional boundary-value problem into a low-order linear model in the frequency domain. 

Battery Coupled Electro-Thermal Model

The battery coupled electro-thermal model captures the battery’s electric (current, voltage, SoC) and thermal (surface and internal temperature) behaviors simultaneously. Several coupled electro-thermal models have already been developed. A 3D electro-thermal model estimates battery SoC and calculates heat generation and distribution under both constant and dynamic currents. This model contains a 2D potential distribution model and a 3D temperature distribution model. 

A reduced low-temperature electro-thermal model has been validated by batteries with three cathode materials. This model is accurate for developing fast heating and optimal charging approaches under low-temperature conditions.

The 3D electro-thermal model is used to analyze the influences of different battery operation conditions on the battery temperature, such as coolant flow-rate and discharge current. Based on the analysis of this model, the contact resistance also plays an important role in the battery temperature.

Coming Up Next

The subject of battery management systems is a very important area of research, and it is the focus of many companies handling different battery applications. However, there is yet a lot to learn about BMS and how it works. The market offers many different functional BMS series (Renesas, Texas Instruments etc.) which could be used for corresponding applications skipping complex algorithms. As new EVs emerge in the market, the BMS collects new data and evolves to a much smarter, reliable and user-friendly system.

In part two of our BMS series, we’ll discuss battery internal state estimation, and in part three, we’ll discuss battery charging.

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