Battery Management Systems – Part 2: Battery State Estimation
Edis Osmanbasic posted on February 03, 2020 |
An in-depth look at estimating SOC, SOH, internal temperature and joint state.
(Image courtesy of DV Power.)
(Image courtesy of DV Power.)

In part one of this series, we introduced the battery management system (BMS) and explained the battery modeling process. For part two, we’ll look at another important aspect of the BMS: battery state estimation.

Battery state estimation is necessary to optimize a battery’s safety and performance as well as its lifetime predictions and aging diagnostics. Aging batteries accrue a solid electrolyte interface at the negative electrode. Cell design, battery operation and environmental conditions are among the many factors affecting a battery’s lifespan. Aging decreases a battery’s available usable capacity and increases its internal resistance, etc. Figure 1 shows the main degradation factors that affect battery condition.

Figure 1. Various battery aging and degradation factors are presented inthis Ishikawa diagram. (Image courtesy of MDPI Article Harting et al., 2018.)
Figure 1. Various battery aging and degradation factors are presented in this Ishikawa diagram. (Image courtesy of MDPI Article Harting et al., 2018.)

Battery state estimation includes four key states: State of Charge (SOC), State of Health (SOH), internal temperature, and joint state estimations (see Figure 2).

Figure 2. The four key states of battery state estimation.
Figure 2. The four key states of battery state estimation.

SOC Estimation

SOC battery estimation provides information about the battery’s remaining capacity as a percentage value of its total capacity. SOC estimation has two commonly used approaches: direct estimation and model-based estimation.

Direct Estimation Approach

This approach is based on the direct measurement of electrical battery parameters (voltage and current). The two calculation methods used are Ampere-hour (Ah) and open-circuit voltage (OCV)-based methods.

Ah method uses a simple measurement of charging or discharging current. As a result, this approach should be a logical choice for SOC estimation. The SOC calculation can be performed by using the following equation:

  • SOC(n0) is the known initial SOC
  • η is battery charging/discharging efficiency
  • I(t) current value during the charging/discharging process
  • CN is battery nominal capacity

However, determining the initial SOC and measurement accuracy can be a challenging process when adapting the Ah method for the SOC estimation algorithm.

This method is highly dependent on the measured current, where errors accumulated over time significantly affects the accuracy of the SOC estimation. It is also difficult to determine the accurate initial SOC in real-world applications (e.g., in the case where a battery is charged only within a limited range, from 10 percent to 90 percent).

On the other hand, the OCV-based method provides high estimation accuracy and has been accepted as an effective and popular method for SOC estimation (Baccouche et al., 2017). There is a nonlinear relationship between a battery’s SOC and OCV. The method requires sufficient battery resting (the battery needs to be disconnected from chargers and loads). The main limitation of this method is the resting time. It usually takes a long time to reach equilibrium after disconnecting the battery from its load (it can take more than two hours under low temperature conditions). The OCV-SOC relationship also depends on the battery’s age and temperature. These disadvantages prevent the OCV method from being used widely in EV applications. However, the method can be improved by using a real-time OCV calculation that allows SOC estimation during driving.

The Model-Based Method

This model has been developed to provide a calculation of the OCV enabling online SOC estimation. With this method, a corresponding battery model needs to be designed, as is described in the previous article. The most common models are the battery equivalent circuit model and the electrochemical model. The accuracy of the model-based method is dependent on the training of the battery models, the adopted state observers, and the parameter tuning. The SOC estimation performance is validated under limited conditions of the test data, so the estimation performance under various real operating conditions cannot be guaranteed.

SOH Estimation

SOH indicates the battery’s ability to store and deliver energy, as well as provides information about the battery’s condition compared to its optimal conditions. SOH is 100 percent in new batteries and decreases overtime. However, the initial SOH can be less than 100 percent when a new battery’s performance does not meet its specifications.The battery SOH can be described with the following equation:

  • SOH(t0) is the initial battery SOH
  • δfunc (x) an aging rate function
  • X—different factors that strongly influence an aging rate function are current, temperature, SOC, and stress factors such as mechanical vibrations and over potential

Battery aging lowers its capacity and causes increased battery internal resistance. The battery’s internal resistance measurement can be used for battery SOH estimation. Different approaches can be used for battery SOH estimation, and they can be categorized into three methods: model-free, model-based, and data mining methods.

The model-free method estimates the battery SOH by using parameters called the aged capacity(Caged) or the increased internal resistance (Rinc). The model is presented simply by the equations below, where Cn and Rn are the nominal capacities and internal resistance for a new unused battery:

For the direct measurement method, a standard capacity test or pulse current test is used to measure the battery aged capacity (Caged) and increased internal resistance (Rinc). This method is not practical for EV applications because it requires full battery discharge, thus interrupting normal EV operations.

An additional method, battery electrochemical impedance spectroscopy (EIS), has been introduced to provide more information about battery health. However, this method requires onboard measurement and specific instruments, which limit its applicability. In addition, the full EIS test takes a long time.

Researchers are focused on developing battery cycle life models that can predict battery capacity degradation and provide an analysis of the effects of stress factors. Battery capacity degradation is mostly influenced by dynamic factors such as current, temperature, SOC, and charging methods. Therefore, researchers have introduced various dynamic cycle life models to assess battery aging parameters. For example, Omar et al.(2014) propose a battery aging model that predicts the capacity degradation that occurs during discharging and fast charging, and Ecker et al.(2012) present the cycle life model validated for the Li-ion battery based on the profiles proposed by the VDA (German Association of the Automotive Industry). These cycle life models are important to optimize the real-time operations that can prolong a battery’s service life.

Since the battery SOH changes much more slowly than the battery SOC, the battery cycle life models require wider ranges of battery operation, and more test data, to train the battery model.

Data-mining SOH estimation approaches have become popular for diagnosing and predicting the cell condition of Li-ion batteries. Commonly used data-driven diagnostic algorithms for identifying the complex aging of Li-ion batteries apply artificial neural networks as well as support vector machines (SVMs). SVMs rely only on measurable battery data, including voltage, current and operating temperature. According to the historical distributions of measured data (battery current, voltage and temperature), clustering and neural network technologies are proposed for an SOH estimation by using the data-mining approach. The average accuracy of the estimated SOH can be within 2.2 percent (You et al., 2016).

Internal Temperature Estimation

Battery temperature is an important factor that affects battery performance, lifespan, efficiency and safety. Thermal sensors are suitable for measuring a battery’s surface temperature. However, this information alone is not sufficient because the internal temperature of the battery is a crucial parameter for proper battery management. High internal temperature accelerates the battery’s aging and causes safety issues (e.g., fire). The internal battery temperature is usually significantly different than the surface temperature (up to 12°C in high-power applications [Zang et al., 2016]). Designing a proper approach for internal battery temperature estimation prevents accelerated aging of batteries and assists the BMS algorithm in optimizing battery energy discharging.

There are different methods for battery internal temperature estimation. An efficient but costly and complex method is mounting micro-temperature sensors into the battery cell. Different model-based approaches have been proposed to achieve this, such as a distributed battery thermal model and a lumped-parameter battery thermal model. These approaches can also be used in online battery internal temperature estimation. However, the model-based methods require the tuning parameters and acquisition of useful thermal data, which can make this approach challenging.

The electrochemical impedance spectroscopy (EIS) method can be used for battery internal temperature estimation. There is an intrinsic relationship between the internal cell’s temperature and its electrical parameters—the phase shift between applied sinusoidal current and the induced voltage. This allows instantaneous measurement of the internal cell’s temperature. The measurement depends mostly on the temperature and does not depend on the battery SOC. The optimal frequency range of the applied signal is between 40 and 200Hz.

Battery impedance measurement at a single frequency can also be used for the battery internal temperature estimation. Under inhomogeneous or transient temperature distribution conditions, this approach gives only information about the average temperature, but not the temperature distribution field or the peak value.

Figure 3. Battery internal resistance is a function of battery temperature. The low internal resistance value provides smaller internal heating losses. (Image courtesy of the article “Advanced Electric Vehicle Fast-Charging Technologies,” Yu Miao, Baylor University - Energies 12(10):1839, May 2019.)
Figure 3. Battery internal resistance is a function of battery temperature. The low internal resistance value provides smaller internal heating losses. (Image courtesy of the article “Advanced Electric Vehicle Fast-Charging Technologies,” Yu Miao, Baylor University - Energies 12(10):1839, May 2019.)

Hybrid data-driven methods (based on linear neural networks) can capture nonlinear performance of battery dynamics and estimate Li-ion battery internal temperatures. The extended Kalman filter (EKF) provides good estimation accuracy. The method can be adapted to other types of batteries as well.

Joint State Estimation

The joint state battery estimation (SOC and internal temperature) can be obtained based on the coupled electro-thermal models. These models simultaneously capture a battery’s electric and thermal behaviors. Designing a simple and accurate battery electro-thermal model is a first and key step for joint state estimation. The joint state (battery SOC and internal temperature) can be estimated simultaneously based on the interaction between battery resistance and internal temperature.

Coming Up Next

In the third and final part of our BMS series, we’ll discuss battery charging.


[1] State-of-Health Identification of Lithium-Ion Batteries Based on Nonlinear Frequency Response Analysis: First Steps with Machine Learning, Nina Harting, René Schenkendorf, Nicolas Wolff, and Ulrike Krewer, 19 May 2018.

[2] Improved OCV model of a Li-ion NMC battery for online SOC estimation using the extended Kalman filter, Baccouche I, Jemmali S, Manai B, Energies, 2017, 10(6): 764.

[3] Lithium iron phosphate-based battery—Assessment of the aging parameters and development of cycle life model. Omar N, Monem M A, Firouz Y, Applied Energy, 2014, 113: 1575–1585.

[4] Development of a lifetime prediction model for lithium-ion batteries based on extended accelerated aging test data, Ecker M, Gerschler J B, Vogel J, Journal of Power Sources, 2012, 215: 248–257.

[5] Real-time state-of-health estimation for electric vehicle batteries: A data-driven approach, You G, Park S, Oh D, Applied Energy, 2016, 176: 92–103.

[6] Rapid self-healing and internal temperature sensing of lithium-ion batteries at low temperatures, Zhang G, Ge S, Xu T, et al. Electrochimica Acta, 2016, 218: 149–155.

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