Development of dual polarization battery model with high accuracy for a lithium-ion battery cell under dynamic driving cycle conditions

Abstract

Lithium-ion batteries are a key technology for electric vehicles. They are suitable for use in electric vehicles as they provide long range and long life. However, Lithium-ion batteries need to be controlled by a Battery Management System (BMS) to operate safely and efficiently. The BMS continuously controls parameters, such as current, voltage, temperature, state of charge (SoC), and state of health (SoH), and protects the battery against overcharging and discharging, imbalances between cells, and thermal runaways. The battery models and several prediction algorithms that the BMS uses to carry out these checks are essential to the system's performance. This research assesses the Dual Polarization (DP) model's ability to mimic actual battery performance in different dynamic driving conditions. In the study, a battery model for a Lithium–Nickel–Manganese–Cobalt-Oxide (Li-NMC) cell with a nominal capacity of 2 Ah is developed. A DP model was used in the study. Modeling and parameter estimation were performed in MATLAB Simulink/Simscape. Firstly, the model parameters are estimated depending on the SoC using the current and voltage data obtained from the Hybrid Pulse Power Characterization (HPPC) test. A further validation study of the model for low dynamic and high dynamic driving cycles is then presented. Dynamic Stress Test (DST), the US06 Supplemental Federal Test Procedure (SFTP) and Worldwide harmonized Light vehicles Test Procedure (WLTP) cycles were used for model validation. As a result of the study, the model's Root Mean Square (RMS) error values were obtained as 0.0053 V for DST, 0.0059 V for US06, and 0.008 V for WLTP. The obtained model is particularly successful for simulating a battery under dynamic current conditions and for use in control and prediction algorithms.

1. Introduction

Lithium-ion batteries are preferred in electric vehicles due to their advantages such as high single-cell voltage, high energy and power density, and long life [1]. However, Lithium-ion batteries can be damaged by overcharge-discharge, high temperatures, and overcurrent. Therefore, a Battery Management System (BMS) is used to ensure the safe and efficient operation of the battery [[2], [3], [4], [5]]. BMS continuously monitors important parameters of the battery such as current, voltage and temperature, state of charge (SoC) and state of health (SoH) and optimizes the operating conditions to ensure efficient operation in the safe region [6,7]. While parameters such as current and voltage can be measured directly with sensors, SoC and SoH values cannot be measured directly. BMS uses battery models to estimate these parameters that cannot be measured directly [3,8,9]. Hence, the accuracy of the battery model used is critical for the battery to operate efficiently within safe operating limits. Therefore, BMSs are one of the topics that need to be developed in electric vehicles [10].

Three main classifications are used in the literature to classify battery models: electrochemical, mathematical, and electrical circuit models [11,12]. In addition to these three basic cell model methodologies, data-driven models such as artificial neural networks and Support Vector Machine (SVM) are employed [13,14]. However, these g conditions [15]. To effectively model battery behavior in learning-based algorithms like as artificial neural networks, a large ammethods rely on the accuracy of experimental data and are unable to explain the changing electrochemical behavior under various operatinount of data must be defined as input to the network during the learning stage. This approach is not preferred because it is not efficient to process and store large data by the BMS [14,16]. Electrochemical models can model chemical phenomena inside the battery, such as ion diffusion, ion distribution, mass, and charge balance, with high accuracy. However, modeling the phenomena occurring inside the battery requires the use of partial differential equations with a large number of unknowns. This makes the model complex and increases the computational and storage overhead [17]. Various simplified electrochemical models are also available in the literature. However, these models are unsuccessful over wide SoC ranges [18]. In addition, determining parameters and solving non-linear equations is also difficult for simplified models [19]. For this reason, electrochemical models are mostly used to design new batteries and are not preferred for battery management in electric vehicles [14,20,21]. Mathematical models model battery behavior using various equations such as Nernst and Butler-Volmer equations [22,23]. The most important feature of these models is that the parameters can be easily determined from a typical discharge curve provided by the manufacturer without needing cell testing. Although this approach has the advantages of simplicity and low computational cost, the accuracy of the model depends on the accuracy of the data provided by the manufacturer, and the equations do not allow for physical interpretation of the model parameters [22,[24], [25], [26]]. The electrical equivalent circuit model is an approach that simulates voltage behavior using circuit elements such as voltage source, resistor and capacitor. They can model battery behavior with high accuracy if simulation efficiency is achieved. The most common time domain equivalent circuit models in the literature are the Rint model, Thevenin model, Partnership for a New Generation of Vehicles (PNGV) model, Dual Polarization (DP) model [27,28]. The Rint model is the simplest equivalent circuit model consisting of a voltage source and an internal resistor. Only ohmic losses can be modeled with series-connected resistor. In a real battery, the voltage varies according to the SoC level and other factors, while the Rint model is SoC-independent and models the voltage behavior with a fixed internal resistance value [29]. When a resistor and capacitor element (RC) are connected in parallel to the Rint model, the Thevenin model, or 1-RC model, is obtained. The Thevenin model characterizes ohmic losses as well as electrochemical polarization. Unlike the Thevenin model, the PNGV model uses a capacitance connected in series with the circuit to utilize the time variation of the current [30]. Although the PNGV model is successful in modeling voltage behavior in short-term simulations, the error value increases in long-term simulations [11,31]. DP model or also known as the 2-RC model is obtained by adding a second parallel connected RC circuit to the Thevenin model. In the DP model, the second RC element characterizes the concentration polarization. The DP model is more accurate in representing the voltage characteristics than the other three models [[31], [32], [33], [34]]. More RC circuits can also be added to the DP model. Such models are called multi-order models. For example, a model with 3-RC circuits connected in series is called a 3-RC model. However, while the increase in RC elements increases model complexity and computational cost, it does not affect model accuracy much [15,33,35,36].

The DP model is widely used in the literature. Huo et al. [14] used a DP model for SoC prediction with Extended Kalman Filter. They explained the relationship between temperature and battery behavior with Open Circuit Voltage (OCV) tests at different temperatures. They validated their model using OCV and Dynamic Stress Test (DST) data. The model they obtained was able to simulate the experimental voltage curve of OCV test at 25 °C with 0.011 V RMSE and the voltage curve of DST with 0.008 V RMSE. A similar study was done by Pang et al. [33]. Pang et al. proposed an Improved DP model for SoC prediction with Kalman Filter. In their study, they added a series-connected resistor to the DP model to include the temperature effect. They used the Exponential Function Fitting (EFF) method to estimate the model parameters. They performed a comparison of the improved model with the DP model for Hybrid Pulse Power Characterization (HPPC) and US06 cycles. Gurjer et al. [37] made a comparison between the Thevenin model and the DP model using battery test data from Center for Advanced Life Cycle Engineering (CALCE) for different temperatures. The root mean square percentage error (RMSPE) of the Thevenin model at 25 °C under DST was 6.66%, while the RMSPE of the DP model was 1.77%. Another study comparing the DP model with the Thevenin model was presented by Nemes et al. [38]. The error values of the models were compared for HPPC test and the Root Mean Square Error (RMSE) value for the Thevenin model was calculated as 0.1171 V and the RMSE value for the DP model was calculated as 0.0825 V.

In the case of electric vehicles, a vehicle is often subjected to highly dynamic driving behavior during travel. Therefore, it is important to evaluate the models considering all the load conditions that an EV battery can be subjected to. The existing studies mostly have present results based on data obtained from tests under static load, even if dynamic load conditions are compared, the procedures used appear to be mild dynamic procedures. One of the emphasis in this study is to provide an analysis according to the Worldwide harmonized Light Vehicles Test Procedure (WLTP). Because WLTP is the most current and valid driving cycle that most realistically reflects the driving behavior of a vehicle. Vehicle manufacturers evaluate the energy consumption of the vehicle according to this cycle. Therefore, it is important for vehicle manufacturers or those who will design battery management systems to examine the performance of the models under these driving cycle conditions.

In this study, a DP battery model was built in MATLAB R2022b Simscape environment. The model is aimed to be able to simulate the real voltage behavior under highly dynamic driving cycles with high accuracy. HPPC testing was used to obtain the model parameters. DST, US06, and WLTP cycles were used to evaluate the model's ability to simulate actual voltage behavior. A validation of the model with respect to dynamic cycles is important to examine its usability in electric vehicles. The more accurately the model can model dynamic conditions, the more accurately the battery management system can control the battery pack. As a result, the battery pack is ensured to fulfill its expected lifetime and operate efficiently. The energy consumption of the vehicle is also optimized. For this reason, model validation is done for DST, US06 and WLTP cycles in this article. The DST current profile is a relatively low dynamic procedure. Therefore, validation was also carried out for the US06 and WLTP driving cycles in order to evaluate how well the battery model can mimic the battery behavior under the realistic driving conditions of an electric vehicle. The US06 cycle was chosen because it represents a dynamic driving profile with high speed, high accelerations, rapid speed fluctuations, and sudden stop-start behavior. The WLTP cycle is the most up-to-date test procedure developed in 2018 to report more realistic fuel efficiency values. It has a more comprehensive range of data with low, medium, high and extra-high driving zones [[39], [40], [41]]. It is therefore important that the model can simulate the voltage with high accuracy, especially for the most aggressive WLTP cycle. As stated in Table 2, the lack of results for WLTP cycles in DP model studies in the literature is one of the aspects that makes this study original.

Table 2.

A comparison of the current study's results with those of other studies.

	Battery Model	SoC range (%)		RMSE (V)
			HPPC	DST	US06	UDDS	WLTP
Shin et al. [47]	Thevenin	100–10	–	–	0.0229	–	–
Geng et al. [16]	PNGV	100–10	–	–	–	0.0170	–
Huo et al. [14]	DP	100–10	–	0.008	–	–	–
Pang et al. [33]	DP	100–10	0.0245	–	0.0285	–	–
	Improved DP		0.0126	–	0.0156	–	–
Gurjer et al. [37]	DP	80–10	0.0078	0.0177	–	–	–
Nemes et al. [38]	DP	100–0	0.0825	–	–	–	–
Current paper	DP	100–10	0.0031	0.0053	0.0059	-	0.008

The article structure is as follows: In the first part of Section 2, information about the battery cell used in the study and the experiments performed are given, and in the second part, the battery model used in the article and identification of the model parameters are introduced. In Section 3, the obtained parameter values are presented. The model's performance under various current profiles is compared with the results of different studies. Finally, a discussion is presented in Section 4.

2. Material and methods

2.1. Experiments

In this study, a new INR18650-20R battery cell manufactured by Samsung is used. Table 1 lists the cell characteristics. All tests were carried out in the experimental setup shown in Fig. 1. Neware BTS4000-5V-12A battery cell tester was used. The ambient temperature was maintained at a constant range of 23–25 °C in the laboratory conditions. First, a static capacity test was carried out to assess the cell's real capacity. The value was found to be 2.048 Ah. Following that, HPPC, DST, US06, and WLTP driving cycle testing were conducted. For each test, current and voltage were measured at 1-s intervals. After completing one test, the cell was rested for enough time to achieve equilibrium. Then, it was charged using the Constant Current-Constant Voltage (CC-CV) charging method indicated by the manufacturer in the datasheet before moving on to the next step.

Table 1.

Characteristics of the battery cell.

Item	Specification
Nominal discharge capacity	2000 mAh Charge: 1A, 4.20V,CC-CV 100 mA cut-off, Discharge: 0.2C, 2.5V discharge cut-off
Cell chemistry	LiNiMnCoO2/Graphite
Nominal voltage	3.6 V
Discharge cut-off voltage	2.5 V
Charge cut-off voltage	4.2 V
Standart Charge	CC-CV, 1A, 4.2 ± 0.05 V, 100 mA cut-off
Cell weight	45.0 g max
Cell dimension	Height: 64.85 ± 0.15 mm Diameter: 18.33 ± 0.07 mm

Fig. 1.

Experimental setup.

The model parameters were defined using the voltage data collected from the HPPC test. Different HPPC procedures [[42], [43], [44]] are used in the literature. In this study, the HPPC profile developed by The United States Advanced Battery Consortium (USABC) [45] was used. According to this process, an HPPC cycle consists of 30 s of discharge, 40 s of hold, and 10 s of charge. Following this cycle, the battery is discharged at a current rate of C/3 until 10% of its capacity has been depleted, and then rested for 1 h to allow the open circuit voltage to reach equilibrium. This is repeated until the cell is fully discharged. As a result, the dynamic properties of a battery at each SoC level can be identified. After identifying model parameters, the DST, US06, and WLTP driving cycle tests were used to validate model performance. Fig. 2 depicts the current and voltage profiles obtained during the experiments. The graphs on the left side of the diagram show the current profile of a single cycle in each test. The middle section shows the current profile for the entire cycle, while the graphs on the right side show the voltage profile collected for the whole cycle.

Fig. 2.

Applied current profiles and recorded voltages a) HPPC, b) DST, c) US06, d) WLTP (Left side one cycle current profile, middle side entire current profile, right side voltage profile. Discharge is represented by negative current and charge by positive current.).

2.2. Battery model and parameter identification

The DP model was used in this study, which is the most preferred model for SoC and SoH estimation. The DP model electrical equivalent circuit diagram is given in Fig. 3.

Fig. 3.

Dual Polarization model.

The voltage measured across the battery terminals is equal to the open circuit voltage V_OC when no load is applied to the cell and the cell is in chemical equilibrium. The open circuit voltage drops due to losses as soon as the discharge current is applied to the battery cell. This transient response is represented by resistance and capacitance components. In Fig. 3, the series-connected resistor R₀ represents the internal resistance caused by the electrolyte and other electrical components. Parallel connected R_p and C_p represent polarization resistance and polarization capacitance, respectively. R_p and C_p together give the polarization time constant τ (tau). R_p,1 and C_p,1 give the short-time constant τ₁, and R_p,2 and C_p,2 give the long-time constant τ₂ [37,46].

For the find out of these parameters, the HPPC test is used. The resulting voltage curve can be used to determine these values. Fig. 4 shows the voltage curve obtained when a pulse of discharge current is applied to a battery at a given SoC level.

Fig. 4.

Battery voltage response.

The voltage value is equal to the open circuit voltage (V_OC) when no current is drawn from the battery cell. The first parameter to be determined is this. The voltage drops sharply when the first time the current pulse is applied. The ohmic resistance is the reason of this drop, as described by Equation (1).

$${\mathrm{R}}_0=\frac{\Delta \mathrm{V}}{\Delta \mathrm{I}}=\frac{{\mathrm{V}}_2-{\mathrm{V}}_1}{\mathrm{I}}$$ (1)

For the DP model, Equations (2), (3), (4), (5) express the polarization resistances and capacitances that cause the slower drop following the sudden drop in voltage ($\Delta$ t₁ period in Fig. 4). The battery state of charge continues to decrease as the current continues to drawn in this region. When the current is discontinued, the state of charge stays constant, and the cell voltage begins to increase slowly. This is because different Li-ion concentration gradients exist throughout the battery cell when the current is discontinued. In this relaxation period, which is shown as the $\Delta$ t₂ region in Fig. 4, the concentration gradient equalizes over time and the voltage reaches a constant value. The value read at the end of the relaxation period is the new open circuit voltage.

$${\mathrm{R}}_{\mathrm{p},1}=\frac{{\mathrm{V}}_3-{\mathrm{V}}_2}{\mathrm{I}}$$ (2)

$${\mathrm{R}}_{\mathrm{p},2}=\frac{{\mathrm{V}}_4-{\mathrm{V}}_3}{\mathrm{I}}$$ (3)

$${\tau }_1=R_{p,1}{C}_{p,1}$$ (4)

$${\tau }_2=R_{p,2}{C}_{p,2}$$ (5)

As a result of the polarizations, the voltage between the battery terminals is calculated by Equation (6).

$$V_T=V_{OC}-R_{0}I-R_{p,1}I\left(1-e^{-\frac{\Delta t_1}{R_{p,1}{C}_{p,1}}}\right)-R_{p,2}I\left(1-e^{-\frac{\Delta t_2}{R_{p,2}{C}_{p,2}}}\right)$$ (6)

3. Results and discussion

3.1. Parameter identification

The HPPC voltage curve was used to estimate the model parameters. The battery cell model was built in MATLAB Simscape environment. MATLAB/Simulink Parameter Estimation Toolbox was used to identify the parameter values. Non-linear Least Squares was chosen as the solver method and Trust-Region-Reflective, and Parallel Computing Toolbox was used for faster estimation. In the Toolbox, the minimum and maximum values for each model parameter were set manually by observing the error values of the model. The determined parameter values are defined as 1-D look-up tables in the model.

Fig. 5 shows the performance of the model after parameter estimation to mimic the real voltage curve obtained from the HPPC test. All results and graphs are given for SoC range of 1 and 0.1. After 0.1 SoC the cell does not show normal voltage behavior, there is a sudden drop in voltage. The model fails to model this unusual behavior. Therefore, the low SoC region is not taken into account to avoid misleading. In Fig. 5, the voltage error is calculated by the expression (V_experimental-V_model). Maximum voltage error of the model for HPPC test is 0.0326 V. The RMSE value formulated in Equation (7) is also given at the end of the section. In the equation, N indicates the number of samples. It is preferred because it is a widely used measure for evaluating model performance and allows for easier comparison with different studies.

$$RMSE=\sqrt{\frac{\sum _{i=1}^N{\left(V_{experimental}\left(i\right)-V_{model}\left(i\right)\right)}^2}{N}}$$ (7)

Fig. 5.

a) Cell voltage and error value under HPPC test b) the zoomed voltage section.

3.2. Model validation and evaluation

In this section, after obtaining the SoC-dependent parameter values, DST, US06 and WLTP cycles are used to examine the performance of the model under dynamic current conditions.

First, a comparison of the model and experimental voltage curve for DST is given in Fig. 6. In Fig. 6-a, the entire voltage curve up to 0.1 SoC and the voltage error are given. In Fig. 6-b, a zoomed-in voltage region is shown to better see the difference between the experimental and model voltage curves. The maximum voltage error for DST is 0.0279 V.

Fig. 6.

a) Cell voltage and error value under DST b) the zoomed voltage section.

The second cycle used for model validation is the US06 cycle. The US06 cycle is an aggressive driving cycle with rapid accelerations and sudden stops and starts. Fig. 7 shows the model performance. For US06, the model was able to mimic the real voltage curve with an error value of 0.0383 V.

Fig. 7.

a) Cell voltage and error value under US06 b) the zoomed voltage section.

And finally, the performance of the model for the WLTP driving cycle is analyzed. As mentioned before, the WLTP driving cycle is important as it reflects real driving behavior and allows for a more comprehensive assessment of fuel economy. The maximum error value of the model for WLTP is 0.0374 V. A comparison of the voltage curves under WLTP is presented in Fig. 8.

Fig. 8.

a) Cell voltage and error value under WLTP b) the zoomed voltage section.

Table 2 shows a comparison of the model errors obtained in different studies using the Thevenin, PNGV and DP model and the model errors obtained in the present study. The results at 25 °C are given for all studies. When the results in Table 2 are analyzed, it is seen that the results obtained for the PNGV and Thevenin models are limited. However, better results were obtained in the PNGV model compared to the Thevenin model. The DP model gave better results compared to these two. Although it is not possible to compare the three models in different variations according to the table, it is seen that the DP model is better in adapting to different dynamic conditions. When the results obtained in the present paper are compared with the others, it is seen that a more accurate model is achieved. The reason for obtaining a better result than others for the same model approach may be the parameter extraction method used. In the other studies presented in the table, the parameters were extracted by exponential function fitting and curve fitting methods, while in the current study, the variation of the parameters depending on the SoC was extracted using the Simulink Parameter Estimation toolbox. However, it should be noted that uncertainties in the data, data size and experimental conditions allow for a limited discussion.

4. Conclusion

In this study, a further investigation of the DP model's performance in simulating voltage behavior is presented by considering low dynamic and high dynamic driving cycles. In particular, the ability to simulate the actual battery voltage under driving conditions such as sudden acceleration, high speed and dynamic speed variations is important for BMS control. Therefore, a DP model is created and the modeling performance under DST, US06 and WLTP driving cycles is investigated. The model parameters were found out by HPPC testing. Since all tests were performed only at room temperature, the model parameters depend only on the SoC value. DST, US06 and WLTP cycles were used to examine the performance of the model to mimic the real voltage behavior. As a result, the following conclusions were reached.

The model accurately mimicked the real voltage behavior for all cycles. Especially in the WLTP driving cycle, the maximum voltage error is 0.0374 V and the RMSE value is 0.008 V. This is a remarkable result considering how dynamic the WLTP driving cycle is.

When the error values obtained under all test conditions are compared with the error values obtained in previous studies, a more successful model is obtained in the current study. One of the reasons for this may be the different approaches used to obtain the model parameters. In addition, it was observed in the study that the limits and scales set for the parameter values in the Toolbox during the identification of the model parameters with the Parameter Estimation Toolbox also significantly affect the estimation results and consequently the model performance.

As a result, the DP model is very suitable for use in BMSs due to its simple structure and its ability to reasonably mimic the battery performance of the battery. Another advantage is its low computational cost and efficiency. It should be noted that the effect of battery health status and ambient temperature is not considered in this study. The parameters of the model are only a function of the SoC. However, the behavior of the battery is affected by factors such as temperature and aging level. Although the DP model can successfully simulate the voltage behavior, its performance may deteriorate in real application when the battery health and temperature effects are not included in the model. Another issue is the cells are stacked in the battery pack. In future studies, taking into account the effects such as health status, temperature, pressure caused by the stacking of cells, etc. at the package level of the model created at the cell level will increase the adaptability of the model to different operating conditions.

Author statement

During the preparation of this work the authors used Grammarly and Quillbot in order to check grammar and improve readability. After using this tools, the authors reviewed and edited the content as needed and takes full responsibility for the content of the publication.

Data availability statement

The authors do not have permission to share data.

CRediT authorship contribution statement

Merve Tekin: Writing – original draft, Formal analysis, Conceptualization. M. Ihsan Karamangil: Writing – review & editing, Supervision, Project administration, Formal analysis.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Nomenclature

CALCE

Center for Advanced Life Cycle Engineering

CC-CV

Constant Current- Constant Voltage

DST

Dynamic Stress Test

HPPC

Hybrid Pulse Power Characterization

Li- NMC

Lithium–Nickel–Manganese–Cobalt-Oxide

OCV

Open Circuit Voltage

PNGV

Partnership for a New Generation of Vehicles

RMSE

Root Mean Square Error

SoC

State of Charge

SoH

State of Health

US06

Supplemental Federal Test Procedure

USABC

The United States Advanced Battery Consortium

WLTP

Worldwide harmonized Light Vehicles Test Procedure

$C_p$

the polarization capacitance (F)

$R_0$

the internal resistance ($\mathrm{\Omega })$

$R_p$

the polarization resistance ($\mathrm{\Omega })$

$V_{OC}$

open circuit voltage (V)

$V_T$

battery terminal voltage (V)

I

current (A)

V

voltage (V)

τ

time constant (s)