Lithium-Ion Polymer Battery for 12-Voltage Applications: Experiment, Modelling, and Validation

Modelling, simulation, and validation of the 12-volt battery pack using a 20 Ah lithium–nickel–manganese–cobalt–oxide cell is presented in this paper. The cell characteristics influenced by thermal effects are also considered in the modelling. The parameters normalized directly from a single cell experiment are foundations of the model. This approach provides a systematic integration of actual cell monitoring with a module model that contains four cells connected in series. The validated battery module model then is utilized to form a high fidelity 80 Ah 12-volt battery pack with 14.4 V nominal voltage. The battery cell thermal effectiveness and battery module management system functions are constructed in the MATLAB/Simulink platform. The experimental tests are carried out in an industry-scale setup with cycler unit, temperature control chamber, and computer-controlled software for battery testing. As the 12-volt lithium-ion battery packs might be ready for mainstream adoption in automotive starting–lighting–ignition (SLI), stop–start engine idling elimination, and stationary energy storage applications, this paper investigates the influence of ambient temperature and charging/discharging currents on the battery performance in terms of discharging voltage and usable capacity. The proposed simulation model provides design guidelines for lithium-ion polymer batteries in electrified vehicles and stationary electric energy storage applications.


Introduction
Lead-acid-based batteries have a long-term historical usage in the automotive and stationary standby power market, ranging from 12-volt high-power such as automotive starting-lighting-ignition (SLI) applications, low-power applications such as emergency lighting or uninterruptible power supplies (UPSs) for individual computers, to high-power, high-voltage electric energy storage in renewable energy systems or UPSs telecommunications facilities. Typical lead-acid batteries have several problems including high self-discharge rate, relatively heavy and large, and shallow depth of discharge (DOD). For the past decades, lithium-ion batteries have been widely used in portable electronics due to their features of high energy density, high discharge power, and long cycle life. The emerging applications of the lithium-ion batteries to electric-drive vehicles and large-scale energy storage systems for renewable energy make them a promising solution for challenges of environmental preservation and resource conservation [1,2]. The lithium-ion battery is also a suitable replacement for the conventional 12-volt SLI lead-acid battery; for example, Porsche offers an option of a lithium-ion SLI battery [3], and some medium-duty truck manufacturers use a lithium-ion battery for 12/24 V electrical systems [4,5]. The lithium-ion polymer battery uses a high conductivity semisolid (gel) polymer electrolyte instead of a liquid electrolyte. The battery cell voltage depends on the electrode material UPS applications, this paper investigates the ambient temperature effect on the battery performance in terms of discharging voltage and usable capacity. The proposed simulation model provides design guidelines for lithium-ion polymer batteries in electric-drive vehicle and stationary UPS applications.

Battery Modelling from Cell to Pack
A high-fidelity single cell model is a foundation to form a reliable battery module and pack with statistical confidence. The equivalent circuit technique is commonly used for electrochemical impedance characterizations in a cell model. This study uses parameters normalized directly from single cell experiments, which provide a systematic integration of actual cell monitoring with a module model. The approach begins with single cell model development and validation. A module with four cells connected in series is also validated. A high fidelity SLI battery pack model is then achieved.

An Enhanced Equivalent Electric Circuit Cell Model
The equivalent electric circuit approach has been adopted by many researchers to model battery cells ranging from lead-acid to lithium-ion batteries. The most commonly used equivalent electric circuit models are the Thevenin-based model [17][18][19], impedance-based model [20][21][22], and the runtime-based model [23,24]. The Thevenin-based model can predict battery response to the transient load at a certain SOC due to a series resistor and resistor-capacitor parallel network in the model. An impedance-based model is formed by an AC-equivalent impedance model in the frequency domain and the electrochemical impedance spectroscopy method. The runtime-based model utilizes a capacitor and controllable current source to predict battery capacity, SOC, runtime, and open circuit voltage (OCV). The battery operation time and DC voltage response under a constant discharge C-rate also can be simulated by the runtime-based model. The advantages of the runtime-based model and Thevenin-based model are combined in a model presented by [26], as shown in Figure 1. Based on [27], an equivalent electric circuit model with improved features is presented in this paper. In the developed Simulink model shown in Figure 2, three inputs (discharging current, initial SOC ranging from 0 to 1, and battery capacity) replace the battery runtime model. Since the initial SOC is an input variable, the developed model can simulate batteries that are not fully-charged. The OCV is calculated according to real-time SOC, which is predicted from three inputs to the model. Subtracting both voltages of the resistor-capacitor (RC) parallel networks and series resistor (R S ) from the OCV gives the cell terminal voltage (Vt), which is an output of the developed model. The real-time SOC, OCV, RC value, RC parallel network voltages, and series resistor voltage are calculated by five developed submodels.  Equation (1) calculates the real-time SOC, in which SOC 0 denotes the initial SOC, I denotes the discharging current, and UC denotes the usable capacity. A submodel calculating SOC is presented in Figure 3a, in which three inputs are SOC 0 , I, and UC and output is real time SOC. Equation (2) is derived from numbers of experimental discharging curves using the method presented in [26] that provides relationship between the SOC and OCV. The interpolation-extrapolation lookup method is applied to calculate and determine the most suitable RC values, as a submodel presented in Figure 3b. The transient response of the battery cell voltage in the developed model is computed by the voltages of RC parallel networks. Equation (3) calculates the voltages of RC parallel networks in the s-domain, as a submodel shown in Figure 3c. For a typical lithium-metal-oxide polymer cell, the series resistor is 0-0.01 ohms in the 20%-100% SOC range, and 0.01-0.06 ohms within the 0%-20% SOC range [26]. Therefore, the developed model uses 0.001 ohms for 20%-100% SOC and 0.03 ohms for 0%-20% SOC in all discharging currents. The voltage on the series resistor (V S ) is calculated by Equation (4) where R S is the series resistor resistance, and a submodel is presented in the Figure 3d. Equation (5) calculates the terminal voltage (V t ) of the battery cell. A more detail description of the submodels and their paraments is presented in [30].

Cell Thermal Model
The lithium-ion polymer cell thermal model was built in the Simulink battery block platform, which implemented similar equations as those discussed in Section 2.1 with thermal effects. In the discharge model (i * > 0), Equations (6)-(11) are implemented to represent the temperature effect on the battery model parameters [31]. The temperature tab requires several parameters, which are determined by battery discharging test under 20 • C ambient temperature. The initial cell temperature is set to the ambient temperature because each cell is cooled down or warmed up to the ambient temperature before starting the discharging test. The "nominal ambient temperature T1 ( • C)" parameter is the ambient temperature during nominal operations. It is assumed that all parameters in the parameters tab are obtained at 20 • C ambient temperature. The procedures of establishing the cell thermal model in the Simulink platform are presented in [32]. Figure 4 shows the Simulink battery cell discharging model considering ambient temperature effects. (11) where: T ref (K) nominal ambient temperature, T (K) cell or internal temperature, T a (K) ambient temperature, E/T (V/K) reversible voltage temperature coefficient, α Arrhenius rate constant for the polarization resistance, β Arrhenius rate constant for the internal resistance, (Ah/K) maximum capacity temperature coefficient, C∆Q/∆T (V/Ah) nominal discharge curve slope.

Battery Module and Pack Model
A battery module model containing four cells connected in series was created in the Simulink platform, as shown in Figure 5. The controlled current source, four battery cells, breakers with control algorithms to perform the battery management system (BMS) function, and voltage measurement with scopes are the four submodels in the module model. The charging and discharging current to each cell model are generated by the controlled current source sub-model, which has two parameters, namely DC source type and zero initial amplitude (A). The controlled current source block is connected to a constant block for generating a continuously constant charging or discharging current. A value in the constant block is the constant charging/discharging current. The pulse generator block is applied to generate a pulse charging/discharging current. Cell breaker, bypass breaker, cell voltage tag, and cell control tag form a BMS submodel for each cell. When the cell is charged to a voltage higher than 4.3 V or discharged to a voltage lower than 2.3 V, the control tag opens the cell breaker and closes the bypass breaker to prevent the cell from becoming over-charged or over-discharged. Each submodel contains one pair of tags for the breakers. Figure 5 shows only one pair of tags for a better display. Each cell voltage curve is shown in its scope and a terminal voltage is displayed in total voltage scope. All the parameters in this model are determined from the continuous and pulse discharge tests. A more detail description of the submodels and their paraments is presented in [33].

Experiment and Model Validation
The lithium-ion polymer cells used in this study were EiG ePLB C020 lithium-nickel-manganese-cobalt-oxide-based cathode and graphite-based anode with 3.6 V nominal voltage and 20 Ah capacity. Figure 6 shows the test equipment using in this study, namely a Digatron charge/discharge cycler, a computer with Digatron Battery Manager 4 (BM4) software

Battery Cell Model Calibration and Validation
An initial battery performance evaluation test was conducted on 27 cells disassembled from a hybrid electric vehicle battery pack. Each cell was charged to 4.17 V and then fully discharged to 2.46 V using 1 C rate in the initial evaluation test. The cell model parameter determination, correlation, and validation utilized six cells with best performance in the initial evaluation test. Figure 7a shows an experimental curve generated by averaging curve data for each testing case (1/3, 1/2, 1, 1.5, and 2 C discharging current). These tests were used to calibrate the cell model parameters. The determination of cell model parameters is presented in [30]. Examples of simulated and experimental discharging curves are shown in Figure 7b. A 7% or less discrepancy between simulations and experiments existed in the 0% to 80% DOD range during constant current discharge.

Cell Thermal Experiment and Validation
To ensure the battery cell completely cooled down or warmed up to a specific ambient temperature, the battery cell was kept charging by a small current to sustain its voltage in the neighbor of 4.17 V. The temperature chamber was then set to a specific temperature for 15 minutes before applying the discharging current. The validation process consisted of 12 discharging tests, which were 10 A, 20 A, and 40 A constant discharging currents, and each discharging test was conducted under 4 different ambient temperatures (−20, −10, 0, 20, and 50 • C). The simulated discharging curves from each discharging current with specified ambient temperature were compared to corresponding experimental discharging curves. Examples of comparisons between simulated and experimental discharging curves using constant currents, 10 A, 20 A, and 40 A, under four different ambient temperatures are shown in Figure 8. A full comparison results is shown in [32]. In each discharging test, the experimental and the simulated discharging curves matched well in the range from 0% to 80% DOD (assuming 100% DOD at 2.5 V). The discrepancy between each comparison was under 7%. From the range of 80% to 100% DOD, the discrepancy became much larger. This large discrepancy might be due to the fact that battery model parameters were acquired in the nominal voltage of 3.6 V. The accuracy of the model was acceptable because most of the batteries only used up to 80% DOD. The experimental and simulated discharging time to reach 2.5 V were correlated in most test cases. Under higher ambient temperature (50 • C), the battery usable capacity increased so the total discharging time was longer than 1 hour for the one C-rate (20 A) discharging test. A similar phenomenon occurred in the one-half C-rate (10 A) test, which showed more than two hours discharging time. However, the Simulink model could not simulate the increase of battery usable capacity under high ambient temperature. Table 1 summarizes two correlated data under different ambient temperatures and discharging currents; discharging voltage at 50% DOD (assuming 100% DOD at 2.5 V) and total discharging time to reach 2.5 V are compared.

Battery Module Experiment and Validation
For the module testing, four series-connected cells formed a battery module, where the four cells were numbered from #1 to #4. This section was abstracted from [33]. The inconsistency of the cells was taken into account in the experiments and analytical models. All tests were conducted at a constant temperature of 25 • C in the chamber. Figure 6c shows the assembled-module experimental setup in the cycler. The four cells selected for the experiments had slightly different aging, internal resistance, and voltage, although they performed very similarly to each other (voltage variation between four cells was smaller than 0.08 V) under loads, as the example shows in Figure 9a. At any specific time, the difference between the highest and lowest voltage among the four cells was always no larger than 0.08 V. Figure 9b indicates that the module terminal voltage measured by the cycler was higher than the summation value of each cell terminal voltage (measured by individual voltmeter) during continuous charging. This phenonium might be due to internal resistances existing in the connecting wires between cells. The difference between cycler measurement and summation voltage became larger as the charging current increased (0.04 V for 10 A, 0.1 V for 20 A, 0.25 V for 30 A, and 0.5 V for 40 A). In continuously constant current discharge tests, each cell had very similar 10 A and 20 A discharging voltage curves. At any timeframe, the difference between the highest and lowest voltage among the four cells was always no larger than 0.15 V, as the example shows in Figure 9c. The internal resistances in the connecting wires between cells resulted in that module voltage measured by the cycler always being lower than the summation value of each cell terminal voltage measured by each individual voltmeter. As the discharging current increased, the voltage difference between the cycler measurement and summation became larger (0.05 V for 10 A, 0.2 V for 20 A, 0.3 V for 30 A, and 0.5 V for 40 A). This discrepancy was clearly observed during the 40 A discharging test shown in Figure 9d. Comparing the simulated module voltage curves with experimental voltage curves generated by the summation of four individual cells was conducted for module model validation. The module voltage curve measured by the cycler was not used for comparison because it was affected by the resistance of the connecting wires. Figure 10a-d shows that all the simulated curves matched well with the experimental ones during continuous charging and discharging. An up to 9% discrepancy occurred at the end of each charging and discharging cycle. Figure 10e and f indicate that simulated pulse charging and discharging curves matched with the experimental ones, particularly in the beginning of the cycle. The largest discrepancy was 7.8%, which occurred at the end of the 30 A pulse discharge curve. The validation of the developed battery module model presented an acceptable discrepancy.
The BMS function was simulated in the battery module model with predefined initial conditions. In one example of 25 A continuous charge current to the model, Cell #4 reached 4.3 V earlier than other cells because Cell #4 had a higher initial voltage. Therefore, the BMS opened the cell breaker and closed the bypass breaker to prevent Cell #4 from being overcharged. The voltage of Cell #4 then dropped to 4.08 V, as shown in Figure 11a. In the other example of 35 A continuous discharge current, Cell #4 reached 2.3 V first because it had a lower initial voltage. The BMS opened the cell breaker and closed the bypass breaker to prevent Cell #4 from being overdischarged. The Cell #4 voltage then increased back to 2.8 V.

Twelve-Volt Battery Pack Model
The new designed or future vehicle needs an SLI battery with a higher capacity to support increasing vehicle accessory or auxiliary loads [35,36]. Additionally, the 12-volt battery pack could

Twelve-Volt Battery Pack Model
The new designed or future vehicle needs an SLI battery with a higher capacity to support increasing vehicle accessory or auxiliary loads [35,36]. Additionally, the 12-volt battery pack could become a building module to form a high-voltage battery pack (such as 48-volts or higher) used in electrified vehicle and stationary electric energy storage for renewable energy. An 80 Ah SLT-type battery pack with 14.4 V nominal voltage is proposed in this study. This battery pack contains four modules connected in parallel where each module (14.4 V, 20 Ah) has four ePLB-C020 cells connected in series. A Simulink model of the proposed battery pack is shown in Figure 12. The model scope displays the battery pack voltage, which is a summation of each module voltage. Both simulated battery pack and module have the same shapes of constant current charging/discharging voltage curves. Obviously, the pack has four times charging/discharging durations of the module. The pack voltage curves have large fluctuations in each pulse during 20 A pulse charge simulation (180 seconds charge, 120 seconds pause, and repeat) and 30 A pulse discharge simulation (180 seconds discharge, 120 seconds pause, and repeat), as indicated in Figure 13. Figure 14 shows the simulated discharging curves of a 14.4 V 80 Ah SLI battery with one C-rate (20 A) and two C-rate (40 A) under five ambient temperatures.

Conclusions
Modelling, simulation, and validation of SLT-type 12-volt lithium-ion polymer battery are presented in this paper. The MATLAB/Simulink-based modelling starts from using parameters deduced directly from single cell experiments, which provide convenient integration with actual cell monitoring, to a module containing four cells connected in series. A validated module model is utilized to model a high fidelity 80 Ah SLI-type battery pack with 14.4 V nominal voltage. The battery cell thermal effectiveness and battery management system functions are also considered. The experimental tests are carried out in an industry-scale setup with a charge/discharge cycler, temperature chamber, and computer-controlled software for battery testing.
In the cell-level model validation, either with or without thermal effectiveness, the experimental and the simulated discharging curves match well in the range from 0% to 80% DOD (assuming 100% DOD at 2.5 V). The discrepancy between each comparison is under 7%. From the range of 80% to 100% DOD, the discrepancy becomes much larger. The module model validation indicates a 9% or less discrepancy in all continuous and pulse charge/discharge simulation results. An 80 Ah SLI-type battery pack model with 14.4 V nominal voltage then can be achieved with statistical confidence.
The 12-volt lithium-ion battery packs might be ready for mainstream adoption in automotive SLI, stop-start engine idling elimination, and UPS applications. Additionally, the 12-volt battery pack could become a building module to form a high-voltage battery pack (such as 48-volts or higher) used in electrified vehicle and stationary electric energy storage for renewable energy. The proposed simulation model provides design guidelines for lithium-ion polymer batteries in electric-drive vehicle and stationary energy storage applications.