Cranking Capability Estimation Algorithm Based on Modeling and Online Update of Model Parameters for Li-Ion SLI Batteries

Abstract

The terminal voltage of a starting–lighting–ignition (SLI) battery can decrease to a value lower than the allowable voltage range because of the high discharge current required to crank the engine of a vehicle. To avoid the safety problems generated by this voltage drop, this paper proposes a cranking capability estimation algorithm. The proposed algorithm includes an equivalent circuit model for describing the instantaneous voltage response to the cranking current profile. This algorithm predicts the minimum value of the terminal voltage for the cranking transient period by analyzing the polarization voltage and dynamic characteristic of the equivalent circuit model. The estimation accuracy is adjusted by an online update for the parameters of the equivalent circuit model, which varies with temperature, aging, and other factors. The proposed algorithm was validated by experiments with a 60Ah LiFePO4-type SLI battery.

1. Introduction

A starting–lighting–ignition (SLI) battery is used to supply power to operate the electrical devices and implement the electrical loads of a vehicle. The rapid expansion of the electrical functions and devices in vehicles has accelerated the need for accurate state estimation algorithms for SLI batteries [1,2,3,4,5]. In particular, a state-of-function (SOF) algorithm that determines the cranking capability of the SLI battery is necessary because the steep voltage drop associated with an instantaneous discharge current can decrease the terminal voltage (v_terminal) beyond the lower-limit voltage (V_limit), as shown in Figure 1. Moreover, the reliable estimation of SOF is becoming more important because contemporary vehicles generate more frequent cranking by an idle stop and go (ISG) process, which automatically stops and recranks the engine to reduce the amount of time the engine spends idling [6,7].

SOF is defined as the minimum value of the terminal voltage reached for the cranking transient period. SOF can be calculated as follows:

$$SOF=V_{\mathrm{t}0}-V_{\mathrm{drop}}$$

(1)

where V_t0 is the relaxation voltage immediately before cranking the engine, and V_drop indicates the voltage drop when the engine is cranked, as shown in Figure 1. This SOF is compared with the lower limit voltage to determine that the engine is permitted to be stopped or keeps running to charge the SLI battery. Therefore, in order to estimate SOF, V_t0 and V_drop should be predicted in real time.

V_t0 is associated with the polarization voltage that makes the relaxation voltage change although there is no current applied on the battery [8,9,10]. This polarization voltage causes SOF to vary according to when the driver attempts to crank the engine. Therefore, there is a need for a V_t0 prediction method to determine the cranking capability whenever the driver attempts to crank. The V_drop in Equation (1) can be predicted by calculating the voltage induced at the internal impedance of an equivalent circuit model (ECM) when the cranking current profile is applied. Thus, the ECM and ECM parameters that can describe the instantaneous voltage response are required to accurately calculate V_drop. Moreover, an online update process for ECM parameters is necessary because ECM parameters change nonlinearly according to operating conditions such as temperature and aging [11,12,13,14].

In conventional studies, many ECMs for Li-ion batteries and ECM parameter identification methods have been proposed for battery management system (BMS) applications: the high-order resistor–capacitor (RC)-ladder model, Randle model, Thevenin model, and partial differential equations model [15,16,17,18,19,20,21]. These models are sufficiently reliable for general state estimation algorithms, such as state-of-charge (SOC) and state-of-health (SOH), but not directly applicable to SOF, which is required to simulate the fast voltage response.

In [22,23,24], the characteristics of the cranking load were analyzed, and an ECM for simulating voltage during cranking transient was proposed. However, [22] analyzed just the cranking loads, and [23] and [24] focused on estimating SOH using the internal resistance extracted from the voltage drop measured during cranking transient, rather than SOF. Moreover, in [25], an online electrochemical impedance spectroscopy (EIS) technique to extract the parameters of the ECM was utilized, and the extracted parameters were used to estimate the voltage drop caused by cranking. However, this algorithm is inefficient because it requires analysis of the entire frequency range to identify all of the ECM parameters. In [26] and [27], a fractional model was used for battery modeling, and the terminal voltage during cranking transient was simulated with high accuracy. However, this method cannot predict SOF before cranking is attempted because the parameters for the fractional model are extracted based on the measured terminal current and voltage during the cranking transient period. Moreover, conventional studies of SOF algorithms are difficult to apply directly to Li-ion batteries, which have high energy and power density, because these methods have been designed for lead–acid batteries [28,29].

This paper proposes a SOF estimation algorithm for Li-ion batteries that predicts V_t0 and V_drop in Equation (1) with an online update process for ECM parameters. The rest of the paper is structured as follows. In Section 2, a new ECM that can be used to accurately describe the instantaneous voltage response to the cranking current is presented. Section 3 proposes a prediction method for V_t0 in order to estimate SOF considering the polarization voltage response to the applied current. Additionally, V_drop is calculated using the parameters of the proposed ECM with the cranking current profile. Moreover, an online update process for ECM parameters is suggested based on the analysis of dynamic characteristics of the proposed ECM. To validate the developed SOF estimation algorithm, experiments performed with a LiFePO4 (LFP)-type SLI battery installed on a vehicle are discussed in Section 4. Section 5 concludes the paper.

2. Equivalent Circuit Model for SOF Estimation

2.1. Conventional Model Based on 1st RC-Ladder

Figure 2a shows a conventional ECM based on the 1st RC-ladder, which consists of R_s, R₁, and C₁. R_s denotes the internal resistance of the battery and describes the ohmic voltage drop generated by an instantaneous change in the terminal current [15,16,17,18,19,20,21]. Moreover, the 1st RC-ladder simulates the polarization voltage as the curve of the exponential function, of which the time constant is determined by R₁ and C₁. The parameters are identified using the current profile shown in Figure 2b, which repeats a discharge with a pulsed current and relaxation for an hour until the battery is discharged from SOC 90% to 10%.

R_s is determined by Ohm’s law between the variation of the terminal voltage and current for 10 s after the SLI battery is allowed to relax, as follows:

$$R_{\mathrm{s}}=\frac{V_{10\mathrm{s}}-V_{0\mathrm{s}}}{I_{\mathrm{pulse}}}$$

(2)

where V_0s and V_10s indicate the terminal voltage immediately before starting the relaxation and after 10 s, respectively, and I_pulse represents the magnitude of the pulsed current used in the experiment, as shown in Figure 2c. This time condition, 10 s, is typically used to extract R_s under a hybrid pulse power characterization (HPPC) test, which identifies the power performance of batteries [30,31]. Open-circuit voltage (OCV), R₁, and C₁ can be identified by fitting the relaxation curve of the terminal voltage measured after 10 s to the voltage equation of ECM. Figure 3a–c shows R_s, R₁, and C₁ of the SLI battery, extracted by a charging and discharging test unit in Section 4.

This ECM is widely used for state estimation algorithms, such as SOC and SOH, because it can describe the voltage response with high accuracy when the SLI battery supplies the power to the general electrical devices and functions in a vehicle. However, this ECM has limited applicability to the SOF algorithm as the ECM for the SOF algorithm is required to describe an instantaneous voltage response that is generated for a much shorter period than the 10 s used to identify R_s and the time constant of the 1st RC-ladder.

2.2. Proposed Equivalent Circuit Model for SOF Estimation

This paper proposes an ECM expanded on the basis of the conventional model to describe the fast voltage response for SOF estimation, as shown in Figure 4. The proposed model divides R_s in the conventional model into R_s1 and another RC-ladder consisting of R_s2 and C_s2 (s-ladder). Additionally, the stray inductance (L_s) is added to the ECM because the sharp slope of the cranking current profile can cause an additional voltage drop, which can be ignored in the general driving profile.

In order to describe instantaneous voltage changes, R_s1 is extracted using an ohmic drop for 1 s (V_1s), the shortest sampling period of the charging and discharging test unit, as shown in Equation (3). Considering that R_s1 and the s-ladder are separated from R_s in the conventional model, the total resistance of R_s1 and R_s2 should be equal to R_s. Moreover, the time constant of the s-ladder (τ_s2) has to be determined as a quarter of 10 s to saturate the s-ladder 10 s after the pulsed current is applied, as shown in Equations (4) and (5):

$$R_{\mathrm{s}1}=\frac{V_{1\mathrm{s}}-V_{0\mathrm{s}}}{I_{\mathrm{pulse}}},$$

(3)

$$R_{\mathrm{s}}{}_2=R_{\mathrm{s}}-R_{\mathrm{s}1},$$

(4)

$$\mathrm{and}{C}_{\mathrm{s}2}=\frac{{\mathsf{\tau }}_{\mathrm{s}2}}{R_{\mathrm{s}2}}=\frac{10\mathrm{s}\times \frac{1}{4}}{R_{\mathrm{s}2}}.$$

(5)

In order to identify L_s, the voltage induced at L_s (v_Ls) that is generated by the slope of the terminal current should be analyzed. v_Ls can be measured at the transient period when the terminal current decreases or increases with a slope caused by the settling time of the charging and discharging test unit. Figure 5a,b shows the conceptual figures of a part of the parameter identification experiment during the transient period when the terminal current changes from I_pulse to 0 A.

As shown in Figure 5b, v_Ls occurs only until the terminal current reaches 0 A, and OCV, v₁, and v_s2 can be assumed to be constant considering the brevity of this settling time. Thus, L_s can be calculated using the change in v_Ls (∆v_Ls) measured from the terminal voltage immediately before the terminal current becomes 0 A, as follows:

$$L_{\mathrm{s}}=\Delta v_{L\mathrm{s}}\cdot \frac{dt}{d{i}_{\mathrm{terminal}}}.$$

(6)

The parameter extraction results of the proposed model are shown in Figure 6a–c.

In order to verify the accuracy of ECMs, a cranking experiment was performed after the SLI battery was charged to SOC 70% at 20 °C, as shown in Figure 7a, and the measured terminal voltage was compared with the voltage simulated by the conventional and proposed ECM. Figure 7b shows that the proposed model had an accuracy of 96.73%, which is 23.56% higher than the conventional model for estimating SOF. Conversely, after the engine was cranked completely, the conventional model was more accurate than the proposed ECM, as shown in Figure 7c. Therefore, it is more suitable to apply the proposed model for SOF estimation, although the conventional model is used to estimate general state factors such as SOC and SOH.

Figure 8 shows the proportions of the voltages induced at each impedance component according to ECMs when V_drop, 2.17 V, was simulated. In the proposed model, v_s1 and v_Ls accounted for most of the V_drop (98.9%). Conversely, the voltages induced at the s-ladder and 1st RC-ladder (v_s2 and v₁) occupied very small fractions of 1.1% because the time constant of each ladder was too large to generate a significant voltage response to the cranking current profile. Thus, the proposed model was simplified by neglecting the s-ladder and 1st RC-ladder, as shown in Figure 4, and the simplified model had an accuracy of 95.71%, similar to the expanded model, as shown in Figure 7b and Figure 8.

3. Proposed SOF Estimation Algorithm with Online Update of ECM Parameters

3.1. Prediction of V_t0 Considering Polarization Voltage

The terminal voltage after the engine is shut off changes over time because of the polarization voltage. This polarization voltage causes SOF to vary according to when the driver attempts to crank the engine, as shown in Figure 9a,b. Thus, it is necessary to determine V_t0 as the smallest relaxation voltage considering the polarization voltage to prevent the terminal voltage from exceeding the lower-limit voltage whenever a driver attempts cranking.

When the SLI battery is allowed to relax after charging, the relaxation voltage decreases to OCV exponentially, as shown in Figure 9a. Therefore, V_t0 should be determined as the OCV that minimizes SOF, as follows:

$$V_{\mathrm{t}0}=OCV(\mathrm{after}\mathrm{charge}).$$

(7)

Conversely, V_t0 for the battery after discharge, as shown in Figure 9b, should be determined as the terminal voltage immediately after starting the relaxation, which minimizes SOF as follows:

$$V_{\mathrm{t}0}=v_{\mathrm{terminal}}-i_{\mathrm{terminal}}\cdot R_{\mathrm{s}1}(\mathrm{after}\mathrm{discharge}).$$

(8)

Therefore, SOF in Equation (1) can be expressed using Equations (7) and (8) as follows:

$$SOF=\{\begin{array}{ll}OCV-V_{\mathrm{drop}}& (\mathrm{after}\mathrm{charge})\\ \left\{v_{\mathrm{terminal}}-i_{\mathrm{terminal}}\cdot R_{\mathrm{s}1}\right\}-V_{\mathrm{drop}}& (\mathrm{after}\mathrm{dischare})\end{array}.$$

(9)

This V_t0 makes it possible to estimate SOF before stopping the engine contrary to [26] and [27] because V_t0 is determined as one of the predicted relaxation voltages that causes the smallest SOF.

3.2. V_drop Estimation Using ECM and Simplified Cranking Current Profile

V_drop is equal to the sum of the voltage induced at the impedance components of the proposed ECM, R_s1 and L_s, when the cranking current is applied, as follows:

$$V_{\mathrm{drop}}=v_{\mathrm{s}1}(t_{\mathrm{c}})+v_{L\mathrm{s}}(t_{\mathrm{c}})=-R_{\mathrm{s}1}\cdot i_{\mathrm{terminal}}(t_{\mathrm{c}})-L_{\mathrm{s}}\frac{d{i}_{\mathrm{terminal}}(t_{\mathrm{c}})}{dt}$$

(10)

where t_c indicates the time when the cranking current attains the minimum value. Equation (10) shows that V_drop is affected by only the magnitude and the slope of the cranking current at t_c. Additionally, there is no need to consider the cranking current profile after t_c because the terminal voltage has the smallest value at t_c and then increases gradually, as shown in Figure 10a,b.

Therefore, the cranking current profile can be equalized as a ramp function (i_{crank_eq}), as shown in Figure 10a, which contains only i_terminal(t_c) and the slope of the terminal current at t_c, as follows:

$$i_{\mathrm{crank}\_\mathrm{eq}}(t)=\{\begin{array}{cc}0,& (t\le t_c-\Delta t_{\mathrm{c}})\hfill \\ \frac{i_{\mathrm{terminal}}(t_{\mathrm{c}})}{\Delta t_{\mathrm{c}}}\times (t-t_c+\Delta t_{\mathrm{c}}),& (t_c-\Delta t_{\mathrm{c}}\le t<t_c)\hfill \\ 0,& (t_c\le t)\hfill \end{array}$$

(11)

where ∆t_c indicates the time to reach i_terminal(t_c), as shown in Figure 10a. t_c, ∆t_c, and i_terminal(t_c) in Equation (11) are recorded at every cranking transient to predict V_drop when the vehicle is cranked again. Using i_{crank_eq}, Equation (10) can be expressed as

$$V_{\mathrm{drop}}=-R_{\mathrm{s}1}\cdot i_{\mathrm{crank}\_\mathrm{eq}}(t_c)-L_{\mathrm{s}1}\frac{i_{\mathrm{crank}\_\mathrm{eq}}(t_c)}{\Delta t_{\mathrm{c}}},$$

(12)

and Equation (8) can be substituted as follows:

$$SOF=\{\begin{array}{cc}OCV-\left\{-R_{\mathrm{s}1}\cdot i_{\mathrm{crank}\_\mathrm{eq}}(t_c)-L_{\mathrm{s}}\frac{i_{\mathrm{crank}\_\mathrm{eq}}(t_c)}{\Delta t_{\mathrm{c}}}\right\}& (\mathrm{after}\mathrm{charge})\hfill \\ \left\{v_{\mathrm{terminal}}-i_{\mathrm{terminal}}\cdot R_{\mathrm{s}1}\right\}-\left\{-R_{\mathrm{s}1}\cdot i_{\mathrm{crank}\_\mathrm{eq}}(t_c)-L_{\mathrm{s}}\frac{i_{\mathrm{crank}\_\mathrm{eq}}(t_c)}{\Delta t_{\mathrm{c}}}\right\}& (\mathrm{after}\mathrm{discharge})\hfill \end{array}.$$

(13)

Figure 10b shows the SOF estimation result using Equation (13) when the cranking current in Figure 7a is applied to the SLI battery. The red mark indicates the SOF calculated by Equation (13), and the green circle indicates the simulated terminal voltage based on the proposed ECM in Figure 4. The accuracy of the SOF calculated by Equation (13) is 95.57%, which is similar to that of the simulated terminal voltage (95.71%).

3.3. Online Update through Analysis of Dynamic Characteristic of ECM Parameters

The ECM parameters vary depending on operating conditions such as SOC, the temperature, the aging conditions, and C-rate. Therefore, if ECM parameters are not updated in real time, the accuracy of the SOF estimation can be reduced. Because R_s1 and L_s cannot be directly measured from the terminal voltage and current, the online update for R_s1 and L_s should utilize the dynamic characteristics of v_s1 and v_Ls as follows:

$$R_{\mathrm{s}1}=-\frac{\Delta v_{\mathrm{s}1}}{\Delta i_{\mathrm{terminal}}},$$

(14)

$$L_{\mathrm{s}}=-\Delta v_{L_{\mathrm{s}}}\times \frac{\Delta t_{\mathrm{s}}}{\Delta i_{\mathrm{terminal}}}$$

(15)

where ∆t_s indicates the sampling period of the terminal current and voltage.

However, ∆v_s1 and ∆v_Ls cannot be directly extracted from the terminal voltage because both occur simultaneously when i_terminal changes (∆i_terminal). Thus, the proposed online update process updates R_s1 and L_s through the following process:

(1)

Record i_terminal, ∆i_terminal, and v_terminal during two consecutive sampling sequences, t_k−1 and t_k.

(2)

Assume that OCV is given, and the changes in R_s1 and L_s for these sequences (∆t_s) are negligible.

(3)

Calculate the sum of v_s1 and v_Ls at t_k−1 and t_k using

$$v_{\mathrm{s}1}(t_{\mathrm{k}-1})+v_{L\mathrm{s}}(t_{\mathrm{k}-1})=v_{\mathrm{terminal}}(t_{\mathrm{k}-1})-OCV(t_{\mathrm{k}-1}),$$

(16)

and

$$v_{\mathrm{s}1}(t_{\mathrm{k}})+v_{L\mathrm{s}}(t_{\mathrm{k}})=v_{\mathrm{terminal}}(t_{\mathrm{k}})-OCV(t_{\mathrm{k}}).$$

(17)

(4)

Express Equations (16) and (17) through R_s1 and L_S as follows:

$$v_{\mathrm{terminal}}(t_{\mathrm{k}-1})-OCV(t_{\mathrm{k}-1})=-R_{\mathrm{s}1}(t_{\mathrm{k}})\cdot i_{\mathrm{terminal}}(t_{\mathrm{k}-1})-L_{\mathrm{s}}(t_{\mathrm{k}})\cdot \frac{\Delta i_{\mathrm{terminal}}(t_{\mathrm{k}-1})}{\Delta t_{\mathrm{s}}},$$

(18)

and

$$v_{\mathrm{terminal}}(t_{\mathrm{k}-1})-OCV(t_{\mathrm{k}-1})=-R_{\mathrm{s}1}(t_{\mathrm{k}})\cdot i_{\mathrm{terminal}}(t_{\mathrm{k}})-L_{\mathrm{s}}(t_{\mathrm{k}})\cdot \frac{\Delta i_{\mathrm{terminal}}(t_{\mathrm{k}})}{\Delta t_{\mathrm{s}}}.$$

(19)

(5)

Calculate R_s1(t_k) and L_s(t_k) by solving a simultaneous equation between Equations (18) and (19).

The assumption in step 2 above is reasonable because ∆t_s is short enough to neglect the changes in the ECM parameters caused by SOC, SOH, and temperature.

3.4. Verification of Online Update of ECM Parameters

In order to verify the proposed online update process, a simulation based on the battery model, consisting of look-up tables in Figure 5a,c, was performed. The parameters of ECM were set to change according to SOC variation when the battery was charged or discharged by the current profile. Figure 11a,b shows the current profile used to verify the proposed online update process and the simulated terminal voltage of ECM. This current profile was measured when the SLI battery was charged by an alternator and supplied the electrical loads of the vehicle.

As shown in Figure 12a,b, both R_s1 and L_s, which were updated based on the proposed online update process, had instantaneous errors because a few changes in R_s1 and L_s were caused by the small variation of SOC over ∆t_s. Therefore, these updated results should be filtered through a low-pass filter (LPF), which improves both values to over 99.99% accuracy. This indicates that the proposed online update process can prevent misjudgments of SOF despite variations in ECM parameters due to the operating conditions. The proposed online update for the model parameters is more intuitive and requires smaller calculation than other mathematical methods, such as the adaptive filter and computational intelligence [32,33,34].

4. Experimental Verification

4.1. Experimental Setup

The SLI battery (12.0 V, 50 Ah) used in the experimental verification was connected with 2-parallel and 4-series LFP-type battery cells, as shown in Figure 13a,b; the specifications of the SLI battery pack are listed in

Table 1. Specification of battery pack.

Parameter	Value
Battery type	LiFePO4 (LFP)
Manufacturer	Top Battery
Current density	50 [Ah]
Voltage range	8.0–14.4 [V]
Nominal voltage	12.0 [V]

. The battery was installed in a vehicle, specifically a Korando-C manufactured by SsangYong, with a battery management system (BMS) and voltage/current sensors, as shown in Figure 14. The BMS recorded the terminal current and voltage at measurement intervals for time, current, and voltage of 1 ms, 1 mA, and 1 mV, respectively.

Look-up tables of the ECM parameters in Figure 3 and Figure 5 were identified at 20 °C with the charging and discharging test unit in Figure 15. These look-up tables were utilized to verify the accuracy of the proposed online update by comparing the SOF estimation results based on the look-up tables and the updated parameters. Before the engine was cranked, the SLI battery was charged to SOC 80% (Experiment 1) and SOC 90% (Experiment 2); for further validation, each experiment was performed at different temperatures (20 °C and −25 °C). As shown in Figure 16a,b, when the SLI battery attempted to crank the engine at a lower temperature, the magnitude of i_terminal(t_c) increased from −703.32 to −907.29 A because more output power is required for cold cranking [35,36].

4.2. Cranking Experiment Results

Figure 16a,b shows the waveforms of the terminal current and voltage measured for Experiments 1 and 2. In section t₁, the engine was running, and the SLI battery was charged by the alternator and supplied power to electrical devices and functions. The measured terminal current and voltage in t₁ were utilized to update the ECM parameters in order to estimate SOF, and the updated parameters right before the engine was stopped are shown in

Table 2. Cranking experiments and SOF estimation results.

Purpose		Experiment 1	Experiment 2
SOC of SLI battery		80%	90%
Temperature		20 [°C]	−25 [°C]
iterminal(tc)/∆tc		−703.32 [A]/4 [ms]	−907.29 [A]/5 [ms]
Updated parameters	Rs1	1.09 [mΩ]	2.02 [mΩ]
	Ls	13.55 [μH]	16.70 [μH]
Estimation error with look-up table		1.34%	−17.99%
Estimation error with online update		0.87%	1.40%

. In Figure 16a,b, the estimation results based on the updated parameters are indicated by a red line, and a blue line represents the SOF estimated using look-up tables in Figure 5a,c. Because the estimated SOFs were higher than the lower limit voltage, the engine was stopped in both Experiments 1 and 2.

After section t₂, when the SLI battery was allowed to relax, cranking the engine was attempted, as shown in section t₃. The minimum terminal voltages in the cranking transient period were compared with the estimated SOF, as summarized in Table 2. Because Experiment 1 was performed under the same temperature in which the look-up tables were composed, the SOF estimated through the look-up tables was 1.34%, similar to the SOF with online update (0.87%). This result verifies the accuracy of the SOF calculation using V_t0 and V_drop. Conversely, because Experiment 2 was proceeded at a low temperature, −25 °C, the SOF estimation based on the look-up tables had an average error (−17.99%) that was higher than Experiment 1. These estimation errors tended to increase as the operating conditions differed from the conditions used to extract the look-up tables of the ECM parameters. With the online update, the estimation errors in Experiment 2 decreased to 1.40%, confirming that the proposed online update is sufficiently accurate for correct estimation and can prevent the safety risks caused by inaccurate judgment of the cranking capability. The engine was stopped after being completely cranked, as shown in section t₄.

5. Conclusions

In this paper, a SOF estimation algorithm is proposed to determine the cranking capability of a Li-ion SLI battery. In order to accurately estimate SOF, an ECM suitable for describing the instantaneous voltage response to the cranking current profile is also proposed. On the basis of the parameters of the proposed ECM, the SOF is estimated by predicting the terminal voltage after the battery starts the relaxation and the voltage drop caused by cranking. In addition, to correct the variation of ECM parameters with operating conditions such as temperature and aging, an online update process based on the dynamic characteristics of the proposed ECM is presented. This algorithm can prevent the BMS from inaccurately estimating SOF, thereby eliminating the possibility of the occurrence of related safety problems. The accuracy of the proposed SOF algorithm was validated experimentally using a vehicle fitted with an LFP-type SLI battery. In future works, the proposed algorithm will be validated in various operating conditions, such as SOC, SOH, and temperature. Moreover, the applicability of the high-performance computing and computational intelligence will be reviewed and researched to improve the accuracy and calculation burden.