Hardware-in-the-loop Implementation of ANFIS based Adaptive SoC Estimation of Lithium-ion Battery for Hybrid Vehicle Applications

Journal of Energy Storage 27 (2020) 101124

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Hardware-in-the-loop Implementation of ANFIS based Adaptive SoC Estimation of Lithium-ion Battery for Hybrid Vehicle Applications

T

Krishna Veer Singha, , Hari Om Bansala, Dheerendra Singha ⁎

a

Power Electronics & Drives Lab, Department of Electrical and Electronics Engineering, Birla Institute of Technology and Science, Pilani, Rajasthan, India

ARTICLE INFO

ABSTRACT

Keywords: Open circuit voltage state-of-charge state-of-health lithium-ion battery and hardware-in-the-loop and hybrid vehicle

This paper presents an effective method to estimate the state of charge (SoC) of a Lithium-ion battery. This parameter is very crucial as it indicates the performance and health of the battery. The battery SoC estimation equivalent circuit provided in MATLAB has been modified by adding the 3- RC pairs in series with its internal resistance. The values of the RC pairs have been calculated mathematically by solving the circuit model, based on charging and discharging dynamics of the battery. The values of these parameters have also been optimized using a “lsqnonlin” function. The SoC of the battery is estimated using the combination of coulomb counting and open-circuit voltage methods to minimize the error in estimation. The obtained SoC is further corrected for errors using ANFIS based algorithms. The effect of temperature has also been accounted for modelling the battery and in SoC estimation. These obtained SoCs for 3 cases, i.e. without RC/with RC pairs and then tuned with ANFIS based optimization are compared for the same load. The parameter calculation method adopted here results in an efficient and accurate model that keeps track of correct battery SoC. The complete system is validated in real-time using hardware-in-the-loop laboratory setup.

1. Introduction The electric vehicles (XEVs) are gaining a lot of popularity, as they are the sustainable mode of transportation and are also the alternatives of the international combustion engine (ICE) based vehicles. The XEVs are an effective way to overcome the fossil fuel crisis and environmental pollution, which are considered as the prominent hurdles for the automobile sector. The battery management system is an integral part of any XEV. The more energy storage capacity means a higher driving range of the vehicle and its better fuel economy. However, more capacity requires the bigger size battery which will increase the weight of the vehicle and occupy more space, so a trade-off is needed between capacity and the size of the energy storage system (ESS). There are various batteries available in the market, but the lithiumion batteries are gaining popularity[1]. They are equipped with several advantages such as high specific energy, low self-discharge rate, high energy density, prolong life, high charge/discharge and high cell potential, therefore, they have found a unique place in EV applications as ESS. Traction batteries need attributes like high energy density and power density. However, it is also associated with some demerits such as high cost, safety issues, ageing and immature technology. The selection of Li-ion batteries for traction application can be held true by Fig. 1 where various batteries have been compared based on energy ⁎

density [2–5]. The batteries yield non-linear and complex characteristics making their behaviour unpredictable. The batteries undergo certain cycles with consideration of environmental condition, therefore battery circuit modelling is a prominent task in determining the accurate state of charge (SoC) and its performances. The model validation using parameter optimization is an essential tool to accurately predict the behaviour. The major objectives and outcomes of this paper are as below: 1 The modelling of the battery by adding the multiple RC circuits. 2 Identification of time constant and then the calculation of the corresponding resistance and capacitances (RC). 3 Optimization of the obtained parameters from step 2 by “lsqnonlin” function provided in MATLAB. 4 Estimation of SoC using hybrid of coulomb counting and OCV methods and then the obtained results were fine-tuned using ANFIS based algorithm to minimize the error between proposed and realistic data. 5 Analysis of temperature variation on battery behaviour. 6 Real-time validation of entire system on HIL testing platform.

Corresponding author. E-mail address: [email protected] (K.V. Singh).

https://doi.org/10.1016/j.est.2019.101124 Received 25 July 2019; Received in revised form 14 November 2019; Accepted 30 November 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.

Journal of Energy Storage 27 (2020) 101124

K.V. Singh, et al.

Nomenclature ESS OCV SoC XEVs SoH ANFIS ICE ANN SoF KF CC MHE GA PSO BMS DEKF EKF UKF NN EV SoH SoE PI FIS BP MF DSO

Vter Voltage across terminal of battery Voc Open circuit volatge Voltage across R0 V0 V1 Voltage across R1 V2 Voltage across R2 V3 Voltage across R3 R0 Internal resistance of battery R1 Resistance across C1 R1 Resistance across C2 R2 Resistance across C3 I Current flowing in the circuit Tem Operating temperature C1 Capacitor of the branch R1C1 C2 Capacitor of the branch R2C2 C3 Capacitor of the branch R3C3 τ1 Time constant of the branch R1C1 τ2 Time constant of the branch R2C2 τ3 Time constant of the branch R3C3 ToT0 and T0+ Initial condition V1zero, V2zero and V3zero Zero input response of voltages V1,V2 and V3 T1, T2 and T Various time instant of the waveform a0 Battery terminal voltage when SoC = 0% Battery terminal voltage when SoC = 100%. a1 Cp Battery capacity in Ah Reaction constant K0 R Gas constant Ea Activation energy pi Firing strength

Energy storage system Open circuit voltage State of charge (BEVs, HEVs & PHEVs) State of health An adaptive neuro-fuzzy inference system Internal combustion engine Artificial neural network State of function Kalman filter Coulomb counting Moving horizon estimation Genetic algorithm Particle swarm optimization Battery management system Dual extended Kalman filter Extended Kalman filter Unscented Kalman filter Neural network Electric vehicle State of health State of energy Proportional integral Fuzzy inference system. Back propagation Membership function Digital storage oscilloscope

1.1. Literature review on the SoC estimation methods

estimation of SoC. Here, OCV was divided into three parts based on charging, discharging, and neutral mode and were fed to NN for correct estimation of SoC. In [17], the reuse of EV batteries in the applications other than transportation has been suggested. The flow management of energy has also been explained. The author in [18] has discussed the role of the dual EKF (DEKF) for battery SoC and state of health (SoH) estimation. Based on the comparison of simulation results using KF and DEKF, they recommended DEKF. In [19], a new method of combining DEKF algorithm and charging voltage curve for SoC estimation has been proposed. In [20], the adaptive SoC estimator has been proposed under various assumption and condition. The error estimate in SoC is less than 3% for both the constant current-voltage charging conditions and the dynamic discharging conditions. In[21], the SoC and state-of-energy (SoE) are evaluated by the particles filter method and EKF by minimizing the errors in voltage or current signal measurement. The [22] addresses the estimation of battery SoC from the joint perspectives of dynamic datadriven and model-based recursive analysis. In [23], the battery degradation capacity and the corresponding SoC has been estimated by using three-dimensional response surface-based battery OCV. In [24], a SoH estimation method has been proposed for lithium-ion batteries. Here, OCV and Thevenin's equivalent circuit model was used to improve the model accuracy and also to discuss the relation between internal parameters and states of the battery. In [25], a new kind of battery model which gets turned on/off based on the load response has been proposed. The various switching algorithm for the load has also been designed as well. The SoC and online model parameters co-estimation for liquid metal batteries has been proposed in [26]. In [27], SoC estimation of battery has been carried by applying two proportional-integral (PI) filters to minimize the sate error. In [28] a comparative study of ANN/KF for on-board SOC estimation has been carried out. They concluded that UKF presents the best overall performance. In [29] the SoC estimation with accuracy has been proposed. An attempt to estimate the OCV and SoC of the battery during normal

There are various papers reported in the literature citing different SoC estimation methods. Some recent papers have been presented in this section. The SoC basically is the measure of the remaining capability of the battery. The various methods which have been proposed to estimate the SoC can be categorized as: simple calculation methods, informationdriven strategies, and model-based methods. The simple calculation method can further be divide into impedance, open-circuit voltage (OCV) and ampere-hour counting methods. The information-driven strategies are alike simple calculation methods except they use intelligent (neural networks, fuzzy logic, etc.) algorithms to train the model. Model-based methods consider battery as a dynamic system and involve state space to carry out battery modelling. This also uses observers like extended Kalman filter (EKF) and unscented Kalman filter (UKF) to estimate the state. Model-based techniques have some merits like high accuracy, fast convergence, and a good computing power [6–15]. In [16], the author has used the neural network (NN) for

Fig. 1. Comparison of various batteries based on power density and energy density 2

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Table. 1 Literature review of papers based on SoC, SoE, SoF, SoH, cell balancing and parameters estimation. REF.

PARAMETER ESTIMATED

METHOD/APPROACH USED

OUTCOME/ FINDINGS

[2]

SoC

Model-Based and Data-Driven Methods

[6]

SoC

Ampere-hour and Kalman filter

[7]

SoC and SoH

OCV

[8]

SoC

[10]

SoC

Advanced binary search pattern for impedance spectra OCV and unscented Kalman filter

[11]

SoC

Fuzzy based control

[12]

SoC

EKF

[14]

SoC

[16]

SoC

EKF system based on a round-robin approach ANN

1 . A review has been carried out on various model-based and data-driven methods. 1. The estimation error and the accumulated error of current is reduced to obtain maximum accuracy. 1. SoC estimation accuracy has been improved compared to existing OCV method. 1. This work deals with accuracy, efficiency, tolerance of disturbances and temperature dependence of the methods which were proposed. 1 . A model has been developed which is based on the temperature effect to estimate SoC. 1 . A novel fuzzy model is proposed to characterize lead-acid battery discharging. 2. An EKF based on a fuzzy model is proposed for SoC estimation. 3. The polarization resistance can be estimated using the algorithm proposed. 1. The average error of SoC estimation has been reduced by the proposed algorithm. 1. The SoC has been accurately estimated based on voltage measurement.

[18]

SoC and SoH

DEKF

[19]

SoC

DEKF and Charging voltage

[20]

SoC

Improved adaptive battery state estimator

[21]

SoC and SoE

The particle filter is used for simultaneous SoC and SoE

[22]

SoC

[23]

SoC and SoH

A combination of symbolic time series analysis and linear least-squares filtering GA (genetic algorithm)

[24]

SoH

PSO

[25]

SoC

UKF and H-infinity observer for state estimation

[26] [27]

SoC SoC

Adaptive unscented Kalman filter Two proportional-integral filters

[28]

SoC

ANN/KF

[29] [31]

SoC SoC

ANFIS Hybrid algorithm with UKF

[32]

SoC and SoH

KF

[33]

SoC

DEKF

[34]

SoC

DEKF

[35]

SoC/Capacity

DEKF

[36]

SoC

DEKF

[37]

SoC

DEKF

1. The proposed method results in a reduction of average estimation error. 2. The result depicts that the NN has boarder choice of training data and low computational cost. 1. The paper presents that the DEKF is responsible for increasing the accuracy in SoC estimation as compared to EKF. 1. Based on the DEKF algorithm, the SoC is estimated. The results show that the estimation error is within 3%. 1.An adaptive battery state estimator has been proposed for SoC estimation of the lithium-ion battery. 2. The SoC estimation precision is evaluated under various operating conditions. 3. Generality, robustness and dynamic characteristics are evaluated. 4. The error in SoC estimation is within the range of 3%. 1. Co-estimation of both SoC and SoE has been proposed. 2. The temperature effect was analysed to verify the robustness of the proposed method. 1. “Markov machine representation for dynamic data-driven analysis has been presented.” 1. “A three-dimensional response surface-based battery OCV model was constructed.” 2. The proposed method has high accuracy and robustness. 3. The efficiency of online computation reported being increased. 1. The proposed method is compared with other methods and the advantage of the PSO has been presented. 1. The proposed algorithm offers high accuracy under various load conditions. 2. An online optimization problem is formulated to find the best suitable battery model. 3. Comparisons of the proposed algorithm with several existing ones are also presented. 1. Accuracy and robustness of SoC estimation have been proved to be higher. 1. In order to compensate error two PI filters have been proposed. 2. In two RC equivalent circuit model of the battery, the presence of error were analysed. 3. The fusion of the weights of the PI filter has been proposed as well. 1. ANN and KF, SoC estimation methods are compared. ANN is proved superior over KF. 1. SoC is compared to coulomb counting (CC) computation and ANFIS. 1. The SoC estimation has considered the effect of series batteries and the differences between each cell i.e cell unbalancing 2. Error in the SoC estimation has been reduced. 1. This paper describes the use of KF in order to estimate the parameters of battery for photovoltaic applications 1. KF overcomes the defects of the simplified battery modelling and separates the sequence for estimation of the state and weight filter. 1. Estimation of the remaining useful life with suitable margins of uncertainty has been proposed. 1. DEKF algorithm combined with the pattern recognition based on the hamming network for identification of suitable cell model parameters in order to obtain improved SoC/battery capacity estimation has been presented. 1. Reliable SoC and battery parameter estimation algorithm with DEKF has been proposed. 1. This paper focuses on the behaviour of the modified DKF, based on the state and parameter estimation and on the ideal tuning of the algorithm. 2. The algorithm enables an estimating error in SoC of less than 1.5%.

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Table. 1 (continued) REF.

PARAMETER ESTIMATED

METHOD/APPROACH USED

OUTCOME/ FINDINGS

[38]

SoC/ Capacity

EKF

[39] [40]

SoC SoC

DKF KF

[41] [42]

SoC, SoP and SoH SoC

DEKF EKF

[43]

SoC

GA

[44]

SoC

ANFIS

[43]

SoC and battery parameters

GA

[45]

SoC

[46]

SoC

EKF filter and least square identification method NN

[47] [48]

SoC SoC and Cell balancing

EKF AEKF

[49]

SoC

ANFIS in combination with CC

[50] [51]

SoC SoC

EKF EKF and ANFIS

[52]

SoC

CC and SoC-OCV relationship

[53] [54]

SoC SoC

EKF ANN and ANFIS

[55] [56]

SoC SoC

AEKF ANN

[57]

SoC

OCV

[58]

SoC

KF

[59]

SoC

UKF and H-infinity filter

[60]

SoC

Split battery model

[61]

SoC and Cell balancing

Quasi-sliding mode

[62]

SoC, SoH and SoF

EKF

[63]

SoC

Review

[64]

SoC

CC, KF and OCV

[65]

SoC

[66]

SoC

A joint moving horizon estimation (jointMHE) approach EKF and AEKF

[67]

SoC

Gravitational search algorithm

1. The proposed approach can estimate battery parameter, capacity and SoC concurrently. 2. Less computation efficiency but higher estimation accuracy has been suggested. 1. The behaviour of the DKF is analysed at various temperature. 1. The benchmark proposed shows the same accuracy in the estimation of the SoC with a one and two RC-term equivalent battery circuit. 2. The strong effect of temperature due to high-dynamic loads is observed. 3. By tuning individual filter, the temperature dependence is found to be reduced. 1. Online estimation of the battery's capacity and SoH 1. Parameterization and algorithm evaluation has been conducted. 2. Computational complexity is analysed. 3. Robustness and accuracy of the algorithms are compared. 1. Multi-objective GA is utilized for extracting performance parameters. 2. Battery performance is accurately predicted once parameters are optimally extracted. 1. Accurate estimation of the state of available capacity under variable discharge currents. 1. Battery charging/discharging characteristics are accurately predicted once parameters are optimally extracted 1. The results demonstrate the effectiveness of the fractional-order model and the estimation method. 1. Increased SoC estimation accuracy and robustness by adding noise to training data has been presented. 1. Accurate SoC for battery in automotive applications. 1. To obtain the OCV a data-driven filtering process is proposed 2. Parameter uncertainties are developed and analysed. 3. An adaptive SoC estimator which reduces the cell unbalancing. 1. SoC is estimated with a mean error of 4% and a maximum error of 7% in a realistic driving scenario. 1. The proposed SoC estimation is accurate in terms of the error in estimation. 1. EKF and ANFIS have been compared. 2. It has been concluded that ANFIS-based SoC estimation has greater precision and don't require iterations. 1. The CC algorithm has the drawback as it is associated with cumulative errors and measurements uncertainties,to avoid them, the OCV has been used, thus a linear SoC-OCV relationship has been established and recalibration of the battery capacity periodically has been conducted. 1. Accurate estimation of SoC has been presented. 1. Comparisons of the two approaches have highlighted the potential of ANFlS in modelling and prediction of the behaviour of complex nonlinear dynamic systems. 1. SoC estimation error is less than 2% compared to EKF. 1. The proposed technique showed that very accurate SoC estimation results can be obtained provided enough training data are used to train the ANN models. 1. The superiority of the adaptive SoC estimation which is based on the parameter identification algorithms and SoC estimation schemes over the existing methods has been demonstrated in terms of accuracy and robustness. 1. The fractional-order model has higher accuracy in SoC estimation, and the error can reach up to 0.5% SoC. 1. The joint SoC estimation method has high accuracy, fast convergence, excellent robustness and adaptability. 1. The cross-interference between RC voltages and SoC is reduced, which effectively reduces the oscillation in the estimation and improves the estimation accuracy 1. Bidirectional Modified ´Cuk converters are utilized as the cell equalizers due to their advantages of integrated infrastructure and modular design. 1. The continuous online upgrading of battery capacity and its related parameters helps in accurate state estimation. 1. This paper presents the reviews the SoC estimation methods that are suitable for online usage and classify them into five categories. 1. Hybrid (which is a combination of CC and OCV SoC estimation technique to improve accuracy under varying conditions. 1. Compared to joint EKF, the proposed approach based on MHE can offer a more reliable, robust, and accurate SoC estimation. 1 . A moving window technology and partial least squares (PLS) regression can establish a series of piecewise linear battery models automatically. 2. Results have been compared with EKF and Adaptive-EKF (AEKF). 1 . A detailed comparative study between the proposed model and existing SoC strategies is conducted, which also demonstrates the superiority of the proposed.

(continued on next page)

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Table. 1 (continued) REF.

PARAMETER ESTIMATED

METHOD/APPROACH USED

OUTCOME/ FINDINGS

[68]

SoC

Long Short-Term Memory Network

[69]

SoC

Gaussian process regression and polynomial regression

[70] [71]

SoC SoC and cell balancing

SoC estimation strategies ANFIS

[72]

SoC

Estimation strategies

[73]

SoC

Estimation and management strategies

[74]

SoC

OCV

[75]

SoC

KF

[76]

SoC, capacity, impedance parameters, available power, SoH, and remaining useful life. Characterization of lithium-ion batteries

Review on monitoring of lithium-ion batteries in electric and hybrid vehicles

[79]

On-line adaptive impedance and state estimation of battery. Cell balancing

Butlere volmer kinetics on the chargetransfer process chain structure of the switched capacitor

[80]

SoC and battery parameter estimation

DEKF

[81]

SoH

DEKF

[82]

SoC

ANFIS

[83]

SoC and battery parameters

[84]

Battery capacity, resistance and power capability.

Reference performance test Methodology

[85]

Battery parameters and SoC

OCV and Prediction-error minimization algorithm

[86]

SoC

[87]

Battery degradation

Bayesian filters, EKF, UKF and a particle filter. Reference performance test Methodology

[88]

Review on batteries

Review paper

1. The proposed method have the advantage of quick convergence to the true SoC, with root mean square errors within 2% and mean average errors within 1%. 1. The proposed method reports great improvement in SoC estimation with the bias characterization. 2. The polynomial regression model and the gaussian process regression model are proposed to examine the effects of the two methods on bias modelling and SoC estimation using a typical battery circuit model. 1. Review on SoC estimation strategies for HEVs and EVs 1. The proposed method has the potential to overcome the drawbacks of traditional SoC estimators caused by cell-to-cell variations in a battery pack, and the corrected SoC is more reasonable than the traditional “averaged SOC.” 1. The paper presented the common methods currently adapted by researchers in estimating battery SoC by analysing their pros and cons. 1 . A review of lithium-ion battery SoC estimation and management system in EV applications has been proposed. 1. An algorithm to determine the battery system's impedance and SoC are presented including parameter and state estimation techniques. 1. An adaptive co-estimator is presented to update pack parameters in dual time-scale using an optimized recursive least squares algorithm and to estimate the battery pack SoC using an EKF. 1. The methods for monitoring of the battery life are reviewed with the focus on the elaboration of their strengths and weaknesses for the use in on-line BMS applications. 1. The cell impedance is presented and analyzed and strong nonlinear temperature correlation has also been demonstrated for Li-ion battery 1 . A critical review of methods, modelling and requirement has been presented. 1. To improve cell balancing speed, two circuits with chain structure are proposed to increase balancing speed, particularly among outer cells. 1. Compared to the other estimators the proposed estimator is found to be between 16.4% and 28.2% more accurate for SoC estimation. 1. The DKEF estimate the parameters of equivalent circuit network and maximum available power of the battery at any specified instant irrespective of the age of the battery. 1. It has been proposed that the identification error can change unknown battery parameters. 2 . A novel analytical formula for identification has also been presented.. 1. The results demonstrate that even with a high noise level in measured data, the proposed identification and estimation algorithms are able to work well in real-time. 1. The reference performance test methodology is typically used to evaluate the performance of the batteries in terms of capacity, shuttle current, resistance and power capability. 1. An SoC observability analysis was also performed for both case studies, NiMH and Li-S. The results show that the system is observable in the case of NiMH whereas it is not fully observable for Li-S because of its flat OCV–SoC curve. 1. The estimators (Bayesian filters, EKF, UKF and a particle filter) are tested through practical experimentation. 1 . A methodology for a reference performance test for the Li-S batteries is proposed. 1. The transition from the use of lithium-ion to lithium-sulphur battery has been proposed in the form of review.

[77] [78]

Electrochemical impedance spectroscopy

operation of EV was made by means of charge/discharge current and voltage in [30]. The various paper related to SoC, SoH (state of health), SoF (state of function), SoE (state of energy), cell balancing and parameters estimation of battery has been listed in Table 1. From the above literature, it has been concluded that the major challenges which make battery inefficient are as follows: cell unbalancing, battery modelling, life of a battery, the effect of temperature, self-discharge, rate of charge and discharge, challenges of monitoring battery health, estimation of maximum capacity and communication method. Out of these challenges, the battery modelling and temperature effect has been taken into consideration for our work and for cell balancing it has been assumed that the cell equalizer has been incorporated with BMS which will uniformly distribute the SoC of an

individual cell. 1.2. Fixing the number of time constants (RC branches) It has also been observed that many of the researchers have used different combination of RC circuits in battery modelling (Table 2). To accurately estimate the SoC, the fixing of RC circuits in battery model is a must and the same is explained below. In Fig. 2, five different time constant combinations have been considered. The OCV is compared for these five combinations (1/2/3/4/5 RC pairs respectively) and for a realistic battery. The zoom-in a portion of the waveform has been shown on the right side so that the clear waveform of all five times constants can be seen. In Fig. 2, it can be clearly seen that out of five combinations, the one with single RC pair is not at all acceptable. Out of remaining combinations, the blue dotted 5

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Table. 2 The various RC model reported literature review: Reference

Model used

Estimate

Initialization (Tuned/Measured)

Year

[32] [33] [34] [35] [36] [89] [37] [38] [39] [40] [41] [90] [42]

Ro model 1-RC model 2-RC model 1-RC model Ro model 3-RC model 1-RC model 1-RC model 1-RC model 2-RC model 2-RC model 2-RC model 2-RC model

State/parameters State/parameters State/parameters State/parameters State/parameters State/parameters State/parameters State/parameters State/parameters State/parameters State/parameters State/parameters State/parameters

Tuned N.S N.S N.S N.S Tuned Measured N.S N.S Tuned Tuned Measured Tuned

2007 2008 2009 2013 2013 2013 2014 2014 2014 2016 2016 2017 2018

N.S*: Not Specified.

Fig. 2. Time constant comparison by curve fitting method

line (3-RC pair) is in close resemblance with the data of the OCV (green line). This also provides a minimal error in SoC estimation with realistic data. Therefore 3- RC combination is chosen here which is less explored in the literature.

3 The obtained parameters are optimized by means of “lsqnonlin” function. 4 A combination of coulomb counting and open-circuit voltage methods is used to estimate the SoC. 5 The obtained SoC is further corrected (calibrated) using ANFIS method. 6 The effect of temperature variation on battery behaviour is analyzed. 7 Real-time validation of a complete system using dSpace MicroLabBox.

1.3. Paper organization This paper has been organized in various sections where section 1 is an introduction, literature review, paper organization, and Novelty. Section 2, establishes the Thevenin equivalent circuit model with 3-RC for Li-ion battery. The detailed procedures for identifying the model parameters and SoC estimation are also presented in this section. Section 3 presents the simulations results and discussion. Section 4 gives the ANFIS optimized SoC. Section 5 presents the variation of SoC and OCV with temperature. Section 6 reveals the real-time validation and hardware setup, Section 7 is the validation of the proposed work in ADVISOR tool and Section 8 draws the conclusion.

2. Equivalent circuit model In this study, a Li-ion battery model is established. A reliable and

1.4. Novelty or peculiarity of the paper 1 3-RC model of battery has been proposed, which has not been much explored. 2 The various parameters of the battery, namely (R0, R1, C1, R2, C2, R3, and C3) have been estimated. Where R0 is the internal resistance, R1, R2, & R3 and C1, C2, & C3 are the resistance-capacitance pairs, as shown in Fig. 3.

Fig. 3. The equivalent circuit battery model 6

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accurate battery model is required to estimate battery SoC while using the model-based method. The third-order RC model of battery is crafted here in order to imitate the behaviour of the real battery. The model considered in this work consists of DC source, Ro, i.e. internal resistance and 3-parallel RC circuit in series as shown in Fig. 3. In a Li-ion battery, Li-ions move from anode to cathode through an organic electrolyte during discharging. During charging the reverse process is followed. Anode and cathode have a layered structure and Liions move in between layers. The governing chemical reactions are as follows:

response

Atcathode: Li1 x CoO2 + xLi+ + xe Atanode:Lix C6 xLi++xe + 6C

V1zero = V1 (T1) V2zero = V2 (T1) V3 zero = V3 (T1) From Eq (3), (4) and (5)

LiCoO2

T T1 2

V3 (T

T1) = V3zero e

T T1 3

H (T

V1 (T

C1

dV1 V + 1 =I dt R1

C2

dV2 V + 2 =I dt R2

X (T

T1) = Voc

T1) =

T1) =

+ V2zero e

Vter (T

T T1 2

+ V3zero e

T T1 3

(12)

(13)

T1)

H(

T1) d

X(

T1) d

T1) = (V1zero 1 + V2zero

(1)

Y (T

T T1 1

(14)

(15)

+ (V1zero

2 1

2

+ V3zero 3)

+ V2zero e

T1) = (V1zero 1 + V2zero (V1zero

2

+ V3zero e

+ V3zero 3)(T 2 2

+ V2zero

2 T T1 1e 1

T T1 2

T T1 3 )

(16)

T1)

+ V3zero 32 )

+ V2zero

2 T T1 2e 2

+ V3zero

2 T T1 3e 3 )

(17)

By using Eq. (13), (16) and (17)

Y (T

T1) =

X (T

T1)( 1 +

+ (V1zero 1 + V2zero

2

+ 3)

H (T

T1)

2

+ V3zero 3)(T

T1)

+ (V1zero + V2zero + V3zero)

1 2 3

1 2 3

(18)

When these expressions are substituted into the third equation, a regression equation is obtained as follows, which has no exponential terms in it: Table. 3 Specification of the Li-ion battery [91,92]:

Determination of Voc: Since the battery has been at rest for sufficiently long and the test starts from zero state, we have: (7)

The R0 can be obtained by

I

T T1 1

(V1zero e

(6)

Vter (T0+)

(11)

T1)

T1

The time constant of the circuit can be expressed as

Vter (T0 )

V3 (T

T

Y (T

(5)

VOC = Vter (T0 )

T1)

T1

(4)

1 = R1 C1 2 = R2 C2 3 = R3 C3

V2 (T

T

X (T

(3)

dV V C3 3 + 3 = I dt R3

T1)

T1) = V1zero e

(2)

V0 = IR 0

(10)

To establish a regression equation that can be used for parameter identification, the following two variables are taken from [93].

Where Vter is the terminal voltage, Voc open-circuit voltage, Vo is the voltage across the resistance Ro, V1 voltage across resistance R1, V2 voltage across resistance R2 and V3 voltage across resistance R3

R0 =

T1) = V2zero e

From Eq (10)

From Fig. 4, it is clear that the response voltage has a downward jump to discharge the battery once the battery is at rest for long enough. Similarly, the response voltage has an upward jump for charging the battery. The voltage drop due to Ro is sudden, whereas it is gradual for the RC combination. According to the principle of the circuit, the calculation of ohmic resistance could be obtained by the formula

V3

V2 (T

H (T

1 Rest the single battery for more than 24 hours, to ensure that the polarization voltage of the battery is reduced to zero. 2 Discharge the single battery with a constant current. 3 Rest the battery at the end of the experiment.

V2

T T1 1

Considering H = V1 + V2 + V3 This yields

The battery performance depends on three main parameters, i.e. SoC, operating temperature, and ageing. The battery model parameter identification is obtained by the discharging/charging current pulse experiments, and the specific experimental steps are described as follows:

V1

T1) = V1zero e

Vter = Voc

2.1. Identification of battery model parameter

V0

V1 (T

Since I = 0, from (1) and (2)

The specification of the battery used has been shown in Table 3.

Vter = VOC

(9)

(8)

Where T0 and the initial conditions The time duration from the T0+ to T2 has been used to calculate the three time constants. During this period the circuit is in zero input

T0+represent

7

Commercialization year

1992

Cell voltage Energy by weight (Wh/kg) Specific power (W/kg) Energy by volume (Wh/L) Maximum discharge rate Recharge time Cycle life cycle Self-discharge per month Temperature range 0C Preferred charge method Average energy cost

3.7 90-180 760 220 –350 40C < 3 Hours 1200 5% – 10% -20°C to + 60°CConstant voltage and constant current $250

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Y (T

T1)

=[

X (T

T1)

H (T

1+

2

+

T1) (T

T1) 1]

3

1 2 3

V1zero 1 + V2zero 2 + V3zero 3 (V1zero + V2zero + V3zero) 1 2 3

(19)

The time constants and initial states V1zero, V2zero and V3zero can be calculated by Eq (19) by considering all the sampling point from T1+ to T2 Then from Eq. (19) we have

Y1 X1 H1 T T1 Y2 = X2 H2 T2 T1 … … … … … … …… Yn X2 Hn Tn T1

1 1 … 1

1

1

+

2

+

2

+

3

V1zero 1 + V2zero 2 + V3zero (V1zero + V2zero + V3zero) 1

Y1 X1 H1 T T1 X2 H2 T2 T1 2 A = B= Y … …… …… …… Yn X2 Hn Tn T1

Fig. 4. Discharge test at constant current pulse

+

1 2 3 3 2 3

(20)

1 1 … P 1

3

1 2 3

= V 1zero 1 + V2zero 2 + V3zero (V1zero + V2zero + V3zero) 1

3

(21)

2 3

The Eq. (20) can be written as (22)

B = AP By least squared error solution

(23)

P = (AT A) AT B T1

V1zero = IR1 (1

e 1)

V2zero = IR1 (1

e 2)

V3zero = IR1 (1

e 3)

T1

T1

(24)

Since V1zero and V2zero are already obtained, R1 and R2 can be calculated from (24) and subsequently, C1 and C2 can be calculated from (6). 2.2. State of charge estimation: The output voltage can be calculated as [94]

Vter = Voc (t ) R1 + 2R0 e R1 C1

i (t ) R 0

R3 + 2R 0 e R3 C3

( t1 )

( t3 )

R2 + 2R 0 e R2 C2

( t2 ) (25)

A) SOCV Calculation: Cell voltage when all the reactions are balanced, is called equilibrium voltage, which is occasionally referred to as OCV. With this OCV, voltages based SoC (SoCv) can be estimated using [64,95–97]

SoCv = Fig. 5. Flow chart of estimation of parameters

1 (OCV a1

a0)

(26)

Where a0 is battery terminal voltage when SoC = 0% and a1 is battery terminal voltage when SoC = 100%. But, due to change in temperature, equilibrium voltage of the battery at any temperature (Tem) gets changed as

V (Tem) = V298 + ( dV is dTem

8

dV )(Tem dTem

298)

(27)

temperature coefficient and is constant for the considered

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Fig. 6. The data of the battery and the located pairs due to R0 and RC

Fig. 7. The real-time data and simulated data of battery

temperature range. So the consideration of this OCV with temperature effect will lead to modifying SOCV and will contribute in the final SOC calculation. B) SoC Calculation: The coulomb counting (CC) method involves the current integration flowing through the battery to get SoC

SoCi =

1 cp cp

Idt

depends on temperature. As for every 10 °C temperature increase, the current gets doubled so for ΔTem temperature change, final equation can be written as.

I(s

Ea R × Tem

=

1 K 0 (Tem) e cp

(ln 2( 10R ) ) (Tem×(Tem+10))

(30)

Temperature effect and self-discharge current are included for analyzing run-time characteristics. A number of Li-ion cells are connected in series and in parallel to simulate a powerful battery to be used in hybrid vehicles. The output voltage is calculated as Eq.(25) where V (t) is time-dependent OCV, i(t) is the time-dependent current, and multiplier term associated with i(t) represents the impedance offered. From Eq. (26), temperature-dependent voltage-based SoC, that is, SoCV(Tem), can be intended as Eq. (31) and from Eq. (28) temperaturedependent current based SoC, that is, SoCi(Tem), can be calculated as Eq. (32)

(28)

Cp is battery capacity in Ah. Due to change in temperature, the cell reaction rate gets changed. The Arrhenius equation, the reaction rate is given as

K = K0 × e

d)

(29)

K0 is reaction constant, R is gas constant, Ea is activation energy, and Tem is operating temperature. During the electron transfer reaction, electrons require the additional amount of energy to surmount the energy barrier called the activation energy (Ea = J⋅mol−1) which 9

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Fig. 8. The parameter obtained for the 3-RC circuit

Fig. 9. The optimized parameter obtained for the 3-RC circuit

SoCv (Tem) =

1 a1

Vter (t ) + i (t ) × 2( R1 + 2R0 e R1 C1

Fig. 10. The new and original SoC comparison with the time

SoCi (Tem ) =

1 cp cp

) + I(s

d)

(t ) × R 0

R2 + 2R 0 e R2 C2

( t1 )

R3 + 2R0 e R3 C3

Tem 10

( t3 )

+

{

( t2 )

dV (Tem dTem

i (t ) × 2(

Tem 10

) + I(s

298)

d)

}

(t ) dt

a0

(31) (32)

3. Simulations Results and Discussion The SoC indicates the power available in a battery and its correct information is of utmost importance. The parameters namely resistance and capacitance, play a vital role in system dynamic performance so to accurately estimate the SoC, these parameters are first optimized. The procedure of parameter estimation starts with the data 10

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Fig. 11. The MATLAB/Simulink circuit used to simulate and analyze SoC

Fig. 12. Structure of ANFIS

collection of the battery, which involves OCV and charge/discharge current pulse data collection. The collected data is processed to identify the effects of Ro and the RC pairs on OCV while tracking the charge/ discharge current pulse. The OCV is sampled so that its magnitude can be located at various time intervals concerning the current pulse. Then parameters are mathematically estimated by the Eq.(1) to Eq.(24). The obtained parameters are again optimized with the help of a function called “lsqnonlin” provided in the MATLAB. The obtained parameters are put up in the battery block, and an accurate SoC can be obtained. The obtained SoC with the 3-RC circuit is compared with the original circuit (circuit having no change). The procedure of the parameter estimation of the 3-RC circuit has been shown in Fig. 5 in the form of a flowchart: The simulation has been carried out in MATLAB/Simulink, and the temperature has been kept 303° K to 315° K for the whole experiment. The data of a real battery has been collected and is fed in the MATLAB

with the help of a lookup table. After that the OCV and current discharge pulse have been tracked with the SoC at the same time. The pairs due to Ro and RC also need to be identified for a sampling of the data, as shown in Fig. 6: The difference in the behaviour of the real data of a battery and the simulated battery, which has been demonstrated in Fig. 7: By locating the pairs and by sampling the OCV and corresponding current pulse for the time interval T0 to T2, the parameters can be calculated using the equations described in section 2. The obtained parameters have been shown in Fig. 8. The time constant and resistance are calculated by applying the equations mentioned in section 2 and are given below. The obtained parameters have been optimized utilizing “lsqnonlin” function provided in MATLAB. The values have been provided using the graphs shown below in Fig. 9: The obtained parameters have been fed to the modified block of 311

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consideration, as the authors can generate the data set. As expected, the ANFIS optimized SoC provides lesser variation in parameters during dynamically load change and lesser settling time. The real‐time verification ensures that this can be implemented practically. ANFIS is a hybrid of ANN and FLC, which enjoys the benefits of both. A dynamic and parallel processing system estimates input‐output functions. A fuzzy method adaptively deduces and alters its fuzzy relationship from representative mathematical samples. The NN, on the other hand, can erratically create and refine fuzzy rules from the training data. The fuzzy sets are thought to be constructive in the intelligent field and in dealing with higher processing. The performance of FLC depends on the rule basis, number, and forms of membership functions (MFs). In this work, various MFs like triangular, trapezoidal, and Gaussian are evaluated. Out of these, triangular is chosen here as it offers minimum error and less computational burden. The authors have tested the system with fuzzy MF rules like 3*3, 5*5, and 7*7, but they all yield the same result and settling time. Therefore, 3*3 rules are chosen here because of the lesser computational burden. The fuzzy input, along with triangular MF, is fed into the NN block. The NN block consists of a rule base, which is connected to the fuzzy inference system (FIS). Here, back propagation (BP) algorithm issued to train the FIS, and the BP learning algorithm has been used for training feedforward NNs. The most commonly used FIS are Mamdani and Sugeno. In this work, the Sugeno‐type FIS is used because it is computationally efficient than the Mamdani type, and can be trained by real data as opposed to the latter, which is more susceptible on an expert system. Also, the output MF of the Sugeno system is either linear or constant. Takagi Sugeno FIS is executed here using ANFIS and has a five‐layered structure, as shown in Fig. 12. Fuzzification of the input variable has been done in the first hidden layer and T‐standard operators to compute the rule are conveyed to the second hidden layer. Third and fourth hidden layers standardize the rule strengths and determine consequent parameters of the rule, respectively. The fifth layer computes the overall input by summing all the incoming signals. ANFIS architecture is an adaptive, feedforward network structure. Every node plays out a specific function on input signals as well as on the set of parameters of that node. Some of the nodes are adaptive, which means that the node parameters are dependent on the other nodes; whereas others are fixed nodes, where the node parameters are independent. The MF chosen should be able to minimize the error between the actual output data and ANFIS input sketched output data. The parameters connected with the MF will change within the learning process. Layer 1: This layer contains two inputs, one as error and other as a change in error represented by x and y respectively. It is commonly known as the fuzzification layer [98]. Layer 2: Every node of the 2n (the number of fuzzy if‐then rules) is fixed and labelled as Π. It multiplies the input signal and forwards and outputs the product as given by Eq. 33

Fig. 13. Flowchart showing the operation of an adaptive neuro‐fuzzy inference system (ANFIS) algorithm

RC pair circuit and are compared with the SoC of the original circuit, as shown in Fig. 10 below. In the Fig.10 the new SoC is the SoC obtained by modifying the battery model by incorporating 3-RC branches and original SoC is the SoC of the battery without any modification or for default battery model. The curves show the real value curve of SoC estimation. The coulomb-counting and OCV methods have been used to estimate the SoC. 4. The ANFIS based Optimized SoC The obtained parameters have been installed in the circuit shown in Fig. 11 and are used to obtain the new SoC. The obtained SoC has again been optimized by ANFIS, as shown below: ANFIS algorithm: The ANFIS has many advantages like it does not necessitate the use whole mathematical model only input‐output data are required generated from the simulation. The rousing features of the NN are its ability to learn and adapt, whereas the ability of a fuzzy system is to consider imprecision and prevailing uncertainties. In order to exploit the advantages of both methods, an adaptive neuro-fuzzy inference system (ANFIS) algorithm comprising of both the NN and the fuzzy logic is adapted for the proposed work. The ANFIS do have a high computational cost but due to the redundancy, complementarity, heterogeneity and its performance make it a fascinating tool for such case. As the learning rate of the NN is relatively low, which makes it less suitable as a stand-alone technique for time-critical applications, integrating it with fuzzy logic brings a better real-time response. The EV applications deals with high uncertainty of the power demand, temperature, and load variations. Concurrently, the system should also be designed in such away so that it could be adaptive and responsive to these changes. Therefore, application of ANFIS is appropriate for the proposed system. Further, the literature survey establishes that ANFIS results in accurate modelling of the system provided a good data bank is available. This is the icing on the cake for the system under

pk =

ai (x )

×

bi (y )

(33)

Where k = 1, 2, 3… 9. The output of each node represents the firing strength pi (i = 1 to 2n) of the i the fuzzy if‐then rule given by Eq. 34 as

pi =

pi 2n p i=1 i

(34)

Layer 3: Each node in this layered circle calculates the ratio of the individual rule's firing strength to the sum of all rules given by Eq. 35, as shown in Fig. 13. The ANFIS model for the controller design uses the architecture of the adaptive network. Fig. 12 shows the flow chart for the working operation of the ANFIS algorithm. The ANFIS model is designed, trained, and analyzed using MATLAB 2017b Neuro‐Fuzzy Designer tool‐box and graphical user interface (GUI). A data set is collected and stored in the MATLAB workspace to train 12

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Fig. 14. A) Training data, B) Epochs and test data error, and C) Training data testing. The predicted output is indicated by red, and the test data is represented by blue circles

Fig. 15. A) SoC comparison with 3-RC and ANFIS optimized & without 3-RC circuit B) OCV versus SOC curve

the ANFIS. The ANFIS is tested with different MFs such as triangular, trapezoidal, and Gauss MFs, and it is found that the training error is minimum with triangular MF. The epochs (iterations) and error are shown in Fig. 14 3

= pi =

pi p1 + p2

, i = 1, 2, 3.

individual output values “f” from the inferring of the rule base. Each node in this layer is a square node, with the function as given by Eq 36 4 i

= pi fi = pi (gi x + h1 y + ri),

(36)

Where i = 1, 2, 3 and pi is the output of layer 3 and {g1, h1, ri} is a parameter set. Parameters in this layer are also referred to as consequent parameters. Layer 5: This layer is called as the output layer. There is a single

(35)

Layer 4: This layer is called a defuzzification layer. It calculates the 13

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Fig. 16. . Effect of temperature on SoC and voltage of battery A and battery B

circle of the output neuron labelled as Σ, and the output signal is obtained by adding up input signals as it can be seen in the following Eq 37 5 i

=

i pi fi

=

ipi fi

ipi,

Step 7: Implement the “. fis” in the fuzzy toolbox and obtain the results. Step 8: Implement the same work in hardware to check its validity in real-time. Step 9: The algorithm uses an ANFIS based system for fusing the data from multiple sources. The two inputs are given to the ANFIS based algorithm by means of taking the Input/ Output data in the workspace of the MATAB tool. The generated “. mat” file is loaded in the ANFIS. The training has been carried by setting the epoch value and MF is generated using “trimf.” The output which is “. fis” file is loaded in a fuzzy toolbox in the simulation model then the output is taken, and the same is checked in the HIL.

(37)

Comparison of simulated SoCs: Fig. 15 (A) provides the comparison of estimated SoCs, where red line indicates estimation without RC, and the blue line indicates with the 3-RC circuit. The circuit with 3-RC involves more losses due to the impedance whereas in another case losses due to internal resistance are only considered. The results obtained using RC pairs are closer to that of real data available in [38]. Therefore, the proposed approach provides a faster and accurate estimation of SoC in real-time. Fig. 15 (B) provides the OCV Vs SoC curve of the battery. This paper presents the design of a data fusion algorithm based on ANFIS and provides minimal root mean square error and mean absolute percentage error. The redundancy, complementarity, timeliness, heterogeneity etc. are the advantages of the systems based on data fusion algorithms. As the learning rate of the NN is relatively low, which makes it less suitable as a stand-alone technique for time-critical applications, integrating it with fuzzy logic brings a better real-time response. The fuzzy logic creates a fuzzy engine based on the rules derived from the input/output data set. The neural network trains the engine for more precision. The steps of the algorithm have been presented below:

5. Variation of SoC and OCV with temperature Two batteries, namely, A and B, have been taken with the 3-RC circuits. The behaviour of battery A has been captured for temperature variations from 40 °C to – 40 °C as shown in Fig. 16 below. The effect of temperatures is neglected in Battery. The current pulse of 2A has been considered for this purpose. 5.1. Simulation and analysis At t = 0s, the Battery A and B are discharged with 2A at an ambient temperature of 40°C. At t = 150s, the internal temperature has increased to its steadystate value of 42.2°C due to heat losses from the discharge process. This causes the output voltage of Battery A to slightly increase, while battery B output voltage continues to decrease. At t = 1000s, the ambient temperature is decreased to -40°C. This causes the output voltage of Battery A to greatly decrease as the internal temperature decreases rapidly. Also, the SoC of Battery A decreases due to the reduction of its capacity. The battery B output voltage continues to decrease slowly to its steady-state voltage. At t = 2000s, the ambient temperature is increased from -40°C to 0°C. As the internal temperature increases, the output voltage of Battery A increases. Also, as the capacity increases, the SoC of Battery A

Algorithm Step 1:Collect the data from individual sensors. Step 2: Create a fuzzy engine with pre-determined input/output variables using ANFIS. Step 3: Train/re-train the fuzzy engine until there is no improvement in the accuracy. Step 4: Train the engine to obtain the minimum root mean square error. Step 5: If No, go to step 4. Step 6: If Yes, stop training further and save the “. fis” file.

14

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Fig. 17. A) Hardware setup and B) SoC comparison.

increases. The Battery B output voltage remains constant to its steadystate value. At t = 2500s, the Battery A and B are charged with 3A at an ambient temperature of 0°C. This causes the internal temperature to increase due to heat losses during the charging process, which increases the charging voltage of Battery A. Afterwards, Battery A and B continue to charge up until fully charged. The variation of SoC has also been taken care of in the developed design.

calculations and to write all outputs. The interval size is known as the step size, Ts. Fixed-step solvers solve the model at regular time intervals from the beginning to the end of the simulation. Physical test system setups are large, costly, and required highly experienced people to handle the repetitive occupations of setting up networks and maintaining extensive inventories of difficult hardware. With the improvement of microprocessor and floating-point digital signal processing technologies, physical test systems have been replaced with completely real-time simulator. The HEVs are highly nonlinear and complex in nature, and testing on the actual network is very expensive, tedious, and risky. Hence, a speedier approach to test and validate a new algorithm or research in a real-world environment using real-time simulator is an essential part of the design and improvement of the system. There are various types of real-time simulators; the popular realtime platforms are Opal-RT, Typhoon HIL, and MicroLabBox (dSPACE). In this work, authors have used MicroLabBox hardware

6. Hardware setup and Real-time results Real-time is often used to describe the time-critical technology in various industries. MicroLabBox uses real-time in reference to an embedded system. These systems are devices which interface with the real world and provide control. The embedded device is given a pre-set time, like 1,5,20ms to read input signals, to perform all necessary 15

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Fig. 18. SoC comparison.

estimation, this estimated SoC was compared with real data and error was minimized using ANFIS based. The system has been tested on HIL platform by applying MicoLabBox hardware controller. The HIL results are very close to the simulated results. Proposed SoC estimation shows very little deviation from the real battery data, thus verifies the utility of the proposed design in real-time systems.

controller. The laboratory setup of HIL has been presented in Fig. 17 (A). The whole system has been simulated in the MATLAB, and then it is burnt in the MicroLabBOX to verify the results obtained in real-time. The waveform in Fig. 17 (B) shows two different lines corresponding to two SoCs. The blue line is the SoC due to the original battery (without RC) and the yellow line shows the ANFIS optimized SoC of the 3-RC circuit. The results obtained on the HIL platform are in line with the simulated results. Further, the results obtained using ANFIS based algorithm is very close to the real data, thus verifies the proposed design. In the MicroLabBox it is difficult to show the exact waveform as the signal division is quite large and digital storage oscilloscope (DSO) can only display till M 50s the signal magnitude is further divided by 100so that it can be step down and can be displayed in DSO in real-time. The MATLAB file needs to undergo some setting like fixed solver is selected, step time needs to be fixed and will have to be kept the same for the whole system. In figure 17(B) the original SoC indicates the default SoC of the battery i.e battery without any modification which is indicated by the blue line and the SoC of the battery with ANFIS with the 3-RC and has been indicted by the yellow line which runs parallel to blue line but lesser in magnitude. The result shown in 17(B) is only for 500s as the sampling time of the DSO is 50s so in display at a time in one screen it can show result for 500s.

Declaration of Competing Interest All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version. This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue. The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript Reference [1] H. Budde-Meiwes, J. Drillkens, B. Lunz, J. Muennix, S. Rothgang, J. Kowal, D.U. Sauer, A review of current automotive battery technology and future prospects, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 227 (2013) 761–776, https://doi.org/10.1177/ 0954407013485567. [2] D.N.T. How, M.A. Hannan, M.S. Hossain Lipu, P.J. Ker, State of Charge Estimation for Lithium-Ion Batteries Using Model-Based and Data-Driven Methods: A Review, IEEE Access 7 (2019) 136116–136136, https://doi.org/10.1109/access.2019. 2942213. [3] Battery Performance Characteristics – How to specify and test a battery, (n.d.). https://www.mpoweruk.com/performance.htm (accessed October24, 2019). [4] G. Zubi, R. Dufo-López, M. Carvalho, G. Pasaoglu, The lithium-ion battery: State of the art and future perspectives, Renewable and Sustainable Energy Reviews 89 (2018) 292–308, https://doi.org/10.1016/j.rser.2018.03.002. [5] Battery Comparison of Energy Density – Cylindrical and Prismatic Cells, (n.d.). https://www.epectec.com/batteries/cell-comparison.html (accessed October24, 2019). [6] L. Guo, C. Hu, G. Li, The SOC estimation of battery based on the method of improved Ampere-hour and Kalman filter, Proceedings of the 2015 10th IEEE Conference on Industrial Electronics and Applications, ICIEA 2015 (2015) 1458–1460, https://doi.org/10.1109/ICIEA.2015.7334337. [7] C. Weng, J. Sun, H. Peng, A unified open-circuit-voltage model of lithium-ion batteries for state-of-charge estimation and state-of-health monitoring, Journal of Power Sources 258 (2014) 228–237, https://doi.org/10.1016/j.jpowsour.2014.02. 026. [8] P. Jansen, M. Vollnhals, D. Renner, D. Vergossen, W. John, J. Götze, Advanced binary search pattern for impedance spectra classification for determining the state of charge of a lithium iron phosphate cell using a support vector machine, Advances in Radio Science 14 (2016) 55–62, https://doi.org/10.5194/ars-14-55-2016. [9] D.I. Stroe, V. Knap, M. Swierczynski, T. Stanciu, E. Schaltz, R. Teodorescu, An Electrochemical Impedance Spectroscopy Study on a Lithium Sulfur Pouch Cell, ECS Transactions 72 (2016) 13–22, https://doi.org/10.1149/07212.0013ecst. [10] Y. Xing, W. He, M. Pecht, K.L. Tsui, State of charge estimation of lithium-ion batteries using the open-circuit voltage at various ambient temperatures, Applied Energy 113 (2014) 106–115, https://doi.org/10.1016/J.APENERGY.2013.07.008. [11] C. Burgos, D. Sáez, M.E. Orchard, R. Cárdenas, Fuzzy modelling for the state-of-

7. Validation of the proposed work by ADVISOR tool To reconfirm the accuracy of the proposed work for SoC estimation, it has been implemented in the ADVISOR tool (for Toyota Prius) that is developed by NREL and considered as a very significant tool for carrying out the research on XEVs. The Fig. 18 demonstrates the difference between the estimated SoC (after implementation of the proposed work) and the default SoC (without any modification). The proposed results are in line with the default battery and are close to realistic situation. 8. Conclusion This paper presents an accurate SoC estimation involving parameter optimization for a hybrid electric vehicle. In this work whole battery system of 420V has been considered instead of a single cell. 3-RC pairs are included in the circuit in series with the internal resistance which has produced realistic results for EV applications. The values of the parameters have been calculated mathematically and then installed in the circuit to find the new SoC from the modified battery. The obtained parameters are then optimized to get accurate results. To get a precise 16

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