Optimization based System Identification of HEV Li-Ion Battery

Controls, Measurement & Calibration Congress

Optimization based System Identification of HEV Li-Ion Battery Ramesh Kumar Junnuri, Shivaram Kamat, Ramanathan Annamalai, Nitin Goyal Engineering and Industrial Services, TATA Consultancy Services Limited, Pune, India

Hiroshi Tashiro, Nobuya Miwa ePF R&D Division, DENSO CORPORATION, Kariya, Japan

ABSTRACT The battery management system in hybrid electric vehicle relies on reasonably accurate model of its high voltage Li-ion battery pack primarily to estimate the state of the charge and health of the battery. There have been many approaches for modeling or system identification of the battery system using experimental lab data and the dynamic data of the HEV operation. In this paper we have proposed an approach of system identification for the HEV battery pack using only the dynamic data. To capture the dynamics of the electrical equivalent circuit parameters and the characteristics, a variety of drive cycles have been designed and conducted on the test vehicle at various operating conditions. The equivalent circuit for the HV battery is formulated as discrete state space equations. The Open Circuit Voltage (VOC), Offset Voltage at zero load conditions (VZL), Internal Resistance (Rbatt), battery pack RC filter states are considered as the states of the discrete state space (SS) equation at various operating temperature conditions. The system identification problem is then posed as the problem of simultaneously estimating the parameters of all the coefficients formulated in the state space equations. This is posed mathematically as a constrained nonlinear optimization problem. The optimization problem is solved using MATLAB ®’s constrained nonlinear multivariable optimization routine. The model is implemented in MATLAB ®/Simulink ® tools and validated with the dynamic data generated during vehicle run for various driving cycles.

The results obtained by the proposed approach are closely matching with the actual battery responses for various drive cycles. The simulation results of the developed model are compared against one of the popular models in normalized form as benchmarking exercise.

INTRODUCTION System identification deals with the techniques for building mathematical models for dynamical systems using the measured input / output data. It is a pre-requisite to the analysis of a dynamic system towards the design of an appropriate controller to improve its closed loop performance and fault diagnosis. Various approaches are found in the literature to obtain such mathematical models for the physical systems [2, 9].

In this paper, a new approach is proposed for system identification of HV Li-Ion battery pack of an HEV. Fairly accurate HV battery model is required to validate the HV battery control algorithms. It is important to calculate the state-of-charge (SOC), open-circuit voltage (VOC), and the terminal voltage (Vbatt) with acceptable accuracy for the arbitrary current profiles at various operating conditions of the vehicle. An accurate and fast simulation model with good runtime prediction and voltage response characteristics has been crucial requirement for the development and validation of a Battery Management System (BMS).

Several approaches are available in the literature [8, 9, 13, and 15] to model various types of batteries. In most of the approaches that are reported and used to develop the battery pack model, it is important to have the cell level data and measurements. Using this data an equivalent battery cell model has been developed and further integrated to create the entire battery pack model. This requires additional instrumentation for the battery pack and laboratory set up to conduct specialized tests to extract the dynamics of battery cell behavior. In this paper, the battery model structure uses the measured parameter values by the available sensors on the battery pack rather than using the cell level data, which inturn saves the cost of additional instrumentation.

The problem of estimation of parameters of HV battery pack is formulated as a constrained optimization problem that minimizes an objective function (error function) between the measured and simulated output. The constrained optimization problem is solved using MATLAB ®’s constrained nonlinear multivariable optimization routine. The main advantages of the proposed approach are given below:

  

No additional data acquisition instrumentation either at cell or pack level.

Uses of existing pack level sensors data.

No special lab set up and lab tests

The model has been implemented using MATLAB ®/ Simulink ®. The developed model is validated and compared against available benchmark [16] model for various standard drive cycles data collected at various operating conditions of the vehicle and battery temperatures.

PROPOSED MODELLING APPROACH A number of approaches and models are available in the literature to characterize and simulate Li-ion cells. Various HV battery equivalent electrical circuits are available in the literature [7, 9 and 10]. HV battery equivalent electrical circuit considered in the proposed approach is shown in Figure 1. The equivalent electrical circuit is composed of open circuit voltage (VOC), series battery resistance (Rbatt) and two RC filters (RC1, RC2) as shown in Figure 1.

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Figure 1: Battery Equivalent Electrical Circuit From the equivalent circuit, HV battery pack terminal voltage is calculated using (1) given below: yˆ  VOCSOC ,Temp  Rbatt * i  h( RCFilters )

(1)

Where, VOC SOC ,Temp   open circuit voltage as function of SOC and Battery Temperature R batt  series battery resistance i  battery current h(RC Filters )  effective voltage across RC1 & RC2 filters yˆ  estimated battery voltage

In this approach, the linear dynamics of the RC filters are mathematically represented using discrete state space equations (h(dSS)). Equation (1) can be further modified to the equation shown below in (2). yˆ  VOC SOC ,Temp  Rbatt * i  h(dSS)

(2)

While carrying out several simulations, it is observed that, at zero load conditions, the VOC (SOC, Temp) alone is not able to result the desired terminal voltage and hence an offset voltage function has been added to obtain the desired terminal voltage at zero load conditions. Again, the offset voltage is found to be function of the SOC and battery temperature, The Equation (2) is further modified as shown in (3). yˆ  VOC SOC ,Temp  VZLSOC ,Temp  Rbatt * i  h(dSS)

(3)

Where, VZLSOC ,Temp   Offset Voltage at zero load conditions as function of SOC & battery temperature

PROPOSED ALGORITHM The approach for system identification of battery pack is given in the flowchart shown in Figure 2. As a matter of simplification and a time saving measure, the SOC v/s VOC characteristic curves for Li-Ion cell are inherited from the literature [15], Where they are available for constant ambient temperatures of 30C, 270C and 62.50C. As the data is

available for constant ambient temperature conditions, we have made an assumption that, while creating the VOC data, the battery cell temperature and ambient temperature are maintained around the same value. The inherited characteristic curves for the HV battery pack are shown in Figure 3.

The VZL Look-up-Table curves for some of the selected battery temperatures (-4.30C and 28.30C) are shown in Figure 4.

The profile curves shown in Figure 4 are normalized data curves rather than the actual VZL data.

The linear dynamics of the RC filter states is represented using discrete state space equations [8, 11, 13 and 15] as given below in (4): h( k  1)  diag(  ) * h( k )  B * i ( k ) (4) k   C * h( k ) The vector α has N number of filter ―poles‖, with | α(N) | <1 for ensuring the stability [13], corresponding to the time constants of the filter states. In this work, we have chosen two poles, i.e, N = 2. The vector B is the input weight matrix, C is output coefficient matrix and i(k) is the battery pack current at the k th time instant and Ф(k ) is the effective voltage across the RC filters. The battery pack model parameter estimation problem is posed mathematically as a constrained optimization problem [3]. The formulated constrained Non Linear Program (NLP) is solved using Sequential Quadratic Program (SQP) solver from MATLAB ®' Optimization Toolbox, which allows explicit definition of the objective function and constraint equations. The SQP solver internally uses finite-difference based hessians and gradients of both the objective function and constraints. The objective function to be minimized is a function of the simulation error i.e. some function of error between model simulated output ŷ(t) and the actual measured output y(t). This constrained optimization problem can be represented as given in (5). Min [ e(y  yˆ )] θ (5) s . t . θ lower  θ  θ upper Where, θ  R batt α, B , C

In (5), a set of the decision variables is actually a set of parameters to be estimated i.e. θ = { Rbatt, filter coefficients, input matrix coefficients, output matrix coefficients }, whereas θlower and θupper are lower and upper constraints (bounds) on the parameters to be estimated.

Select the VOC v/s SOC characteristics data for available temperatures

Calculate VZL v/s SOC data for various battery temperatures

Implement the state space (SS) equations as a function of state space filters

For mulate the constraints for the unknow n parameters

Estimate the parameters using Optimization Techniques

Validate the converged mode l using other Drive Cycles data

Figure 2: Proposed procedural flow chat for System Identification of HV battery pack model

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Figure 3: SOC v/s VOC at various ambient temperatures 30C, 270C and 62.50C 1 0.8

Normalized Offset Volatge

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Figure 4: SOC v/s Normalized offset Voltage at Zero Load conditions (VZL) at selected constant battery temperatures -4.30C and 28.30C

BENCHMARK REFERENCE MODEL A number of models have been developed in the past to characterize and simulate Li-ion cells and battery. The Li-ion battery cell model presented in [16] has been chosen as a benchmark reference model in this paper. In the reference model, an equivalent circuit model with one voltage source, one series resistor, and a single RC block were used to account for the discharge dynamics. The electrical equivalent of battery cell used in the reference model is represented in Figure 5. The reference model also simulates the thermal behavior of an internal cell.

R0

+ -

RC

Em

Figure 5: Equivalent Battery Cell circuit represented in the reference model Each element of the equivalent circuit used in Figure 5 is a function of SOC and battery temperature. Where E m is the electromotive force of the main branch, R1 and C1 are the resistance and capacitance of RC circuit, R0 is the series branch resistance and V is the terminal voltage of the battery. The parameters were determined using the parameter estimation tool in Simulink Design Optimizationâ&#x201E;˘.

Battery Current

SOC

Battery Model

Battery Voltage

Ambient Temperature Battery Temperature

Figure 6a: Reference model Interface Battery Current

SOC

Battery Model Battery Temperature

Battery Voltage

Figure 6b: Modified reference model interface

For the purpose of comparison, the reference model input interface as shown in Figure 6a has been modified to accept battery temperature as an input parameter rather than the output parameter as shown in Figure 6b. The reference model contains ambient temperature as an input signal and the battery temperature is estimated by it. For comparison with the proposed battery model the reference model has been modified and the battery temperature calculation has been removed and provided as an input signal.

SIMULATION RESULTS The proposed model has been validated against various HEV test drive cycles data sets at various vehicle and battery temperature conditions. The validated data sets comprised of the standard drive cycles (NEDC, UDDS, etc) and generic vehicle road trial data sets. For comparing the proposed battery model responses with the reference model, estimated battery resistance and open circuit voltage offset values are slightly tuned to match the characteristics of the reference battery model.

The battery current and the corresponding battery temperature profiles of selected test drive cycle data sets (NEDC and UDDS) considered in this paper are shown in the Figure 7 and Figure 10 respectively. Figure 8 shows the comparison of the battery voltage and estimated SOC of the proposed model with respect to the measured vehicle test data for NEDC drive cycle. Figure 11 shows the comparison of the battery voltage and estimated SOC of the proposed model with respect to the measured vehicle test data for UDDS drive cycle. Comparison results show that the battery model responses are closely matching with the actual measured responses. Figure 9 shows the comparison of the normalized battery model terminal voltage and SOC estimates of the proposed model with respect to the reference model responses for NEDC drive cycle test dataset. The comparison of NEDC drive cycle data show that the results are closely matching with each other. The Figure 12 shows the comparison of the normalized battery model terminal voltage and SOC response of the proposed model with respect to the reference model responses for UDDS drive cycle test dataset. The comparison of UDDS drive cycle data shows that the results are closely matching with each other.

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Figure 7: Battery Current & Battery Temperature Input Profiles of NEDC Test data

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Figure 8: Comparison of battery voltage & SOC of Actual Measured data & Proposed Model for NEDC Test data 1 0.9 0.8 0.7 0.6

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Figure 9: Comparison of battery voltage & SOC of Proposed Model and Reference Model for NEDC Test data

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Figure 10: Battery Current & Battery Temperature Input Profiles of UDDS Test data

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Figure 11: Comparison of battery voltage & SOC of Actual Measured data & Proposed Model for UDDS Test data

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Figure 12: Comparison of battery voltage & SOC of Proposed Model and Reference Model for UDDS Test data

CONCLUSION The proposed approach is new in a way that the system identification of HEV HV Li-Ion battery pack problem is posed as a discrete state space parameters estimation problem which is solved as a constraint optimization problem using MATLAB 速 constrained nonlinear multivariable optimization routine. The HV battery pack model identified by the proposed approach is found to be reasonably accurate. The developed model simulates the electrical dynamic behavior across the operating conditions within the constraints of the limitations and assumptions mentioned in this paper. The HV battery model is validated using various standard vehicle drive cycle data sets (UDDS, UDC, NEDC) at various operating conditions (hot and cold drive cycles). The comparison of the results of the developed model with the selected reference battery model shows that there is significant improvement over the reference model. The comparison results show that an accurate battery can be developed using the proposed approach using the available and specialized drive cycle data at the battery pack level and does not require the cell level data and specialized cell/battery level lab tests. Thus, the approach is proved to be cost effective.

ACKNOWLEDGMENTS The authors acknowledge the support from Hiroshi Hayakawa, Director, EE Core, DENSO Corporation, and Sanjeev Madhav, Sunil Viswanathan, Sanjay Peshin of Engineering and Industrial Services, TATA Consultancy Services Limited, without which this work could not have been possible.

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CONTACT Ramesh Kumar Junnuri was born in INDIA. He received Bachelor Degree in Electrical & Electronics Engineering from J.N.T.U, Hyderabad, India in 2002 and Masters Degree in Control Systems from University of Pune, India in 2004. He has been working with Engineering & Industrial Services division of TATA Consultancy Services Limited, Pune, INDIA since 2004. He has been working in the areas of Advanced Process Control, Marine Engineering, Automotive control and Diagnostics, Model Predictive Control, Data Analysis and Model Based Development. His research interests include modelling, optimization and control of various components in HEV, EV, Power Train and Energy Storage Systems. He has multiple publications in conferences and journals in these areas. He is reachable at ramesh.junnuri@tcs.com.

Shivaram Kamat was born in INDIA. He received Bachelor Degree in Electrical Engineering from Walchand College of Engineering, Sangli, India in 1987 and Masters Degree in Power Electronics from IIT, Delhi, India in 1990. He has been working with Engineering & Industrial Services division of TATA Consultancy Services Limited, Pune, INDIA since 2000 and is Senior Member of IEEE and contributes as reviewer for IEEE Transactions on Neural Networks and Learning Systems. He has been working in the areas of Advanced Process Control, Automotive Control and Diagnostics, Model Predictive Control, Machine Learning, Data Analysis and Model Based Development. His research interests include modelling, optimization and control of various components in HEV, EV, Power Train and Energy Storage Systems. He has multiple publications in conferences and journals in these areas. He is reachable at shivaram.kamat@tcs.com, shivaram.kamat@ieee.org.

Ramanathan Annamalai was born in INDIA. He received Bachelor Degree in Production Engineering from Annamalai University, India and the Masters Degree in Manufacturing Systems from Birla Institute of Technology & Science Pilani, India in 1998 and 1999, respectively. He worked for Sundaram Clayton Limited for 7 years in area of control system development of Active safety systems for heavy commercial vehicles. He is working with Engineering & Industrial Services division of TATA Consultancy Services Limited, Pune, INDIA in the areas of Automotive Control and Diagnostics, Model Based Development. He is reachable at ramanathan.annamalai@tcs.com.

Nitin Goyal was born in INDIA. He holds a Bachelor Degree in Electronics and Communication from Gulbarga University, Karnataka India in 2000. He has been working with Engineering & Industrial Services division of TATA Consultancy Services Limited, Bangalore, INDIA since 2004, associated with R&D and key customer Engagements. His key interest areas include new technology incubation, convergence and process optimization. He is reachable at nitin.go@tcs.com.

Hiroshi Tashiro was born in JAPAN. He received his Masters Degree in Mechanical Engineering from Tokyo University of Science, Japan in 1989. He is working with electronics platform R&D division of DENSO CORPORATION, Kariya, JAPAN. His research interests include multi domain modelling and optimization of automobile. He is reachable at hirosi_tasiro@denso.co.jp.

Nobuya Miwa was born in JAPAN. He graduated in Electrical Engineering from Doushisya University, Japan in 1993.

He is working with electronics platform R&D Division of DENSO CORPORATION, Kariya, Japan. His research interests include multi domain modelling and optimization of automobile. He is reachable at nobuya_miwa@denso.co.jp.

DEFINITIONS, ACRONYM S, ABBREVIATIONS BMS: Battery Management System C1: RC circuit Capacitance of the reference model Em: Electromotive force of the main branch of the reference model HEV: Hybrid Electrical Vehicle HV: High Voltage Li-Ion: Lithium Ion NEDC: New European Driving Cycle NLP: Non Linear Program R0: Internal battery Resistance of the reference model R1: RC circuit Resistance of the reference model Rbatt: Internal battery Resistance RC: Resistance Capacitance SOC: State Of Charge SQP: Sequential Quadratic Program UDDS: Urban Dynamometer Driving Schedule UDC: Urban Driving Cycle VOC: Open Circuit Voltage V: Battery Terminal Voltage of the reference model Vbatt: Battery Terminal Voltage VZL: Offset Voltage at zero load conditions