978-1-4673-2605-6/12/$31.00©2012 IEEE

Bidirectional Contactless Charging System using Li-Ion Battery Model

Ezhil reena Joy T.P. Kannan Thirugnanam Praveen KumarDept. of EEE/ Indian Institute of

Technology Guwahati , India ezhil@iitg.ac.in

Dept. of EEE/ Indian Institute of Technology Guwahati,India

kannan@iitg.ac.in

Dept.of EEE/Indian Institute of Technology Guwahati,India

Praveen_kumar@iitg.ac.in

Abstract—In this paper, the performance of Bidirectional Contactless Charging System (BCCS) have been assessed by an electric circuit based battery model suitable for Electric Vehicles applications. The time, C-rate and SOC dependent electric circuit parameters of charge /discharge model are calculated using a polynomial equation. The charging system along with battery model is tested by simulation for a 2kW BCCS system and is able to transfer power in both the direction. The simulation results show that, the charging scheme could effectively maintain the longetivity of EV’s and can supply power during Vehicle to Grid (V2G) operations.

Keywords- Battery Model, Bidirectional Contactless Charging system, Electric Vehicles, Grid-to Vehicle and Vehicle-to-Grid, Plug-in -Hybrid Vehicles.

I. INTRODUCTION Contactless charging is safe, efficient and easy to use for

the Electric Vehicles (EV). Contactless charging systems in EV’s improve the drawbacks such as failure connection, sparking and the risk of electrical shock of the conventional charging system [1]-[3]. Although, EV’s have emerged as the way to green and clean transport, they can also be used as a distributed energy resources by supplying power back to the grid [4]. In such situation, the power interface (charging system) should necessarily be bi-directional to allow for both charging and discharging of EV’s. Therefore, Bidirectional Contactless Charging System (BCCS) is emerging as a viable choice for EV applications, as they meet most of the aforementioned attributes [1]-[3].

The performance of EV’s are largely depends on the charge/discharge rate characteristics of the batteries [5]-[11]. Presently, Lithium ion (Li-ion) batteries have attracted a great interest in EV applications due to their high energy and power density, wide temperature range and long cycle life [6]-[11]. Consequently, to investigate the system performance of Vehicle-to-Grid (V2G) and Grid-to-Vehicle (G2V) technology an effective battery model is critically needed [11].

Various battery models have been developed in literatures based on experimental, electrochemical and mathematical model [6]-[11]. The electrochemical models are the most accurate models, but they require complex nonlinear differential equations and detailed knowledge of the chemical actions in the cells of the batteries [7]. Experimental models require experimentation to determine the parameters of the battery model [8]. The mathematical models are based on stochastic approaches to predict the efficiency, runtime and

capacity of the batteries [6] and [9]. Moreover, due to complexity and intensive computations, all these models are difficult to use in real-time power management and circuit simulations to predict the performance of the systems [10]. Therefore, to investigate the performance of power converter-based BCCS for V2G applications, an effective circuit based battery models are critically needed to perform simulations [11].

In this work a simple Electric Circuit (EC) based battery model is used with BCCS unit to analyze the performance of V2G systems [5]. This model is computationally less expensive and is based on Thevenins equivalents and impedances [10]-[11]. Basically, an EC based model consists of the combination of batteries internal resistors and capacitors. The parameters of these models are based on multivariable functions of SOC, current, temperature, Charge and Discharge cycle’s etc [11]. In order to predict the real time performance of V2G through BCCS model, it is important to determine the parameters of the circuit based battery model as accurate as possible. Here, the parameters of EC’s are determined by Genetic Algorithm (GA) approach.

Despite, a large number of publications assessed the benefits of V2G technology through BCCS, so far there are no publications have explored the entire BCCS with a real time battery model [1]-[3]. As a solution, this work examines a complete new BCCS with dc/dc interface connected with EC based battery model. The proposed BCCS unit associated with its controllers are designed for a 2kW system and tested with the battery model interfaced with a single node of real time grid condition of Guwahati city [14]. Due to the uncertain behavior of EV batteries, Fuzzy logic Controllers (FLC) are used in the proposed BCCS unit; which is found to be flexible enough to handle EV batteries of different ratings such as terminal voltage, Ampere hour (Ah) and SOC levels.

The rest of the sections are organized as follows: Section II, III and IV explain the battery model, architecture of BCCS and its modeling. Section IV, presents the controller descriptions and Section V, reports the simulation results and discussion based on the performance of the battery model with BCCS during G2V and V2G operations.

II. BATTERY MODEL To understand the behavior of EV’s batteries, Electric

Circuit (EC) based battery models are used [10]-[11]. This section explains, equivalent circuit based battery model of Lithium-ion (Li-ion) battery and its mathematical descriptions.

A. Battery Equivalent Circuit Fig.1. shows the EC based battery model, where 1R and

2R are internal resistance, C represents the internal capacitance, battV and oV are the battery terminal and open circuit voltages of the battery.

Fig. 1. Electric equivalent circuit for Li-ion battery

The parameters 1R , 2R , C and oV can be represented in terms of polynomial equation to represent the nonlinear phenomenon in the battery [5]. These equations are expressed as a function of State of Charge ( )SOC and charge or discharge rates ( , )r rC D .

)()( 2765

23211 4 rr

SOCarr CaCaaeCaCaaR ×+×++××+×+= ×−

(1)

)()( 2141312

210982 11 rr

SOCarr CaCaaeCaCaaR ×+×++××+×+= ×− (2)

)()( 2212019

21716151 18 rr

SOCarr CaCaaeCaCaaC ×+×++××+×+−= ×−

(3)

23130

329

2282726

22423220

)(

)( 25

rr

SOCarr

CaCaSOCaSOCaSOCaa

eCaCaaV

×+×−×+×+×+

+××+×+= ×−

(4)

Where 1 2 31, ,............a a a , is the coefficients of the polynomial and rC are the rate at which the battery is charged or discharged and SOC is the current state of charge of the battery. In the above equations (1)-(4), the parameters are expressed as a function of SOC , rC and rD . Under constant current condition, the time dependent cell voltage is given by equation (5)

( )( )21012

2 exp RRIVCR

tRI

CQV c

ccbatt +×−+⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛×

−×⎟⎠

⎞⎜⎝

⎛ ×+= (5)

Where, Q is the nominal capacity, oV is the nominal SOC dependent cell Open Circuit Voltage ( )OCV . The coefficients of the polynomial equation from (1) to (4) can be determined using Genetic Algorithm approach [11].

B. Charge/Discharge Model Fig.2. shows the block representation of the battery model

during charging and discharging scenario. The model is developed using the polynomial equation mentioned in (1)-(4).

The input given to the model are constant current ( )I ,

initial capacity of the battery ( )Q , nominal voltage ( )V , time

taken ( )t , charge ( )rC and discharge ( )rD rate and values of the coefficients from 1a to 31a . If current is positive, charging

takes place and when current is negative, battery discharges. The output of this model is battV , if the battery is discharging and oV , if it is charging.

Fig. 2. Schematic representation of charging and discharging conditions

III. BIDIRECTIONAL CONTACTLESS CHARGING SYSTEM (BCCS)

In the previous section, the details about the battery model and its related equations are explained. The battery model explained in Fig.1 is analyzed with the BCCS unit shown in Fig.3. This section explains the general scheme background of BCCS with its theoretical descriptions.

A. BCCS system Structure Fig.3. shows the layout of the BCCS System. The system

basically consists of two main units, charging station in primary side and EV battery system in the secondary side. Two coreless coils are arranged on either side of the units. The primary side is connected to the utility grid and it consists of transformer, filter and bidirectional ac-dc and dc-ac converter. The secondary side corresponds to EV battery system. It has a bidirectional rectifier with a Buck-Boost (BB) converter. As the EV batteries represents different nominal voltages, Ah ratings and variable 'SOC s . Here, the BB converter is essentially required to step up or down the voltage depending on the battery terminal voltage and C-ratings.

B. Analysis of Operation

The Bidirectional charging systems are basically intended to operate in two modes, charging and discharging mode. In discharging mode or inverting mode, the battery supplies power to the grid. This operation is termed as V2G operation. In charging or rectification mode, the power is provided by the grid to the battery. This operation is termed as G2V operation. The overall design must use the same hardware for two modes of operation and thus it has the bidirectional power flow functionality. The entire power flow of the BCCS system during G2V and V2G operation is based on the command from the grid.

Cp

AC to AC

EV’s Battery system

SVPWM Controller

High frequency controller

Fuzzy logic based controller board

Charging station

AC - DC Driver Board

SVPWM Controller

DC - DC Driver Board

Fuzzy Logic control

Cs

AC-DC-AC Driver Board

Fig. 3. Typical layout of the single unit of Bidirectional Contactless Charging System

IV. MODELLING OF THE SYSTEM The modeling of the complete BCCS system involves the

design of contactless coils and Parameter extraction of battery model using Genetic Algorithm (GA) approach. This section explains the design details of contactless coil and Extraction of polynomial coefficient of the circuit based battery model.

A. Design of Contactless Coils The design process of contactless coil requires the

determination of a number of electrical parameters such as maximum operating frequency, primary and secondary voltage and current, input power and output power transferred to the load etc. Considering all the above factors, a detailed design procedure for rectangular with planar coil distribution has been already reported in literature [3], only a brief description is given here. The design of contactless coil involves the calculation of self ( , )p sL L and mutual ( )M inductance with

compensation capacitors ,p sC C . The design of BB converter

includes boost inductor ( )bL with input-output capacitors

1( )bC and 2( )bC . The values of , , ,p s pL L M C and sC are designed based on Neumann’s formula and equations explained in [3]. Coupling factor k of 0.17 is chosen, which provides a measure of total coupling within the system. The input filters ( , )f fL C and the charging station inverter’s filter ( )C are designed based on the equations [15].

B. Extraction of Polynomial Coefficients of Battery As mentioned earlier, the EC based battery models

accurately determines the performance of V2G system. The parameters of Electric Circuit (EC) based battery model explained in section II are represented in terms of polynomial equations. The polynomial coefficients are extracted using Genetic Algorithm (GA) approach. The optimization procedure used for extracting the parameters using GA approach is reported in literature [11]. Table I and II below shows the extracted polynomial coefficient of 300V, 7Ah

battery for charging and discharging scenarios. TABLE III

POLYNOMIAL COEFFICIENTS FOR CHARGING CONDITION

Polynomial Coefficients(Coeff) for charging scenario (Coeff) Values (Coeff) Values (Coeff) Values

a1 0.000225 a11 25.471252 a21 0.000637 a2 0.000987 a12 0.006872 a22 0.000126 a3 0.000035 a13 0.000426 a23 36.780107 a4 32.879520 a14 0.000035 a24 314.068640 a5 0.014569 a15 9.654871 a25 0.188108 a6 0.000453 a16 0.459870 a26 0.032145 a7 0.000031 a17 0.000028 a27 0.002864 a8 0.008412 a18 0.0066821 a28 0.269874 a9 0.000482 a19 154.235634 a29 0.023145 a10 0.0000031 a20 0.001105 a30 120.000602

a31 10.000422

TABLE III

POLYNOMIAL COEFFICIENTS FOR DISCHARGING CONDITION

Polynomial coefficients (Coeff) for charging scenario(Coeff) Values (Coeff) Values (Coeff) Values

a1 0.000050 a11 20.001425 a21 0.002661 a2 0.003021 a12 0.010070 a22 1.000000 a3 0.000398 a13 0.000880 a23 15.00000 a4 30.210540 a14 0.000029 a24 310.236547 a5 0.040125 a15 1.120032 a25 0.2301240 a6 0.003147 a16 0.010693 a26 0.1001201 a7 0.000300 a17 0.004548 a27 0.020001 a8 0.020000 a18 50.909916 a28 0.015002 a9 0.001000 a19 1.503659 a29 0.000101 a10 0.000100 a20 0.0012389 a30 0.010000

a31 70.232012

V. CONTROLLER DESCRIPTIONS Suitable controllers are used in BCCS system during G2V

and V2G operation. This section explains the description about the controllers.

A. G2V Controllers During G2V operation, the diode rectifier in the BCCS

system converts 50Hz, grid voltage to dc voltage. The dc voltage in turn converted to high frequency ac voltage by the

resonant inverter and is given to contactless system. The high frequency is generated, by sensing the inductor primary current in conjunction with the square wave pulse generator of frequency 25 kHz. The secondary side of the coreless coil has a bidirectional converter, which convert’s ac to dc. Further, the dc voltage is given as input to the dc/dc interface connected, the battery. The charging current of the dc-dc converter is controlled by a fuzzy controller shown in Figure.4

Fig.4. Controllers in G2V operations

B. V2G Controllers During V2G operation, the voltage from the EV battery

supplies power to the grid. Fig.5. shows the controller descriptions in V2G mode. During this mode, the BB converter in the EV battery system maintains the 440V dc irrespective of the battery voltage. It is further converted to high frequency ac voltage for contactless system.

Fig.5. Controllers in V2G operations

The contactless system transfers the power to charging station inverter at a transmission frequency of 25 kHz. In the charging station inverter, the high frequency ac voltage is converted to dc voltage using the reversible diode. The dc voltage is converted to 50Hz ac voltage by the inverter using SVPWM (Space-Vector PWM) technique, which gives a linear control of output voltage over the whole modulation range.

C. Fuzzy P controller Fuzzy based Proportional (Fuzzy P) controller is used to

control the current in the battery as shown in Fig.4 and 5. Seven fuzzy subset NB (Negative Big), NM (Negative Medium), NS (Negative Small), Z (Zero), PS (Positive Small), PM (Positive Medium), PB (Positive Big) have been chosen for iL and for the output VVS (Very Very Small), VS (Very

Small), S (Small), M (Medium),B (Big), VB (Very Big), VVB (Very Very Big) are chosen in order to obtain the required control action. The membership functions and rule bases are shown in Fig.6.

Error

Reference

Fig.6. FLC a) Input b) Output c) Rule Base

VI. RESULTS AND DISCUSSION BCCS system with battery model explained in sections II,

III, IV and V has been modeled for the parameters shown in Table III. The entire system is designed with contactless coil for the power handling capacity of 2kW at a frequency rating of 25 kHz.

TABLE III CIRCUIT PARAMETERS OF THE PROPOSED BCPT SYSTEM

Parameter Value Parameter

Value

1 2, ,b b bL C C

4.5mH, 0.36mF, 3.97mF ,p sL L

1.384mH, 1.384mH

C 454μF ,M k

0.24017mH, 0.1735

,f fL C 35mH, 109μF ,p sC C

0.023μF, 0.023μF,

The complete BCCS unit with circuit based battery model and its associated controllers are tested by simulation for the parameters shown in Table III, with a single node a real time grid data of Guwahati city [14]. The system is tested for both V2G and G2V to examine its bidirectional functionality. This section reports, the simulated results of the system during V2G and G2V operations, which is shown in Fig.7-19.

Fig.7. Charge and discharge rate characteristics of battery model at 1C rate

Fig.8. Charge and discharge rate characteristics of battery model at 2C rate

Fig.7-8, shows the charge and discharge rate characteristics of 300V, 7Ah battery at 1C and 2C ratings.

Fig.9. Battery terminal voltage, during G2G mode

Fig.10. Battery terminal voltage, during V2G mode

Fig.11. Line-Line voltage across the transformer, during G2V

Fig.12. Rectified voltage of charging station converter during G2V

Fig.9-10, shows the battery terminal voltage during charging and discharging operating modes. Fig.11 shows the three phase output waveform of the charging station transformer supplied from the grid. Fig. 12 shows the output of the 540V charging station converter during G2V operation.

Fig.13. Voltage input of dc/dc interface during G2V mode

Fig.13. shows the load voltage of 200V, as the output of ac-dc converter in EV battery system. The charging current of the BCCS system with battery model is controlled by a simple fuzzy based P controller explained in section V. Fig.14 shows the regulated battery current of the BCCS system maintaining 6.5A at 1 C rating. Fig.15 shows the controller maintains 2kW power during G2V mode.

Fig.14.Charging current of 300V, 7Ah at 1C, G2V mode

Fig.15. 2kW power supplied from the grid, during G2V mode

Fig.16 shows the inverter maintains a constant DC voltage of 640V. Then further it is converted to ac using SVPWM explained in Fig.4. The synchronization event is shown in Fig.17, before and after the closing of Circuit Breaker (CB). The grid voltage and inverter voltage is in floating condition before giving the CB signal. When the circuit breaker signal is given, the inverter or grid voltage leads or lag with respect to the grid voltage for power transfer. In Fig.17, the inverter voltage leads the grid voltage; due to this phase difference inverter supplies power to the grid.

Fig.16. Inverter input voltage at charging station during V2G mode

Fig.17. Inverter Voltage leads grid voltage while supplying power to Grid

Fig.18-19, shows the discharging current and power during V2G mode. The battery discharges at 1C and supplies 2kW power to the grid. The performance curves are matching with the reference, which shows the effectives of the proposed controllers in V2G mode.

Fig.18.Discharging current of 300V, 7Ah at 1C, G2V mode

VII. CONCLUSION This paper describes the performance of the Bidirectional

Contactless Charging System (BCCS) with an electric circuit based battery model. The time, C-rate, and SOC dependent electric circuit parameters of the battery model are calculated using a polynomial equation. The coefficients are calculated by an optimization process using Genetic Algorithm approach. Suitable controllers are developed for the functioning of BCCS unit. The performance of V2G system is accurately predicted by the BCCS unit with this battery model. The simulation results of the system reveals that the overall efficiency of the proposed battery model with charging system can achieve an efficiency of 92%.

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Fig.19. Power supplied to the grid during V2G mode