1

Individual Cell Equalization for Series Connected Lithium-Ion Batteries

*Yuang-Shung Lee,1a) Ming-Wang Cheng,2,3b) Shen-Ching Yang1, Co-Lin Hsu1 1Department of Electronic Engineering Fu-Jen Catholic University 510 Chung-Cheng Rd., Hsin-Chuang, Taipei 24205, Taiwan Tel: +886-2-29031111-3791 Fax: +886-2-29042638 2Graduate Institute of Applied Science and Engineering, Fu-Jen Catholic University 3Industrial Technologies Research Institute, Blog77,195-5 Chung Hsing Rd. Section 4, Chutung, Hsinchu, 31015, Taiwan a) lee@ee.fju.edu.tw b) MWCheng@itri.org.tw

Abstract: A systematic approach to the analysis and design of a bi-directional Ck converter for the cell voltage balancing control of a series-connected lithium-ion battery string is presented in this paper. The proposed individual cell equalizers (ICE) are designed to operate at discontinuous-capacitor-voltage mode (DCVM) to achieve the zero-voltage switching (ZVS) for reducing the switching loss of the bi-directional DC/DC converters. Simulation and experimental results show that the proposed battery equalization scheme can not only enhance the bi-directional battery equalization performance, but also can reduce the switching loss during the equalization period. Two designed examples are demonstrated, the switch power losses are significantly reduced by 52.8% from the MOSFETs and the equalization efficiency can be improved by 68~86.9% using the proposed DCVM ZVS battery equalizer under the specified cell equalization process. The charged/discharged capacity of the lithium-ion battery string is increased by using the proposed ICEs equipped in the battery string.

Keywords: Bi-directional converter, DCVM Ck converter, Lithium-ion battery, Individual cell equalizer, ZVS References 1. H. V. Venkatasetty, and Y. U. Jeong, Recent Advanced in Lithium-Ion and Lithium-Polymer Batteries, Proceeding of

Battery Conference on Applications and Advances, The Seventeenth Annual, Jan. 2002, pp. 173-178. 2. J. McDowell, A. Brenier, M. Broussely, and P. Lavaur, Industrial Lithium-Ion Batteries: From The Laboratory to Real

Telecom Application, Proceeding of Telecommunications Energy Conference, INTELEC 24th Annual International, Sept. 2002, pp. 373-378.

3. N. H. Kutkut, A Modular Nondissipative Current Diverter for EV Battery Charge Equalization, Proceeding of Applied Power Electronics Conference and Exposition, APEC'98, Thirteenth Annual, Vol. 2, 1998, pp. 686 -690.

4. K. Nishijima, H. Sakamoto, and K. Harada, A PWM Controlled Simple and High Performance Battery Balancing System, Proceeding of IEEE Power Electronics Specialists Conference, PESC00, IEEE 31st Annual, Vol. 1, 2000, pp 517 -520.

5. Z. Zhang, and S. Ck, A High Efficiency 1.8 kW Battery Equalizer, Proceeding of IEEE Applied Power Electronics Conference and Exposition, APEC '93, Eighth Annual, 1993, pp. 221 227.

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6. Toshio Matsushima, Shinya Takagi and Seiichi Muroyama, Rack-Mounted DC Power Supply Utilizing Li-Ion Batteries for Backup, IEICE Transactions on Communications, Vol. E88-B, No. 11, 2005, pp. 4353-4359.

7. W. F. Bentley, Cell Balancing Considerations for Lithium-Ion Battery Systems, Proceeding of the 1997 Battery Conference on Applications and Advances, Twelfth Annual, 14-17, Jane, 1997, pp. 223-226.

8. S. W. Moore, and P. J. Schneider, A Review of Cell Equalization Methods for Lithium Ion and Lithium Polymer Battery Systems, SAE Technical Paper Series, 2001-01-0959, March, 5-8, 2001, pp. 1-5.

9. Y. S. Lee and C. W. Jao, Fuzzy Controlled Lithium-Ion Battery Equalization with State-of-Charge Estimator, Proceeding of 2003 IEEE International Conference on System, Man and Cybernetics, IEEE CSMC2003, pp. 4431-4438.

10. J. Chatzakis, K. Kalaitzakis, N. C. Voulgaris, and S. N. Manlas, Designing A New Generalized Battery Management System, IEEE Transaction on Industrial Electronics, Vol. 50, No. 5, 2003, pp. 990-999.

11. Tosiba Matsushima, Shinya Takagi, Seiichi Muroyama and Toshio Horie, Fundamental Characteristics of Stationary Lithium-Ion Secondary Cells and A Cell-Voltage-Equalizing Circuit, IEICE Transactions on Communications, Vol. E88-B, No. 8, 2005, pp. 3436-3442.

12. P. Melin and O. Castillo, Intelligent Control of Complex Electrochemical System with A Neuro-Fuzzy-Genetic Approach, IEEE Transaction on Industrial Electronics, Vol. 48, No. 5, 2001, pp. 951-955.

13. D. Maksimovic and S. Ck, A Unified Analysis of PWM Converters in Discontinuous Modes, IEEE Transactions on Power Electronics, Vol.6 No.3, July 1991, pp. 476 490.

14. M. Brkovic and S. Ck, Automatic Current Shaper with Fast Output Regulation and Soft-Switching, Telecom Energy Conference, INTELEC93, 15th International Conference, Vol. 1, Sept. 1993, pp. 379-386.

15. K. K. Tse, M. T. Ho, H. S. H. Chung and S. Y. Hui, A Novel Maximum Power Point Tracker for PV Panels Using Switching Frequency Modulation, IEEE Transaction on Power Electronics, Vol. 17, No. 6, 2002, pp. 980-989.

16. Bo-Tao Lim and Yim-Shu Lee, Power-Factor Correction Using Ck Converter in Discontinuous Capacitor Voltage Mode Operation, IEEE Transaction on Industrial Electronics, Vol. 44, No. 5, 1997, pp. 648-653.

17. D. S. L. Simonetti, J. Sebastian and J. Uceda, The Discontinuous Conduction Mode Sepic and Ck Converter Power Factor Preregulators: Analysis and Design, IEEE Transaction on Industrial Electronics, Vol. 44, No. 5, 1997, pp. 630-637.

18. G. Spiazzi, P. Mattavelli, L. Rossetto and S. Buso, High-Quality Rectifier Based on Ck Converter in Discontinuous Capacitor Voltage Mode, European Power Electronics Conference, Vol. 2, Sept. 1995, pp. 385-390.

19. H. S. H. Chung, K. K. Tse, S. Y. Ron Hui, C. M. Mok and M. T. Ho, A Novel Maximum Power Point Tracking for Solar Panels Using a Sepic and Ck Converter, IEEE Transaction on Power Electronics, Vol. 18, No. 3, 2003, pp. 717-724.

20.Yan-Fei Liu, Requirements and Technologies in Telecom Power System, International Power Electronics and Motion Control Conference, PIEMC2000, Vol. 3, August 2000, pp. 1478-1482.

21.Yuang-Shung Lee and Jiun-Yi Duh, Fuzzy Controlled Individual-Cell Equalizer Using Discontiunous Inductor Current Mode Ck Converter for Lithium-Ion Chemistries, IEE Proceedings Electric Power Applications, Vol. 152, No. 5, September 2005, pp. 1271-1282.

* To whom all correspondence should be addressed.

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1. Introduction

Because a single battery cell voltage is limited due to the active materials chemistry, battery cells connected in

series are usually employed in many applications, such as electric vehicles (EV), hybrid electric vehicles (HEV),

or telecom battery energy systems. Imbalanced cell voltage within a series string can be attributed to the

differences in the cells internal resistance, imbalanced state-of-charge (SOC) between cells, degradation and the

ambient temperature gradients of the battery pack during charging and discharging. Voltage monitoring and

current diversion equalization schemes and battery management systems (BMS) have been presented in the

literature to prevent imbalances during charging and discharging in a series connected battery cells [1]-[3].

Integrated individual cell equalization schemes (ICE) for battery pack applications have been proposed to

equalize battery strings [3]-[6]. The bidirectional battery equalization scheme has many advantages such as

higher equalization efficiency for non-dissipative current diverters, and a modular design approach [3]. The

disadvantage of this equalization scheme is that the stored energy in the inductor is transferred to the weaker cell

only in the (1-D)Ts duty cycle. The equalization time and efficiency of this equalization scheme are therefore

poor for practical battery equalization applications in a smart battery management system (SBMS) [6]-[11].

Battery equalization control should be implemented to restrict the charge-discharge current to the allowable cell

limitations in the battery string. Cell balancing control is designed to obtain the maximum usable capacity from

the battery string. However, battery string charging and discharging are limited by any single cell reaching its

end-of-charge voltage and by low voltage threshold, respectively. Cell balancing algorithms search to efficiently

remove energy from a stronger cell and transfer that energy into a weaker one until the cell voltage is equalized

across all cells. This enables additional charging capacity for the entire battery string [4]. Complete cell voltage

balancing is performed using a bi-directional dc-dc converter based on the Ck converter [9], [11]. This unit can

be designed to operate at the DICM or DCVM to obtain soft switching in MOSFET switches [11]-[15].

The discontinuous conducting mode of a Ck converter is generally of used in applications of the power

factor correction technology [16]-[18] and the maximum power point tracker of PV panels [15],[19]. The analysis

and design of the uni-directional power flow control scheme Ck converter in discontinuous capacitor voltage

mode (DCVM) was already discussed in [15],[16],[18]. The aforementioned analysis and design method of the

uni-directional Ck converter operated at DCVM can not be totally adopted for the battery equalization

4

application due to the alternating characteristics of the cell voltage balancing process in the charge/discharge of

battery string [3],[4],[7]-[9]. The continuous and discontinuous inductor current modes of the bi-directional Ck

converter application for cell voltage balancing control of lithium-ion battery strings were investigated in

literatures [11] and [20,21], respectively. The main contribution of this paper is the first application of the

bi-directional Ck converter operating at DCVM in the design and analysis of the individual cell equalization

control of the lithium-ion battery strings. Two designed cases are used to demonstrate the performance in the

proposed ICEs for reducing the switching power losses of the MOSFET switches and increasing the equalization

efficiency and battery string capacity.

The consideration and experience for the cell balancing control system of a lithium ion battery

string are summarized as follows [8,11,21]:

The equalization algorithm will be started when the voltage difference between two adjoining cells

exceeds 0.0196 (V) (hardware resolution limit of A/D converter, ADC0804) to minimize the

cell-to-cell imbalance.

During the charged equalization state, the cell voltage can not exceed its end-of-charge voltage

(about 4.1V/cell) to prevent overcharging to damage the active materials.

During the discharged equalization state, the cell voltage can not go below its low voltage threshold

(about 2.8 V/cell) to prevent overdischarge and damaging the cell capacity and life.

When the voltage difference between adjoining cells is large then it needs a higher equalization

current to speed up the time required to execute a balancing algorithm, the maximum equalization

current limit is 2.5 A.

When the voltage difference between adjoining cells is small then it needs a small equalization

current to prevent low voltage cell overdischarge, the minimal equalization current limit is 0.5 A.

If either a cell voltage in the battery string exceeds its end-of-charge voltage during charge

equalization state, or one cell voltage in the battery string reaches its low voltage threshold during

discharge equalization, the BMS will send a command to stop the cell voltage balancing process.

5

Fig. 1 Studied battery charging system with ICE and microprocessor based BMS

2. Topologies description of the ICEs

The studied battery charging system with the proposed ICEs and the microprocessor based BMS is shown in

Fig. 1. The system is composed of N battery cells and (N-1) ICEs. The jth module is comprised of two inductors

Lj and Lj+1, an energy transfer capacitor Cj, and two power MOSFETs with body diodes as the battery

cell-balancing switches. The single module of the ICE is redrawn and simplified in Fig. 2. The cell voltage

balancing control algorithm for this equalization scheme is instructed by a microprocessor-based BMS. The

energy between the adjoining battery cells is transformed through the energy transferring capacitor for cell

6

voltage balancing. The energy transfer direction is determined by the cell voltage and/or SOC difference in the

battery string and conduction from the controlled power MOSFET switches [9]. The two adjoining cells voltages

are balanced by switching the MOSFETs on/off according to the PWM signals generated from the BMS. The

PWM signals correspond to the respective cell voltage through the microprocessor-based BMS, which controls

the switches Qj and Qj+1. The initial capacitor voltage VCj equals VBj+VBj+1. For example, the PWM control signal

turns on/off the Qj to transfer some of the stronger cell voltage, VBj, to the weaker cell, VBj+1. The stronger cell

energy is transferred from cell VBj to cell VBj+1. Conversely, if the cell VBj+1 is stronger than cell VBj, the stored

chemical energy is transferred from cell VBj+1 to cell VBj by controlling the Qj+1. The equalization process will be

uninterrupted until the voltages in the remaining cells are all equalized to the same end-of-charge or

end-of-discharge level. The proposed bidirectional battery equalizer is designed to operate at DCVM for

achieving the zero voltage switching to reduce the MOSFETs switching losses. The DCVM operation principle

of proposed ICE is described in the following section.

Fig. 2 Single stage of the proposed ICE

7

Fig. 3 Equivalent circuit of DCVM for VBj > VBj+1

(a) Qj turn-on, (b) Qj and Dj+1 turn-on, and VCj = 0, (c) Qj turn-off and Dj+1 turn-on

8

Fig. 4 Equivalent circuit of DCVM for VBj < VBj+1

(a) Qj+1 turn-on, (b) Qj+1 and Dj turn-on and VCj = 0, (c) Qj+1 turn-off and Dj turn-on

9

5. (a)

5. (b)

Fig. 5 Typical switching waveforms of ICEj for (a) VBj>VBj+1, (b) VBj

10

in Figs. 3 and 4 during the various time intervals for the different cell voltage, VBj > VBj+1 and VBj < VBj+1,

respectively. The corresponding typical switching waveforms for various operating states are depicted in Figs. 5

(a) and 5 (b), respectively. Referring to the capacitor voltage waveform and the dynamic state equations of the

ICE in Fig. 5 (a) for VBj > VBj+1 can be explained as follows:

Assume the capacitor voltage cj has reached a maximum before the main switch Qj is turned on. From the duty

cycle t0 to t1 = D1Ts, the switch Qj is turned on and diode Dj+1 is turned off at the beginning of the switching cycle

t0 = 0, as shown as Fig. 3 (a). The inductor Lj is charged by input voltage VBj and the current iLj+1 through inductor

Lj+1 is discharged by capacitor Cj. The energy stored in Cj is completely transferred to the cell VBj+1, and cj

becomes to zero at t1 = D1Ts. From the duty cycle t1 = D1Ts to t2 = DTs, the switch Qj was still on and Dj+1 starts

conducting to allow iLj+1 to flow since cj is equal to zero during this interval, as shown as Fig. 3 (b), VBj

continues to charge Lj and the stored energy in Lj+1 is still discharged to VBj+1 for cell voltage balancing control.

From duty cycle t2 = DTs to t3 = Ts, the switch Qj is turned off at t2 = DTs, and Dj+1 is still on for cell voltage

balancing. Capacitor Cj is charged from zero voltage by iLj. The capacitor voltage cj reaches maximum value at t3

= Ts, as shown in Fig. 3 (c). The proposed ICE has more than one stage, in contrast to a Ck converter operating

in CICM, where both the MOSFET switch Qj and flywheel diode Dj+1 are conducting in the DCVM operation, as

shown in Fig. 3(b). The dynamic equations of the equivalent circuit for VBj > VBj+1 in Fig.3 can be expressed by

the following:

Stage 1 ( 0 1t t t < ), Fig.3 (a) shows that Qj is turned on and Dj+1 is turn-off, and denoted the switching variable u

=1 (HIGH state):

( )Lj

j S Lj Bj BjI i Rdi

L Vdt

= + , 0 0( )L ji t I= (1)

11 1 1 1( )

Ljj S Lj Bj C j Bj

diL I i R v V

dt+

+ + + += + + , *

1 0 0( )Lji t I+ = (2)

1C j

j L j

d vC i

d t += , 0( )C j C Pv t V= (3)

Stage 2 ( 1 2t t t < ), Fig. 3 (b) shows that Qj is still turned on and Dj+1 is forced to start turn-on when cj = 0, and

denoted the switching variable u = 0.5 (FLOATING state):

( )Lj

j S Lj Bj BjI i Rdi

L Vdt

= + , [ ]1 1 01

( )( ) PL j

D I D D Ii t

D+

= (4)

11

11 1 1 1( )

Ljj S Lj Bj Bj

diL I i R V

dt+

+ + + += + ,* *

1 1 01 1

( )( )

PLj

D I D D Ii t

D+ + = (5)

0C jv = (6)

Stage 3 ( 2 3t t t < ), Qj is turned off and Dj+1 is still turned on, and denoted the switching variable u = 0 (LOW

state):

1( )Lj

j S Lj Bj Cj Bj

diL I i R v V

dt += + + , 2( )Lj Pi t I= (7)

11 1 1 1( )

Ljj S Lj Bj Bj

diL I i R V

dt+

+ + + += + , *

1 2( )Lj Pi t I+ = (8)

C jj L j

d vC i

d t= , 2( ) 0C jv t = (9)

The compact state equation for describing of the three states mentioned above can be combined and simplified as:

1 1 111

1 1 1

1(1 )( ) 220

12 ( )20

1 12(1 )( ) 2 ( )2 2 00

j

j j

j j j

BB s B

Lj j jj

LjB B s BLj

Ljj j j

CjCj

j j

u uRV I Rdi L L

Ldt iu uR V I Rdii

dt L L Lvdv

u u u udtC C

+ + +++

+ + +

+ + = +

(10)

where u is a tri-state switching control variable. It is also suggested that u = 1 (HIGH state) denotes Qj turn-on

and Dj+1 turned off shown as Fig. 3 (a), u = 0 (LOW state) denotes Qj is turned off and Dj+1 is turned on shown as

Fig. 3 (c), and u = 0.5 (FLOATING state) denotes Qj and Dj+1 are both turned on and cj = 0 shown as Fig. 3 (b).

The internal resistance of battery cell RB is neglected to simplify the steady state circuit analysis, and the

charging/discharging source effect is absent in the principle operation of the converter.

If Lj and Lj+1 are large enough, the ripples in iLj and iLj+1 are small. The time average values of iLj and iLj+1 are

denoted as ILj and ILj+1, respectively. From Fig. 5(a), the conditions of DCVM operation can be derived as follows.

The instantaneous capacitor voltage in the full duty cycle of the DCVM Ck converter can be expressed by

12

11 S

1 S S

S S

(1 ), for 0 t D T

0, for D T t DT ( )

, for DT t T

Lj S Lj

j

Cj

j S

j

I D T I tC

I t DTC

+ <

13

1

1

1(1 )

2

B j

S j

jDV

Lf I

+

+

+

(22)

The switching boundary surface of the converter to operate between DCVM and continuous-capacitor-voltage

mode (CCVM) is depicted in Fig. 6. However, the proposed converter may not operate in DCVM when VBj is

small because the cell voltages do not have constant dc voltage and depending on the equalization current of the

ICE, therefore, the inequalities (20), (21) and (22) are used to design the proposed ICE that can be guaranteed to

operate in DCVM [15], [16].

Voltage (V)

Dut

y cy

cle

(D)

Current (I) Voltage (V)

Dut

y cy

cle

(D)

Current (I)

DCVM

CCVM

Voltage (V)

Dut

y cy

cle

(D)

Current (I) Voltage (V)

Dut

y cy

cle

(D)

Current (I)

DCVM

CCVM

Fig. 6 Switching boundary surface between DCVM and CCVM

14

Fig. 7 Configuration of MATLAB/SimuLink model

15

Fig. 8 Simulation results

9. (a)

(s) (V)

(V)

(V)

(A)

(A)

Time (ms)

16

Vgs Vc

Vc(V)

Vgs

(V)

5V/div 1A/div 20us/div Time(sec)

Vgs Vc

Vc(V)

Vgs

(V)

5V/div 1A/div 20us/div Time(sec)

9. (b)

9. (c) Vgs VT

VT(V

) V

gs(V

)

5V/div 5V/div 10us/div Time(sec)

Vgs VT

VT(V

) V

gs(V

)

5V/div 5V/div 10us/div Time(sec)

9. (d)

Fig. 9 Simulation and experimental results of MOSFET control signal Vgs and drain-source voltage VT for VB1>VB2>VB3, (a)(c) Simulations, (b)(d) Experiments

4. Simulation and experimental results

4.1 Three lithium-ion cells module (n=3)

In order to validate the performance of the proposed bi-directional battery equalizer, a Matlab/Simulink

simulation and an experiment were carried out for a three cells battery module (n=3) with the two proposed

battery equalizers (2 ICEs). Matlab/Simulink simulation was performed for mathematical model of ICEs. A

three-modular battery stack with two proposed equalization schemes was used to verify the analysis results

mentioned above. The simple signal flow graph is defined using Matlab/Simulink simulation for the proposed

(s) (V)

17

ICE Matlab/Simulink model for a three battery-cell, the ICE1 (composed of L1, L2, C1, Q1 and Q2) and the ICE 2

(composed of L3, L4, C2, Q3 and Q4) comprise the block diagram shown in Fig. 7. The battery storage elements

were simply assumed for the battery charge/discharge model, which was established by a battery

charge/discharge profile with equivalent series resistor (ESR) from the library of the Matlab/simulink block

model. The battery initial voltages, inductors and energy transferring capacitor with ESR were set as VB1 = 4.0

(V), VB2 = 3.9 (V), VB3 = 3.6 (V), L1 = L2= L3= L4 = 230H and C1 = C2 = 0.66F with ESR = 0.001,

respectively. The switching frequency was 16.67 kHz and the duty ratio was D = 0.53 for both VB1>VB2>VB3 and

VB1VB3 are shown in Figs.

9 (a) and 9 (c). The simulation results of the cell voltage trajectories under static state, added 1A charging and

discharging current states of the proposed battery equalizer are illustrated in the Figs. 10 (a), (c) and (e),

respectively. The cell balancing process is stopped when the cell voltage is equalized to the same end-of-charge

or end-of-discharge state.

The experimental installation of a three-modular lithium ion battery stack with the proposed equalization

scheme is used to verify the equalization performance of the three cells battery stack with the proposed ICEs. The

driving signals for the equalization schemes are controlled using a microprocessor-based battery management

system according to each cell voltage. The driving signals are constructed using a logical switching algorithm,

and instructed by the BMS processor of AT89C52. Cell voltages were balanced within 0.0196 (V), due to the

hardware resolution, which was limited by the analogue to digital converter (ADC0804). The voltage balancing

process is stopped when the BMS sends an executable command to cut off the MOSFET. The experimental

parameters of the batteries and the designed ICEs are listed as follows: The initial voltages of the three lithium

ion batteries MRL/ITRT 10AH are 4.0 (V), 3.5 (V), and 3.0 (V), respectively. The MOSFETs with body diodes

are IRF530. The inductances are L1~L4 = 230H, C1 = C2 = 0.66F. The switching frequency and the duty ratio of

the battery equalizer are 16.67 kHz and 0.53, respectively.

18

Figs. 9 (b) and 9 (d) show the measured voltages of Vgs, Vc, and MOSFET drain-source voltage VT,

respectively. The transient oscillations in the drain-source voltage of MOSFET due to the fast switching transient

effect can be suppressed by well designed turned off DRC snubber circuits in the switching devices. Figs. 10 (b),

(d) and (f) show the experimental results of the cell voltage trajectories under static state, added 1A charging and

discharging current states of the proposed battery equalizers. Therefore, the equalization method can balance all

the adjoining cell voltages of the battery string to the same voltage level. Consequently, each cell can be

simultaneously charged to the end-of-charge voltage, so the total charging capacity of the battery string would be

increased. Fig. 11 shows the waveform and the corresponding FFT spectrum of MOSFET switch power losses,

PT = VT * iT. The experimental results of the equalization efficiency of ICE under various operating modes for the

specified equalization processing are shown in Fig. 12 (a). The average equalization efficiency of the ICE

operated as DICM can be improved from 52% to 60% compared with the equalizer operated as CICM, the

maximum equalization efficiency can achieved 62% for this designed test sample. When it is designed as DCVM,

the total power losses of the MOSFETs in the battery equalizer can be significantly reduced from 33.5% to 52.8%

compared with the same equalizer operated at CICM. The average equalization efficiency can be improved from

52% to 68% compared with the equalizer operating as CICM, and the maximum equalization efficiency can

achieve above 70% for this designed case. Using optimally designed passive elements and active devices the

equalization efficiency can reasonably improve. The experimental installation of the proposed equalizer is

redesigned by the following devices: The MOSFET is chosen as a SBL1040, Schottky diode is selected

AM20N06-90D, and the low ESR inductor is wound by a stranded-wires PVF (0.4mm4) around a SENDUST

core. Fig. 12 (b) shows the equalization efficiency of the reformed equalization scheme under a specified

equalization process, the average and the maximum equalization efficiency can achieve 86.9% and 89.8%,

respectively. The alternating soft switching technology in the ICE design for a future study can significantly

improve efficiency. Table 1 shows the differentially designed results and performance comparison of the ICEs

operated at CICM, DICM and DCVM under the specified equalization procession and equalizing current,

respectively. Several observations and comparison about the proposed battery equalizer can be summarized as in

the following section.

19

10(a) 10(b)

10(c) 10(d)

10(e) 10(f)

Fig. 10 Simulation and experimental results of cell voltage trajectories for VB1>VB2>VB3, (a) (b) static state, (c) (d)

added 1A charging current, (e) (f) added 1A discharging current

(ms)

(ms)

(ms)

VB1 VB2

VB3

VB1 VB2

VB3

VB1

VB2

VB3

(V)

(V)

(V)

20

11. (a) 11. (b)

Fig. 11 (a) Waveform and, (b) FFT spectrum of MOSFET switch power losses

Fig. 12 (a)

21

Fig. 12 (b)

Fig. 12 Equalization efficiency of ICE under various operating modes

(a) Original equalization scheme (b) Reformed equalization scheme

22

Table 1 Comparisons between continuous and discontinuous modes

CICM DICM DCVM

Inductor (Lj) 98.3H 100.5H 229.2H

Inductor (Lj+1) 100.7H 101.2H 230.3H

Capacitor (Cj) 470F 470F 0.66F

Switching Frequency (fs)

18.1 kHz 16.67 kHz 16.67 kHz

Duty Cycle (D) 0.53 0.5 0.5

Boundary Condition

1

11

1

21

2)1(

2)1(

+

++

+

+

>

>

j

jsj

j

jsj

IDV

fL

IDDV

fL

1

11

1

21

2)1(

2)1(

+

++

+

+

23

initial voltages of the twelve lithium ion batteries MRL/ITRT 50AH in charging and discharging test are shown

in the below of Figs. 13, 14, 15 and 16, respectively. The MOSFETs with body diodes are IRF530. The design

parameters, switching frequency and the duty ratio of the eleven ICEs are the same as the aforementioned testing

case. Figs. 17 (a) and 17 (b) show the photography of the 12-cells lithium-ion battery pack and the prototype of

the proposed ICEs. Two schemes, one is battery string without ICEs and the other is with ICEs are used to

demonstrate the performance of the proposed equalization method. The automatic battery testing equipment is

MACCOR 4000, the charging and discharging testing cycles are set as follows:

CHARGING

STEP_1 I=25A

A: Voltage50.4V NEXT STEP

B: Cell Voltage4.2V NEXT STEP

C: T50 STOP

STEP_2 I=10A

A: Voltage50.4V NEXT STEP

B: Cell Voltage4.2V NEXT STEP

C: T50 STOP

STEP_3 I=5A

A: Voltage50.4V NEXT STEP

B: Cell Voltage4.2V NEXT STEP

C: T50 STOP

STEP_4 I=2.5A

A: Voltage50.4V STOP

B: Cell Voltage4.2V STOP

C: T50 STOP

DISCHARGING

I=50A

A: Voltage33V STOP

B: Cell Voltage2.75V STOP

C: T50 STOP

24

Figs. 13 and 14 show the charging/discharging cell voltages and the modular capacity under the charging test

for the string without and with the proposed ICEs. The final states of the battery string are: the maximal cell

voltage deviation is 52mV, the total charging capacity is 2440 Whr and the charging time for reaching the

end-of-charge state is 131.45 minutes for the string without ICEs. When the system is equipped with the

proposed ICEs, the maximal cell voltage deviation is decreased to 20 mV, the total charging capacity is increased

to 2480 Whr and the charging time for reaching the end-of-charge state is extended to 143.36 minutes. Figs. 15

and 16 show the discharging cell voltages and the modular capacity under discharging test for the same testing

schemes. The final states of the battery string are: the maximal cell voltage deviation is 0.63V, the total

discharging capacity is 2343 Whr and the discharging time for reaching the end-of-discharge state is 61.46

minutes under the string without ICEs. When the system is equipped with the proposed ICEs, the maximal cell

voltage deviation is decreased to 37 mV, the total discharging capacity is increased to 2379 Whr and the

discharging time for reaching the end-of-discharge state is extended to 65.43 minutes. By using the proposed

ICEs for the lithium-ion battery string, each cell can be simultaneously charged/discharged to the

end-of-charge/discharge state. The total charging/discharging capacity of the battery string is improved under the

safe operation specifications.

25

0.00 2000.00 4000.00 6000.00 8000.00 10000.00

3.20

3.40

3.60

3.80

4.00

4.20

Legend Title

Cell 1

Cell 2

Ceii 3

Cell 4

Cell 5

Cell 6

Cell 7

Cell 8

Cell 9

Cell 10

Cell 11

Cell 12

0.00

500.00

1000.00

1500.00

2000.00

2500.00

Legend Title

Whr

Initial and final cell voltage for charging test

Module Data Cell Voltage

Time Voltage Ahr Whr Cell_1 Cell_2 Cell_3 Cell_4 Cell_5 Cell_6 Cell_7 Cell_8 Cell_9 Cell_10 Cell_11 Cell_12

Time Voltage Ahr Whr Cell_1 Cell_2 Cell_3 Cell_4 Cell_5 Cell_6 Cell_7 Cell_8 Cell_9 Cell_10 Cell_11 Cell_12

Initial 60 42.30 0.4 17 3.493 3.534 3.536 3.491 3.529 3.550 3.540 3.540 3.529 3.535 3.533 3.539

Final 8487 50.06 50.8 2440 4.200 4.186 4.182 4.197 4.183 4.182 4.148 4.180 4.183 4.157 4.158 4.155

Fig. 13 Charging curves of 12 cells without ICEs

Cel

l Vol

tage

(V)

Module Capacity

Time(sec)

Mod

ule

Cap

acity

(Whr

)

Cell Voltage

26

0.00 2000.00 4000.00 6000.00 8000.00 10000.00

3.20

3.40

3.60

3.80

4.00

4.20

Legend Title

Cell 1

Cell 2

Ceii 3

Cell 4

Cell 5

Cell 6

Cell 7

Cell 8

Cell 9

Cell 10

Cell 11

Cell 12

0.00

500.00

1000.00

1500.00

2000.00

2500.00

Legend Title

Whr

Initial and final cell voltage for charging test

Module Data Cell Voltage

Time Voltage Ahr Whr Cell_1 Cell_2 Cell_3 Cell_4 Cell_5 Cell_6 Cell_7 Cell_8 Cell_9 Cell_10 Cell_11 Cell_12

Time Voltage Ahr Whr Cell_1 Cell_2 Cell_3 Cell_4 Cell_5 Cell_6 Cell_7 Cell_8 Cell_9 Cell_10 Cell_11 Cell_12

Initial 60 42.24 0.4 17 3.400 3.378 3.390 3.357 3.379 3.400 3.410 3.413 3.405 3.414 3.412 3.421

Final 8602 50.03 51.0 2480 4.195 4.194 4.192 4.195 4.192 4.188 4.192 4.189 4.189 4.190 4.190 4.190

Fig. 14 Charging curves of 12 cells with ICEs

Cel

l Vol

tage

(V)

Module Capacity

Time(sec)

Mod

ule

Cap

acity

(Whr

)

Cell Voltage

27

0.00 1000.00 2000.00 3000.00 4000.00

2.40

2.80

3.20

3.60

4.00

4.40

Legend Title

Cell 1

Cell 2

Ceii 3

Cell 4

Cell 5

Cell 6

Cell 7

Cell 8

Cell 9

Cell 10

Cell 11

Cell 12

-2500.00

-2000.00

-1500.00

-1000.00

-500.00

0.00

Legend Title

Whr

Initial and final cell voltage for discharging test Module Data Cell Voltage

Time Voltage Ahr Whr Cell_1 Cell_2 Cell_3 Cell_4 Cell_5 Cell_6 Cell_7 Cell_8 Cell_9 Cell_10 Cell_11 Cell_12

Initial 60 48.36 -0.8 -40 4.042 4.034 4.036 4.044 4.039 4.047 4.020 4.037 4.045 4.025 4.017 4.028

Final 3688 37.29 -51.2 -2343 2.727 3.147 3.186 2.731 3.157 3.262 3.218 3.197 3.188 3.177 3.136 3.206

Fig. 15 Discharging curves of 12 cells without ICEs

Cel

l Vol

tage

(V)

Module Capacity

Time(sec)

Mod

ule

Cap

acity

(Whr

)

Cell Voltage

28

0.00 1000.00 2000.00 3000.00 4000.00

2.40

2.80

3.20

3.60

4.00

4.40

Legend Title

Cell 1

Cell 2

Ceii 3

Cell 4

Cell 5

Cell 6

Cell 7

Cell 8

Cell 9

Cell 10

Cell 11

Cell 12

-2500.00

-2000.00

-1500.00

-1000.00

-500.00

0.00

Legend Title

Whr

Initial and final cell voltage for discharging test Module Data Cell Voltage

Time Voltage Ahr Whr Cell_1 Cell_2 Cell_3 Cell_4 Cell_5 Cell_6 Cell_7 Cell_8 Cell_9 Cell_10 Cell_11 Cell_12

Time Voltage Ahr Whr Cell_1 Cell_2 Cell_3 Cell_4 Cell_5 Cell_6 Cell_7 Cell_8 Cell_9 Cell_10 Cell_11 Cell_12

Initial 60 48.36 -0.8 -40 4.034 4.038 4.037 4.041 4.040 4.043 4.032 4.034 4.040 4.032 4.025 4.026

Final 3926 32.849 -52.2 -2379 2.741 2.749 2.749 2.758 2.756 2.758 2.739 2.740 2.747 2.736 2.721 2.730

Fig. 16 Discharging curves of 12 cells with ICEs

Cel

l Vol

tage

(V)

Module Capacity

Time(sec)

Mod

ule

Cap

acity

(Whr

)

Cell Voltage

29

Fig. 17 (a) ICEs module

Fig. 17 (b) Battery pack module

Fig. 17 Photography of 12-cells lithium-ion module

5. Comparison of battery equalizer in DICM and DCVM

In order to obtain a more complete comparison about the use of bi-directional converters operating in continuous

and discontinuous modes for the battery equalizer, design results and performance will be further evaluated in

detail, based on the same equalization conditions as in the Table 1. The proposed ICE schemes operating in

CICM, DICM and DCVM can perform the cell voltage equalization, selecting a suitable operating mode is based

on various system desired features [15], [21]. The current ripple in the CICM and DCVM are smaller than that in

the DICM. Consequently, the equalization current in the DCVM is smaller, it needs a compensating controller to

improve the equalization time during cell balancing process. For the intrinsic characteristics, the maximum

voltage stress on a MOSFET switch, Vds max, occurs in the time interval when the switch is turn-off and the diode

is turned on. The maximum voltage stress on a diode, VD max, occurs when switch is turned on and the diode is

turned off. The voltage stress can be expressed as

30

Cj 1

ds max max Cj 1

V for CICM

V = V V for DICM

2 for DCVM

1

Bj Bj

D Bj Bj

Bj

V V

V V

VD

+

+

+= +

(23)

The voltage stress in DCVM is higher than that in the CICM and DICM under the same terminal and specified

equalization conditions. The maximum current stress on a MOSFET switch and diode, Ids max and ID max at the

specified time duration, it can be shown as

Pk1

1max max

1

Pk1

I (1 ) for CICM

2I I ( ) for DICM

I (1 ) for DCVM

j

j

Bj jds D Lj

Bj j

Bj

Bj

LL

V LI

V L D

VV

+

+

+

+

+

= = +

(24)

where IPk = VBjDTs/Lj and ILj = VBj(D+)DTs/2Lj, and denotes the duty ratio when a switch is turned on in

DICM. The current stress in DICM is higher than that in CICM and DCVM under the same equalization

conditions. Table 1 shows a comparison of ICE characteristics in CICM, DICM and DCVM, respectively.

Detailed illustration and observation from Figs. 8-12, 13-16, and Table 1 show several features of the proposed

battery equalizers that are summarized and revealed as follows:

The maximum voltage stresses in the switch and the diode in the DCVM are higher than in the other two

modes. The maximum current stress is significantly reduced compared with the equalizer designed to operate

at DICM. The stresses are compared and illustrated in (23) and (24).

The power MOSFET switches of the proposed battery equalizer are turned off in the zero voltage state. The

total power losses of the MOSFETs in the battery equalizer can be significantly reduced from 33.5% to

52.8% compared with the same equalizer operated at CICM.

The average equalization efficiency can be improved from 52% to 68~86.9% compared with the equalizer

operated at CICM. The maximum equalization efficiency of 72~89.8% can be achieved for the DCVM

designed sample.

31

The charged and discharged capacities in the 12-cells lithium-ion battery-stack module are increased 1.64%

and 1.54% compared with the battery string without equipped the proposed ICEs, respectively.

The DCVM ZVS and DICM ZCS Ck converter have spent slightly more equalization time to balance the

cell voltage to reach the end-of-charge state. Therefore, as a future studied of a smart lithium-ion battery

management system, it is necessary to design an equalization controller, which speeds up the equalization

processing.

6. Conclusion

An ICE for the ZVS soft-switching of DC/DC converters has been proposed. The zero-voltage-switching

technique can greatly reduce the power losses of MOSFET switch was implemented. The proposed ICEs

MOSFET is turned off and the body diode is turned on at zero voltage of the capacitor in DCVM. When the

capacitor voltage approaches zero then the body diode of the MOSFET is turned on until the capacitor energy is

completely transferred to a weaker battery cell. Therefore, the MOSFET switch power losses are reduced by

about 52.8% more than in CICM. The MOSFET switch power losses and the corresponding FFT frequency

spectrums of the proposed battery equalizer in the DVCM are reduced than they are in the DICM and CICM.

The energy harmonic spectrum is concentrated in the low frequency for CICM, and is dispersed low to higher

frequencies in DCVM. Hence, the high frequency EMI emission is improved in a series-connected battery

energy system with DCVM designed ICEs. The performance and capacity of the series connected lithium-ion

battery string are improved by using the proposed battery equalization technology.

Acknowledgments

This work was financially supported by the National Science Council of Taiwan, under grant NSC

92-2213-E-030-020 and NSC 93-2745-E-030-002-URD. The authors would like to thank the MRL, ITRI, Taiwan

for supplied the MRL/ITRI 10AH and 50AH lithium-ion batteries and testing.

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