Individual Cell Equalization for Series
Connected Lithium-Ion Batteries
*
Yuang-Shung Lee,1a) Ming-Wang Cheng,2,3b) Shen-Ching Yang1, Co-Lin Hsu1
1
Department 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
2
Graduate Institute of Applied Science and Engineering, Fu-Jen Catholic University
3
Industrial 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 Cûk 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 Cûk converter, Lithium-ion battery, Individual cell equalizer, ZVS
References
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1
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* To whom all correspondence should be addressed.
2
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 cell’s 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 Cûk 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 Cûk 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 Cûk converter in discontinuous capacitor voltage
mode (DCVM) was already discussed in [15],[16],[18]. The aforementioned analysis and design method of the
uni-directional Cûk converter operated at DCVM can not be totally adopted for the battery equalization
3
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 Cûk
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 Cûk 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.
4
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
5
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
6
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
7
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
8
t0
t1 t2
t3
Vcc
t0
t1 t2
t3
VBj
VGSj
VLj
t
Vcp
t
iLj
IP
VLj+1
t
- VBj+1
IP
IO
iDSj
t
t
iLj+1
I *P
I *O
t
- VBj+1
VBj
V Cj
t
0
D1 Ts DTs
iDSj+1
I *P
0
Ts
t
D1 Ts DTs
Ts
5. (a)
t0
t1 t2
t3
Vcc
t0
t
VCj
t
IP
iLj+1
IO
t3
VBj+1
VGSj+1
Vcp
t1 t2
VLj+1
t
-VBj
VBj+1
VLj
t
-VBj
IP
iDSj+1
t
I *P
t
iLj
IO*
0
t
D1 Ts DTs
iDSj
I *P
0
Ts
t
D1 Ts DTs
Ts
5. (b)
Fig. 5 Typical switching waveforms of ICEj for (a) VBj>VBj+1, (b) VBj<VBj+1
3. Circuit analysis of the jth ICE
The inductors Lj and Lj+1 are assumed to be large enough to operate in continuous inductor current. In addition,
the capacitor is also sufficiently small so it can be fully discharged during the switching period. Where Ts is the
converter switching period, the detail equivalent circuit of the proposed battery equalization schemes are shown
9
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 υcj 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 υcj
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 υcj 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 υcj reaches maximum value at t3
= Ts, as shown in Fig. 3 (c). The proposed ICE has more than one stage, in contrast to a Cûk 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 ( t0 ≤ t < t1 ), Fig.3 (a) shows that Qj is turned on and Dj+1 is turn-off, and denoted the switching variable u
=1 (HIGH state):
di Lj
Lj
dt
L j +1
C
= ( I S − i Lj ) R Bj + V Bj ,
di L j + 1
dt
d vCj
j
dt
iLj (t0 ) = I 0
(1)
= − ( I S + i L j + 1 ) R B j + 1 + v C j − V B j + 1 , iLj +1 (t0 ) = I 0
= iL j +1 , v C j ( t 0 ) = V C P
*
(2)
(3)
Stage 2 ( t1 ≤ t < t2 ), Fig. 3 (b) shows that Qj is still turned on and Dj+1 is forced to start turn-on when υcj = 0, and
denoted the switching variable u = 0.5 (FLOATING state):
Lj
di Lj
dt
= ( I S − i Lj ) R Bj + V Bj ,
i L j ( t1 ) =
[ D1 I P
+ ( D − D1 ) I 0 ]
D
10
(4)
L j +1
di L j + 1
dt
⎡ D I * + ( D − D1 ) I 0 * ⎤
⎦
= − ( I S + i L j + 1 ) R B j + 1 − V B j + 1 , iLj +1 ( t1 ) = ⎣ 1 P
D
vCj = 0
(5)
(6)
Stage 3 ( t2 ≤ t < t3 ), Qj is turned off and Dj+1 is still turned on, and denoted the switching variable u = 0 (LOW
state):
di L j
Lj
dt
L j +1
C
= ( I S + i L j + 1 ) R B j − v C j + V Bj , iLj (t2 ) = I P
di L j + 1
dt
d vCj
j
dt
= − ( I S + i L j + 1 ) R B j + 1 − V B j + 1 , iLj +1 (t2 ) = I P
(7)
*
= iL j , vCj (t2 ) = 0
(8)
(9)
The compact state equation for describing of the three states mentioned above can be combined and simplified as:
⎡
RB
⎢
− j
⎢
⎡ diLj ⎤
Lj
⎢
⎥ ⎢
⎢ dt ⎥ ⎢
⎢ diLj +1 ⎥ ⎢
0
⎢ dt ⎥ = ⎢
⎢
⎢
⎥
⎢ dvCj ⎥ ⎢
1
⎢ dt ⎥ ⎢ 2(1 − u )( − u )
2
⎣
⎦ ⎢
⎢
Cj
⎢⎢
⎣
0
−
RB j+1
L j +1
1
−2u (u − )
2
Cj
1
⎤
−(1 − u )( − u ) × 2 ⎥
2
⎡ VB j + I s RB j ⎤
⎥
Lj
⎥
⎢
⎥
Lj
⎥
⎢
⎥
1
2u (u − )
⎥ ⎢⎡ iLj ⎥⎤ ⎢ VB + I s RB ⎥
j +1
2
⎥
⎥ ⎢iLj +1 ⎥ + ⎢− j+1
⎥
⎢
L j +1
L
⎥⎢ ⎥
j +1
v
⎢
⎥
Cj
⎥⎣ ⎦
⎢
⎥
⎥
⎢
⎥
⎥
0
0
⎢
⎥⎦
⎣
⎥
⎥⎥
⎦
(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 υcj = 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 Cûk converter can be expressed by
11
⎧ I Lj (1 − D )TS − I Lj +1t
, for 0 < t < D 1TS
⎪
Cj
⎪
⎪
= ⎨ 0,
for D 1TS < t < DTS
⎪ I ( t − DT )
S
⎪ j
,
for DTS < t < TS
⎪⎩
Cj
ν Cj
(11)
The power MOSFETs of the modified QRZVS battery equalizer are turned off at the zero current. The sub-duty
ratio D1 in terms of the duty ratio D can be governed as:
D
I
= (1 − D )
1
I
Lj
(12)
L j +1
The time-average of voltages of
υ cj
and υ D j + 1 are denoted as Vcj and VDj+1, respectively. This can be
determined from (11) as
V cj =
Ts
I L j (1 − D )(1 − D + D )
2C
Ts
V D j +1 = −
(13)
1
j
I L j (1 − D ) D
2C
(14)
1
j
Therefore, the terminal voltages of the battery cells and the voltage conversion ratio are
Ts
V Bj +1 = − V D j +1 =
V Bj = V D j +1 + VC j =
V
B j+1
V
=
Bj
I Lj (1 − D ) D
D
(15)
1
2Cj
Ts
2C
I
Lj
(1 − D )
2
(16)
j
1
(17)
1 − D
Combining (12) and (15) and substituting into (17) to yield
=
I Lj
D
1
2 fs C jV B j
(1 − D )
V
2 fsC j
I
=
(18)
2
B j+1
(19)
L j+1
To operate the proposed ICE in DCVM, the inequality should be satisfied, or equivalent
D ≥
L j ≥
2 fSC
V
j
V Bj + 1
Ij + 1
B j + 1 (1
− D)
2 D fS I
(20)
2
(21)
j +1
12
L j +1 ≥
V
B j + 1 (1
2 fS I
− D)
(22)
j +1
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
Duty cycle (D)
operate in DCVM [15], [16].
DCVM
CCVM
Voltage (V)
Current (I)
Fig. 6 Switching boundary surface between DCVM and CCVM
13
Fig. 7 Configuration of MATLAB/SimuLink model
14
(V)
(A)
(V)
(A)
Time (ms)
Fig. 8 Simulation results
(s)
(V)
9. (a)
15
Vc(V
) Vgs(V)
Vgs Vc
5V/div 1A/div 20us/div
Time(sec)
9. (b)
(s)
(V)
9. (c)
VT(V) Vgs (V)
Vgs
VT
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
16
ICE Matlab/Simulink model for a three battery-cell, the ICE 1 (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 = 230µH and C1 = C2 = 0.66µF with ESR = 0.001Ω,
respectively. The switching frequency was 16.67 kHz and the duty ratio was D = 0.53 for both VB1>VB2>VB3 and
VB1<VB2<VB3 to ensure that the proposed bi-directional dc-to-dc converter could be designed to operate in
DCVM. This can obtain a zero voltage switching (ZVS) to reduce the MOSFET switching loss in the proposed
ICEs.
Fig. 8 shows the simulation voltages and currents for the capacitor and inductor in ICE1, respectively. The
MOSFET control signal Vgs and the corresponding drain-source voltage VT for VB1>VB2>VB3 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 = 230µH, C1 = C2 = 0.66µF. The switching frequency and the duty ratio of
the battery equalizer are 16.67 kHz and 0.53, respectively.
17
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 (0.4mm×4) 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.
18
VB1
VB2
VB3
(V)
(ms)
10(a)
10(b)
VB1
VB2
VB3
(V)
(ms)
10(c)
10(d)
VB1
VB2
VB3
(V)
(ms)
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
19
11. (a)
11. (b)
Fig. 11 (a) Waveform and, (b) FFT spectrum of MOSFET switch power losses
Fig. 12 (a)
20
Fig. 12 (b)
Fig. 12 Equalization efficiency of ICE under various operating modes
(a) Original equalization scheme (b) Reformed equalization scheme
21
Table 1 Comparisons between continuous and discontinuous modes
CICM
DICM
DCVM
Inductor (Lj)
98.3µH
100.5µH
229.2µH
Inductor (Lj+1)
100.7µH
101.2µH
230.3µH
Capacitor (Cj)
470µF
470µF
0.66µF
Switching
Frequency (fs)
18.1 kHz
16.67 kHz
16.67 kHz
Duty Cycle (D)
0.53
0.5
0.5
Boundary
Condition
Lj ⋅ fs >
V j +1 (1 − D) 2
2 D ⋅ I j +1
L j +1 ⋅ f s >
V j +1 (1 − D)
2 I j +1
Lj ⋅ fs <
V j +1 (1 − D) 2
2 D ⋅ I j +1
L j +1 ⋅ f s <
V j +1 (1 − D)
D > 2 f sC j
V j +1
I j +1
2 I j +1
Voltage Stress
Eq. (23)
Eq. (23)
Eq. (23)
Current Stress
Eq. (24)
Eq. (24)
Eq. (24)
Soft Switching
Characteristic
NO
ZCS
ZVS
Applications
Low power
Low current,
High voltage
High current,
Low voltage
Equalization
time
Short
Long
Long
4.2 Twelve lithium-ion cells module (n=12)
The other experimental installation of a twelve lithium ion batteries stack with the eleven proposed
equalization schemes (11 ICEs) is used to verify the equalization performance of the proposed ICEs. The driving
signals for the equalization schemes are from a microprocessor-based battery management system according to
each cell voltage. The experimental parameters of the batteries and the designed ICEs are listed as follows: The
22
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
STEP_2
STEP_3
STEP_4
I=25A
A: Voltage＞50.4V
NEXT STEP
B: Cell Voltage＞4.2V
NEXT STEP
C: T＞50℃
STOP
I=10A
A: Voltage＞50.4V
NEXT STEP
B: Cell Voltage＞4.2V
NEXT STEP
C: T＞50℃
STOP
I=5A
A: Voltage＞50.4V
NEXT STEP
B: Cell Voltage＞4.2V
NEXT STEP
C: T＞50℃
STOP
I=2.5A
A: Voltage＞50.4V
STOP
B: Cell Voltage＞4.2V
STOP
C: T＞50℃
STOP
DISCHARGING
I=50A
A: Voltage＜33V
STOP
B: Cell Voltage＜2.75V
STOP
C: T＞50℃
STOP
23
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.
24
4.20
2500.00
4.00
2000.00
Legend
Title
Cell
Voltage
Cell 1
3.80
Cell 2
1500.00
Ceii 3
Cell 4
Cell Voltage (V)
Cell 6
1000.00
Module Capacity (Whr)
Cell 5
3.60
Cell 7
Cell 8
Cell 9
3.40
Cell 10
Legend
Title
Module
Capacity
500.00
Cell 11
Whr
Cell 12
0.00
3.20
0.00
2000.00
4000.00
6000.00
8000.00
10000.00
Time(sec)
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
Final
8487
50.06
50.8
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
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
25
4.20
2500.00
4.00
2000.00
Cell
Voltage
Legend
Title
Cell 1
3.80
Cell 2
1500.00
Ceii 3
Cell 5
3.60
Cell 6
Module Capacity (Whr)
Cell Voltage (V)
Cell 4
1000.00
Cell 7
Cell 8
Cell 9
3.40
Cell 10
Module Capacity
Legend Title
500.00
Cell 11
Whr
Cell 12
0.00
3.20
0.00
2000.00
4000.00
6000.00
8000.00
10000.00
Time(sec)
Initial and final cell voltage for charging test
Module Data
Initial
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
60
Final 8602
42.24
0.4
50.03
51.0
17
3.400 3.378 3.390 3.357 3.379 3.400 3.410 3.413 3.405
3.414
2480 4.195 4.194 4.192 4.195 4.192 4.188 4.192 4.189 4.189 4.190
Fig. 14 Charging curves of 12 cells with ICEs
26
3.412
4.190
3.421
4.190
4.40
0.00
4.00
-500.00
Legend
Title
Cell
Voltage
-1000.00
Cell 1
3.60
Cell 2
Module Capacity (Whr)
Cell Voltage (V)
Ceii 3
Cell 4
Cell 5
3.20
-1500.00
Cell 6
Cell 7
Cell 8
Cell 9
2.80
Cell 10
Cell 11
-2000.00
Module
LegendCapacity
Title
Whr
Cell 12
-2500.00
2.40
0.00
1000.00
2000.00
3000.00
4000.00
Time(sec)
Initial and final cell voltage for discharging test
Module Data
Time Voltage Ahr
Cell Voltage
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
27
4.40
0.00
4.00
-500.00
Legend Title
Cell Voltage
Cell 1
3.60
-1000.00
Cell 2
Module Capacity (Whr)
Cell Voltage (V)
Ceii 3
Cell 4
Cell 5
3.20
-1500.00
Cell 6
Cell 7
Cell 8
Cell 9
2.80
Cell 10
Cell 11
-2000.00
Module
LegendCapacity
Title
Whr
Cell 12
-2500.00
2.40
0.00
1000.00
2000.00
3000.00
4000.00
Time(sec)
Initial and final cell voltage for discharging test
Module Data
Initial
Final
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
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
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
28
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
29
Vds max = VD max
⎧ VCj V Bj + V Bj +1
⎪
⎪⎪
= ⎨ VCj V Bj + V Bj +1
⎪
⎪ 2V Bj
⎩⎪ 1 − D
for CICM
for DICM
(23)
for DCVM
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
I ds max = I D max
⎧
Lj
)
⎪ I Pk (1 +
L
j +1
⎪
⎪
2V Bj L j +1
⎪
)
= ⎨ I Lj (
V
L
D
1
+
Bj
j
⎪
⎪
V
⎪ I Pk (1 + Bj )
V Bj +1
⎪⎩
for CICM
for DICM
(24)
for DCVM
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.
30
•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 Cûk 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 ICE’s
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.
31