Impedance analysis of_battery_bidirectional_dc-dc_

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/ACCESS.2020.2972647, IEEE Access
VOLUME XX, 2017 1
Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
Digital Object Identifier 10.1109/ACCESS.2017.Doi Number
Impedance Analysis of Battery Bidirectional
DC-DC Converter
Jun Liu
School of Electrical and Electronic Engineering, Eastchina Jiaotong University, Nanchang, 330013, China
Corresponding author: Jun Liu (e-mail: jimliujun@ 163.com).
This work was supported in part by Project Supported by National Natural Science Foundation of China under Grant 51467006 and 51567009, Key R&D
Project of Jiangxi Provincial Department of Science and Technology under Grant 20192BBE50017, Science and Technology R&D Plan of China Railway
Electrification Bureau Group under Grant 2018-47.
ABSTRACT When a converter is composed of cascaded system with another unknown converter, the
optimal design of the converter is especially important owing to stability of the cascaded systems. Battery ‘s
model is introduced to analysis. Battery converter’s different work conditions are considered. Battery
converter is the front stage when it discharges, and it is the rear one when it charges in a cascade DC system.
From the view of impedance, it’s good for the cascaded system stability to reduce output impedance of
battery converter when the converter is the first stage. Another, increasing the converter’s input impedance
could improve the cascade system stability when the converter becomes the rear one. The battery equivalent
circuit model is introduced as a key component of system. Battery bidirectional converter should act as the
front or rear stage of cascaded system. Selection rules of LC filter are put forward according to analyzing
the inductor and capacitor’s effects on two conditions. The PI controller parameters’ effects on impedance
are analyzed to furnish the basis for the PI controller parameters selection. Finally, experiment is carried out
to verify the correctness of the analyses.
INDEX TERMS Battery Equivalent Model, Bidirectional DC-DC Converter, Cascade System, Impedance
Analysis, Small-Signal Model
I. INTRODUCTION
When a converter is composed of cascaded system with
another unknown converter, the optimal design of the
converter is especially important considering stability of the
cascaded systems. Battery bidirectional DC-DC converter is
more complex since battery is intricate element thinks to its
electrochemistry characteristic and there are two operation
modes of discharge and charge. However, it’s significant to
optimize the battery converter design for cascaded stability.
Many research institutes have established different battery
equivalent models. Swiss researchers proposed an enhanced
battery energy storage system model to reflect the effect of
charge distribution on lithium batteries [1]. Beijing
University of Technology established a second-order RC
circuit equivalent model of lead-acid battery. The researchers
used the model to simulate the charging and discharging
process [2]. The Institute of Electrical Engineering of
Chinese Academy of Sciences established a battery variable
order equivalent circuit model based on the electrode
impedance spectrum theory [3]. University of Kansas,
Mitsubishi Electric Research Laboratories and Zhejiang
University worked together to focus nonlinear parameter
identification of a Thevenin equivalent circuit model for
lithium-ion batteries [4]. Aalto University and Hybria Oy
presented an analytical time-domain-based parameter
identification method for Thevenin equivalent circuit based
lithium-ion battery model [5]. University of California at
Davis investigated relationship between the estimation
accuracy of input current and output voltage [6].
Battery bidirectional DC-DC converter often cascade with
the other converter to constitute a cascade system. The other
side of the cascade system is often unknown. Then, the
design of the battery converter should be more careful to
make the cascade as large stable margin as possible so that
the cascaded system has enough stability.
Harbin Institute of Technology thought that a small bus
capacitance should introduce poor cascade system stability.
They proposed virtual impedance control method to reduce
the source stage output impedance for improving the stability
of cascade system [7]. Adding bus capacitance should be
simpler rather than virtual impedance. University of
Washington improved bus voltage stability by reducing the

VOLUME XX, 2017 9
output impedance of the source-level converter for DC-DC
cascade system [8]. The way also points DC bus voltage
stability. Norway and French researchers adopt a discrete-
time model to analyse the stability of a nonlinear DC
distribution system [9]. The former is a Buck converter, the
circuit is simple. It is not practical in real scene that DSPACE
was used for real time control owing to cost. EastChina
JiaoTong University suppressed second harmonics of two-
stage single-phase inverter DC bus [10]. The researchers
improved the system stability by bus, but no further research
plan was proposed.
The PFC cascade system was studied by Nanyang
Technological University. They thought the rear stage active
load converter could be looked as a constant power load and
constructed a small signal model of the system [11]. This
study pointed to a low voltage DC Boost cascade system.
The conclusion is not necessary to suit to the other type
systems. North China University of Technology gave
attention to bidirectional DC-DC converter system. They
employed double close-loop PI control to the former
bidirectional DC-DC converter and an improved model
predictive control strategy to the rear one [12]. This scheme
is based on Buck cascade system, and there is error that the
rear converter was considered as constant power load.
University of Birmingham and Sheffield University
researched discussed the stability of the hybrid battery
system. They analysed the stability issue and the limitations
of the conventional approach [13]. They also proposed a
control method based on Lyapunov functions for stability of
the system [14]. Whatever, the batteries and its own
converters were cascaded for higher voltage to provide the
PWM inverter in the hybrid battery system. They didn’t
discuss the circuit parameters’ influence on the stability of
the system. North China Electric Power University proposed
a coordinate impedance behaviour to reshape the low-
frequency negative impedance of the constant-power sub
converter to a positive resistance. The first stage was a DC-
DC converter with phase-shifted control, the rear one was an
inverter [15]. This scheme need design the two sub-
converters at same time and point at coordinative control
method. Polytechnic University of Madrid and Tampere
University of Technology thought circle-like forbidden
region to ensure robust stability only if the impedance-based
minor-loop gain was determined at the very input or output
of each subsystem within the interconnected system [16].
The investigation discussed impedance-based stability and
transient-performance assessment applying maximum peak
criteria. They analysed the stray inductor and equivalent
series resistor’s influence. Tampere University of
Technology presented the small signal model for inverter-
current-feedback converter as well as output impedance
properties using only the inverter-side inductor current
feedback for both control and active damping [17]. They
improved output impedance of grid-connected converter with
active damping and feed-forward schemes. The filter is LCL
filter, the filter is often used in three-phase system rather than
DC system. Moreover, they didn’t show how to choose the
filter parameters. Shenzhen Graduate School of Harbin
Institute of Technology investigated stability improvement of
the cascaded DC-DC converters power supply system [18].
They adopt a control method based on output voltage AC
signal sampling feedback to improve the cascaded stability.
Whatever, the cascaded DC-DC system was comprised two
Buck converters, the structure was relatively simple.
University of Sheffield together with Illinois Institute of
Technology researched a cascaded dc/dc converter system
stability via magnitude compensation and phase
compensation [19]. The comparison is carried out for the
parallel-virtual-impedance and series-virtual-impedance
control strategies. A load converter cascaded with three
different source converters is fabricated to validate the
effectiveness of the proposed adaptive SVI control strategy.
The system’s source converter was variable, the load
converter was a Buck converter. The source and load
converters are single directional.
Whatever, it’s good for the cascaded system stability to
optimize output and input impedances of the battery
bidirectional converter especially when the other cascade
converter’s parameters are not known.
First, as a key component of system, a battery’ s model is
introduced to the whole system analysis to increase the
confidence level and practicability. Secondly, the battery
converter is bidirectional DC-DC. The stability of cascade
systems must be considered on two conditions that the
battery converter works as a front or rear stage with another
unknown converters. The paper analyses the output and input
impedance of the two conditions and derives the design rules
of LC filter and PI control parameters. Finally, experiment is
carried out to verify the correctness of the analyses.
II. Battery Model
The battery rated voltage is 144V, the rated capacity is
10Ah. Firstly, the parameter identification of the battery
circuit model is carried out. Conducting "FreedomCAR
Battery Test Manual for Power-Assist Hybrid Electric
Vehicles" mixed pulse test, the electrical performance
parameters of the battery are identified by the data obtained
from the experiments.
The experimental scheme was designed according to the
Hybrid Pulse Power Characterization Test (HPPC Test).
There are 100 seconds in a HPPC Test. The first is 2C pulse
discharge current for 10 seconds, such as t0-t1 of FIGURE 1. .
Then the battery is stood for 40 seconds, as shown as t1-t2.
Then 1.5C pulse charge current is carried out for 10 seconds,
such as t2-t3. Finally, the battery is stood for 40 seconds again,
as shown as t3-t4.
The battery is tested according a series of equal interval
SOC points. First, the battery is filled with electricity, then
discharges to 0.8 SOC, and stand for 30 minutes before the
next HPPC cycle. The battery’s voltage and current are

VOLUME XX, 2017 9
measured in real time. After that, the battery is discharged to
0.7 SOC, set it quiet for 60 minutes. Then the next HPPC
cycle is began again, measuring the battery’s voltage and
current. The else SOC points’ test are similar. After obtaining
data of the battery HPPC experiments, the Thevenin model
parameter identification is carried out.
1
t
0
t
3
t
2
t
d
I
c
I
I
t
4
t
FIGURE 1. Cyclic process of HPPC
Thevenin equivalent circuit model is shown as FIGURE 2.
UOC corresponds the open circuit voltage, RO delegates the
ohm internal resistance, RP is the polarization resistance, CP
corresponds the polarization capacitor. I is the battery current,
IP is the current through polarization resistance. The
polarization capacitor CP is added because of the capacitance
effect of battery, and the polarization resistance RP represents
the mutation of the capacitance effect.
UOC
CP
RP
+
-
UL
I
+ -
UO
+
-
UP
RO
IP
FIGURE 2. Thevenin model of battery
According to the above method, the parameters of the
battery Thevenin circuit model are simulated by formula 1
and the results are shown as Table 1.
, , ,
1 1
L i O L i p p j oc
p p
p p p
U R I R I U
U U I
C R C

   



  


(1)
TABLE 1. Test data of battery Thevenin model
SOC UOC (V) RO (mΩ) RP (mΩ) CP (F)
0.3 151.55 126 267 14.94
0.4 152.98 116 274 14.55
0.5 153.76 112 281 14.20
0.6 154.41 110 286 13.94
0.7 155.27 109 292 13.66
0.8 156.76 112 295 13.53
Finally, the parameters of the battery Thevenin model are
obtained as shown as Table 2.
TABLE 2. DATA OF BATTERY THEVENIN MODEL
RO (mΩ) RP (mΩ) CP (F)
114 283 14.14
III. IMPEDANCE ANALYSIS
Buck-Boost half-bridge circuit is used to the battery
bidirectional DC-DC converter, the main circuit is shown as
FIGURE 3. Battery rated voltage is 144V, operating voltage
is 150-180V and DC bus rated voltage is 75V.
G1
G2
E2
D2
Q1 D1
Q2
+
-
UBUS
UBat CB1 E1
CB2
LB
FIGURE 3. Main circuit of battery converter
When the battery converter works on Buck condition, the
battery discharges and provides energy to the load. When the
battery converter works on Boost condition, the battery is
charged and acquires energy. G1 and G2 are interlocked, and
a 10μs dead time is added while the two operation conditions
are switched to avoid short circuit. On Buck condition, Q1
works and -5V is imposed between G2 and E2 to ensure Q2
turn-off. Similarly, on Boost working conditions, Q2 works
and -5V is imposed between G1 and E1 to ensure Q1
shutdown.
A. IMPEDANCE CHARACTERISTICS ON BUCK
CONDITION
The battery converter works as a front converter on Buck
condition. Its output impedance is expected as small as
possible according to impedance matching theory. when the
battery converter works on Buck condition, the simplified
main is shown as FIGURE 4.
+
-
+
-
UBat
CB1
Ubus
CB2
LB
G1
D2
D1
E1
Q1
UC1
FIGURE 4. Main circuit of battery converter on Buck condition
While the battery Thevenin model is introduced, the
output impedance circuit model of the converter on Buck
condition is modeled as shown as FIGURE 5.

VOLUME XX, 2017 9
+
-
rLB
Zout_B
LB
Ubus
rCB2
CB2
rCB1
CB1
114mohm
UOC
14.14F
CP
283mohm
RP
+ -
UO
+
-
UP
RO
UBat
1:DB1
+
-
FIGURE 5. Output impedance model of battery converter on Buck
condition
The battery impedance based on Thevenin model is such
as formula 2.
( )
1
P P O O P
B
P P
SC R R R R
Z S
SC R
 


(2)
The output impedance of the battery converter on Buck
condition is such as formula 3.
2 1 1
1
1
2 2
2
1
( ) [ ( || ) ]
1
||
+
B CB
OO B B B LB
B
B CB
B
SC r
Z S D Z SL r
SC
SC r
SC

 

(3)
While CB2=4000μF, the size of LB is changed to observe
its effect on the open-loop output impedance of the converter
on Buck condition and Bode diagram is shown as FIGURE 6.
FIGURE 6. Output impedance Bode diagram of battery converter on
Buck condition (CB2=4000μF, variable LB)
The real line corresponds to LB=250μH, the dotted line
corresponds to LB=500μH, the short horizontal dotted line
corresponds to LB=1000μH, and the dash dotted lines
corresponds LB=2000μH.
While LB=500μH, the size of capacitor CB2 is changed to
observe its effect on the open-loop output impedance of the
battery converter on Buck condition and its Bode diagram is
shown as FIGURE 7. Where, the real line corresponds to
CB2=2000μF, dotted line corresponds to the CB2=4000μF,
short horizontal dotted line corresponds to the CB2=10000μF,
dash dotted lines corresponds to CB2=20000μF.
FIGURE 7. Output impedance Bode diagram of the converter on Buck
condition (LB=500μH, variable CB2)
Open-loop output impedance magnitude of battery
converter on Buck condition rises with the frequency
increasing in low frequency band. It rises firstly then drops
after in the medium frequency band. There is a peak near the
LC filter resonant frequency. With the frequency near the
high frequency band, the impedance magnitude declines and
tends to constant value at last. The impedance phase angle
increases with the frequency rise in the low frequency band.
In the medium frequency band, it increases with the
frequency but drops abruptly after. The impedance phase
angle rises and tends to constant in the high frequency band.
It can be seen from the figures that the output impedance is
small in high frequency and low frequency band, especially
in low frequency band.
The output impedance magnitude and has also phase angle
all increase with the inductor increasing. And the impedance
peak point frequency is decreased with the inductor increase.
So, the filter inductor should not be too large. With the
capacitor increasing, the open loop output impedance
magnitude and phase angle become smaller. The changes are
not obvious in the low frequency band but the changes are
obvious in the high frequency band.
The peak frequency of the open loop output impedance
reduces with the increase of the capacitor. In addition, the
impedance of the middle frequency band shifts left with the
increase of capacitor and inductor.
The small signal equivalent circuit model of the battery
converter on Buck condition is shown as FIGURE 8.

VOLUME XX, 2017 9
O
ˆ
I d( S )
(S)
in
ˆ
U d
in in
ˆ
I i

2
CB
r
O O
ˆ
I i

2
B
C
O O
ˆ
U u

1: D


d̂( S )
(S)
ref
û
(S)
m
K
V
K ( S )
(S)
V
G
B
L
LB
r
1
CB
r
1
B
C
OC
U
O
R
P
C
P
R
(S)
in in
ˆ
U u

FIGURE 8. Small signal equivalent circuit model of the converter on
Buck condition
The control to the output’s transfer function is expressed
as formula 4.
2
2
_
2
2
1
( ) ||
1
( ) ||
in CB O
B
vd B
B LB CB
B
U r R
SC
G
SL r r R
SC


  
(4)
The battery converter’s closed-loop impedance on Buck
1
OO _ B
O
OC _ B
O VB
Z S
û S
Z ( S )
î S T S
 

( )
( )
( ) ( )
(5)
Where, the battery converter’s open-loop impedance on
Buck condition is such as formula 6.
2 1 1
_ 1
1
2 2
2
1
( ) [ ( || )
1
1
]||
P P O O P B CB
OO B B
P P B
B CB
B LB
B
SC R R R R SC r
Z S D
SC R SC
SC r
SL r
SC
  



 
(6)
Voltage gain function of the battery converter o Buck
VB vd _ B m _ B V _ B v _ B
T S G S K S G S K S

( ) ( ) ( ) ( ) ( ) (7)
The close-loop output impedance of the battery converter
on Buck condition is shown as FIGURE 9. The point line is
the open loop output impedance, the dashed line is control
parameter P=6, I=0.05, the dotted line is the PI control
parameter P=2, I=1, and the real line is P=1, I=0.05.
FIGURE 9. Output impedance Bode diagram of converter on Buck
condition
The closed-loop output impedance of battery converter
should reduce on Buck condition by closed-loop control. So,
closed-loop control is beneficial to reduce the output
impedance. The I parameter is not significant effect on the
output impedance, and the P parameter could make the
impedance down. So, larger P is welcomed for cascade
system stability because it brings less output impedance.
B. IMPEDANCE CHARACTERISTICS ON BOOST
CONDITION
The battery converter works as a rear converter on Boost
condition. Its input impedance is expected as large as
possible according to impedance matching theory. The
simplified main is shown as FIGURE 10. when the battery
converter works on Boost condition.
G2
E2
D2
D1
Q2
+
-
+
-
UBat
CB1
Ubus
CB2
LB
FIGURE 10. Main circuit of the converter on Boost condition
The input impedance circuit model of the converter on
Boost condition is shown as FIGURE 11. while the battery
Thevenin model is introduced.

VOLUME XX, 2017 9
Zino_B
1:D'
B2
+
-
rLB
LB
Ubus
rCB1
CB1
114mohm
UOC
14.14F
CP
283mohm
RP
+ -
UO
+
-
UP
RO
UBat
+
-
FIGURE 11. Equivalent circuit of the converter on Boost condition
The open-loop input impedance circuit model of the
converter on Boost condition is shown as formula 8 while the
battery Thevenin model is introduced.
'2 1 1
2
1
1
( ) ( || )
1
P P O O P B CB
inO B
P P B
B LB
SC R R R R SC r
Z S D
SC R SC
SL r
  


 
(8)
The size of the inductor LB is changed to observe its effect
on the input impedance of the battery converter Boost
condition while CB1=4000μF. Its Bode diagram is shown as
FIGURE 12. Where, the solid line corresponds to LB=250μH,
dotted line corresponds to the LB=500μH, short horizontal
dotted line is LB=1000μH, dash-dotted lines corresponds to
LB=2000μH.
-40
-20
0
20
40
60
Magnitude
(dB)
10
0
10
1
10
2
10
3
10
4
10
5
-45
0
45
90
Phase
(deg)
Bode Diagram
Frequency (Hz)
FIGURE 12. Input impedance Bode diagram of the converter on Boost
condition (CB1=4000μF, variable LB)
The size of the inductor LB is changed to observe its effect
on the input impedance of the battery converter Boost
condition while CB1=4000μF. Its Bode diagram is shown as
FIGURE 12. , where the solid line corresponds to
CB2=2000μF, dotted line corresponds to the CB2=4000μF,
short horizontal dotted line corresponds to CB2=10000μF,
dash-dotted lines corresponds to CB2=20000μF.
Magnitude
(dB)
Phase
(deg)
FIGURE 13. Input impedance Bode diagram of the converter on Boost
condition (LB=500μH, variable CB1)
As the capacitor of battery, the size of CB1 shows little
effect with the open-loop input impedance from FIGURE 13.
The open-loop input impedance magnitude of battery
converter on Boost condition decreases with the frequency
increasing in all frequency bands. The impedance phase
angle increases with the frequency increasing in the low and
medium frequency bands, and tends to constant in the high
frequency band. The open-loop input impedance magnitude
and phase angle increase with inductor rising.
The converter’s input impedance magnitude on the
boost decreases with the increase in the low frequency band.
And the impedance emerges a peak value in the medium
band near the LC filter resonant frequency. Then it
descends and tends to stabilize in high frequencies. The
phase angle declines first and then rises with the frequency
in the low frequency band with frequency. It ascends firstly
and descends abruptly in the medium frequency band with
frequency. It goes up and finally tends to stabilize with
frequency in high frequency. It can be seen from the figures
that the output impedance is small in high frequency or low
frequency. As the inductor increasing, the input impedance
magnitude and phase angle all become larger and larger.
While the inductor becomes larger, the inflexion
frequencies of the impedance’s magnitude and phase angle
are smaller.
As the capacitor CB2 increasing, the input impedance
magnitude and phase angle all become smaller and smaller.
While the inductor becomes larger, the inflexion frequencies
of the impedance’s magnitude and phase angle are smaller
too. With the inductor and CB2 increasing, the medium
frequency band of the output impedance shifts left.
The small signal equivalent circuit model of the battery
converter on Boost condition is shown as FIGURE 14.

VOLUME XX, 2017 9


d̂( S )
ref
i ( S )
m
K ( S )
i
K (S )
in in
ˆ
I i

in in
ˆ
U u ( S )

O O
ˆ
I i

O O
ˆ
U u

1
D' :
i
G ( S )
OC
U
O
R
P
C
P
R
1
B
C
1
CB
r
B
L
LB
r
in
ˆ
I d
O
ˆ
U d
FIGURE 14. Small signal model of the converter on Boost close-loop
condition
The closed-loop input impedance of the battery converter
on Boost condition is described as formula 9.
2
inC _ B O i _ B B LB CB in i _ B
Z ( S ) U T SL r Z D' I T D'
    
( ) (9)
Where, the Boost current gain function of battery
converter is described as formula 10.
i _ B id _ B m _ B i _ B i _ B
T S G S K S S K S

( ) ( ) ( )G ( ) ( ) (10)
The current to control function of Battery converter on
Boost condition is expressed as formula 11.
_ ˆ 0
ˆ 0
ˆ
ˆ
in
id B O
in
o
u
i
i
G I
d


  (11)
Observe the closed-loop input impedance of the battery
converter on Boost condition by changing PI control
parameters, the result is shown as FIGURE 15.
The point line is open loop input impedance and the others
are close loop input impedance. The real line is P=2, I=0.05,
the dot line is P=6, I=0.05, the dotted line is P=2, I=1.
-50
0
50
100
150
10-4
10-2
100
102
104
106
108
-90
-45
0
45
90
Bode Diagram
Frequency (rad/sec)
FIGURE 15. Input impedance Bode diagram of the converter on close-
loop condition
The closed-loop input impedance of the battery converter
is bigger on Boost condition than open-loop input impedance.
So, closed-loop control is beneficial to increase the input
impedance. The I parameter is not significant effect on the
input impedance, and the P parameter could make the
impedance up. So, larger P is welcomed for cascade system
stability because it brings larger input impedance.
When the battery converter operates on Buck or Boost
condition, the output or input impedance all increase with the
inductor increasing. Lager inductor is harmful to decrease the
output impedance of the battery converter and is good to
increase input impedance. So, the filter inductor should select
appropriate size. Lager CB2 is benefit to reduce the output
impedance on Buck converter.
The open-loop output impedance magnitude becomes
smaller and smaller with increasing of filter capacitor CB2, as
is the phase angle. Then, the frequency on the peak
magnitude is decrease too. So, the large CB2 should be
welcomed for reducing output impedance. On contrast, larger
CB1 brings less input impedance, it is unwise to increase
CB1.The close control is good to reduce the output impedance
or to increase the input impedance, whether the battery
converter work on Buck or Boost condition. If the PI control
is used, the P parameter has more valuable influence on
impedance and the I parameter has little effect on it.
IV. EXPERIMENTAL RESULT
Obviously, when the battery converter is the front
converter, it should reduce its output impedance, and when it
is the back one, it should increase its input impedance for the
cascade system stability. Then, it is easy to choose the
suitable LC filter parameters and the control parameters of
the converter according to above analyses.
The battery converter’s control target is to get a stable 75V
voltage when it operates on buck mode as a front stage of the
cascade system. The battery is discharged by a way. The
battery converter’s control target is that output current is
constant while it operates on boost mode as a rear stage of
the cascade system. And the battery is charged.
A prototype is produced for proving the above analyses.
The rate power of the bidirectional DC-DC converter is 5kW
and the peak power is 10kW. The DC bus voltage is 75V and
the battery rate voltage is 144V. The inductor LB is chosen to
250uH which peak-peak current fluctuations is design with
8%. Amorphous core CF140 of Advanced Technology &
Materials Co., Ltd. is chosen and air gap is 2*3mm and coil
is 64 turns by 18mm2
insulated copper strip. The
capacitorsCB1 and CB2 are all 4000uF which is the four
HCGF5A2G102Y of Hitachi AIC Inc. in parallel. Half
bridge IGBT Module SKM200GB063D of Semikron Co. is
elected as the power switch. The switch frequencies are all
18kHz on the two conditions.
The battery converter uses the current linear sampled
circuit joined a DC bias to avoid the negative voltage. The

VOLUME XX, 2017 9
physical picture of the battery converter is shown as FIGURE
16.
FIGURE 16. Picture of the battery converter
The control target is 75V when the battery converter
works on Buck condition, the rear converter is connected to
another Buck converter as the load. And the other converter’s
parameters don’t intentionally coordinate to the battery
converter for the stabilization of the cascade system. The
battery converter output power is 750W and the output
voltage is 75V. The experimental result is shown as FIGURE
17.
0 0.1 0.2 0.3 0.4 0.5
74
74.2
74.4
74.6
74.8
75
75.2
75.4
75.6
75.8
76
t(s)
U(V)
FIGURE 17. Experimental result of the converter on Buck condition
The experiment result shows that the converter works
stably with power electronic load. There are a certain
switching voltage spikes to cause ripple voltage, but it is still
within the controllable range, and overall electrical
performance is good to meet the operation requirements.
When the converter works on Boost condition, the control
target is input constant current -42.5A while the front stage is
a Buck converter. And the other converter’s parameters don’t
intentionally coordinate to the battery converter for the
stabilization of the cascade system too. The experimental
result is shown as FIGURE 18.
350 400 450 500 550 600
-46
-45
-44
-43
-42
-41
-40
-39
t(ms)
I(A)
FIGURE 18. Experimental result of the converter on Boost condition
The current error is slightly large owing to current
sampling accuracy. The converter is stable and the cascade
system is stable too.
V. CONCLUSION
When the battery converter operates on Buck or Boost
condition, the output or input impedance all increase with the
inductor LB increasing. Lager inductor LB is harmful to
decrease the output impedance of the battery converter, but it
is good to increase input impedance. So, the filter inductor
should select appropriate size. Lager CB2 is benefit to reduce
the output impedance on Buck converter.
The open-loop output impedance becomes smaller with
increasing of the capacitor CB2. Then, the frequency on the
peak is decrease too. So, the large CB2 should be welcomed
for reducing output impedance. Larger CB1 brings less input
impedance but it seems unwise to increase CB1.The close
control is good to reduce the output impedance or to increase
the input impedance. If the PI control is used, the bigger P
parameter is good choice considering to the impedance for
the cascade system’s stability. However, the I parameter
manifests little effect on it. Adopt suitable LC and control
parameters and then implement experiments.
Battery module is introduced to the impedance analyses
for better practicability. The output and input impedance of
the battery converter two conditions are respective analyzed
and design rules of the LC filter and PI parameters are
given together consideration. The experiments results prove
the correctness of the analyses.
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Jun Liu was born in Nanchang, China in 1975.
He received the M.S. degree from Nanchang
University, China in 2005. He received the Ph.D.
degree from Chinese Academy of Sciences
(CAS), China in 2011. From 2011, he was a
lecturer of East China Jiaotong University, China.
His research interests include power electronics,
EV, WPT. Email: jimliujun@163.com.
He worked in Wuxi Si-da electric company
from 1998 to 2002 and worked in Nanchang
campus of Jiangxi of Science and Technology
from 2005 to 2007.

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