High Current Battery Impedance Testing for Power
Electronics Circuit Design
Ke Zou, Stephen Nawrocki, Renxiang Wang and Jin Wang*
Department of Electrical and Computer Engineering, The Ohio State University
Columbus, USA
*Email: Wang@ece.osu.edu
the passive component design and control strategy optimization
of the power electronics circuits.
Abstract—In hybrid electric vehicles, the operation of the power
electronics circuits usually generates great amount of switching
frequency related current ripple. This current ripple would be
absorbed by both the battery and the passive components at the
front end of the power electronics circuits. The amount of the
current ripple that goes into the battery is largely decided by the
battery impedance. So, in this paper, a high power converter
based impedance tester and an impedance test of nickel-metal
hydride (NiMH) battery at power converter switching frequency
with high DC offset current are presented. The test method and
test platform introduced in this paper can also be used for other
different types of batteries, ultra capacitors, fuel cells, and as well
as photovoltaic modules.
This paper proposed a battery impedance tester that is
suitable for HEV applications. In the proposed test setup,
ripple on a battery from a HEV system is mimicked through the
use of a DC/DC boost converter and a high-accuracy DC-link
film capacitor in parallel with the battery. Instantaneous
currents are measured from both the battery and the capacitor.
Because the capacitance of the film capacitor is known for a
given frequency and remains stable throughout short testing
cycles, the battery impedance can be determined.
The proposed system only utilizes current measurements,
so the accuracy is better than methods involving voltage
measurement. Also, due to the current measurement, within
the power rating of the tester, the test method and test setup
shown in this paper would be suitable for both battery cells and
battery pack. Other energy storage devices such as ultra
capacitors, fuel cells, and photovoltaic modules can also be
tested using the same test setup and test method.
Keywords-battery, impedance, current ripple, HEV, fuel cell,
NiMH
I.
INTRODUCTION
Every motor and generator in the hybrid electric vehicles
(HEV) is driven by power electronics circuits which would
introduce high-frequency current ripple into the battery and
paralleled dc-link capacitor. Fig. 1 shows one example of the
AC current on the DC-link of the inverters when both motor
and generator in a full hybrid vehicle are operating at their full
power. If a bidirectional DC/DC converter is used before the
inverters, the ac ripple would have a triangular waveform.
The next section of this paper reviews the existing battery
impedance testing methods. Section III describes the proposed
high current battery impedance tester, including the test setup
and test method. Then preliminary test results on a nickelmetal hydride (NiMH) battery from hybrid vehicle in current
production are shown. These results include the impedance
under different frequencies and different DC offset currents. A
simple battery model in high current, high frequency condition
is presented. Then in the next section the future work
involving a new tester and is discussed. The conclusion is
presented in the last section.
II.
The widely used method [2][3] of measuring the battery
impedance under different frequencies involves the using of
electrochemical impedance spectroscopy (EIS) to get the
battery impedance spectra. The EIS sends a small ac current or
voltage signals to the battery and get the corresponding voltage
or current response and thus calculate the battery impedance.
Nyquist Plots can be used to see the impedance over a wide
range of frequencies using this method. One obvious flaw of
this approach in vehicular battery impedance tests is that it only
gives the impedance under small signal situations. Since the
battery is delivering power to the load or receiving power from
the generator, a high DC current exists in the circuit which
ranges from several amps to several hundred amps. This high
Figure 1. Simulated DC link capacitor ripple resulting from IGBT operation.
Because the battery is in parallel with the DC-link
capacitor, the current ripple would be shared by the battery and
the dc link capacitor. The amount of shared ripple into the
battery is mainly decided by the impedance of the battery and
the impedance of the capacitor at the switching frequency.
Previous research has shown that the battery impedance
changes with operation frequency [1]. Since the current ripple
into the battery would cause extra heat generation and possible
state of charge (SOC) estimation error, the understanding of the
battery impedance at switching related frequencies is the key to
978-1-4244-2601-0/09/$25.00 ©2009 IEEE
EXISTING BATTERY IMPEDANCE TESTING METHODS
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DC offset may affect the battery both chemically and
physically and change its impedance.
calculation of battery impedance, the capacitor also works as
an impedance reference since its capacitance is known and
remains almost unchanged during our operation frequency
range.
A test setup utilizes a current sink consists of ten power
MOSFETS in parallel is described in [4]. Using this test setup,
high DC current testing is achieved while a low terminal
voltage is maintained to enable single battery cell
measurement. In [5][6], different DC offsets are superimposed
to the EIS to measure the battery impedance under different
battery working points. The above methods, although useful,
are mainly focus on frequencies less than several kilo-hertz and
small AC ripple situations. However, in hybrid electric
vehicles (HEV) applications, although the dc-capacitor does
absorb some of the AC ripple, the switching related frequency
ripple that goes in to the battery is still usually much larger than
spectroscopy can produce.
il
ib
Cin
Figure 2. General diagram of the test setup
Due to the above reasons, small signal methods using
impedance spectroscopy are not suitable for predicting the
battery impedance at real high current operation conditions. So
the purpose of this paper is mainly to find the battery
impedance characteristics under high frequency, high DC
charging/discharging current and high AC ripple situations. A
novel test setup and measurement method is proposed in this
paper.
Battery models have been studied extensively [7][8]. For
vehicular application, electrical battery models are easier to
understand and use in analysis. The tests results shown in this
paper indicate that an inductive component is need in this highfrequency, high-current conditions. However, most electrical
models did not include inductive components in them. In [9],
Buller gave a model that includes an inductor to represent the
inductive behavior of the battery in high frequency region.
However, that model is still based on the test data on relatively
low frequency (below 6 kHz) and small signal experiments,
which resulted in some extra components included in the model
to simulate the low frequency behavior of the battery. A
simplified and specific model for vehicular application in high
frequency, high current condition could be derived based on the
tester and testing method describe in this paper.
III.
ic
Figure 3. Mechanical design of the three-phase tester
THE BATTERY IMPEDANCE TESTER AND TEST METHOD
A. Test Setup
The test setup diagram is shown in Fig.2. It mainly
consists of two parts: the DC/DC converter based ripple and
DC current generator and a high-accuracy film capacitor in
parallel with the battery under test.
The current ripple and DC current generator is achieved by
configuring a universal 1200 Volt 200 Amp three-phase tester,
which is shown in Fig.3 and Fig.4, as a single phase bidirectional boost converter. A DSP (TI TMS320F2812) is
used as the controller to generate PWM waveform to control
the duty ratio of the DC/DC boost converter. The operation of
boost converter will generate certain amount of current ripple,
which is decided by the inductance of the inductor in the boost
converter, the operation frequency and duty ratio of the boost
converter, and the output voltage.
Figure 4. Realization of the three-phase tester
Battery side components, including the battery, a film
capacitor and a contactor used to protect the battery under
fault or other undesired situations, are shown in Fig.5. Note
that the cables connecting the capacitor to the battery in Fig. 5
are twisted together to reduce the stray inductance. These
cables will be replaced by a laminated busbar in the next step
The high accuracy film capacitor was used as the filter to
filter out the current ripple and protect the battery. In our
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to achieve minimized stray inductance and more accurate test
results.
method presented in this section is more accurate than voltage
measurement based methods.
IV.
PRELIMINARY TEST RESULTS
The experimental goal of this preliminary test is to find the
affection of high AC current ripple and DC current offset to
the battery impedance under switching frequency in real
vehicular applications. So the experimented DC current
ranges from 5 amps to 100 amps and the switching frequency
of the boost converter ranges from 5 kilo-hertz to 20 kilo-hertz,
which are the normal working conditions of the power
electronics devices in HEV.
During the preliminary test, a nickel-metal hydride (NiMH)
battery from a current mass production hybrid vehicle was
charged and discharged through the DC/DC boost converter to
provide power to the load or absorb energy from a high power
DC supply.
Figure 5. The test setup on the battery side
Three currents in the circuit are measured in the
experiment: , and , although it is known from the last
section that two of them are enough to calculate the battery
impedance. As examples, the measured current waveform at
the condition of 5A DC offset, 10 kHz switching frequency
and 100 A DC offset, 10 kHz switching frequency were shown
in Fig. 6 and Fig.7, respectively.
B. Impedance Calculation
In the above test setup, three currents are measured using
current probes (TCP4041XL, 500A DC maximum) and
sampled in an oscilloscope (Tektronix MSO4054): the battery
current , capacitor current , and the current of the inductor
in the DC/DC converter . Using discrete Fourier transforms
(DFT) on the sampled currents reveals their switching
frequency components.
For these switching frequency
components of the currents, the inductor current is divided
into and based on the capacitor and battery impedance.
Then the relationship of the three measured currents can be
written as shown in (1).
ib ∠ib = iL ∠iL + ic ∠ic
(1)
Since the capacitor and the battery are in parallel, they
share the same voltage on the switching frequency, so
ib ∠ib × Z ∠Z + ic ∠ic ×
1
=0⇒
jωC
(2)
1
ib Z × ∠(ib + Z ) = ic ×
(∠ic − 90D + 180D )
ωC
Figure 6. Current waveforms at 10 kHz, 5 A DC offset
Based on (1) and (2), the impedance of the battery can be
calculated as:
Z =
ic
1
×
, ∠Z = ∠ic − ∠ib + 90D
ib ωC
Thus, from the above analysis, only two currents
to be measured to get the battery impedance.
(3)
,
need
Most battery impedance testing methods measures the
terminal voltage of the battery. A common problem for this
kind of method is that since the battery impedance is a small
value, the resulted voltage is also small, which reduces the
measurement accuracy.
Also, voltage signal is more
vulnerable to interferences than the current signal. So the
Figure 7. Current waveforms at 10 kHz, 100 A DC offset
Two groups of tests were performed in the preliminary
experiment. The first group is at the situation of no DC load
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current and the switching frequency varied from 5 kHz to 20
kHz, which is to test the impedance characteristics under
different switching frequency. The second group is at constant
switching frequency of 10 kHz and the dc current offset varied
from 5A to 120 A. This group is to examine the influence of
DC working point to the battery impedance. The results for
the first group are shown in TABLE I and plotted in Fig. 8.
TABLE I.
BATTERY IMPEDANCE UNDER DIFFERENT SWITCHING
FREQUENCY
Switching Frequency (kHz)
Battery Impedance (Ω)
5
0.0262+0.0328j
7
0.0308 + 0.0422j
10
0.0363 + 0.0550j
12
0.0379 + 0.0630j
15
0.0379 + 0.0742j
17
0.0391 + 0.0813j
20
0.0412 + 0.0932j
Figure 9. Equivalent inductance vs. switching frequency
From the battery impedance spectra over the test frequency,
a battery model for high frequency, high current condition is
developed, which is shown in Fig.10. It only contains 4
components, two resistors and two inductors, which is much
simpler than most mainly used models. The value of each
passive component is shown in TABLE 2. The detailed
derivation and possible improvement of the model will be
addressed in the follow up papers.
Figure 10. The proposed battery model
TABLE II.
Component
L1
R1
L2
R2
Figure 8. Battery impedance vs. switching frequency
The test result of group 1 shows that the battery impedance
amplitude and angle increase almost linearly with the
increasing of switching frequency. It also shows that the
battery impedance is inductive throughout the given frequency
range (5-20 kHz) since the impedance angle is positive. This
inductive attribute of battery impedance at switching
frequency is quite different from that at low frequency, which
is capacitive. It also can be seen that the equivalent resistance
of the battery also increases as the switching frequency. This
linearity of the impedance frequency response indicates that a
simple impedance model with small number of components
should be enough to describe the high-frequency, high current
behavior of the Ni-MH battery under test.
PASSIVE COMPONENTS PARAMETERS IN THE PROPSED
BATTERY MODEL
Value
0.680 µH
0.0184 Ω
0.562 µH
0.0252 Ω
The results for the second group are shown in TABLE III
and plotted in Fig. 11. The test on group 2 shows that, when
the dc offset current increase, the amplitude of the battery
impedance decreases slightly and the phase angle increases.
This change of impedance is mainly due to the increase of the
battery resistance as the increasing of DC offset. It can be
seen that the equivalent battery resistance at 116.7 A DC
offset dropped to almost one half of the value when the DC
current is 5.3 A, while the reactance of the battery only
changed slightly. This result indicate that the battery will have
different models under different DC current situation, or one
component that could reflect this resistance change should be
included in the model.
The equivalent inductances at different frequencies are
plotted in Fig. 9. It can be seen a nonlinear decreasing of the
measured inductance as the switching frequency increases.
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TABLE III.
BATTERY IMPEDANCE UNDER DIFFERENT DC OFFSET
DC offset (A)
5.3
31.0
Battery Impedance (Ω)
0.0361 + 0.0582j
0.0281 + 0.0545j
38.9
0.0271 + 0.0540j
46.0
0.0262 + 0.0534j
75.1
0.0235 + 0.0518j
80.3
97.0
0.0233 + 0.0517j
0.0229 + 0.0507j
109.1
0.0218 + 0.0500j
116.7
0.0215 + 0.0504j
method will be used calculate the SOC and ensure
experiments are performed in the same SOC condition; 3.
Feed power back to the grid. The 3-phase tester described in
this paper will be configured as a boost converter + a single
phase inverter. Under this structure, current control as well as
the power flow control could be realized and battery power
could be sent to the power grid.
Based on the new tester, new tests that covering most
switching frequencies used in hybrid vehicle traction drives
(0-30 kHz) would be tested. Then a new battery model will be
derived with more test data. Control strategy and stability
analysis will be made based on the battery model to help the
power electronics design. Furthermore, the test method and
test setup will not be restricted to Ni-MH battery testing. The
goal of this work is to develop a test method and test platform
that would be suitable for different types of batteries, ultra
capacitors, fuel cells, and photovoltaic modules.
VI.
CONCLUSION
This paper presented a high-current, high-frequency battery
impedance tester and relevant testing methods specifically
designed for real applications such as vehicular application. A
DC/DC converter is used in the tester as the AC ripple
generator. Current measurement method is adopted, which
has better accuracy than voltage based methods. The test
results showed that the battery impedance at high frequency
conditions is inductive. Based on this, a simple impedance
model is built. More detailed about battery model derivation
and relevant control strategy will be addressed more in the
follow up papers.
Figure 11. Battery impedance vs. DC offset current
REFERENCES
It should be noted that the tests presented in this paper are
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Firstly the battery impedance is affected by many other factors
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preliminary test, this can cause the loss of accuracy for the test
results. In fact, all tests were performed at roughly 50% SOC
and room temperature. Although each test is controlled to be
performed for less than 3 seconds, the SOC still could change
for more than 10% after several rounds of high current tests.
Since the duty ratio and the output voltage remained
unchanged for each test, the AC current ripple for different
test frequencies varies. So proper procedures should be taken
to ensure all the tests are performed under the same
temperature, SOC and AC ripple conditions.
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be charged/discharged at a desired current accurately; 2. Track
SOC and temperature automatically. A current integration
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