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

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.

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.

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

the passive component design and control strategy optimization of the power electronics circuits.

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.

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 nickel-metal 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. EXISTING BATTERY IMPEDANCE TESTING METHODS 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

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DC offset may affect the battery both chemically and physically and change its impedance.

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.

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 high-frequency, 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. 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 bi-directional 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.

The high accuracy film capacitor was used as the filter to filter out the current ripple and protect the battery. In our

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.

inCbi ci

li

Figure 2. General diagram of the test setup

Figure 3. Mechanical design of the three-phase tester

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

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to achieve minimized stray inductance and more accurate test results.

Figure 5. The test setup on the battery side

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).

ccLLbb iiiiii ∠+∠=∠ (1)

Since the capacitor and the battery are in parallel, they share the same voltage on the switching frequency, so

)18090(1)(

01

+−∠×=+∠×

⇒=×∠+∠×∠

ccbb

ccbb

iC

iZiZi

CjiiZZii

ω

ω (2)

Based on (1) and (2), the impedance of the battery can be calculated as:

90,1 +∠−∠=∠×= bcb

c iiZCi

iZ

ω (3)

Thus, from the above analysis, only two currents , need to be measured to get the battery impedance.

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

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.

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.

Figure 6. Current waveforms at 10 kHz, 5 A DC offset

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 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.

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.

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. PASSIVE COMPONENTS PARAMETERS IN THE PROPSED BATTERY MODEL

Component Value L1 0.680 µH R1 0.0184 Ω L2 0.562 µH R2 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.

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TABLE III. BATTERY IMPEDANCE UNDER DIFFERENT DC OFFSET

DC offset (A) Battery Impedance (Ω) 5.3 0.0361 + 0.0582j

31.0 0.0281 + 0.0545j

38.9 0.0271 + 0.0540j

46.0 0.0262 + 0.0534j 75.1 0.0235 + 0.0518j 80.3 0.0233 + 0.0517j 97.0 0.0229 + 0.0507j

109.1 0.0218 + 0.0500j

116.7 0.0215 + 0.0504j

Figure 11. Battery impedance vs. DC offset current

It should be noted that the tests presented in this paper are the preliminary tests and could be improved in several aspects. Firstly the battery impedance is affected by many other factors such as ambient temperature, the SOC of the battery, as well as the AC ripple. All these factors are not considered in the 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.

V. FUTURE WORK

Now that preliminary data has been acquired, a clear map of future work is emerging. More accurate and all-rounded tests need to be performed. An automatic impedance tester will be built which utilize a dSPACE controller board. The new tester can: 1. Control the DC current dynamically, so the battery will be charged/discharged at a desired current accurately; 2. Track SOC and temperature automatically. A current integration

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.

REFERENCES [1] A. Jossen, “Fundaentals of battery dynamics,” J. Power Sources, vol.

154, no. 2, March 2006, pp. 530-538. [2] P. Mauracher and E. Karden, “Dynamic modelling of lead/acid batteries

using impedance spectroscopy for parameter identification,” J. Power Sources, vol.67, no.1-2,August 1997,pp.69-84.

[3] X.Feng and Z. Sun, “A battery model including hysteresis for State-of-Charge estimation in Ni-MH battery”, Vehicle Power and Propulsion Conference,2008. Sept. 2008, pp.1 – 5

[4] B. Schweighofer, K. Raab, and G. Brasseur, “Modeling of High Power Automotive Batteries by the Use of an Automated Test System,” IEEE Transactions on Instrumentation and Measurement, vol. 96, no. 4, August 2003, pp. 1087-1091.

[5] Marc Thele, Oliver Bohlen, Dirk Uwe Sauer. “Development of a voltage-behavior model for NiMH batteries using an impedance-based modeling concept”. J. Power Sources, 2008,175 (2008) 635-643

[6] Eckhard Karden, Stephan Buller, Rik W. De Doncker, “A method for measurement and interpretation of impedance spectra for industrial batteries,” J. Power Sources, vol 85,no.1, 2000.pp.72–78

[7] M.Chen, G.Rincon-Mora, “Accurate Electrical Battery Model Capable of Predicting Runtime and I–V Performance,” IEEE Transactions on Energy Conversion, vol.21, no.2, June 2006, pp.504-511.

[8] R. Kroeze and P. Krein, “Electrical Battery Model for Use in Dynamic Electric Vehicle Simulations,” Power Electronics Specialists Conference, June 2008, pp.1336-1342.

[9] S. Buller, M, Doncker and E. Karden, “Impedance-Based Simulation Models of Supercapacitors and Li-Ion Batteries for Power Electronic Applications,” IEEE Transactions on Industry Applications, vol. 41, no. 3, MAY/JUNE 2005, pp.742-747.

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