A Modified Equivalent Circuit for Common-Mode Current of Single-Phase Full-Bridge Inverters Kai Zhang*, Yunbin Zhou, Yonggao Zhang, and Yong Kang Huazhong University of Science and Technology 1037 Luoyu Road, Wuhan 430074 CHINA *
[email protected] Abstract – A modified equivalent circuit for common-mode (CM) current of single-phase full-bridge inverters is proposed. The circuit allows application of superposition theorem, and it provides more insights into the propagation mechanism of the CM noise. Simulations and experiments are conducted on an inverter test setup to validate the proposed circuit. Three operation conditions are studied: (1) with one of the two legs detached from the dc bus; (2) with that leg installed back in place but not switching; (3) with normal unipolar PWM switching of both the two legs. Based on the proposed equivalent circuit and measured parameters from the test setup, simulations with MATLAB software predicted the CM current both in time and frequency domains with reasonable precision.
current flows through the two phase legs. Due to the same reason, the well-known theorem of superposition does not apply to this typical multi-source circuit, which is rather counter-intuitive. In this paper, a modification is made to that circuit so as to overcome this disadvantage. The paper is organized in this way: section II describes the derivation of the proposed equivalent circuit, a theoretical analysis is also given on that circuit; section III gives simulation and experimental results on a test setup to validate the proposed circuit; and section IV concludes the paper.
I. INTRODUCTION
Fig.1 shows the main circuit of a single-phase full-bridge inverter. The two power semiconductor devices of each leg usually come in one single module. For reducing the thermal resistance within each power device, there is only a thin insulation layer between the chip area of the device and the metal base plate, with the latter fixed on a heat sink. The heat sink is in turn fixed to the chassis, which is usually grounded for safety reasons. This gives rise to a significant stray capacitance (see Cp1 and Cp2 in Fig.1) from the midpoint of each leg to the ground. As the devices switch on and off with high speed, high dv/dts at the leg midpoints generate currents through the stray capacitors. These currents converge into the chassis/ground, forming a major part of the CM current. This CM current then will find its way into the dc bus through capacitors C1 and C2 at the front end. These two capacitors, usually of feedthrough type and 10µF in value, are connected for obtaining repeatable CM EMI measurement results. They can also be replaced with a line-impedance-stabilizing network (LISN).
To reduce volume and weight, and improve dynamic response, there has been a continuing demand for increasing the switching frequency of power electronic converters. As a result, high-speed power devices find more and more applications. However, high dv/dt associated with high speed switching can cause severe common-mode electromagnetic interference (CM EMI) [1]. The CM EMI usually constitutes a major part of total conducted EMI, especially beyond MHz level. CM EMI also acts as a major cause of radiated EMI because of the significant “antenna effect” of the CM current loop. It has been understood that the general mechanism (noise source and propagation path) of CM EMI emission in a PWM inverter is similar to a Buck dc-dc converter, whereas the former one is much more complicated due to the fact the it contains multiple switching devices. In recent years, there has been some notable progress reported in the modelling, simulation, and prediction of CM EMI for PWM inverters [2]-[8]. However, quite a lot of the above research work was on ac motor drive applications and focused on the motor side of the systems. Discussion on the CM EMI equivalent circuit of the inverter itself, especially when more than one phase leg is involved, is relatively limited. In [8], an equivalent circuit model of CM EMI for a single-phase full-bridge inverter was proposed, where it has been shown that a simplified, 2nd-order lumped circuit model together with a trapezoidal characterization of CM noise source can give a prediction of the CM EMI spectrum with reasonable precision. A drawback of this equivalent circuit model is that it fails to clearly demonstrate how the CM
II. DERIVATION OF THE EQUIVALENT CIRCUIT
E
D1
T2
D2
Cd Cp1 Cp2 T3
D3
T4
D4
C1 C2
Fig.1 A single-phase full-bridge inverter.
This work was sponsored by the National Natural Science Foundation of China (NSFC), under project 50407011.
1-4244-0136-4/06/$20.00 '2006 IEEE
T1
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To simplify the analysis, it has been assumed that the stray capacitance between the windings of the output filter inductor is negligible. Otherwise this capacitance will also make a significant contribution to the total CM current. A. CM Current Path for a Single Leg The CM current path for each leg of the inverter is the same as that of a basic Buck converter [9,10], as shown in Fig.2. Lcab
R in E
V1
i cm Cn
20uF
tr Cp
tf
L cm
Although this circuit is easy to handle, it fails to demonstrate clearly how the CM current is flowing through the two phase legs. Due to the same reason, the theorem of superposition cannot be applied to this circuit or it would produce a wrong result. For example, if we let the left hand side leg act alone, (that is, let V2 =0,) then the equivalent circuit will go back to the form shown in Fig.2. In that figure, there is no trace of any impact of right hand side leg, no matter whether it is connected or not. This does not seem to reflect the real situation. To clarify this, a special experiment was designed and conducted on a single-phase full-bridge inverter product with only one phase leg working (i.e. switching on and off), and the CM current waveforms are recorded as shown in Fig.4. The upper trace in Fig.4 is with the other leg in place (but not switching); and the lower one is with the other leg detached from the dc bus. Noticeable change in both magnitude and frequency of the CM current can be observed, which cannot be explained with the circuit given in Fig.3.
Fig. 2. Equivalent CM current path for a single leg.
In Fig.2, Lcm is the stray inductance from the heat sink to the ground point where the feedthrough capacitors are connected. For high frequencies, the dc bus are effectively short-circuited by the bulk capacitor Cd, therefore the two feedthrough capacitors are parallel connected to form the 20µF capacitor in the figure. Lcab and Rin are respectively the stray inductance and stray resistance of the dc bus from feedthrough capacitors to the bulk capacitor. Cn is the stray capacitance from the dc bus to ground after the bulk capacitor. Cp is the stray capacitance from the leg midpoint to ground. (It is supposed that Cp1 = Cp2 = Cp.) The voltage source V1 is equal in value to the voltage across T1 and is the source of CM noise current. For theoretical analysis, V1 can be considered as a trapezoidal pulse train with rise time tr and fall time tf, as already shown in that figure. For simplicity, it is often assumed that tr = tf.
Fig. 4. Impact on the CM current of the non-switching leg. (0.5A/div; 500nS/div)
To address this problem, the voltage source side of Fig.3 is modified into the parallel form in the proposed equivalent circuit, as shown in Fig.5. Lcab
B. Adding the Second Leg To establish the equivalent circuit of CM current for the whole inverter, the second leg has to be included. In [8], this is done by simply adding the two noise source voltages V1 and V2 together. The resulting circuit is shown in Fig.3. Lcab
i cm
Cn
20uF
Cn
20uF
R in
i cm
R in
V1
V2
Cp1
Cp2
L cm Fig. 5. The modified equivalent circuit for the CM current of the whole inverter.
V1 +V2 Cp
L cm Fig. 3. Previously proposed equivalent circuit for the CM current of the whole inverter.
C. Analysis of the Proposed Equivalent Circuit From Fig.4 it can be observed that the presence of the second leg, although not switching, does have significant impact on the CM current. Specifically, the oscillation frequency is lower; and the magnitude of the current is also 2868
Lcab
Again the admittance in the first case is higher, which is also in consistence with Fig.4. A physical explanation of Fig.6 is: although the second leg is not switching, the midpoint potential of this leg can only be equal to that of the positive or negative dc bus, depending on the (constant) driving signal of the two power devices. In either case, this provides a path for the CM current to flow through the associated stray capacitor Cp2. When both the two legs are in high frequency switching, which is the normal operating condition, the theorem of superposition can be applied to Fig.5 so as to obtain the total CM current as:
R in
i cm
V1
Cn
20uF
Cp2
Cp1
L cm Fig. 6. The equivalent circuit with the second leg in place but not switching.
lower. With the modified equivalent circuit, this phenomenon now can be readily explained. First of all, if the second leg is detached, then Fig.5 reduces to Fig.2. The expression of the CM current icm in s domain can be derived as: I ' cm (s) =
sC p L(C p + C n )s 2 + R(C p + C n )s + 1
V1 ( s) ,
sC p L(2C p + C n )s 2 + R(2C p + C n ) s + 1
V1 (s)
1
(2)
icm
E
1 L(2C p + C n )
.
(4)
Apparently the frequency in the first case is higher, which is in consistence with what has been shown in Fig.4. As for the magnitude of the CM current, substitute s=jω’ into (1) and s=jω” into (2), and the admittances of the equivalent circuit at the resonant frequencies in these two cases can be derived as: Cp I ' cm ( jω ' ) = V1 ( jω ' ) R(C p + C n )
(5)
Cp I "cm ( jω" ) = . V1 ( jω" ) R(2C p + C n )
(6)
and
Inverter
Feedthrough Capacitors HF current probe
and
ω" =
[V1 (s) + V2 (s)]
To validate the proposed equivalent circuit, a single-phase full-bridge inverter test setup is installed, as shown in Fig.7. Simulation is made based on the proposed equivalent circuit with the parameters measured from the inverter test setup. Then the simulation results are compared with the experimental results. The simulation is made with MATLAB software. The CM current waveforms are recorded with a high frequency current probe. The CM spectra are measured with a spectrum analyser.
(3)
L(C p + C n )
L(2C p + C n )s + R(2C p + C n )s + 1
(7)
Form (1) and (2), the resonant frequencies in these two cases are respectively
ω' =
sC p 2
III. VALIDATION OF THE PROPOSED CIRCUIT (1)
where L = Lcab + Lcm , and R = Rin . Note that the 20µF capacitor is considered short-circuited due to its negligible impedance. If the second leg is in place but not switching, then the voltage source V2 in Fig.5 can be short-circuited, leaving only the stray capacitance Cp2 in that branch, as shown in Fig.6. Suppose Cp1 = Cp2 = Cp, the CM current in this case is: I "cm (s) =
I " ' cm (s) =
Load
Ground plane
Fig.7 The test setup for CM current measurement.
The test setup uses two 600V/50A IGBT half-bridge modules from SEMIKRON. The dc bus voltage is 150V, and the switching frequency is 10kHz. The measured parameters of the equivalent circuit are as follows: Cp =220pF, Cn =400pF, Lcab =1.2µH, Lcm =0.2µH, and Rin = 4Ω. The value of Rin is a little higher than expected. Part of the reason is that the current probe used to measure the CM current is connected throughout the experiment (see Fig.7). The probe is actually a current transformer with measuring resistor connected across its secondary winding, which introduces some extra damping effect. The case with the second leg detached from the dc bus is studied first. Based on (1), the simulated CM current waveform in this case is shown in Fig.8(a). Shown in Fig.8(b) is the recorded CM current waveform. The simulated CM
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2 1.5 1
Current(A)
0.5 0 -0.5 -1 -1.5 -2
7.5
7.525
7.55
7.575
7.6 7.625 Time(s)
7.65
7.675
7.7 x 10
(a)
-5
(b)
Fig.8 Simulated (a) and recorded (b) CM current waveforms with the second leg detached. (0.5A/div, 250nS/div) 90 80 70
Current(dBuA)
60 50 40 30 20 10 0
150kHz 300kHz
1MHz Frequency(Hz)
5MHz 10MHz
30MHz
(b) (a) Fig.9 Simulated (a) and measured (b) CM current spectra with the second leg detached. 2 1.5 1
Current(A)
0.5 0 -0.5 -1 -1.5 -2 5.1
5.125
5.15
5.175
5.2
5.225 5.25 Time(s)
(a)
5.275
5.3
5.325
5.35
x 10
-5
(b)
Fig.10 Simulated (a) and recorded (b) CM current waveforms with the second leg in place but not switching. (0.5A/div, 250nS/div)
current spectrum from 150kHz to 30MHz is shown in Fig.9(a). Shown in Fig.9(b) is the measured spectrum. Next, the second leg is installed back in place. But instead of being driven with normal gating signals, the upper and lower devices are driven into constant on and constant off states, respectively. Based on (2), the simulated CM current waveform is shown in Fig.10(a). Shown in Fig.10(b) is the recorded CM current waveform. The simulated CM spectrum is shown in Fig.11(a). Shown in Fig.11(b) is the measured spectrum.
From the above figures, it is observed that both the time domain and frequency domain simulation results match well with the experimental results. Both the simulation and the experiment demonstrate again the following feature: the presence of another leg, although it is not working, tends to lower the resonant frequency as well as the magnitude of the CM current. The reduction in resonant frequency is relatively more noticeable (from 7MHz to 6MHz in this study). The simulated CM current spectra have good precision up to 10MHz. Beyond this frequency range, the error increases
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90 80 70
Current(dBuA)
60 50 40 30 20 10 0
150kHz 300kHz
1MHz Frequency(Hz)
5MHz
10MHz
30MHz
(b) (a) Fig.11 Simulated (a) and measured (b) CM current spectra with the second leg in place but not switching. 2 1.5 1
Current(A)
0.5 0 -0.5 -1 -1.5 -2 5.1
5.125
5.15
5.175
5.2
5.225 5.25 Time(s)
5.275
5.3
5.325
5.35 -5
x 10 (b) (a) Fig.12 Simulated (a) and recorded (b) CM current waveforms with the inverter under unipolar PWM switching. (0.5A/div, 250nS/div)
90 80 70
Current(dBuA)
60 50 40 30 20 10 0
150kHz 300kHz
1MHz Frequency(Hz)
5MHz 10MHz
30MHz
(b)
(a)
Fig.13 Simulated (a) and measured (b) CM current spectra with the inverter under unipolar PWM switching.
quickly due to the limited precision of the equivalent circuit, which apparently does not cover all the stray parameters. Finally, the inverter is put into normal operation (unipolar PWM switching with both the two legs). Based on (7), the simulated CM current is shown in Fig.12(a). Shown in Fig.12(b) is the recorded CM current in this case. The simulated and measured CM spectra in this case are shown in Fig.13(a) and Fig.13(b), respectively. Again the there is a good agreement between simulation results and experimental results. It can also be noticed that the time domain waveforms
are nearly identical to what have been shown in Fig.10. This is because that under unipolar switching, commutations between the upper and lower devices of the two legs rarely happen simultaneously. As a result, when a commutation happens in one leg, the devices in the other leg are still staying in on or off state. Of course, the number of current pulses during each switching period is now doubled, therefore the CM current spectra are higher.
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IV. CONCLUSION
A modified equivalent circuit for common-mode current of single-phase full-bridge inverters is proposed. Simulations and experiments on the test setup verified the correctness of the proposed circuit. Compared with the previously proposed equivalent circuit, the circuit proposed in this paper have the following advantages: (1) it allows direct application of superposition theorem; (2) it provides more insights into the propagation mechanism of the CM noise; (3) with this circuit, both the noise source voltage and the stray capacitance of each phase leg do not have to be the same. This last benefit is especially useful to explain the working mechanism of certain active CM current compensation technique, in which each phase leg of the inverter can be equipped with an compensatory switching circuit to cancel out the CM current generated by it. V. ACKNOWLEDGMENT The authors would like to thank Huasong Fang and Junling Gao, for their help on the installation of the test setup. VI. REFERENCES [1] Laszlo Tihanyi, Electromagnetic Compatibility in Power Electronics, IEEE Press, 1995. [2] C. Chen, X. Xu, and D. M. Divan, “Conductive electromagnetic interference (EMI) noise evaluation for an Actively Clamped Resonant DC Link Inverter (ACRDCLI) for electric vehicle (EV) traction drive applications,” IEEE-IAS’97,
v 2, 1997, p.1550-1557. [3] L. Ran, S. Gokani, J. Clare, K. J. Bradley, and C. Christopoulos, “Conducted electromagnetic emissions in induction motor drive systems part I: time domain analysis and identification of dominant modes,” IEEE Transactions on Power Electronics. 1998, 13(4): 757-767. [4] L. Ran, S. Gokani, J. Clare, K. J. Bradley, and C. Christopoulos, “Conducted electromagnetic emissions in induction motor drive systems part II: frequency domain models,” IEEE Transactions on Power Electronics, 1998,13(4): 768-776. [5] H. Zhu, J.-S. Lai, A. R. Hefner, Jr., Y. Tang, and C. Chen, “Analysis of conducted EMI emissions from PWM inverter based on empirical models and comparative experiments,” IEEE-PESC’99, v 2, p.861-867. [6] H. Zhu, J.-S. Lai, A. R. Hefner, Jr., Y. Tang, and C. Chen, “Modeling-based examination of conducted EMI emissions form hard- and soft-switching PWM inverters,” IEEE Transactions on Industry Applications, 2001, 37(5): 1383-1393. [7] J.-S. Lai, X. Huang, E. Pepa, S. Chen and T. W. Nehl, “Inverter EMI modeling and simulation methodologies,” IEEE-IECON 2003, v 2, p.1533-1539. [8] X. Pei, K. Zhang, Y. Kang, and J. Chen, “Analytical estimation of common mode conducted EMI in PWM inverter,” IEEE-IAS 2004, p.2651-2656. [9] R. Scheich, J. Roudet, S. Bigot, and J. P. Ferrieux, “Common mode RFI of a HF power converter: phenomenon, its modeling and its measurement. IEE Conference Publication, v 7, n 377, System Engineering, 1993, p.164-169. [10] W. Teulings, J. L. Schanen, and J. Roudet, “A new technique for spectral analysis of conducted noise of a SMPS including interconnects,” IEEE-PESC’97, v 2, p.1516-1521.
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