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Abstract--The designer of power converters must model the
losses of converter switches to optimize the performance of
system. In this paper, the losses of three-phase SPWM VSC are
modeled using switching function concept. This model is
simulated and its results are compared with accurate method,
which is based on the semiconductor characteristics. It is shown
that the suggested method includes simplicity, convergence, and
short run-time of simulation.
Index Terms--Three-Phase SPWM VSC, Switching Function,
Conduction Losses, Switching Losses.
I. INTRODUCTION
N RECENT YEARS, voltage source converters (VSCs) are
widely used as static power converter in AC drives, HVDC
light transmission, FACTS devices, and etc.
The basic elements used in VSC are IGBTs and diodes.
Because of economical and technical importance of powerdissipation, the designers must consider and minimize the
losses of these devices [1]-[5].
The losses of a switching device can be classified in three
groups: off-state, conduction, and switching losses. The
leakage current during the off-state is negligibly small
therefore the power losses during this state can be neglected.
As a result, only conduction and switching losses must be
exactly modeled [1]-[5].
There are several methods to model these losses. In the case
of modeling with PSPICE and SABER, the converter circuits
can be schematically expressed by using actual power
semiconductor device models and passive elements [6]-[9]. In
the case of modeling with MATLAB, the proper stateequations should be obtained in order to describe the power
converter circuit [6]-[9]. However, these models have shown a
number of problems. These problems include complexity,
slow execution times, large amount of generated data, andconvergence [6]-[9].
To understand and to optimize the performance of power
converters, it is shown that the switching function concept is a
powerful tool which can overcome the mentioned problems
[6].
The authors are with the Department of Electrical Engineering, Amirkabir
University of Technology (Tehran Polytechnic), No 424, Hafez Ave., 15914
Tehran, Iran (e-mail: [email protected]; [email protected]).
In this paper, for a three-phase SPWM VSC system the
different modelling methods of conduction and switching
losses based on switching function concept are presented and
compared.
II. SWITCHING FUNCTION THEORY
According to the operation mode of the static power
converters, they can be modeled as a block box with the DC
and AC, input and output variables. The transfer function of
this model should describe the performance of the converter
[6]-[8].
The transfer function can be used to compute, e.g., the
output voltage of VSC (a dependent variable) in terms of the
input voltage (which is an independent variable) [6]-[8].
Fig. 1(a) and (b) show the detailed configuration and black
box presentation of three-phase VSC, respectively. Based on
the switching function theory input current (Iin) and output
voltage (Vab, Vbc and Vca) are the dependent variables andinput voltage (Vd) and output current (Ia, Ib, and Ic) are the
independent variables. The relationship between the input and
output variables can be written as follows:
[Vab, Vbc, Vca]=TF. Vd (1)
Iin=TF. [Ia, Ib, Ic]T
(2)
where TFis the transfer function of three-phase VSC.
Generally, the transfer function consists of the several
switching function, e.g.:
TF= [SF1, SF2, SF3 ]
In order to define switching functions, a switching control
strategy must be selected. In this paper, the sinusoidal PWM
(SPWM) control strategy (Fig. 2(a)) result in the two
switching functions (SF1, SF2), which are shown in Fig. 2(b)
and (c).
The switching function SF1 expresses the Vao, Vbo and Vco
and it is used to calculate the converter line-to-line voltages
(Vab, Vbc and Vca) and phase voltages (Van, Vbn and Vcn). The
switching function, SF2 designates the voltage across the
switch and the load current (Ia, Ib and Ic). SF1 and SF2 can be
written as follows:
=
=1
1 )sin(n
n tnASF (4)
=+= 1
02 )sin(n
n tnBBSF (5)
Modeling of Switching and Conduction Losses
in Three-Phase SPWM VSC Using Switching
Function ConceptM. G. Hosseini Aghdam and G. B. Gharehpetian
I
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Fig. 1. (a) Detailed and (b) Black box presentation of three-phase VSC
III. FUNCTIONAL MODEL
Fig. 3 shows the functional model of three-phase SPWM
VSC. This model consists of nine functional blocks based on
the switching functions SF1 and SF2. The system losses of this
model can be calculated.
To generate the two switching function signals (SF1 and
SF2) for each phase, in the SPWM block, the carrier signal
(Vcarrier) is compared with three different reference signals
(Vref_a, b, c
) and process in the switching function block.
Using the switching function SF1, the Vao, Vbo and Vco can be
obtained as follows:
=
==1
1)sin(.
2.
2 nn
d
a
d
aotnA
VSF
VV
=
==1
1)120(sin.
2.
2 nn
d
b
d
botnA
VSF
VV
=
+==1
1)120(sin.
2.
2 nn
d
c
d
cotnA
VSF
VV (6)
Then, the inverter line-to-line voltages (Vab Vbc and Vca) can be
derived.
=
+==1
)30(sin.2
3
n
ndboaoabtnAVVVV
=
==1
)90(sin.2
3
n
ndcobobctnAVVVV
=
+==1
)150(sin.2
3
n
ndaococatnAVVVV (7)
Also, in order to calculate the inverter phase voltages (Van, Vbn
and Vcn
), Vno
must be calculated.
)(3
1coboaono
VVVV ++= (8)
Now the phase voltages, i.e. the output of the converter block
in Fig. 3, (Van ,Vbn and Vcn), can be derived as follows:
Van=Vao-Vno
Vbn=Vbo-VnoVan=Vco-Vno (9)
Assuming a balanced R-L load, the load currents (Ia, Ib and Ic)
are obtained.
LjR
V
Z
VI an
a
an
an+
==
LjR
V
Z
VI bn
b
bn
bn+
==
LjR
V
Z
VI can
c
cn
cn+
== (10)
Then, the switch currents (IS1, IS3and IS5) can be calculated.
IS1=Ia. SF2-aIS3=Ib. SF2-bIS5=Ic. SF2-c (11)
The switch current (IS1) can be determined as follows:
IS1=IS1-S-IS1-D (12)
where IS1-Sand IS1-Dare the pure switch current and the pure
diode current the switch S1, respectively.
Now, the converter input current (Iin) can be obtained by
following equation.
Iin=IS1+IS3 +IS5 (13)
Fig. 2. SPWM control strategy and switching functions, (a) Carrier (Vcarrier)
and reference (Vref_a) signals, switching functions (b) SF1 and (c) SF2
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Fig. 3. The model of three-phase SPWM VSC.
IV. SWITCHING AND CONDUCTION LOSSES
As it can be seen in Fig. 3, two methods of (a) and (b)have been used to calculate the switching and conduction
losses.
In the method (a) the power dissipation during
conduction is computed by multiplying the on-state
saturation voltage (von) by the on-state current (ic).
onc
vip .= (14)
The absolute value of the on-state current is used in the
above equation, because this current is always positive,
regardless of the direction of load current.
The von voltage can be approximated by [1]-[3]:
conoon
iRVv .+= (15)
Where Vo is the threshold voltage and Ron is the equivalentresistance of the resistive components presenting voltage
drop across the power device.
The average conduction losses of each device is:
=
dpPlossconductionavg
.2
1.
(16)
In the method (a), since the DC link voltage in VSC is
constant, switching energy can be assumed to be a linear
function of current [1]-[5]. Then, the average switching
losses for diode and controllable switch can be written as
follows:
=
dfiEPccreclossswitchingavgD...
2
1.
(17)
+=
dfiEEPccoffonlossswitchingavgS..).(
2
1.
(18)
Where fc is switching frequency, Erec[J/A], Eon[J/A] and
Eoff[J/A] are reverse-recovery energy coefficient, turn-on
switching energy coefficient and turn-off switching energy
coefficient, respectively. It must be noted that since diode
turns on rapidly (compared to the controllable switch) the
switching energy of diode at turn-on can be neglected.
In the other method, i.e. method (b), the conduction
losses are computed by multiplying the on-state voltage by
the on-state current. The on-state voltage is a function of
switch current, gate voltage of IGBT, and etc. Fig. 4(a)
shows the collector current versuscollector-emitter voltage
of IGBT (SKM 400 GB 124D [10]). Fig. 4 (b) shows the
V-Icharacteristic of the diode. These curves can be
approximated by the following equations.
>+
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The most accurate method of switching losses
calculation is the current and voltage waveforms
determination during transitions. The point by point
multiplication of these curves results in the accurate data
[1]. The area under the power waveform is the switching
energy at turn-on or turn-off transitions. Fig. 5 shows theswitching energy versus switch current for IGBT and diode
(SKM 400 GB 124D [10]). These curves are approximate
by:
Erec-diode=0.0001I2
D+0.073ID+0.2111 (21)
Eon-switch=0.0002I2
S+0.0497IS+6.4364 (22)
Eoff-switch=0.1309I2
S+3.8182 (23)
(a)
(b)
Fig. 5. (a) IGBT turn-on/turn-off energy and (b) Diode turn-off energy.
V. SIMULATION RESULTS
The model, shown in Fig. 1 is simulated with the
following parameters:
DC-link input voltage: Vd=300V,
Load: R=5 and L=20mH,Carrier and reference signals frequencies: 1 kHzand 50 Hz,
Modulation index=0.8 and
IGBT type: SKM 400 GB 124D [10].
As shown in Figures 6 and 7, using functional model
(Fig. 3) the switching functions SF1 and SF2 and then, the
converter phase voltage (Van) and line-to-line voltage (Vab)
can be successfully obtained.
Figures 8-10 show the converter current waveforms. Fig.
8 (a) shows the three balanced load currents (Ia, Ib and Ic)
under the balanced load condition. According to equation
(11), the switch S1 current can be calculated as shown in
Fig. 8 (b). The pure switch current (IS1-S) and pure diode
current (IS1-D) are shown in Fig. 9 (a) and (b). Fig. 10shows the converter input current.
Figures 11 and 12 present the VSC losses which are
calculated based on method (a). Fig. 11 (a) and (b) show
the conduction losses and figures 12 (a), (b) and (c) show
the switching losses in IGBT and diode, respectively.
The results of the calculations based on method (b) are
given in figures 13 and 14. Fig. 13 (a) and (b) show the
conduction losses and figures 14 (a), (b) and (c) show the
switching losses in IGBT and diode, respectively.
As it can be seen from simulation results of the both
methods, i.e. figures 11-14, the method (a) presents the
same accuracy as the method (b) and also it is simple to
model, has a fast execution time with MATLAB and has
not any convergence problem.
Fig. 6. Switching functions SF1 and SF2with the SPWM control.
Fig. 7. Voltage waveforms of VSC with the SPWM control, (a) phase
voltage (Van) and (b) Line-to-Line voltage (Vab).
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Fig. 8. Current waveforms of VSC with the SPWM control, (a) load
currents (Ia, Ib and Ic) and (b) switch current (Is).
Fig. 9. Current waveforms of VSC with the SPWM control, (a) pure
switch current (Is-S) and (b) pure diode current (Is-D).
Fig. 10. Inverter input current (Iin)
Fig. 11. Conduction losses of SPWM VSC; method (a), (a) switch (IGBT)
conduction losses [mJ] and (b) diode conduction losses [mJ].
Fig. 12. Switching losses of SPWM VSC; method (a), (a) switch (IGBT)
turn-on switching losses [mJ], (b) switch (IGBT) turn-off switching losses
[mJ] and (c) diode turn-off switching losses [mJ].
Fig. 13. Conduction losses of SPWM VSC; method (b), (a) switch (IGBT)conduction losses [mJ] and (b) diode conduction losses [mJ].
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Fig. 12. Switching losses of SPWM VSC; method (b), (a) switch (IGBT)
turn-on switching losses [mJ], (b) switch (IGBT) turn-off switching losses
[mJ] and (c) diode turn-off switching losses [mJ].
VI. CONCLUSION
Based on switching function concept, the losses of three-
phase SPWM VSC has been modeled. The simulation
results of this model are compared with the method which
is based on IGBT and diode characteristics modeling. The
simulation results verify the accuracy of the suggested
method. It is shown that this method is simple to model and
has a short run-time of simulation, too.
VII. REFERENCES
[1] T. J. Kim, D. W. Kong, Y. H. Lee, and D. S. Hyun, "The Analysis of
Conduction and Switching Losses in Multilevel-Inverter System", Power
Electronics Specialists Conference, 2001. PESC. 2001 IEEE 32nd Annual,
Vol.3 pp. 1363-1368.
[2] K. Berringer, J. Marvin, and P. Perruchoud, "Semiconductor Power
Losses in AC Inverters", in Conf. Rec. IEEE-IAS Annu. Meeting, 1995, pp.
882-888.
[3] F. Casanellas, "Losses in PWM Inverters Using IGBTs", Proc. IEEE-
Elect. Power Applications, Vol. 144, No. 5, Sept. 1994, pp. 235-239.
[4] P. A. Dahono, Y. Sato, and, T. Kataoka, ''Analysis of Conduction
Losses in Inverters", Proc. IEEE-Elect. Power Applications, Vol. 142, No.
4, July 1995, pp. 225-232
[5] H. van der Broeck, "Analysis of the Harmonic in Voltage-Fed Inverter
Drive Caused by PWM Schemes with Discontinuous Switching
Operation", EPE'91, Conf. Proceedings, Vol. 3, 1991, pp. 261-266.
[6] B. K. Lee, and M. Ehsani, "A Simplified Functional Simulation Model
for Three-Phase Voltage-Source Inverter Using Switching FunctionConcept", IEEE Trans. Industrial Electronics, Vol. 48, No. 2, April 2001,
pp. 309-321.
[7] P. D. Ziogas, E. P. Wiechmann, and V. R. Stefanovic, "A Computer-
Aided Analysis and Design Approach for Static Voltage Source Inverter",
IEEE Trans. Industry Applications, Vol. IA-21, Sept. /Oct. 1985, pp. 1234-
1241.
[8] E. P. Wiechmann, P. D. Ziogas, and V. R. Stefanovic, "Generalized
Functional Model for Three-Phase PWM Inverter/Rectifier Converters", in
Conf. Rec. IEEE-IAS Annu. Meeting, 1985, pp. 984-993 .
[9] L. Salazar, and G. Joos, "PSPICE Simulation of Three-Phase Inverter
by Means of Switching Functions", IEEE Trans. Power Electronics, Vol.
9, Jan. 1994, pp. 35-42.
[10] www.semicron.com/Products/IGBT/ SKM 400 GB 124D.
VIII. BIOGRAPHIES
M. Ghasem Hosseini Aghdam was born in
Shabestar, Iran on September 21, 1978. He
received the B.Sc. degree in electrical
engineering from Tabriz University, Tabriz,
Iran, in 2000, and received the M.Sc. degreein electrical engineering from Amirkabir
University of Technology (Tehran
Polytechnic), Tehran, Iran, in 2003. He is
currently working toward the Ph.D. degree
at Amirkabir University of Technology
(Tehran Polytechnic), Tehran, focusing on
control and modulation of multilevel converters.
His research interests include modulation theory, multilevel
converters, and fundamental principles for power electronic
converters.Gevorg B. Gharehpetian was born in
Tehran, in 1962. He received his B.Sc. and
M.Sc. degrees in electrical engineering in
1987 and 1989 from Tabriz University,
Tabriz, Iran and Amirkabir University of
Technology (AUT), Tehran, Iran,respectively, graduating with First Class
Honors. In 1989 he joined the Electrical
Engineering Department of AUT as a
lecturer. He received the Ph.D. degree in
electrical engineering from Tehran
University, Tehran, Iran, in 1996. As a
Ph.D. student he has received scholarship from DAAD (German Academic
Exchange Service) from 1993 to 1996 and he was with High Voltage
Institute of RWTH Aachen, Aachen, Germany. He held the position of
Assistant Professor in AUT from 1997 to 2003, and has been Associate
Professor since 2004.
Dr. Gharehpetian is a Senior Member of Iranian Association of Electrical
and Electronics Engineers (IAEEE), member of IEEE and member of
central board of IAEEE. Since 2004 he is the Editor-in-Chief of the
Journal of IAEEE.
The power engineering group of AUT has been selected as a Center ofExcellence on Power Systems in Iran since 2001. He is a member of this
center and since 2004 the Research Deputy of this center.
He is the author of more than 120 journal and conference papers. His
teaching and research interest include power system and transformers
transients, FACTS devices and HVDC transmission.
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