Modeling of Switching and Conduction Losses in Three - Phase SPWM VSC Using Switching Function...

8/7/2019 Modeling of Switching and Conduction Losses in Three - Phase SPWM VSC Using Switching Function Concept-1

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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.

Modeling of Switching and Conduction Losses in Three - Phase SPWM VSC Using Switching Function...

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