Matlab simulink model three phase voltage source inverter

AtifIqbal, Adoum, Lamine, ImtiazAshraP, Mohibullah Aligarh Muslim University, India (2)Liverpool John Moores University, UK

MATLAB/SIMULINK MODEL OF SPACE VECTOR PWM FOR THREE-PHASE

VOLTAGE SOURCE INVERTER AtifIqbal(') AdoumLamine(2) ImtiazAshraP') Mohibullah(l)

(1) Aligarh Muslim University, India(2) Liverpool JohnMooresUniversity,UK

ABSTRACT Variable voltage and frequency supply to ac drives is invariably obtained from a three-phase voltage source inverter (VSI) Anumber of Pulse width modulation (PWM) scheme is usedto obtain variable voltage and frequency supply The mostwidely used PWMschemes for three-phase VSI are carrier-based sinusoidal PWM and space vector PWM (SVPWM) There is an increasing trend of using space vector PWM (SVPWM) because of their easier digital realisation and better dc bus utilisation This paper focuses on step by step development of MATLAB/SIMULINK model of SVPWM Firstly model of a three-phase VSI is discussed based on space vector representation Next simulation model ofSVPWMis obtainedusing NIATLAB/SIMULINK Simulation resultsarealsoprovided

1 INTRODUCTION diode for protection Leg voltage waveforms is shown

inFig.2for180°conduction mode

Variable voltage and frequency supply for as drives is

invariably obtained from athree-phase VSI A number i

dc bus utilisation by 15.15%, further digital

implementation of this scheme is easier [1,2] The

SVPWM is identified as an alternative method of _ _

determination of switching pulse width and their N

position The major advantage ofSVWPM stem from

the fact that there isadegree of freedom ofspacevector Figure 1 Power circuit of a three-phase VSI placement in a switching cycle This improves the

The main focus of this paper is to develop a simple

MATLAB/SIMULINK model Thereasonfor choice of z73T 2;T3 Z 4;T3 5;T3 2X MATLAB/SIMULINK as a development tool is VB

because it is the most important and widely used VB

simulation software and is an integral part of taught

programme in most of the universities in

Electrical/Electronics Engineering courses Firstly VC

model ofathree-phase inverterinpresentedonthe basis l

ofspace vector representation This is followed bythe Figure2.Leg voltagewaveform ofathree-phase

MATLAB/SIMULINK model for the SVPWM is

presented Various simulation resultsarealso included It is observed fromFig. 2 that one inverter leg's state

changes after aninterval of60° and theirstate remains

2 THREE-PHASE VSIMODELLING REVIEW constant for 60° interval Thus it follows that the leg

voltages will have six distinct and discrete values in one

A mathematical model ofthree-phase is presented here cycle (36O°).

based on space vector representation The power circuit Space vector representation of the three-phase inverter topology ofathree-phase VSI is shown in Fig 1 output voltages is introduced next Space vector is Each switch in the inverter leg is composed of two defined as;

back-to-back connected semiconductor devices One of -* 2

-these two is a controllable device and other one is a v,=jVa +aVb +aVC) (1)

1096

where a=exp(j2UT/3). The space vector is a AL Img.

simultaneous representation of all the three-phase ""I

quantities It is a complex variable and is function of

timein contrast tothe phasors

Phase-to-neutral voltages of a star-connected load are

most easily found by defining a voltage difference

between thestarpointnof the load and the negative rail 7,8

of the dc bus N The following correlation then holds (011) X'.4 '(100) Real true:

VA Va+VnN

VC =Vc+VnN

Substitution of (3) into (2) yields phase-to-neutral The binary numbers on the figure indicate the switch voltagesof the load in thefollowingform: stateof inverter legs Here 1 impliesupperswitch being

Va =(2/3)VA -(I/3)(VB +VC) on and 0refersto the lower switch of the leg being on

Vb =(2/3)VB-(1/ 3)(VA+VC) (4) Themostsignificantbit is forleg A,the leastsignificant

Vc =(2/3) vC -(1/3) (VB+ VA) bit is relatedtolegC and the middle is forlegB

Phase voltages are summarised in Table 1 and their 3 SPACE VECTOR PWM

correspondingspace vectors arelistedinTable2

This section briefly discusses the space vector PWM Table 1Phase voltage values for different switching principle This PWM method is frequently used in

states vector controlled and direct torque controlled drives In

1 1,4,6 (2/3) Vdc -(1/3)Vdc -(1/3)Vdc exercised in rotating reference frame

Itis seen intheprevious section thatathree-phaseVSI

, , | (1/3)Vdc (1/3)Vdc -(2/3)VdC andtwo zero states Thesevectorsform ahexagon (Fig.

3) which can be seen as consisting of six sectors

3 2,3,6 -(1/3)VdC (2/3)Vdc -(1/3)VdC spanning 60° each The reference vector which

represents three-phase sinusoidal voltage is generated

4 |2)35 -(2/3)Vc (I(3) Vc (I(3)Vdc using SVPWMby switchingbetweentwo nearestactive

,,' Z/d))V~,fc ~l/.))vdc ~l/.))vdc vectors and zero vector. To calculate the time of

5 2,4,5 -(1/3)VdC -(1/3)VdC (2/3)vdc application of different vectors, consider Fig 4,

depicting the position of different available space

vectorsand the referencevectorinthe firstsector

6 1,4,5 (1/3)vdC -(2/3)vdC (1/3)vdC

* mg

Table2Phasevoltagespace vectors

12/3) Vdc b - v

2 (2/3) Vdc exp (IjT 13)

6 (2/3) Vdc exp(15w/3) Figure 4 Principle of space vector time calculation

The discrete phase voltage space vector positions are is found from Fig 4 as

shown in Fig 3

Iv Three-phase sinusoidal voltage is generated using

(5) equivalent using Clark's transformation equations [1]

tb =- sin (2;T/3)blocks. Further thetwo-phase equivalent is transformed

to t - ta - tb (6) 'Simulink extras' sub-library.Theoutputof this block is

where Va = vb =(2/3)V,. in order to obtain fixed corresponding angle of the reference as the second switching frequency and optimum harmonic output.

performance from SVPWM, each leg should change its 4.2 SwitchingTime Calculation

sateonly once inone switching period. This is achieved The switching time and corresponding switch state for

by applying zero state vector followed bytwo adjacent

active state vector in half switching period The next blck 'sf sing is (5)uand () the Matiab

half of the switching period is the mirror image of the block 'sfr using expressions (5) and (6). The Matlab first half The total switching period is divided intro 7 the reference and timer signal for comparison The parts,thezero vectorisapplied for 1/4thofthe totalzero

vector time first followed by the application of active angle of the referencevoltage is hold for eachswitching vectors for half oftheir application time and then again period so that its value does not change during time

zero vector is applied for 1/4th of the zero vector time calculation. The angle information is used for sector

- - ., identification in Matlab code 'aaa' Further, a ramping This is then repeated in the next half of the switching time signal S generatedto be used n Matlab code This period This is how symmetrical SVPWM is obtained

The leg voltage in one switching period is depicted in ramp is generatedusing 'repeating sequence' from the Fig.5 forsector1 Flg 5 Iorsecto 1. ts The Matlab code firstly identifies the sector of thesourcesub-library.

P os referencevoltage. The time ofapplicationof active and

t 4 ta/2 :tb/2 to/2 tb/2 : ta/2 to/4 zero vectors are then calculated The times are then

arranged according to Fig 5 This time is then compared with the ramp timer signal. Depending upon

defined This switch state is then passed on to the inverter block The code isgiveninAppendix1

4.3Three-phaseInverter Block

k 8 V V V V , , < The inverter model is build using 'function' blocks

Figure 5 Leg voltages and space vector disposition inverter block is the phase voltages

foroneswitching period insectorI

The sinusoidal reference space vector form a circular 4.4 Filter Blocks

trajectory inside the hexagon The largestoutputvoltage The PWM voltage signal is filtered using first order magnitude that can be achieved using SVPWM is the filter. This is implemented using 'Transfer function' radius of the largest circle that can be inscribed within block from 'Continuous' sub-library The time constant the hexagon This circle is tangential to the mid points ofthefirst-order filter is chosenas0.8ms

ofthe linesjoining the ends of the active space vector

Thus the maximum obtainable fundamental output 4.5 Voltage Acquisition

vs =-V,,cos(/T/6)= > V (7)

Simulation is carriedoutusing the developed model for maximum obtainable referencevoltage and the resulting filteredleg and phase voltagesare shown inFigs. 8 and 9

development of Matlab/Simulink model for SVPWM

The Simulink model is shown in Fig 6 Each block is Asml albSmln oe speetdt further elaborated in Fig. 7 The Matlab code used to

generate the switching patternsub-blocks ofFig. 6 iS described in iS alsotheprovided followingEachsub- of the VSI modelreesnai.AMtabSmikbsdmolfrimlenSVWiSalso reported based on space vectorfothe-asVS.Abefrvw

step-by-1098

La vs

HptinG

RepEating S,equencDe

Figure 6 Matlab/Simulink Model of SVPWM

cosu [1 f2' p if1 1sqr() n

Va ref (2t3)(u[11+ u[2]foosg2 p i/3)+ u[S]foosgcVp iS3)) (7k

Magnitude

Vfd

ocosgu[1]2-pi'f1-2rpi/3ysqrbp) B Mux

Vb ref

| ~~~(13)SIu [2]:si n(2: pi/3)+ u[B]:si n(2:2=p ii3 -1 C W nG)

A ngle

~~~

~~~~~Ca rtesia to

(a)

[ | y~~~(dcI3Sp(2:u[1]- u[2]- u 3]) ]

F on

Figure 7 Sub-blocks of Matlab/Simulink model: (a) Reference voltage generation (b) VSI (c) Filters

A ~~~~~~~~~~~~~~~Va Vb Vc

0.8

0.6

-0.2 0.3

step model development is reported The presented tO=(ts-ta-tb);

model gives an insight into the SVPWM By varying the tl=[tO/4 ta/2 tb/2 tO/2 tb/2 ta/2tO/4];tl=cumsum(tl); magnitude of the input reference different modulation vl=[O 0 0 1 0 0O];v2=[O 11 11 1 O];v3=[O0 1 1 1 0 0];

if(Y<t(I))

end [1] Holmes, G.D and Lipo, T.A., Pulse Width end

Modulation for Power Converters - Principles and sa=vl();sb=v2(j);sc=v3(j);

Practice, IEEE Press Series on Power Eng., John Wiley end

andSons,Piscataway,NJ, USA, 2003 0osectorIV

if(x>=-pi)&(x<-2*pi/3)

Blaabjerg, F., Control in power electronics- selected tb=mag* sin(pi/3 -adv);ta=mag * sin(adv);

problems, Academic Press,California,USA, 2002 tO=(ts-ta-tb);

[3] Implementing SVPWM with AMD, tl=[tO/4ta/2 tb/2 tO/2 tb/2 ta/2tO/4];tl=cumsum(tl);

Application notes, Analogue Electronics vl=[O0 0 1 00 0];v2=[0 0 1 1 1 00];v3=[0 11 11 1 0];

end

%MatlabCode to generate Switching functions sa=vl();sb=v2(j);sc=v3(j);

%0Inputs aremagnitudeu1(:),angleu2(:) end

00andramptime signal for comparison u3(:) 00 sectorV

function[sfl=aaa(u) if(x>=-2*pi/3) &(x<-pi/3)

ts=0.0002;vdc=1;peak_phase max=vdc/sqrt(3); adv=x+2*pi/3;

x=u(2); y=u(3); mag=(u(l)/peakphasemax) *ts; ta=mag*sin(pi/3-adv);tb=mag sin(adv);

if(x>=O)&(x<pi/3) tl=[tO/4ta/2 tb/2 tO/2 tb/2 ta/2tO/4];tl=cumsum(tl);

ta=mag * sin(pi/3-x);tb=mag * sin(x); vl=[O0 1 1 1 00];v2=[0 0 0 1 0 00];v3=[0 11 11 1 0];

tl=[tO/4ta/2 tb/2 tO/2 tb/2 ta/2 tO/4];tl=cumsum(tl); if(y<t1(j))

vl=[O 11 1 1 0];v2=[00 1 1 1 00];v3=[000 1 0 0 0]; break

sa=vl );sb=v2(j);sc=v3(j); if (x>=-pi/3) &(x<O)

tb=mag *sin(pi/3-adv);ta=mag * sin(adv); vl=[O 11111 0];v2=[0 0 0 1 0 00];v3=[00 1 11 00];

tl=[tO/4ta/2 tb/2 tO/2 tb/2 ta/2tO/4];tl=cumsum(tl); if(y<t1(I))

vl=[O0 1 1 1 00];v2=[01 11 1 10];v3=[00 0 1 0 0 0]; break

sa=vl(j);sb=v2(j);sc=v3(j); Corresponding Author: Dr Atif Iqbal, Reader,

if(x>=2*pi/3)&(x<pi) 2901029, Mob ±91 9411210372, Email:

ta=mag * sin(pi/3-adv);tb=mag * sin(adv);

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