Relatorio Final Space Vector

8/11/2019 Relatorio Final Space Vector

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COPPE / UFRJPROGRAMA DE ENGENHARIA ELTRICA

CPE 713 MICROPROCESSADORES APLICADOA ELETRNICA DE POTNCIA

MODULAO SPACE VECTOR EM LINGUAGEM C

PROFESSOR L. G. B. ROLIM

ALUNO: SAMUEL ALVES DE SOUZA

15/12/2011


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CPE713 Terceiro Trabalho Entrega 07/11/11

1) Escrever uma funo em C para calcular os valores instantneos dos sinais de

referncia para modulao space vector, com as seguintes caractersticas: os parmetros de entrada so as coordenadas ve vdo vetor resultante a sersintetizado, com amplitudes normalizadas (-1,0 < {v, v} < 1,0). os parmetros de sada so as referncias (ndices de modulao) ma , mb e mcnormalizadas (-1,0 < {ma , mb , mc} < 1,0) a serem comparadas com as portadorastriangulares para comandar cada fase de um inversor.

2) Criar um projeto no CCS para testar a funo do item 1 e medir seudesempenho (tempo mdio de execuo) usando o simulador para CPU da famliaC2000.

Bibliografia:[1] http://dx.doi.org/10.1109/ISIE.1999.798657[2] http://dx.doi.org/10.1109/IECON.1999.822220[3] http://dx.doi.org/10.1590/S0103-17592005000100002[4] http://dx.doi.org/10.1109/CERMA.2009.42


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1) Cdigo em linguagem C:

/ * 3o. Trabal ho CPE713 2011_03

SPACE VECTOR PWMProf . L. G. B. Rol i mAl uno: Samuel Al ves de Souza */

#i ncl ude / / ut i l i zado par a cal cul o seno/ coseno#def i ne np 1000 / / t amanho do vet or de dados para gr f i co

f l oat v[np]; / / vet or de dados par a gr f i counsi gned i nt p=0; / / i ni ci al i zao do pont ei r o do vet or de dadosunsi gned i nt set or =0; / / set or do space vect orf l oat w=377. 0; / / f r equenci a em r ad/ sf l oat k1=1. 0; / / t enso val pha e vbetha normal i zadaf l oat t =0. 0; / / t empo emsegundosf l oat val pha; / / t enso Val pha normal i zadaf l oat vbet ha; / / t enso Vbeta normal i zadaf l oat t ang; / / t angent e=Vbet a/ Val phaf l oat t emp_1; / / val or t empor r i of l oat t emp_2; / / val or t empor r i of l oat x; / / t empo x cl cul o ndi ce modul ao (r azo c cl i ca) f ase af l oat y; / / t empo y cl cul o ndi ce modul ao (r azo c cl i ca) f ase bf l oat z; / / t empo z cl cul o ndi ce modul ao ( r azo c cl i ca) f ase cf l oat ma; / / ndi ce de modul ao (r azo c cl i ca) f ase af l oat mb; / / ndi ce de modul ao (r azo c cl i ca) f ase bf l oat mc; / / ndi ce de modul ao (r azo c cl i ca) f ase cf l oat t 1; / / t empo de apl i cao vet or espaci al bsi cof l oat t 2; / / t empo de apl i cao vet or espaci al bsi cof l oat t s=0. 0005; / / t s=1/ f s f s=2 kHz f r equenci a de chaveament o

voi d mai n(voi d){

while(1){

/ * s i mul a gerao dos par amet r os de ent r ada: val pha e vbethaobs. : val pha e vbetha normal i zados por Vdc/ r ai z( 3

val pha ( - 1, +1) e vbet ha( - 1, +1) */val pha=k1*cos(w*t );vbetha=k1*si n(w*t );t ang=vbetha/val pha;

/ * t empos ( x, y e z) de apl i cao dos vetores espaci as bsi cost omados como f r ao do per odo de chaveamento */

t emp_1=vbet ha/2;t emp_2=0. 8660254*val pha;x=vbetha;y=t emp_1+t emp_2;z=t emp_1-t emp_2;

/ * i dent i f i ca setor * /if ((val pha==0)&&(vbetha==0))set or =0;else if ((val pha>0)&&(t ang>=0)&&(t ang


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else if ((val pha>0)&&(t ang>1. 73205))set or =2;else if ((val pha


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case 6: / * setor 6: t 1=y, t 2=- x ( ma, mc, mb) */t 1=y;t 2=-x;ma=(1-t 1-t 2)/2; / * taon=( 1- t 1- t 2) / 2 */mc=ma+t 1; / * t con=t aon+t 1 */mb=mc+t 2; / * t bon=t con+t 2 */

break;

}

t =t +0. 00005;v[p]=ma;if(++p==np) p=0;

}

}-


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2) Tempo mdio de execuo no TMS320F28335 usando o simulador Texas:

O tempo mdio de execuo foi aproximadamente 782 ciclos de clock.


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3) Grficos:

As entradas v e v so componentes do vetor espacial resultante e so

normalizadas pela mxima magnitude da tenso de fase ( )3(Vcc .

Entrada (-1,0 < v,< 1,0).

Entrada (-1,0 < v< 1,0).

Setor


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As sadas so os ndices de modulao normalizados.

Sada (-1,0 < ma < 1,0)

Sada (-1,0 < mb < 1,0)

Sada (-1,0 < mc< 1,0)


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4) Observaes;

Para desenvolvimento deste trabalho trabalho revisado a teoria de modulao

space vector, sendo utilizado as apresentaes das aulas da disciplina Controlede Mquinas Eltricas ( prof. Walter), o livro Modern Power Eletronics and ACDives (Bimal K. Bose) ed. 2002 e o material da Texas Instruments referente aobloco space vector (segue em anexo).

Procurou-se seguir a sequncia apresentada pela Texas, porm a determinaodo setor foi definido fazer de outra forma e foram encontados erros nas tabela 69,70 e 71, sendo necessrio fazer todo o desenvolvimento para localizar o erro eento o programa em linguagem C funcionar adequadamente.

Sequncia do cdigo C desenvolvido:

1-Gerao das componentes valpha e vbetha normalizadas (-1, +1);

2-Cculo de x, y e z (trs valores possveis de tempo de aplicao dos vetoresespaciais) ;

3-Determinao do setor aonde se localiza o vetor espacial resultante (baseadonos valores da tangente e nos sinais de valpha e vbetha);

4-Clculo de t1 e t2 (tempos de aplicao) dos vetores espaciais bsicosnormalizados pelo perodo t ( t1+t2+t0).

5-Clculo dos ndices de moduo (razes cclicas) taon, tbon e tcon;

6-Atribuio dos ndices de modulao as pernas (braos) do inversor.


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Background Information

SVGEN_DQ 197


The Space Vector Pulse Width Modulation (SVPWM) refers to a special switching se-

quence of the upper three power devices of a three-phase voltage source inverters(VSI) used in application such as AC induction and permanent magnet synchronous

motor drives. This special switching scheme for the power devices results in 3 pseudo-

sinusoidal currents in the stator phases.

motor phases

VDC +

a cb

Q6Q4Q2

Q5Q3Q1

Va Vb Vc

ca b

Figure 27. Power Circuit Topology for a Three-Phase VSI

It has been shown that SVPWM generates less harmonic distortion in the output volt-

ages or currents in the windings of the motor load and provides more efficient use of

DC supply voltage, in comparison to direct sinusoidal modulation technique.

ca b

VDC

a

A

b

B

c

C

Z

Z Z

N

ACI or PMSM

Figure 28. Power Bridge for a Three-Phase VSI

For the three phase power inverter configurations shown in Figure 27 and Figure 28,

there are eight possible combinations of on and off states of the upper power transis-

tors. These combinations and the resulting instantaneous output line-to-line and

phase voltages, for a dc bus voltage of VDC,are shown in Table 68.


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198 SPRU456

Table 68. Device On/Off Patterns and Resulting Instantaneous Voltages of a3-Phase Power Inverter

c b a V AN VBN VCN VAB VBC VCA

0 0 0 0 0 0 0 0 0

0 0 1 2VDC/3 VDC/3 VDC/3 VDC 0 VDC

0 1 0 VDC/3 2VDC/3 VDC/3 VDC VDC 0

0 1 1 VDC/3 VDC/3 2VDC/3 0 VDC VDC

1 0 0 VDC/3 VDC/3 2VDC/3 0 VDC VDC

1 0 1 VDC/3 2VDC/3 VDC/3 VDC VDC 0

1 1 0 2VDC/3 VDC/3 VDC/3 VDC 0 VDC

1 1 1 0 0 0 0 0 0

The quadrature quantities (in the (,) frame) corresponding to these 3 phase voltagesare given by the general Clarke transform equation:VsVAN

Vs (2VBNVAN) 3

In matrix from the above equation is also expressed as,

VsVs 23

1

0

12

32

12

32

VANVBNVCN

Due to the fact that only 8 combinations are possible for the power switches, VsandVscan also take only a finite number of values in the (,) frame according to the sta-tus of the transistor command signals (c,b,a). These values of Vsand Vsfor the corre-

sponding instantaneous values of the phase voltages (VAN, VBN,VCN) are listed in

Table 69.

Table 69. Switching Patterns, Corresponding Space Vectors and their (,)Components

c b a V s Vs Vector

0 0 0 0 0 O0

0 0 1 0 U0

0 1 0 U120

0 1 1 U60

1 0 0 U240

1 0 1 U300

1 1 0 0 U180

1 1 1 0 0 O111

23

VDC

VDC

3VDC3

VDC3

VDC

3

VDC3

VDC

3VDC3

VDC

3

23

VDC


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SVGEN_DQ 199

These values of Vsand Vs,listed in Table 69, are called the (,) components of thebasic space vectors corresponding to the appropriate transistor command signal

(c,b,a). The space vectors corresponding to the signal (c,b,a) are listed in the last col-

umn in Table 69. For example, (c,b,a)=001 indicates that the space vector is U0.Theeight basic space vectors defined by the combination of the switches are also shown

in Figure 29.

U120(010)

U240(100)

U60(011)

U300(101)

U180(110) U0(001)O111(111) O0(000)

Figure 29. Basic Space Vectors

Projection of the stator reference voltage vector Uout

The objective of Space Vector PWM technique is to approximate a given stator refer-

ence voltage vector Uoutby combination of the switching pattern corresponding to the

basic space vectors. The reference vector Uoutis represented by its (,) components,Ualfa and Ubeta. Figure 30 shows the reference voltage vector, its (,) components

and two of the basic space vectors, U0and U60. The figure also indicates the resultantand components for the space vectors U0and U60. Vsrepresents the sum ofthe components of U0and U60, while Vsrepresents the sum of the componentsof U0and U60. Therefore,

Vs 0VDC3

VDC

3

Vs 2VDC3 VDC3 VDC


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200 SPRU456

0

V

s

U60(011)

UbetaUout

T3T

U60

T1T

U0Ualfa U0(001) Vs

60

Figure 30. Projection of the Reference Voltage Vector

For the case in Figure 30, the reference vector Uoutis in the sector contained by U0and

U60.Therefore Uoutis represented by U0and U60. So we can write,

TT1T3T0

UoutT1T

U0T3T

U60

where, T1 and T3are the respective durations in time for which U0and U60are applied

within period T. T0 is the time duration for which the null vector is applied. These time

durations can be calculated as follows:

UbetaT3T

|U60| sin

UalfaT1T

|U0| T3T

|U60| cos

(60)

(60)

From Table 69 and Figure 30 it is evident that the magnitude of all the space vectors

is 2VDC/3. When this is normalized by the maximum phase voltage(line to neutral),

VDC/3, the magnitude of the space vectors become 2/3 i.e., the normalized magni-tudes are |U0|= |U60| =2/3. Therefore, from the last two equations the time durationsare calculated as,

T1T

2 3

UalfaUbetaT3TUbeta

Where, Ualfa and Ubeta also represent the normalized (,) components of Uoutwithrespect to the maximum phase voltage(VDC/3). The rest of the period is spent in applyingthe null vector T0. The time durations, as a fraction of the total T, are given by,

t1T1T 3 UalfaUbeta

t2T3TUbeta


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SVGEN_DQ 201

In a similar manner, if Uoutis in sector contained by U60and U120,then by knowing

|U60| = |U120| = 2/3 (normalized with respect to VDC/3), the time durations can bederived as,

t1T2T 1

2 3 UalfaUbeta

t2T3T 1

2 3 UalfaUbeta

where, T2is the duration in time for which U120is applied within period T

Now, if we define 3 variables X, Y and Z according to the following equations,

Y 12 3 UalfaUbeta

Z 12 3 UalfaUbeta

XUbeta

Then for the first example, when Uoutis in sector contained by U0and U60,t1= Z, t2=X.

For the second example, when Uoutis in sector contained by U60and U120, t1=Z, t2=Y.

In a similar manner t1 and t2 can be calculated for the cases when Uoutis in sectors

contained by other space vectors. For different sectors the expressions for t1 and t2

in terms of X, Y and Z are listed in Table 70.

Table 70. t1 and t2 Definitions for Different Sectors in Terms of X, Y and ZVariables

Sector U0, U60 U60, U120 U120, U180 U180, U240 U240, U300 U300, U0

t1 Z Z X X Y Y

t2 X Y Y Z Z X

In order to know which of the above variables apply, the knowledge of the sector con-

taining the reference voltage vector is needed. This is achieved by first converting the

(,) components of the reference vector Uoutinto a balanced three phase quantities.That is, Ualfa and Ubeta are converted to a balanced three phase quantities Vref1, Vref1and Vref1according to the following inverse clarke transformation:

Vref1Ubeta

Vref2UbetaUalfa 3

2

Vref3UbetaUalfa 3

2

Note that, this transformation projects the quadrature or component, Ubeta, intoVref1.This means that the voltages Vref1Vref2and Vref3are all phase advanced by 90

O

when compared to the corresponding voltages generated by the conventional inverse

clarke transformation which projects the component, Ualfa, into phase voltage VAN.The following equations describe the (,) components and the reference voltages:


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202 SPRU456

Ualfa sintUbeta costVref1 costVref2 cos(t 120 )Vref3 cos(t 120 )

Note that, the above voltages are all normalized by the maximum phase volt-

age(VDC/3).

907FFFh

0

8000h

Ubeta

Ualfa

Figure 31. (,) Components of Stator Reference Voltage

1207FFFh

0

8000h

Vref1 Vref2Vref3

Figure 32. Voltages Vref1Vref2and Vref3

From the last three equations the following decisions can be made on the sector infor-

mation:

If Vref1> 0 then a=1, else a=0

If Vref2> 0 then b=1, else b=0

If Vref3> 0 then c=1, else c=0

The variablesectorin the code is defined as, sector = 4c+2b+a

For example, in Figure 29 a=1 for the vectors U300,U0and U60. For these vectors the

phase of Vref1are t=300,t=0 and t=60respectively. Therefore, Vref1> 0 when a=1.

The (,) components, Ualfa and Ubeta, defined above represent the output phasevoltages VAN, VBNand VCN. The following equations describe these phase voltages:

VAN sintVBN sin(t )VCN sin(t )

120

120

The Space Vector PWM module is divided in several parts:

Determination of the sector

Calculation ofX, YandZ


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SVGEN_DQ 203

Calculation of t1and t2

Determination of the duty cycle taon, tbonand tcon

Assignment of the duty cycles to Ta, Tband Tc

The variables taon, tbonand tconare calculated using the following equations:

taonPWMPRD t1 t2

2tbontaon t1tconTbon t2

Then the right duty cycle (txon) is assigned to the right motor phase (in other words,

to Ta, Tb and Tc) according to the sector. Table 71 depicts this determination.

Table 71. Assigning the Right Duty Cycle to the Right Motor Phase

Sector U0, U60 U60, U120 U120, U180 U180, U240 U240, U300 U300, U0

Ta taon tbon tcon tcon tbon taon

Tb tbon taon taon tbon tcon tcon

Tc tcon tcon tbon taon taon tbon

Example:

Sector contained by U0and U60.

T

t

t

t

PWM1

PWM3

PWM5

t

Ta

Tc

Tb

tcon

tbon

taon

T04 T62 T62 T04 T04 T64 T44 T04

V0 V6 V4 V7 V7 V6 V4 V0

Figure 33. PWM Patterns and Duty Cycles for Sector Contained by U0andU60

Table 72. Variable Cross Ref Table

Variables in the Equations Variables in the Code

a r1

b r2

c r3

Vref1 Va

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Relatorio Final Space Vector