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
Background Information
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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Background Information
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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Background Information
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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Background Information
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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Background Information
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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Background Information
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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Background Information
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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