Transcript SVPWM - ENCON - ENCON

Space Vector Modulation (SVM)
PWM – Voltage Source Inverter
Open loop voltage control
vref
PWM
AC
motor
VSI
Closed loop current-control
iref
PWM
AC
motor
VSI
if/back
PWM – Voltage Source Inverter
S1
S3
S5
+ va -
Vdc
a
+ vb b
S4
S6
+ vc S2
c
N
va*
vb *
vc*
Pulse Width
Modulation
S1, S2, ….S6
n
PWM – Voltage Source Inverter
PWM – single phase
Vdc
dc
vc
vc
vPulse
width
tri
modulator
qq
PWM – Voltage Source Inverter
PWM – extended to 3-phase  Sinusoidal PWM
Va*
Pulse width
modulator
Vb*
Pulse width
modulator
Vc *
Pulse width
modulator
PWM – Voltage Source Inverter
SPWM – covered in undergraduate course or PE system (MEP 1532)
In MEP 1422 we’ll look at Space Vector Modulation (SVM)
– mostly applied in AC drives
Space Vector Modulation
Definition:
Space vector representation of a three-phase quantities xa(t), xb(t) and
xc(t) with space distribution of 120o apart is given by:

2
x  x a ( t )  ax b ( t )  a 2 x c ( t )
3

a = ej2/3 = cos(2/3) + jsin(2/3)
a2 = ej4/3 = cos(4/3) + jsin(4/3)
x – can be a voltage, current or flux and does not necessarily has to be sinusoidal
Space Vector Modulation

2
x  x a ( t )  ax b ( t )  a 2 x c ( t )
3

Space Vector Modulation


2
vx  vx aa ( t )  av
axbb ( t )  a 22vxcc ( t )
3
Let’s consider 3-phase sinusoidal voltage:
va(t) = Vmsin(t)
vb(t) = Vmsin(t - 120o)
vc(t) = Vmsin(t + 120o)
Space Vector Modulation

2
v  v a ( t )  av b ( t )  a 2 v c ( t )
3
Let’s consider 3-phase sinusoidal voltage:
At t=t1, t = (3/5) (= 108o)
va = 0.9511(Vm)
vb = -0.208(Vm)
vc = -0.743(Vm)
t=t1

Space Vector Modulation

2
v  v a ( t )  av b ( t )  a 2 v c ( t )
3

Let’s consider 3-phase sinusoidal voltage:
b
At t=t1, t = (3/5) (= 108o)
va = 0.9511(Vm)
a
vb = -0.208(Vm)
vc = -0.743(Vm)
c
Three phase quantities vary sinusoidally with time (frequency f)
 space vector rotates at 2f, magnitude Vm
Space Vector Modulation
How could we synthesize sinusoidal voltage using VSI ?
Space Vector Modulation
S1
S3
S5
+ va -
Vdc
a
+ vb b
S4
N
va*
vb *
vc*
S6
+ vc S2
n
c
We want va, vb and vc to follow
v*a, v*b and v*c
S1, S2, ….S6
Space Vector Modulation
S1
S3
S5
+ va -
Vdc
a
+ vb b
S4
S6
+ vc S2
c
van = vaN + vNn
N
vbn = vbN + vNn
From the definition of space vector:

2
v  v a ( t )  av b ( t )  a 2 v c ( t )
3

vcn = vcN + vNn
n
Space Vector Modulation
=0

2
v  v aN  av bN  a 2 v cN  v Nn (1  a  a 2 )
3
vaN = VdcSa, vaN = VdcSb, vaN = VdcSa,
Sa, Sb, Sc = 1 or 0

2
v  Vdc S a  aS b  a 2 S c
3

2
v  v a ( t )  av b ( t )  a 2 v c ( t )
3



Space Vector Modulation
Sector 2
[010] V3
[110] V2
(1/3)Vdc
Sector 3
Sector 1
[100] V1
[011] V4
(2/3)Vdc
Sector 4

2
v  Vdc S a  aS b  a 2 S c
3
[001] V5
Sector 5

Sector 6
[101] V6
Space Vector Modulation
Reference voltage is sampled at regular interval, T
Within sampling period, vref is synthesized using adjacent vectors and
zero vectors
110
V2
If T is sampling period,
V1 is applied for T1,
Sector 1
V2 is applied for T2
T2
V2
T
Zero voltage is applied for the
rest of the sampling period,
T 0 = T  T 1 T 2
T1
V1
T
100
V1
Space Vector Modulation
Reference voltage is sampled at regular interval, T
Within sampling period, vref is synthesized using adjacent vectors and
zero vectors
T0/2 T1
V0
T2
T0/2
V1 V2 V7
If T is sampling period,
V1 is applied for T1,
va
V2 is applied for T2
vb
Zero voltage is applied for the
rest of the sampling period,
T 0 = T  T 1 T 2
vc
T
Vref is sampled
Vref is sampled
T
Space Vector Modulation
How do we calculate T1, T2, T0 and T7?
They are calculated based on volt-second integral of vref
T1
T2
T7
1 T
1  To

v refdt   v 0dt  v1dt  v 2dt  v 7dt 
T 0
T 0
0
0
0






vref  T  v o  To  v1  T1  v 2  T2  v 7  T7
2
2
v ref  T  To  0  Vd  T1  Vd (cos 60o  j sin 60o )T2  T7  0
3
3
2
2
v ref  T  Vd  T1  Vd (cos 60o  j sin 60o )T2
3
3
Space Vector Modulation
q
T  T1  T2  T0,7
110
V2
Sector 1
vref   vref cos  j sin

100
V1o
2
2
v ref  T  Vd  T1  Vd (cos 60o  j sin 60 )T2
3
3
d
Space Vector Modulation
2
2
v ref  T  Vd  T1  Vd (cos 60o  j sin 60o )T2
3
3
2
1
T v ref cos   Vd T1  Vd T2
3
3
1
T v ref sin 
VdT2
3
Solving for T1, T2 and T0,7 gives:
3  T
1

T1  m cos  T sin
2  3
3

T2  mT sin
v ref
m

where
Vd
3
Space Vector Modulation
Comparison between SVM and SPWM
SPWM
a
b
o
c
vao
For m = 1, amplitude of
fundamental for vao is Vdc/2
amplitude of line-line =
Vdc/2
3
Vdc
2
-Vdc/2
Space Vector Modulation
Comparison between SVM and SPWM
SVM
We know max possible phase voltage without overmodulation is
amplitude of line-line = Vdc
3
Vdc
2
x100
3
Vdc
2
Vdc 
Line-line voltage increased by:
 15%
1
Vdc
3