SVPWM

From the definition of space vector:
v
2 3
v
a ( t ) av b ( t ) a v c ( t )
2

vcn = vcN + vNn
Space Vector Modulation
=0
v
2 3
v
aN
av bN a v cN v Nn (1 a a )
o
100 V1 o
d
Space Vector Modulation
v ref T
2 3
Vd T1
2 3 Vd T1
2 3
1 3
Vd (cos 60 j sin 60 ) T2
Vd T2
o
o
T v ref cos
T v ref sin
1 3
Vd T2
Solving for T1, T2 and T0,7 gives:
3 2 Vdc
Vdc/2
-Vdc/2
Space Vector Modulation
Comparison between SVM and SPWM SVM We know max possible phase voltage without overmodulation is
1 3 Vdc
amplitude of line-line = Vdc
T2 T
100 V1
V1
Space Vector Modulation
Reference voltage is sampled at regular interval, T Within sampling period, vref is synthesized using adjacent vectors and zero vectors
vc = -0.743(Vm)
t=t1
Space Vector Modulation
v
2 3
v
a ( t ) av b ( t ) a v c ( t )
2

Let’s consider 3-phase sinusoidal voltage: b At t=t1, t = (3/5) (= 108o)
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 S2 c
+ vc -
n
van = vaN + vNn
N
vbn = vbN + vNn
1 T T1 m cos T sin 2 3 3 3
m v ref Vd 3
T2 mT sin
where
Space Vector Modulation
Comparison between SVM and SPWM SPWM
a
o
b
c
vao For m = 1, amplitude of fundamental for vao is Vdc/2 amplitude of line-line =
Space Vector Modulation (SVM)
PWM – Voltage Source Inverter
Open loop voltage control AC motor
vref
PWM
VSI
Closed loop current-control AC motor
iref
PWM
VSI
if/back
Space Vector Modulation
v
2 3
v
a ( t ) av b ( t ) a v c ( t )
2

Let’s consider 3-phase sinusoidal voltage:
At t=t1, t = (3/5) (= 108o)
va = 0.9511(Vm) vb = -0.208(Vm)
x
2 3
x
a ( t ) ax b ( t ) a x c ( t )
2

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
va = 0.9511(Vm) vb = -0.208(Vm)
vc = -0.743(Vm) c
a
Three phase quantities vary sinusoidally with time (frequency f)
space vector rotates at 2f, magnitude Vm
2
2

vaN = VdcSa, vaN = VdcSb, vaN = VdcSa,
Sa, Sb, Sc = 1 or 0
v
2 3
V dc S a aS b a S c
2

2

v
2 3
v
a ( t ) av b ( t ) a v c ( t )

Space Vector Modulation
If T is sampling period,
V1 is applied for T1, V2 is applied for T2 Zero voltage is applied for the rest of the sampling period, T 0 = T T 1 T 2
V2 T1 T
o o o o
Vd T1
Vd (cos 60 j sin 60 ) T2
Space Vector Modulation
q
T T1 T2 T0 ,7
110 V2
Sector 1
v ref v ref cos j sin

v ref T 2 3 Vd T1 2 3 Vd (cos 60 j sin 60 ) T2
Space Vector Modulation
x
2 3
x
a ( t ) ax b ( t ) a x c ( t )
2

Space Vector Modulation
v x
2 3
v x
( t ) av b ( t ) a 2 v c ( t ) ax x a
2

Let’s consider 3-phase sinusoidal voltage: va(t) = Vmsin(t) vb(t) = Vmsin(t - 120o) vc(t) = Vmsin(t + 120o)
Vdc
3 2 Vdc
Vdc
Line-line voltage increased by:
3 2
x100
15%
PWM – Voltage Source Inverter
S1
S3
S5
+ va -
Vdc
a
+ vb -
b
S4 S6 S2 c
+ vc -
n
N
va * vb* vc* Pulse Width Modulation
S1, S2, ….S6
PWM – Voltage Source Inverter PWM – single phase
Vref is sampled
va
vc T
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
T0/2 T1 V0 T2 T0/2 V1 V2 V7
If T is sampling period,
V1 is applied for T1, V2 is applied for T2 vb Zero voltage is applied for the rest of the sampling period, T 0 = T T 1 T 2
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
How could we synthesize sinusoidal voltage using VSI ?
Space Vector Modulation
S1
S3
S5
+ va -
Vdc
a
+ vb -
b
S4 S6 S2 c
+ vc -
n
N
va * vb* vc*
Reference voltage is sampled at regular interval, T Within sampling period, vref is synthesized using adjacent vectors and zero vectors 110 V2 Sector 1
Vdc dc
vc vc
vPulse width tri
modulator
q q
PWM – Voltage Source Inverter PWM – extended to 3-phase Sinusoidal PWM
Va*
Pulse width modulator
Vb*
Pulse width modulator Vc * Pulse width modulator
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:
1 To v ref dt v 0 dt T 0 T 0 1

T


v 1dt v 2 dt v 7 dt 0 0 0
T1

T2

T7
v ref T v o To v 1 T1 v 2 T2 v 7 T7
v ref T To 0 v ref T 2 3 2 3 Vd T1 2 3 2 3 Vd (cos 60 j sin 60 ) T2 T7 0
Sector 2
[010] V3
(1/3)Vdc
Sector 3
[110] V2
Sector 1
[011] V4
[100] V1
(2/3)Vdc
c S a aS b a S c
Sector 5

2

Sector 6
[001] V5
[101] V6
Space Vector Modulation