1. Space Vector Modulation (SVM)

2. PWM – Voltage Source Inverter
Open loop voltage control AC
motor
PWM
VSI
vref
Closed loop current-control
VSI AC
motor
PWM
iref
if/back

3. Pulse Width Modulation
PWM – Voltage Source Inverter
+ vc -
+ vb -
+ va - n N
Vdc a b c S1 S3 S5 S4 S6 S2
va*
vb*
Pulse Width Modulation
S1, S2, ….S6
vc*

4. PWM – Voltage Source Inverter
PWM – single phase
vtri
Vdc q vc q
Vdc
Pulse width
modulator vc

5. PWM – Voltage Source Inverter
PWM – extended to 3-phase  Sinusoidal PWM
Pulse width
modulator
Va*
Pulse width
modulator
Vb*
Pulse width
modulator
Vc*

6. 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

7. 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:
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

8. Space Vector Modulation

9. Space Vector Modulation
Let’s consider 3-phase sinusoidal voltage:
va(t) = Vmsin(t)
vb(t) = Vmsin(t - 120o)
vc(t) = Vmsin(t + 120o)

10. Space Vector Modulation
Let’s consider 3-phase sinusoidal voltage:
At t=t1, t = (3/5) (= 108o)
va = (Vm)
vb = (Vm)
vc = (Vm)
t=t1

11. Space Vector Modulation
Let’s consider 3-phase sinusoidal voltage: b c a
At t=t1, t = (3/5) (= 108o)
va = (Vm)
vb = (Vm)
vc = (Vm)

12. Three phase quantities vary sinusoidally with time (frequency f)
 space vector rotates at 2f, magnitude Vm

13. Space Vector Modulation
How could we synthesize sinusoidal voltage using VSI ?

14. Space Vector Modulation
+ vc -
+ vb -
+ va - n N
Vdc a b c S1 S3 S5 S4 S6 S2
We want va, vb and vc to follow v*a, v*b and v*c
va*
vb*
vc*
S1, S2, ….S6

15. Space Vector Modulation
+ vc -
+ vb -
+ va - n N
Vdc a b c S1 S3 S5 S4 S6 S2
van = vaN + vNn
vbn = vbN + vNn
From the definition of space vector:
vcn = vcN + vNn

16. Space Vector Modulation
= 0
Sa, Sb, Sc = 1 or 0
vaN = VdcSa, vaN = VdcSb, vaN = VdcSa,

17. 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
Sector 6
[101] V6
[001] V5
Sector 5

18. 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
Zero voltage is applied for the rest of the sampling period,
100 V1
T0 = T  T1 T2

19. 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 V0 V1 T1 V2 T2
T0/2 V7
If T is sampling period, va
V1 is applied for T1,
V2 is applied for T2 vb
Zero voltage is applied for the rest of the sampling period, vc
T0 = T  T1 T2 T T
Vref is sampled
Vref is sampled

20. Space Vector Modulation
How do we calculate T1, T2, T0 and T7?
They are calculated based on volt-second integral of vref

21. Space Vector Modulationq
110 V2
Sector 1 
100 V1 d

22. Space Vector Modulation
Solving for T1, T2 and T0,7 gives:
where

23. Space Vector Modulation
Comparison between SVM and SPWM
SPWM o a b c
vao
Vdc/2
For m = 1, amplitude of fundamental for vao is Vdc/2
amplitude of line-line =
-Vdc/2

24. Space Vector Modulation
Comparison between SVM and SPWM
SVM
We know max possible phase voltage without overmodulation is
amplitude of line-line = Vdc
Line-line voltage increased by:
 15%