1. Submitted by,
Soumya Ranjan Pradhan

2. Introduction:
 Principle of Space Vector PWM
 Treats the sinusoidal voltage as a constant amplitude vector rotating
at constant frequency.
 Coordinate Transformation ( abc reference frame to the stationary d-q frame)
: A three-phase voltage vector is transformed into a vector in the stationary d-q coordinate
frame which represents the spatial vector sum of the three-phase voltage.
 This PWM technique approximates the reference voltage Vref by a combination
of the eight switching patterns (V0 to V7).
 The vectors (V1 to V6) divide the plane into six sectors (each sector: 60 degrees).
 Vref is generated by two adjacent non-zero vectors and two zero vectors.

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

4. PWM – Voltage Source Inverter
PWM – single phase
Vdc
dc
vc vPulse width
tri
vc modulator
qq

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

6. PWM METHODS
 Output voltages of three-phase inverter
where, upper transistors: S1, S3, S5
lower transistors: S4, S6, S2
switching variable vector: a, b, c

7.  The eight inverter voltage vectors (V0 to V7)

8.  The eight combinations, phase voltages and output line to line voltages

9.  Basic switching vectors and Sectors
 6 active vectors (V1,V2, V3, V4, V5, V6)
 Axes of a hexagonal
 DC link voltage is supplied to the load
 Each sector (1 to 6): 60 degrees
 2 zero vectors (V0, V7)
 At origin
 No voltage is supplied to the load
Fig. Basic switching vectors and sectors.

10. 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:
x = ( x a ( t ) + ax b ( t ) + a 2 x c ( t ) )
2
3
a = ej2π/3 = cos(2π/3) + jsin(2π/3)
a2 = ej4π/3 = cos(4π/3) + jsin(4π/3)
x – can be a voltage, current or flux and does not necessarily has to be sinusoidal

11. Space Vector Modulation
v = ( v a ( t ) + av b ( t ) + a 2 v c ( t ) )
2
x x ax x
3
Let’s consider 3-phase sinusoidal voltage:
va(t) = Vmsin(ωt)
vb(t) = Vmsin(ωt - 120o)
vc(t) = Vmsin(ωt + 120o)

12. Space Vector Modulation
v = ( v a ( t ) + av b ( t ) + a 2 v c ( t ) )
2
3
Let’s consider 3-phase sinusoidal voltage:
At t=t1, ωt = (3/5)π (= 108o)
va = 0.9511(Vm)
vb = -0.208(Vm)
vc = -0.743(Vm)
t=t1

13. Space Vector Modulation
v = ( v a ( t ) + av b ( t ) + a 2 v c ( t ) )
2
3
Let’s consider 3-phase sinusoidal voltage:
b
At t=t1, ωt = (3/5)π (= 108o)
va = 0.9511(Vm)
a
vb = -0.208(Vm)
vc = -0.743(Vm)
c

14. Three phase quantities vary sinusoidally with time (frequency f)
⇒ space vector rotates at 2πf, magnitude Vm

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

16. Space Vector Modulation
S1 S3 S5
+ va -
Vdc a + vb -
b + vc -
n
c
S4 S6 S2
van = vaN + vNn
N
vbn = vbN + vNn
From the definition of space vector:
vcn = vcN + vNn
v = ( v a ( t ) + av b ( t ) + a 2 v c ( t ) )
2
3

17. 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
)
v = ( v a ( t ) + av b ( t ) + a 2 v c ( t ) )
2
3

18. 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
) Sector 6
[001] V5 Sector 5 [101] V6

19. Conversion from 3 phases to 2 phases :
For Sector 1,
Three-phase line modulating signals (VC)abc = [VCaVCbVCc]T
can be represented by the represented by the complex vector
VC = [VC]αβ = [VCaVCb]T
by means of the following transformation:
VC α = 2/3 . [vCa - 0.5(vCb + vCc )]
VC β = √3/3 . (vCb - vCc)

20. Space Vector Modulation
Reference voltage is sampled at regular interval, T
Within sampling period, vref is synthesized using adjacent vectors and
zero vectors
If T is sampling period, 110
V1 is applied for T1, V2
V2 is applied for T2 Sector 1
Zero voltage is applied for the
rest of the sampling period,
T2
V2
T 0 = T − T 1− T 2 T
Where, 100
T1 = Ts.|Vc|. Sin (π/3 - θ) T1 V1
T2 = Ts.|Vc|. Sin (θ)
V1
T

21. 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 T2 T0/2
V0 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, vc
T0 = T − T1− T2
T T
Vref is sampled Vref is sampled

22. Space Vector Modulation
How do we calculate T1, T2, T0 and T7?
They are calculated based on volt-second integral of vref
1 T 1  To T1 T2 T7

∫
T 0 T 0 ∫ 0 ∫ 0 ∫
v ref dt =  v 0 dt + v 1dt + v 2 dt + v 7 dt 
0  ∫
v ref ⋅ T = v o ⋅ To + v 1 ⋅ 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

23. Space Vector Modulation
q T = T1 + T2 + T0,7
110
V2
Sector 1
v ref ⋅ = v ref ( cos α − j sin α )
α
100
2 2 V1 d
v ref ⋅ T = Vd ⋅ T1 + Vd (cos 60o + j sin 60 )T2
o
3 3

24. Space Vector Modulation
2 2
v ref ⋅ T = Vd ⋅ T1 + Vd (cos 60o + j sin 60o )T2
3 3
2 1 1
T v ref cos α = Vd T1 + Vd T2 T v ref sin α = Vd T2
3 3 3
Solving for T1, T2 and T0,7 gives:
T1= 3/2 m[ (T/√3) cos α - (1/3)T sin α ]
T2= mT sin α
where,
M= Vref/ (Vd/ √3)

25.  Comparison of Sine PWM and Space Vector PWM
Fig. Locus comparison of maximum linear control voltage
in Sine PWM and SV PWM.

26.  Comparison of Sine PWM and Space Vector PWM
a
o b
c
vao
Vdc/2
For m = 1, amplitude of
fundamental for vao is Vdc/2
∴amplitude of line-line = 3
Vdc
2
-Vdc/2

27.  Comparison of Sine PWM and Space Vector PWM
 Space Vector PWM generates less harmonic distortion
in the output voltage or currents in comparison with sine PWM
 Space Vector PWM provides more efficient use of supply voltage
in comparison with sine PWM
 Sine PWM
: Locus of the reference vector is the inside of a circle with radius of 1/2 V dc
 Space Vector PWM
: Locus of the reference vector is the inside of a circle with radius of 1/√3 Vdc
∴ Voltage Utilization: Space Vector PWM = 2/√3 or (1.1547) times
of Sine PWM, i.e. 15.47% more utilization of voltage.

28. Space Vector Modulation
Comparison between SVM and SPWM
SVM
1
We know max possible phase voltage without overmodulation is Vdc
3
∴amplitude of line-line = Vdc
3
Vdc − Vdc
2 ≈ 15.47%
Line-line voltage increased by: x100
3
Vdc
2

29. 1. Power Electronics: Circuits, Devices and Applications by M. H. Rashid, 3rd edition,
Pearson
2. Power Electronics: Converters, Applications and Devices by Mohan, Undeland and
Robbins, Wiley student edition
3. Power Electronics Handbook: M.H. Rashid, Web edition
4. Modern Power Electronics And Ac Drives: B.K. Bose
5. Extended Report on AC drive control, IEEE : Issa Batarseh
6. Space vector modulation: Google, Wikipedia ; for figures.