Space Vector Modulation (SVM)
Reference:
Bin Wu, High Power Converters and AC Drives, IEEE Press, 2006.
Three Phase Switching States (1)
Three Phase Switching States (2)
Three Phase Switching States (3)
• Eight switching states
Space Vector Review
• Three-phase voltages
v An (t )  vBn (t )  vCn (t )  0
(1)
• Two-phase voltages
2
4  v (t )

 An 
cos0
cos
cos

 v (t )  2 
3
3 

  vBn (t ) 
 v (t )   
   3  sin 0 sin 2 sin 4   v (t ) 

3
3   Cn 
(2)
• Space vector representation

V (t )  v (t )  j v (t )
(3)
(2)  (3)
2
V (t )   v An (t ) e j 0  vBn (t ) e j 2 /3  vCn (t ) e j 4 /3 
3
(4)
Space Vector Diagram


• Active vectors: V1 to V6
(stationary, not rotating)

• Zero vector: V0
• Six sectors: I to VI
Space Vector Example
Switching state [100]  S1, S4 and S6 ON
v AN (t )  Vd , vBN (t )  0, vCN (t )  0
v AB (t )  Vd , vBC (t )  0, vCA (t )  Vd
2
1
v An (t )  Vd , vBn (t )   Vd
3
3
(5)  (4)
 2
V1  Vd e j 0
3
(6)
Similarly,

 2
j ( k 1)
3
Vk  Vd e
3
k  1, 2, ..., 6.
(7)
and
1
vCn (t )   Vd
3
(5)
Active and Zero Vectors
• Active Vector: 6
• Zero Vector: 1
• Redundant switching
states for zero vector:
[111] and [000]
Reference Vector
• Definition

Vref  Vref e j
• Rotating in space at ω
  2 f
(8)
• Angular displacement
 (t ) 

t
0
 dt
(9)
Relationship Between Vref and VAB
• Vref is approximated by two active
and a zero vectors
• Vref rotates one revolution,
VAB completes one cycle
• Length of Vref corresponds to
magnitude of VAB

V2

Vref
Tb 
V2
Ts
SECTOR I
Q

Ta 
V1
Ts

V1
A Simple Method to Decide the Sector Number
A. Calculate the following expression:
N  sign( v An )  2sign( vBn )  4sign( vCn )
where sign(+)=1,sign(-)=0.
B. Use the following look-up table to determine the sector number:
N
1
2
3
4
5
6
Sector
6
2
1
4
5
3
Dwell Time Calculation (1)
• Volt-Second Balancing




Vref Ts  V1 Ta  V2 Tb  V0 T0

Ts  Ta  Tb  T0

V2
(10)
 

• Ta, Tb and T0 – dwell times for V1 , V2 and V0
• Ts – sampling period

Vref
Tb 
V2
Ts
Q

Ta 
V1
Ts
• Space vectors


 2
 2

j
j
3
,
and
Vref  Vref e , V1  Vd V2  Vd e
V0  0
3
3
(11)
(11)  (10)
2
1

Re
:
V
(cos

)
T

V
T

Vd Tb
ref
s
d
a

3
3

Im : Vref (sin  ) Ts  1 Vd Tb

3
SECTOR I
(12)

V1
Dwell Time Calculation (2)
Solve (12)

Ta 


Tb 



T0  Ts
3 Ts Vref
Vd
3 Ts Vref
Vd
sin (

sin 
 Ta  Tb
3
 )
0     /3
(13)
Vref Location versus Dwell Times

V2

Vref
Tb 
V2
Ts
SECTOR I
Q


V1
Ta 
V1
Ts

V ref
Location
Dwell Times
 0
Ta  0
Tb  0
0  

6
Ta  Tb



6
6
T a  Tb
 
Ta  Tb

3


3
Ta  0
Tb  0
Modulation Index


T

T
m
sin
(
 )
s a
 a
3
 T  T m sin 
s a
 b
 T0  Ts  Ta  Tb
ma 
Vref
Vd / 3
(15)
(16)
Replacing  by ’, he above equation (15) can be extended to
the kth sector:

 '    ( k  1)
3
where k  1, 2, ..., 6.
Modulation Range
• Vref,max
2
3 Vd
Vref , max  Vd 

3
2
3
(17)
(17)  (16)
• ma,max = 1

• Modulation range: 0  ma  1
(18)
Switching Sequence Design
• Basic Requirement:
Minimize the number of switchings per
sampling period Ts
• Implementation:
Transition from one switching state to
the next involves only two switches in
the same inverter leg.
Undesirable Switching Sequence
• Total number of switchings: 10
7-Segment Switching Sequence (1)
• Selected vectors:
V0, V1 and V2
• Dwell times:
Ts = T0 + Ta + Tb
• Total number of switchings: 6
7-Segment Switching Sequence (2)
Note: The switching sequences for the odd and ever sectors are different.
7-Segment Switching Sequence (3)
Simulated Waveforms
f1 = 60Hz, fsw = 900Hz, ma = 0.696, Ts = 1.1ms
Waveforms and FFT
Waveforms and Spectrum (1)
Waveforms and Spectrum (2)
( f1  60Hz
and
Ts  1 / 720 sec )
Even-Order Harmonic Elimination (1)
Sector 4
Type-A sequence
(starts and ends with [000])
Type-B sequence
(starts and ends with [111])
Even-Order Harmonic Elimination (2)

V3
b
SECTOR III

V4
a
a
30 
30 
a
a
b
a
b
a

V5
SECTOR I
b
b
SECTOR IV

V2
SECTOR II
SECTOR VI
b
SECTOR V

V1

V6
Space vector Diagram
Type-A sequence
Type-B sequence
Even-Order Harmonic Elimination (3)
Even-Order Harmonic Elimination (4)
( f1  60Hz
and
Ts  1 / 720 sec )
7-Segment Type B sequence (1)
7-Segment Type B Sequence (2)
5-Segment SVM
5-Segment Switching Sequence (1)
5-Segment Switching Sequence (2)
5-Segment Simulated Waveforms
v g1
2 / 3
vg 3
2
vg 5
vAB
0
4
Vd
2
4
iA
0
2
4
• f1 = 60Hz, fsw = 600Hz, ma = 0.696, Ts = 1.1ms
• No switching for a 120° period per cycle.
• Low switching frequency but high harmonic distortion
Comparison of SPWM and SVM
 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 Vdc
 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 =1.155 times of Sine PWM