UNIT-IV
INVERTERS
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1
Single-Phase Inverters
Half-Bridge Inverter
One of the simplest types of inverter. Produces a square wave output.
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2
Single-Phase Inverters
(cont’d)
Full Bridge (H-bridge) Inverter
Two half-bridge inverters combined.
Allows for four quadrant operation.
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3
Single-Phase Inverters
(cont’d)
Quadrant 1: Positive step-down converter
(forward motoring)
Q1-On; Q2 - Chopping; D3,Q1 freewheeling
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4
Single-Phase Inverters
(cont’d)
Quadrant 2: Positive step-up converter
(forward regeneration)
Q4 - Chopping; D2,D1 freewheeling
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Single-Phase Inverters
(cont’d)
Quadrant 3: Negative step-down converter
(reverse motoring)
Q3-On; Q4 - Chopping; D1,Q3 freewheeling
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6
Single-Phase Inverters
(cont’d)
Quadrant 4: Negative step-up converter
(reverse regeneration)
Q2 - Chopping; D3,D4 freewheeling
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7
Single-Phase Inverters
(cont’d)
Phase-Shift Voltage Control - the output of
the H-bridge inverter can be controlled by
phase shifting the control of the
component half-bridges. See waveforms
on next slide.
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8
Single-Phase Inverters
(cont’d)
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9
Single-Phase Inverters
(cont’d)
The waveform of the output voltage vab is a quasisquare wave of pulse width . The Fourier series of vab
is given by:
4Vd
vab  
n 1,3,5... n
  n  
sin  2   cos  n t 
  
The value of the fundamental, a1=
4Vd

The harmonic components as a function of phase
angle are shown in the next slide.
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sin  / 2 
10
Single-Phase Inverters
(cont’d)
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11
Three-Phase Bridge
Inverters
Three-phase bridge inverters are widely
used for ac motor drives. Two modes of
operation - square wave and six-step. The
topology is basically three half-bridge
inverters, each phase-shifted by 2/3,
driving each of the phase windings.
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12
Three-Phase Bridge Inverters
(cont’d)
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Three-Phase Bridge Inverters
(cont’d)
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14
Three-Phase Bridge Inverters
(cont’d)
The three square-wave phase voltages can
be expressed in terms of the dc supply
voltage, Vd, by Fourier series as:
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va 0 
2Vd
vb 0 
2Vd
vc 0 
2Vd




(1) n 1 cos(nt )
n 1,3,5...

(1)
n 1
n 1,3,5...

(1)
2
cos(nt  )
3
n 1
2
cos(nt 
)
3
n 1,3,5...
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15
Three-Phase Bridge Inverters
(cont’d)
The line voltages can then be expressed as:
vab  va 0  vb 0 
2 3Vd
vbc  vb 0  vc 0 
2 3Vd
vca  vc 0  va 0 
2 3Vd
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



cos( t   / 6)  cos(nt   6)

cos( t   / 2)  cos(nt   2)

cos( t  5 / 6)  cos(nt  5 6)
n 1,3,5...
n 1,3,5...
n 1,3,5...
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16
Three-Phase Bridge Inverters
(cont’d)
The line voltages are six-step waveforms and
have characteristic harmonics of 6n1,
where n is an integer. This type of inverter is
referred to as a six-step inverter.
The three-phase fundamental and harmonics
are balanced with a mutual phase shift of
2/3.
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17
Three-Phase Bridge Inverters
(cont’d)
If the three-phase load neutral n is isolated from the the
center tap of the dc voltage supply (as is normally the
case in an ac machine) the equivalent circuit is shown
below.
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18
Three-Phase Bridge Inverters
(cont’d)
In this case the isolated neutral-phase
voltages are also six-step waveforms with
the fundamental component phase-shifted
by /6 from that of the respective line
voltage. Also, in this case, the triplen
harmonics are suppressed.
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19
Three-Phase Bridge Inverters
(cont’d)
For a linear and balanced 3 load, the line currents
are also balanced. The individual line current
components can be obtained from the Fourier series
of the line voltage. The total current can be obtained
by addition of the individual currents. A typical line
current wave with inductive load is shown below.
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20
Three-Phase Bridge Inverters
(cont’d)
The inverter can operate in the usual inverting or
motoring mode. If the phase current wave, ia, is
assumed to be perfectly filtered and lags the phase
voltage by /3 the voltage and current waveforms are
as shown below:
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21
Three-Phase Bridge Inverters
The inverter can also operate in rectification or regeneration
mode in which power is pushed back to the dc side from the ac
side. The waveforms corresponding to this mode of operation
with phase angle = 2/3 are shown below:
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22
Three-Phase Bridge Inverters
(cont’d)
The phase-shift voltage control principle
described earlier for the single-phase
inverter can be extended to control the
output voltage of a three-phase inverter.
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23
Three-Phase Bridge Inverters
(cont’d)
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24
Three-Phase Bridge Inverters
(cont’d)
The three waveforms va0,vb0, and vc0 are of
amplitude 0.5Vd and are mutually phaseshifted by 2/3.
The three waveforms ve0,vf0, and vg0 are of
similar but phase shifted by .
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25
Three-Phase Bridge Inverters
(cont’d)
The transformer’s secondary phase voltages,
vA0, vB0, and vc0 may be expressed as follows:
vA0  mvad  m(va 0  vd 0 )
vB 0  mvbe  m(vb 0  ve 0 )
vC 0  mvcf  m(vc 0  v f 0 )
where m is the transformer turns ratio
(= Ns/Np). Note that each of these waves is a
function of  angle.
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26
Three-Phase Bridge Inverters
(cont’d)
The output line voltages are given by:
vAB  vA0  vB 0
vBC  vB 0  vC 0
vCA  vC 0  vA0
While the component voltage waves va0, vd0, vA0 … etc. all
contain triplen harmonics, they are eliminated from the
line voltages because they are co-phasal. Thus the line
voltages are six-step waveforms with order of harmonics
= 6n1 at a phase angle .
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27
Three-Phase Bridge Inverters
(cont’d)
The Fourier series for vA0 and vB0 are given
by:
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v A0
4mVd
 
n 1,3,5... n
  n  
sin  2   cos  n t 
  
vB 0
4mVd
 
n 1,3,5... n
  n  
sin  2   cos  n t  2 / 3
  
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Three-Phase Bridge Inverters
(cont’d)
The Fourier series for vAB is given by:
vAB  vA0  vB 0
4mVd
 
n 1,5,7,11... n
  n   
2

sin  2   cos  n t   cos n   t  3

   



Note that the triplen harmonics are removed
in vAB although they are present in vA0 and
vB0.
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29
PWM Technique
While the 3 6-step inverter offers simple
control and low switching loss, lower order
harmonics are relatively high leading to high
distortion of the current wave (unless
significant filtering is performed).
PWM inverter offers better harmonic control
of the output than 6-step inverter.
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30
PWM Principle
The dc input to the inverter is “chopped” by
switching devices in the inverter. The
amplitude and harmonic content of the ac
waveform is controlled by the duty cycle of
the switches. The fundamental voltage v1
has max. amplitude = 4Vd/ for a square
wave output but by creating notches, the
amplitude of v1 is reduced (see next slide).
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31
PWM Principle (cont’d)
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32
PWM Techniques
Various PWM techniques, include:
• Sinusoidal PWM (most common)
• Selected Harmonic Elimination (SHE)
PWM
• Space-Vector PWM
• Instantaneous current control PWM
• Hysteresis band current control PWM
• Sigma-delta modulation
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33
Sinusoidal PWM
The most common PWM approach is
sinusoidal PWM. In this method a
triangular wave is compared to a
sinusoidal wave of the desired
frequency and the relative levels of the
two waves is used to control the
switching of devices in each phase leg
of the inverter.
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34
Sinusoidal PWM
(cont’d)
Single-Phase (Half-Bridge) Inverter
Implementation
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Sinusoidal PWM (cont’d)
when va0> vT T+ on; T- off; va0 = ½Vd
va0 < vT T- on; T+ off; va0 = -½Vd
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Sinusoidal PWM
(cont’d)
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Sinusoidal PWM (cont’d)
Definition of terms:
Triangle waveform switching freq. = fc (also called
carrier freq.)
Control signal freq. = f (also called modulation
Peak amplitude
freq.)
of control signal
Amplitude modulation ratio, m = Vp
VT
Peak amplitude
of triangle wave
Frequency modulation ratio,
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38
mf (P)=
fc /byfwww.noteshit.com
Multiple Pulse-Width Modulation
• In multiple-pulse modulation, all pulses are
the same width
• Vary the pulse width according to the
amplitude of a sine wave evaluated at the
center of the same pulse
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39
Generate the gating signal
2 Reference Signals, vr, -vr
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Comparing the carrier and reference signals
• Generate g1 signal by comparison with vr
• Generate g4 signal by comparison with -vr
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Comparing the carrier and reference signals
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42
Potential problem if Q1 and Q4 try to turn ON
at the same time!
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43
If we prevent the problem
Output voltage is low when g1 and g4 are
both high
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44
This composite signal is difficult to generate
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45
Generate the same gate pulses with one
sine wave
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Alternate scheme
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47
rms output voltage
• Depends on the modulation index, M
V V
o
p
S

V



2p
m
S
m 1
Where δm is the width of the mth pulse
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48
Fourier coefficients of the output voltage

4V
n 
3
B 
sin
sin n  
n
4 
4
n  1, 3, 5,..
2p
S
n
m 1
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m
m
m



 
 sin n    

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m
m
4 
49
Harmonic Profile
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50
Compare with multiple-pulse case for p=5
Distortion Factor is considerably less
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51
Series-Resonant Inverter
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52
Operation
T1 fired, resonant pulse of current
flows through the load. The current
falls to zero at t = t1m and T1 is “self –
commutated”.
T2 fired, reverse resonant current
flows through the load and T2 is also
“self-commutated”.
The series resonant circuit must be
underdamped,
R2 < (4L/C)
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53
Operation in Mode 1 – Fire T1
di1
1
L  Ri1   i1dt  vC (0)  VS
dt
C
i1 (0)  0
vC (0)  VC
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54
i1 (t )  A1e

R
t
2L
sin r t
1
2
 1
R2 
r  
 2
 LC 4 L 
Vs  Vc
di1

 A1
dt t 0
r L
Vs  Vc  t
i1 (t ) 
e sin r t
r L
R

2L
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To find the time when the current is
maximum, set the first derivative = 0
di1
0
dt
 Vs  Vc 
 t
 t


e
sin

t


e
cos r t   0


r
r
 r L 
.....
r
 tan r tm

1 r t m
tan
 r t m

1
1 r
tm 
tan
r
2
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56
To find the capacitor voltage, integrate the
current
t
1
vC1 (t )   i1 (t )dt  Vc
C0
t
1  Vs  Vc   t
vC1 (t )   
  e sin r t  dt  VC
C 0  r L 
...
vC1 (t )  (Vs  VC )e  t ( sin r t  r cos r t ) / r  Vs

0  t  t1m ( )
r
The current i1 becomes = 0 @ t=t1m
vC1 (t1m )  VC1  Vs  VC  e
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

r
 Vs
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58
Operation in Mode 2 – T1, T2 Both OFF
i2 (t )  0
vC2 (t )  VC1
vC2 (t2m )  VC2  VC1
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t2m
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60
Operation in Mode 3 – Fire T2
di3
1
L
 Ri3   i3dt  vC3 (0)  0
dt
C
i3 (0)  0
vC3 (0)  VC2  VC1
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i3 (t ) 
VC1
r L
e
 t
sin r t
t
1
vC3 (t )   i3dt  VC1
C0
vC3 (t ) 
VC1 e  t ( sin r t  r cos r t )
r

0  t  t3 ( )
r
m
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vC3 (t3m )  VC3  VC  VC1 e

vC1 (t1m )  VC1  (VS  VC )e

r


r
 VS
.
.
1
VC  VS z
e 1
ez
VC1  VS z
e 1
VC  VS  VC1
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63
Space Vector Modulation
• Space Vector Diagram
jb
r
V3
r
V2
OPO
r
r
• Active vectors: V1 to V6
(stationary, not rotating)
r
• Zero vector: V0
• Six sectors: I to VI
SECTOR
II
SECTOR III
r
V4
r 
Vref
SECTOR I
r
V1
q
PPP
OPP
OOO
SECTOR IV

POO
r
V0
SECTOR VI
SECTOR V
OOP r
V5
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PPO
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r POP
V6
64
Space Vector Modulation
• Space Vectors
• Three-phase voltages
v AO (t )  vBO (t )  vCO (t )  0
(1)
• Two-phase voltages
2

cos
0
cos
v (t ) 
2
3

v (t )

3 sin 0 sin 2
 b 


3
4  v AO (t )
3  v (t ) 
4   BO 
sin
 vCO (t ) 
3 
cos
(2)
• Space
vector representation
r
V (t )  v (t )  j vb (t )
(2)  (3)
r
2
V (t )   v AO (t ) e j 0  v BO (t ) e j 2 / 3  vCO (t ) e j 4 / 3 
3
where e jx  cos x  j sin x
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(3)
(4)
65
Space Vector Modulation
• Space Vectors (Example)
Switching state [POO]  S1, S6 and S2 ON
2
1
1
v AO (t )  Vd , v BO (t )   Vd and vCO (t )   Vd
3
3
3
r 2
V1  Vd e j 0
3
k  1, 2, ..., 6.
(6)
PPO
SECTOR
II
SECTOR III
r
V4
r 
Vref
SECTOR I
r
V1
q
PPP
OPP
OOO
(7)
SECTOR IV

POO
r
V0
SECTOR VI
SECTOR V
OOP r
V5
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r
V2
OPO
Similarly,

r 2
j ( k 1)
3
V k  Vd e
3
jb
r
V3
(5)  (4)
(5)
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r POP
V6
66
Space Vector Modulation
• Active and Zero Vectors
P
Switching State
(Three Phases)
On-state Switch
Vector
Definition
[PPP]
S1 , S 3 , S 5
[OOO]
S4 , S6 , S2
r
V0  0
[POO]
S1 , S 6 , S 2
r
V2
[PPO]
S1 , S 3 , S 2
r
V3
[OPO]
S4 , S3 , S 2
r
V4
[OPP]
S 4 , S3 , S5
[OOP]
S4 , S6 , S5
[POP]
S1 , S 6 , S 5
Space Vector
S1
S3
S5
Zero
Vector
A
r
V1
B
Vd
r
V0
C
S4
S6
S2
N
• Active Vector: 6
• Zero Vector: 1
• Redundant switching
states: [PPP] and [OOO]
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Active
Vector
r
V5
r
V6
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r 2
V1  Vd e j 0
3

r 2
j
V2  Vd e 3
3
2
r 2
j
V3  V d e 3
3
3
r 2
j
V4  Vd e 3
3
4
r 2
j
V5  V d e 3
3
5
r 2
j
V6  V d e 3
3
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Space Vector Modulation
• Reference Vector Vref
• Definition
r
Vref  Vref e jq
SECTOR III
(8)
0  dt
r
V4
PPP
SECTOR I
r
V1
OPP
OOO

POO
r
V0
SECTOR IV
t
r 
Vref
q
SECTOR VI
SECTOR V
(9)
OOP r
V5
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PPO
SECTOR
II
• Angular displacement
q (t ) 
r
V2
OPO
• Rotating in space at ω
  2 f
jb
r
V3
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r POP
V6
68
Space Vector Modulation
• Relationship Between Vref and VAB
• Vref is approximated by two active
and a zero vectors
• Vref rotates one revolution,
VAB completes one cycle
r
Vref
Tb r
V2
Ts
• Length of Vref corresponds to
magnitude of VAB
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r
V2
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SECTOR I
Q
q
Ta r
V1
Ts
r
V1
69
Space Vector Modulation
• Dwell Time Calculation
r
V2
• Volt-Second Balancing
r
r
r
r
Vref Ts  V1 Ta  V2 Tb  V0 T0

Ts  Ta  Tb  T0
(10)
r r
r
• Ta, Tb and T0 – dwell times for V1 , V2 and V0
• Ts – sampling period
r
Vref
Tb r
V2
Ts
SECTOR I
Q
q
Ta r
V1
Ts
r
V1
• Space vectors

r
r 2
r 2
r
j
jq
3
,
and
Vref  Vref e , V1  Vd V2  Vd e
V0  0
3
3
(11)
(11)  (10)
2
1

Re
:
V
(cos
q
)
T

V
T

Vd Tb
ref
s
d
a

3
3

Im : Vref (sin q ) Ts  1 Vd Tb

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3/22/2016
Copyright
(12)
70
Space Vector Modulation
• Dwell Times
Solve (12)

Ta 


Tb 



T0  Ts
3/22/2016
3 Ts Vref
Vd
3 Ts Vref
Vd
sin (

sin q
3
q )
0  q   /3
(13)
 Ta  Tb
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71
Space Vector Modulation
• Vref Location versus Dwell Times
r
V2
r
Vref
Tb r
V2
Ts
SECTOR I
Q
q
r
V1
Ta r
V1
Ts
r
V ref
Location
Dwell Times
3/22/2016
q 0
Ta  0
Tb  0
0 q 

6
Ta  Tb
q


6
6
Ta  Tb
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q 

Ta  Tb
3
q

3
Ta  0
Tb  0
72
Space Vector Modulation
• Modulation Index


T

T
m
sin
(
q )
s
a
 a
3
Tb  Ts ma sin q

T0  Ts  Tb  Tc
ma 
3/22/2016
3 Vref
(15)
(16)
Vd
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73
Space Vector Modulation
• Modulation Range
jb
r
V3
OPO
• Vref,max
2
3 Vd
Vref , max  Vd 

3
2
3
(17)
r
V4
PPP
SECTOR I
r
V1
OOO
SECTOR VI
SECTOR V
r POP
V6
OOP r


POO
r
V0
SECTOR IV
(17)  (16)
r 
Vref
q
OPP
V5
• Modulation range: 0  ma  1
3/22/2016
PPO
SECTOR
II
SECTOR III
• ma,max = 1
r
V2
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(18)
74
Space Vector Modulation
• 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.
3/22/2016
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75
Space Vector Modulation
• Seven-segment Switching Sequence
r
V0
r
V1
OOO POO
• Selected vectors:
V0, V1 and V2
v AN
• Dwell times:
Ts = T0 + Ta + Tb
vBN
r
V2
r
V0
r
V2
r
V1
r
V0
PPO
PPP
PPO
POO OOO
Vd
0
Vd
0
vCN
Vd
0
T0
4
Ta
2
Tb
2
T0
2
Tb
2
Ta
2
T0
4
Ts
• Total number of switchings: 6
3/22/2016
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76
Space Vector Modulation
• Undesirable Switching Sequence
• Vectors V1 and V2 swapped
r
V0
r
V2
OOO PPO
r
V1
r
V0
r
V1
POO
PPP
POO
v AN
r
V2
r
V0
PPO OOO
Vd
0
vBN
Vd
0
vCN
Vd
0
T0
4
Tb
2
Ta
2
T0
2
Ta
2
Tb
2
T0
4
Ts
• Total number of switchings:
10
Copyright by www.noteshit.com
3/22/2016
77
Space Vector Modulation
• Switching Sequence Summary (7–segments)
Sector
Switching Sequence
r
r
r
V2
V0
V2
I
r
V0
r
V1
r
V1
r
V0
II
OOO
r
V0
POO
r
V3
PPO
r
V2
PPP
r
V0
PPO
r
V2
POO
r
V3
OOO
r
V0
III
OOO
r
V0
OPO
r
V3
PPO
r
V4
PPP
r
V0
PPO
r
V4
OPO
r
V3
OOO
r
V0
IV
OOO
r
V0
OPO
r
V5
OPP
r
V4
PPP
r
V0
OPP
r
V4
OPO
r
V5
OOO
r
V0
V
OOO
r
V0
OOP
r
V5
OPP
r
V6
PPP
r
V0
OPP
r
V6
OOP
r
V5
OOO
r
V0
VI
OOO
r
V0
OOP
r
V1
POP
r
V6
PPP
r
V0
POP
r
V6
OOP
r
V1
OOO
r
V0
OOO
POO
POP
PPP
POP
POO
OOO
Note: The switching sequences for the odd and ever sectors are different.
3/22/2016
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78
Space Vector Modulation
• Simulated Waveforms
Sector
V
VI
V
IV
VI
IV
III
II
I
II
I
III
v AB
Vd
0
2

3
v AO
2Vd / 3
0
iA
0

2
3
f1 = 60Hz, fsw = 900Hz, ma = 0.696, Ts = 1.1ms
3/22/2016
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79
Space Vector Modulation
• Waveforms and FFT
v AB
THD =80.2%
Vd
0
2
v AO
THD =80.2%
2V d / 3
0
iA
THD =8.37%
0

2
3
V AB n / V d
THD =80.2%
V AB 1  0.566V d
0.2
0.1
0
3/22/2016
1
5
10
15Copyright
20
25by
30
35
40
45
www.noteshit.com
50
55
60
n
80
Space Vector Modulation
• Waveforms and FFT (Measured)
V AB n
Vd
v AB
THD = 80.3%
23
0.2
14
0.1
v AO
47
10
16
29 34
43
58
8
0
(a) Waveforms 2ms/div
3/22/2016
Copyright by www.noteshit.com
(b) Spectrum (500Hz/div)
81
Space Vector Modulation
• Waveforms and FFT (Measured)
V AB n / Vd
V AB n / Vd
THD
(%)
n 1
n 1
300
0.15
0.15
10
14
16
20
THD
0.10
0.10
n2
4
200
n = 19
8
17
13
11 7
100
0.05
0.05
0
0
0.2
0.4
0.6
0.8
0
ma
0
0.2
0.4
0.6
0.8
ma
0
(b) Odd order harmonics
(a) Even order harmonics
( f1  60 Hz
3/22/2016
5
and
Ts  1 / 720 sec )
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82
Space Vector Modulation
• Even-Order Harmonic Elimination
r
V0
r
V5
r
V4
r
V0
r
V4
OOO
OOP
OPP
PPP
OPP
v AN
r
V5
r
V0
OOP OOO
v AN
Vd
0
vBN
0
vBN
Vd
0
r
V4
r
V5
r
V0
r
V5
r
V4
r
V0
PPP
OPP
OOP
OOO
OOP
OPP
PPP
Vd
Vd
0
vCN
vCN
Vd
0
Vd
0
0
v AB
r
V0
0
v AB
 Vd
Type-A sequence
(starts and ends with [OOO])
3/22/2016
 Vd
Type-B sequence
(starts and ends with [PPP])
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83
Space Vector Modulation
• Even-Order Harmonic Elimination
r
V3
b
SECTOR III
r
V4
a
a
30 
30 
a
a
b
a
b
a
r
V5
SECTOR I
b
b
SECTOR IV
r
V2
SECTOR II
SECTOR VI
b
SECTOR V
r
V1
Type-A sequence
Type-B sequence
r
V6
Space vector Diagram
3/22/2016
Copyright by www.noteshit.com
84
Space Vector Modulation
• Even-Order Harmonic Elimination
V AB n
Vd
v AB
THD = 80.5%
23
0.2
17
v AO
47
13
0.1
41
7
5
65
35
0
(a) Waveforms 2ms/div
(b) Spectrum (500Hz/div)
• Measured waveforms and FFT
3/22/2016
Copyright by www.noteshit.com
85
Space Vector Modulation
• Even-Order Harmonic Elimination
V AB n / Vd
THD
(%)
0.3
THD
300
n 1
200
0.2
17
19
13
0.1
7
0
0
0.2
0.4
( f1  60 Hz
3/22/2016
0.6
and
100
5
11
0.8
ma
0
Ts  1 / 720 sec )
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86
Space Vector Modulation
• Five-segment SVM
r
V0
r
V1
r
V2
r
V1
r
V0
r
V0
r
V2
r
V1
r
V2
r
V0
OOO
POO
PPO
POO
OOO
PPP
PPO
POO
PPO
PPP
Tb
2
T0
2
v AN
Vd
Vd
0
vBN
Vd
Vd
0
vCN
Vd
0
T0
2
Ta
2
Tb
Ta
2
T0
2
T0
2
Tb
2
Ts
(a) Sequence A
3/22/2016
Ta
Ts
(b) Sequence B
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87
Space Vector Modulation
• Switching Sequence ( 5-segment)
Sector
3/22/2016
Switching Sequence (A)
r
r
r
r
V1
V2
V1
V0
I
r
V0
II
OOO
r
V0
POO
r
V3
PPO
r
V2
POO
r
V3
OOO
r
V0
III
OOO
r
V0
OPO
r
V3
PPO
r
V4
OPO
r
V3
OOO
r
V0
IV
OOO
r
V0
OPO
r
V5
OPP
r
V4
OPO
r
V5
OOO
r
V0
V
OOO
r
V0
OOP
r
V5
OPP
r
V6
OOP
r
V5
OOO
r
V0
VI
OOO
r
V0
OOP
r
V1
POP
r
V6
OOP
r
V1
OOO
r
V0
OOO
POO
POP
POO
OOO
Copyright by www.noteshit.com
vCN  0
vCN  0
v AN  0
v AN  0
v BN  0
v BN  0
88
Space Vector Modulation
• Simulated Waveforms ( 5-segment)
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
3/22/2016
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89