Page 1
Inverters circuits will convert DC power to AC power at required voltage & required frequency.
Classification
1) Voltage source Inverter
? Input source is a voltage source.
? Switching device is bidirectional & unipolar.
? Load voltage depends on source voltage & load current depends on load parameters.
2) Current source Inverters
? Input source is a current source.
? Switching device is bidirectional & bipolar
? Load voltage depends on source current & load voltage on load parameters.
Single phase half bridge VSI
When
1
S is ON,
OO
V 0, I 0 ??
When
2
S is ON,
OO
V 0, I 0 ??
When
1
D is ON, ??
OO
V 0, I 0
When
2
D is ON,
OO
V 0, I 0 ??
? The output voltage is a square wave of amplitude
dc
V
2
? The fourier series of output voltage is given by
? ?
?
?
??
?
? O
dc
n 1,3,5
2V
V sin n t
n
? rms value of fundamental components is given by
??
? ? ?
??
??
??
dc
or1 dc
2V 12
VV
2
? rms value of output voltage ?
dc
or
V
V
2
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43%
Page 2
Inverters circuits will convert DC power to AC power at required voltage & required frequency.
Classification
1) Voltage source Inverter
? Input source is a voltage source.
? Switching device is bidirectional & unipolar.
? Load voltage depends on source voltage & load current depends on load parameters.
2) Current source Inverters
? Input source is a current source.
? Switching device is bidirectional & bipolar
? Load voltage depends on source current & load voltage on load parameters.
Single phase half bridge VSI
When
1
S is ON,
OO
V 0, I 0 ??
When
2
S is ON,
OO
V 0, I 0 ??
When
1
D is ON, ??
OO
V 0, I 0
When
2
D is ON,
OO
V 0, I 0 ??
? The output voltage is a square wave of amplitude
dc
V
2
? The fourier series of output voltage is given by
? ?
?
?
??
?
? O
dc
n 1,3,5
2V
V sin n t
n
? rms value of fundamental components is given by
??
? ? ?
??
??
??
dc
or1 dc
2V 12
VV
2
? rms value of output voltage ?
dc
or
V
V
2
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43%
? If load power factor is lagging, then it requires forced commutation.
? If load power factor is leading, then natural commutation occurs.
Single phase Full Bridge VSI
When
1
S ,
2
S conduct
OO
V 0, I 0 ??
When
1
D ,
2
D conduct, ??
OO
V 0, I 0
When
3
S ,
4
S conduct, ??
OO
V 0, I 0
When
34
D ,D conduct,
OO
V 0, I 0 ??
? The output voltage is a square wave of amplitude
dc
V
? The fourier series of output voltage is given by
? ?
?
?
??
?
? O
dc
n 1,3,5
4V
V sin n t
n
? rms value of fundamental components is given by
?
?
or1 dc
2
VV
? rms value of output voltage ?
or dc
VV
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43%
Three phase full bridge VSI
Page 3
Inverters circuits will convert DC power to AC power at required voltage & required frequency.
Classification
1) Voltage source Inverter
? Input source is a voltage source.
? Switching device is bidirectional & unipolar.
? Load voltage depends on source voltage & load current depends on load parameters.
2) Current source Inverters
? Input source is a current source.
? Switching device is bidirectional & bipolar
? Load voltage depends on source current & load voltage on load parameters.
Single phase half bridge VSI
When
1
S is ON,
OO
V 0, I 0 ??
When
2
S is ON,
OO
V 0, I 0 ??
When
1
D is ON, ??
OO
V 0, I 0
When
2
D is ON,
OO
V 0, I 0 ??
? The output voltage is a square wave of amplitude
dc
V
2
? The fourier series of output voltage is given by
? ?
?
?
??
?
? O
dc
n 1,3,5
2V
V sin n t
n
? rms value of fundamental components is given by
??
? ? ?
??
??
??
dc
or1 dc
2V 12
VV
2
? rms value of output voltage ?
dc
or
V
V
2
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43%
? If load power factor is lagging, then it requires forced commutation.
? If load power factor is leading, then natural commutation occurs.
Single phase Full Bridge VSI
When
1
S ,
2
S conduct
OO
V 0, I 0 ??
When
1
D ,
2
D conduct, ??
OO
V 0, I 0
When
3
S ,
4
S conduct, ??
OO
V 0, I 0
When
34
D ,D conduct,
OO
V 0, I 0 ??
? The output voltage is a square wave of amplitude
dc
V
? The fourier series of output voltage is given by
? ?
?
?
??
?
? O
dc
n 1,3,5
4V
V sin n t
n
? rms value of fundamental components is given by
?
?
or1 dc
2
VV
? rms value of output voltage ?
or dc
VV
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43%
Three phase full bridge VSI
180
0
conduction mode
In this mode, each switch will conduct for a period of
0
180 and phase displacement between
any two poles is
0
120
? Phase voltage
? ?
?
ph dc
rms
2
VV
3
? ?
?
??
??
?
?
dc
RN
n 6k 1
2V
V sin n t
n
? ?
R1
V = rms value of fundamental component of
RN
V
?
?
dc
R1
2V
V
Distortion factor, ??
?
R1
ph,rms
V 3
DF
V
? ? ? ?
2
1
THD 1 100 31%
DF
? Line voltage
? ?
?
?
L L dc
rms
2
VV
3
? ? ? ? ? ?
?
??
??
? ? ?
?
?
dc
RY
n 6k 1
4V
n
V sin sin n t
36
n
? ?
RY
1
V = rms value of fundamental component of
RY
V =
? ?
?
?
RY
1
6
V
Distortion factor =
3
?
In each phase, each switch conducts for
0
180 out of
0
360
??
o, rms
r.rms
I
I
2
dc dc
2V V
3R 3R 2
??
?
, Where R = load resistance
Page 4
Inverters circuits will convert DC power to AC power at required voltage & required frequency.
Classification
1) Voltage source Inverter
? Input source is a voltage source.
? Switching device is bidirectional & unipolar.
? Load voltage depends on source voltage & load current depends on load parameters.
2) Current source Inverters
? Input source is a current source.
? Switching device is bidirectional & bipolar
? Load voltage depends on source current & load voltage on load parameters.
Single phase half bridge VSI
When
1
S is ON,
OO
V 0, I 0 ??
When
2
S is ON,
OO
V 0, I 0 ??
When
1
D is ON, ??
OO
V 0, I 0
When
2
D is ON,
OO
V 0, I 0 ??
? The output voltage is a square wave of amplitude
dc
V
2
? The fourier series of output voltage is given by
? ?
?
?
??
?
? O
dc
n 1,3,5
2V
V sin n t
n
? rms value of fundamental components is given by
??
? ? ?
??
??
??
dc
or1 dc
2V 12
VV
2
? rms value of output voltage ?
dc
or
V
V
2
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43%
? If load power factor is lagging, then it requires forced commutation.
? If load power factor is leading, then natural commutation occurs.
Single phase Full Bridge VSI
When
1
S ,
2
S conduct
OO
V 0, I 0 ??
When
1
D ,
2
D conduct, ??
OO
V 0, I 0
When
3
S ,
4
S conduct, ??
OO
V 0, I 0
When
34
D ,D conduct,
OO
V 0, I 0 ??
? The output voltage is a square wave of amplitude
dc
V
? The fourier series of output voltage is given by
? ?
?
?
??
?
? O
dc
n 1,3,5
4V
V sin n t
n
? rms value of fundamental components is given by
?
?
or1 dc
2
VV
? rms value of output voltage ?
or dc
VV
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43%
Three phase full bridge VSI
180
0
conduction mode
In this mode, each switch will conduct for a period of
0
180 and phase displacement between
any two poles is
0
120
? Phase voltage
? ?
?
ph dc
rms
2
VV
3
? ?
?
??
??
?
?
dc
RN
n 6k 1
2V
V sin n t
n
? ?
R1
V = rms value of fundamental component of
RN
V
?
?
dc
R1
2V
V
Distortion factor, ??
?
R1
ph,rms
V 3
DF
V
? ? ? ?
2
1
THD 1 100 31%
DF
? Line voltage
? ?
?
?
L L dc
rms
2
VV
3
? ? ? ? ? ?
?
??
??
? ? ?
?
?
dc
RY
n 6k 1
4V
n
V sin sin n t
36
n
? ?
RY
1
V = rms value of fundamental component of
RY
V =
? ?
?
?
RY
1
6
V
Distortion factor =
3
?
In each phase, each switch conducts for
0
180 out of
0
360
??
o, rms
r.rms
I
I
2
dc dc
2V V
3R 3R 2
??
?
, Where R = load resistance
Voltage Total RMS Fundamental RMS
Phase
dc
2
V
3
dc
2
V
?
Line
dc
2
V
3
dc
6
V
?
? This conversion from total rms to fundamental rms can be performed by multiplication of
?
?
3
DF .
? This conversion from phase to line voltage can be performed by multiplication of 3 .
120
0
conduction mode
For each thyristor, conduction angle is
0
120 & last
0
60 for commutation.
? Phase Voltage
? ?
?
dc
ph
rms
V
V
6
? ? ? ?
?
??
??
? ? ?
?
?
dc
RN
n 6k 1
2V
V sin n sin n t n
36
n
?
?
R1 dc
6
VV
Distortion factor, ?
?
3
DF
THD = 31%
? Line Voltage
? ?
?
dc
L
RMS
V
V
2
? ?
? ? ? ?
?
??
?
? ? ?
?
?
dc
RY
n 6k 1
3V
V sin n t
3
n
? ?
?
?
RY dc
1
3
VV
2
Page 5
Inverters circuits will convert DC power to AC power at required voltage & required frequency.
Classification
1) Voltage source Inverter
? Input source is a voltage source.
? Switching device is bidirectional & unipolar.
? Load voltage depends on source voltage & load current depends on load parameters.
2) Current source Inverters
? Input source is a current source.
? Switching device is bidirectional & bipolar
? Load voltage depends on source current & load voltage on load parameters.
Single phase half bridge VSI
When
1
S is ON,
OO
V 0, I 0 ??
When
2
S is ON,
OO
V 0, I 0 ??
When
1
D is ON, ??
OO
V 0, I 0
When
2
D is ON,
OO
V 0, I 0 ??
? The output voltage is a square wave of amplitude
dc
V
2
? The fourier series of output voltage is given by
? ?
?
?
??
?
? O
dc
n 1,3,5
2V
V sin n t
n
? rms value of fundamental components is given by
??
? ? ?
??
??
??
dc
or1 dc
2V 12
VV
2
? rms value of output voltage ?
dc
or
V
V
2
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43%
? If load power factor is lagging, then it requires forced commutation.
? If load power factor is leading, then natural commutation occurs.
Single phase Full Bridge VSI
When
1
S ,
2
S conduct
OO
V 0, I 0 ??
When
1
D ,
2
D conduct, ??
OO
V 0, I 0
When
3
S ,
4
S conduct, ??
OO
V 0, I 0
When
34
D ,D conduct,
OO
V 0, I 0 ??
? The output voltage is a square wave of amplitude
dc
V
? The fourier series of output voltage is given by
? ?
?
?
??
?
? O
dc
n 1,3,5
4V
V sin n t
n
? rms value of fundamental components is given by
?
?
or1 dc
2
VV
? rms value of output voltage ?
or dc
VV
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43%
Three phase full bridge VSI
180
0
conduction mode
In this mode, each switch will conduct for a period of
0
180 and phase displacement between
any two poles is
0
120
? Phase voltage
? ?
?
ph dc
rms
2
VV
3
? ?
?
??
??
?
?
dc
RN
n 6k 1
2V
V sin n t
n
? ?
R1
V = rms value of fundamental component of
RN
V
?
?
dc
R1
2V
V
Distortion factor, ??
?
R1
ph,rms
V 3
DF
V
? ? ? ?
2
1
THD 1 100 31%
DF
? Line voltage
? ?
?
?
L L dc
rms
2
VV
3
? ? ? ? ? ?
?
??
??
? ? ?
?
?
dc
RY
n 6k 1
4V
n
V sin sin n t
36
n
? ?
RY
1
V = rms value of fundamental component of
RY
V =
? ?
?
?
RY
1
6
V
Distortion factor =
3
?
In each phase, each switch conducts for
0
180 out of
0
360
??
o, rms
r.rms
I
I
2
dc dc
2V V
3R 3R 2
??
?
, Where R = load resistance
Voltage Total RMS Fundamental RMS
Phase
dc
2
V
3
dc
2
V
?
Line
dc
2
V
3
dc
6
V
?
? This conversion from total rms to fundamental rms can be performed by multiplication of
?
?
3
DF .
? This conversion from phase to line voltage can be performed by multiplication of 3 .
120
0
conduction mode
For each thyristor, conduction angle is
0
120 & last
0
60 for commutation.
? Phase Voltage
? ?
?
dc
ph
rms
V
V
6
? ? ? ?
?
??
??
? ? ?
?
?
dc
RN
n 6k 1
2V
V sin n sin n t n
36
n
?
?
R1 dc
6
VV
Distortion factor, ?
?
3
DF
THD = 31%
? Line Voltage
? ?
?
dc
L
RMS
V
V
2
? ?
? ? ? ?
?
??
?
? ? ?
?
?
dc
RY
n 6k 1
3V
V sin n t
3
n
? ?
?
?
RY dc
1
3
VV
2
Distortion factor, =
3
; THD 31% ?
?
In each, phase each switch conducts for
0
120 out of
0
360
o, rms
T, rms
I
I
3
?
dc
V
2R
?
R = load resistance
Voltage Total RMS Fundamental RMS
Phase
dc
V
6
dc
6
V
?
Line
dc
V
2
dc
3
V
2 ?
? The conversion factor remain same as in
0
180 conduction mode.
? In both
00
120 & 180 conduction mode both phase & line voltages are free from even & triplen
harmonics.
Voltage control using PWM techniques
1) Single PWM techniques
In this case, width of positive & negative cycle is not ? but rather equal to 2d.
? ?
? ? ? ?
?
?
?
??
?
? O
S
n 1,3,5
4V
V sin n sin nd sin n t
2
n
To eliminate n
th
harmonics
Sin (nd) = 0
d
n
?
?
Pulse width,
2 4 6
2d , , ,...................
n n n
? ? ?
?
but 2d ??
To eliminate 3
rd
harmonics
2
3d ; d ; 2d
33
??
? ? ? ?
So pulse width of
0
120 is required.
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