Voltage Control of Single-Phase Inverters
• Commonly-used Techniques
– Single-Pulse-Width-Modulation
– Multiple-Pulse-Width-Modulation
– Sinusoidal-Pulse-Width-Modulation
– Modified-Sinusoidal-Pulse-Width-Modulation
– Phase-Displacement Control
ECE 442 Power Electronics
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Single-Pulse-Width-Modulation
ECE 442 Power Electronics
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One Pulse per Half-Cycle
Pulse Width Controls the Output Voltage
ECE 442 Power Electronics
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Carrier and Reference Signals
Gate Pulse
Gate Pulse
• Compare the Reference Signal with the Carrier
• Frequency of the Reference Signal determines
the frequency of the Output Voltage
• Modulation Index = M = Ar/Ac
ECE 442 Power Electronics
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Gate Signals and Output
ECE 442 Power Electronics
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rms value of the Output Voltage

 2
Vo  
2

 


2
V
d
(

t
)
s


 

2
1
2
2

Vo  Vs

0    180
0  Vo  Vs
ECE 442 Power Electronics
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Fourier Series for the Output Voltage
4Vs
n
vo (t )  
sin sin nt
2
n 1,3,5,... n

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Times and angles of the intersections
TS
1
t1 
 (1  M )

2
TS
2
t2 
 (1  M )

2
Pulse width d (or pulse angle δ)

d   t2  t1  MTS

ECE 442 Power Electronics
TS = T/2
8
Harmonic Profile
ECE 442 Power Electronics
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Multiple-Pulse-Width-Modulation
ECE 442 Power Electronics
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Multiple Pulses per Half-Cycle
of Output Voltage
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Gate Signal Generation
• Compare the Reference Signal with the Carrier
• Frequency of the Reference Signal determines the
Output Voltage Frequency
• Frequency of the Carrier determines the number of
pulses per half-cycle
• Modulation Index controls the Output Voltage
ECE 442 Power Electronics
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Gate Signals and Output Voltage
Number of pulses per half cycle = p = fc/2fo = mf /2
where mf = frequency modulation ratio
ECE 442 Power Electronics
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rms Value of the Output Voltage

(  ) / 2


p
2p

2
Vo  
V
d
(

t
)
s


2




(  ) / 2
p


1
2
p
Vo  Vs

0  M 1
0 
0 
T
2p

p
0  Vo  Vs
ECE 442 Power Electronics
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Fourier Series of the Output Voltage
vo (t ) 


n 1,3,5,...
Bn sin nt
4Vs
n 
3

Bn  
sin
sin n( m  )  sin n(   m  

4 
4
4
m 1 n
2p
ECE 442 Power Electronics
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The times and angles of the intersections
m
Ts
tm 
 (m  M )

2
m
TS
tm 
 (m  1  M )

2
The pulse width d (or pulse angle δ)
TS = T/2p

d   tm 1  tm  MTS

ECE 442 Power Electronics
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Harmonic Profile
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