An Investigation into Even Harmonic Injection in Pole Voltages of a Single Phase Inverter: Presented at National Power Electronics Conference (NPEC) 2010 at Roorkee, India.

1. An Investigation into Even Harmonic Injection
in Pole Voltages of a Single-Phase Inverter
Lalit Patnaik*
National Power Electronics Conference 2010
L Umanand*
G Narayanan†
Indian Institute of Science, Bangalore
*Centre for Electronics Design & Technology
†Department of Electrical Engineering

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MOTIVATION
Addition of common mode leads to certain benefits in the case of a 3-phase inverter
• Higher fundamental voltage
• Lesser switching losses
Conventional Space Vector PWM
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3rd harmonic injection PWM

3. Bus Clamping PWM
MOTIVATION
Addition of common mode leads to certain benefits in the case of a 3-phase inverter
• Higher fundamental voltage
• Lesser switching losses
Reference: Pavan Kumar Hari, “Comparative Evaluation of Space Vector Based Pulse Width Modulation Techniques in terms of
Harmonic Distortion and Switching Loss”, M. Sc. (Engg.) Thesis, Department of Electrical Engineering, IISc, Bangalore, August 2008.
*

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Time (seconds)
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Time (seconds)
Volts
Unipolar Sine-Triangle PWM for Single Phase Inverter
ma mb Vab
V =400V
DC
o a b
+V /2
DC
-V /2
DC

5. should be periodic with period = 180°
i.e. should comprise of even harmonics only
we need:
What kind of harmonics can comprise?
No Half-wave Symmetry!

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Can we get a higher fundamental voltage
with even harmonic injection?
n=1
ϕ=0°
k=0.3
n=1
ϕ=45°
k=0.3
n=1
ϕ=90°
k=0.3
n=2
ϕ=0°
k=0.3

7. Can we get a higher fundamental voltage
with even harmonic injection?
NO!
n=1
ϕ=0°
k=0.3
n=1
ϕ=45°
k=0.3
n=1
ϕ=90°
k=0.3
n=2
ϕ=0°
k=0.3

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Can we reduce switching losses
with even harmonic injection?
Bus Clamping PWM
(Waveforms for modulation index =1)
0° to 90° → mb clamped to –VDC/2 & ma> mb
90° to 180° → ma clamped to +VDC/2 & ma> mb
180° to 270° → ma clamped to –VDC/2 & ma< mb
270° to 360° → mb clamped to +VDC/2 & ma< mb

9. (Waveforms for modulation index =0.7)
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Degrees
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-0.5
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Degrees
Bus Clamping PWM

10. Waveforms in a Carrier Cycle
Sine-Triangle PWM
TS TS
Inv. State:++ +- -- -- +- ++
Vao
Vbo
Vab
ma
mb
T1 T1
T /2
0
T /2
0
T /2
0 T /2
0
Bus Clamping PWM
TS
Inv. State: +- --
Vao
Vbo
Vab
-- +-
ma
mb
TS
T0
T0
T1 T1

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Time (seconds)
0 0.005 0.01 0.015 0.02
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-200
0
200
400
Time
Sine-Triangle PWM Bus Clamping PWM
In Bus Clamping PWM, switches half the number of times
it does in Sine-Triangle PWM
Vab Vab
Vab

12. Switching Loss
For Sine-Triangle PWM:
For Bus-clamping PWM:
Switching Loss is halved irrespective of load
power factor and modulation index

13. Conduction Loss
➢ Duty ratio is either 0 or 1 during clamped intervals
(depending on the direction of current)
➢ If VT≃VD (say 2-3 volts) the above weighted sum does
not vary much due to clamping
Conduction Loss does not change much

14. Harmonic Analysis
Unipolar Sine-Triangle PWM
fC = 320 × fMOD = 320 × 50 Hz = 16 kHz
Simulation Experiment

15. Harmonic Analysis
Bus Clamping PWM
Simulation Experiment
fC = 320 × fMOD = 320 × 50 Hz = 16 kHz

16. Current Ripple Analysis
*Assumption: R-L load with L/R >> TS
T1 T0 T1
T0
T1
T1
T /2
0 T /2
0
T /2
0 T /2
0
TS TS
Sine-Triangle PWM
Bus Clamping PWM

17. Current Ripple Analysis
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0
0.01
0.02
0.03
wt (degrees)
RMS
Current
Ripple
(A)
Current Ripple is doubled
fs=20kHz
L=0.1H
Vdc=400V
m=1
*

18. CONCLUSION
Consequences of using
Bus Clamping PWM over Sine-∆ PWM:
1. Switching Loss is halved
2. Conduction Loss does not change much
3. Weighted THD increases
4. Current ripple is doubled

19. THANK YOU
☺

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Equations