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Tutorial 1: Modulation Techniques
1. The VSI in Figure Q1 is applied with selected harmonic elimination PWM. It is necessary
to eliminate 5th, 7th, 9th and 11th harmonics in the line voltage and set the rms value of
the fundamental line voltage to 240 V.
a. What is the required number of switching points per quarter cycle?
b. Write down expressions from which the switching angles corresponding to
switching points can be found.
id
T1
Vd
O
D1
T3
D3
T5
D5
ia
ib
ic
A
B
N
C
T4
D4
T6
D6
T2
D2
Figure Q1
2. A three phase traditional inverter is connected to a Y-connected load and the system
parameters are: Vdc=600 V and switching frequency is 1200 Hz. We want to generate an
output voltage of 240 V (rms) and 50 Hz, using a space vector modulation technique.
a. How many samples happen in each sector?
b. Find duty cycles of each leg over 1/6th of the output cycle
c. Show the voltage vectors in d-q coordinates
d. Show the reference voltage and sampling time in d-q coordinates
3. In a SVM technique, a switching sequence in sector-I is based on the following vectors:
(V0, V1, V2, V1, V0). What are the switching sequences for the rest of the sectors?
Compare it with (V0, V1, V2, V7, V2, V1, V0), What is the difference in terms of switching
losses?
4. In a three-phase inverter, a switching sequence in sector-II is based on (V7, V2, V3, V2,
V7) vectors and time periods for active and zero vectors over one switching cycle are
(T3=0.1 ms, T2=0.2 ms, T0=0.2 ms and Ts=0.5 ms). Sketch the leg voltage waveforms.
What will happen if we change the switching sequence to (V0, V2, V3, V2, V0)? For (V0,
V3, V2, V7, V2, V3, V0), what are the duty cycles (time periods) for each voltage vector?
5. A Space Vector Modulation technique is used in a three-phase inverter with an inductive
load (star connection).
a. Sketch active and zero vectors in d-q coordinates.
b. If we use adjacent voltage vectors and two zero voltage vectors (V7, V0) in each
switching cycle, what are the two switching sequences in sector-I which have
minimum switching losses?
For the following two switching sequences in sector-II,
V2, V3,V0,V3, V2
V7, V2,V3, V0,V3, V7
c. Sketch output voltage waveforms (leg and line voltages)
d. Which switching sequence generates lower harmonics, why? (Describe it based
on the output voltage waveform)
e. Which one generates more switching losses, why? (Describe it based on the
output voltage waveform)
6. Draw a circuit diagram of a three-phase inverter with pure inductive load with star
connection. In one switching cycle, the sequence of the vectors is based on:
[V0 , V1 , V2 , V7 , V2 , V1 , V0 ]
[t0/4, t1/2, t2/2, t0/2, t2/2, t1/2, t0/4]
t0=60 s, t1=80s, t2=60 s
a. Sketch active and zero vectors in d-q coordinate.
b. Sketch the voltage across each inductor (phase a, b and c)
c. What is the switching frequency?
d. What is the switching sequence in sector-II?
e. If the output frequency is 50 Hz, how many switching transitions happen (over
one cycle of 50 Hz)?