8/18/2019 Assignment4-2015

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CONCORDIA UNIVERSITY

DEPARTMENT OF ELETRICAL AND COMPUTER ENGINEERING

ELEC 433/6461 – Power Electronics/Power Electronics I

Assignment #4: dc-ac converters and power electronic interfaces

Due date: November 24, 2015, at 6:00 PM in the mailbox of Dr. Lopes (EV5.175).

1)  Consider an emergency three-phase 5kVA/208VLL /60Hz power supply fed by a 72 V battery bank. It is composed of a

battery bank, a three-phase full-bridge dc-ac converter, a step-up Y:Y transformer and an output LC filter. The dc-ac

converter (inverter) is controlled with SPWM ( f tri = 1980 Hz) with variable amplitude modulation index/ratio (ma) to

compensate for variations in the battery voltage, as it discharges. The system shuts down when the battery voltage

falls below 60 % of its rated value to prevent deep discharge. A) Calculate the turns ratio of the transformer (ideal)

Assume that the converter operates with ma = 1 when the battery voltage is at its minimum value. B) What should be

the value of (ma) when the battery is fully charged? C) Calculate the resonant frequency ( f res) of the output LC filter so

that the magnitude of the dominant harmonic is limited to 3% of the rated fundamental component at all times. Note:

An approach/equation to calculate  f res of a 2nd order LPF is shown below.

 DecdB

dBGain

 fh fres

 DecdB

dBGain fres fhGaindBGain

hVin

hVout Gain

 / 40

)(

10

, / 40

)(loglog ),log(20)(,

_

_

−

=

−

=−==  

2)  Consider a 200Vdc  /1 kW single-phase unity power factor diode rectifier with a boost inductor of 3 mH and a dc

capacitor of 500 µF. It operates with constant switching frequency and is connected to a 120V/60 Hz source. A)

Compute the minimum switching frequency so that the maximum ripple current in the ac side current is smaller than

5% of the input rated current. B) In this case, what would be the value of the minimum ripple current in the ac sidecurrent and when would it occur? C) Compute the magnitude of the output voltage ripple (peak-to-peak) when the

converter supplies half rated power.

3)  Consider a single-phase force-commutated ac-dc converter operating as a rectifier. It operates with hysteresis

(tolerance band) current control and unit power factor. A) Explain how the gating signals for the 4 switches are

generated so that the actual current can follow the sinusoidal reference current waveform within a given tolerance

band. (When does the input current increase and when does it decrease?) B) Assuming that the ac-dc converter is

lossless (Pac = Pdc), compute the magnitude of the dc side (average) voltage when the reference current is 10 A rms,the source is 120 V rms and the dc side load resistor is 50 Ω. C) Assuming that the ac inductor is 4 mH, calculate the

rms value of the fundamental component of the voltage at the ac side of the ac-dc converter. D) Draw the phasor

diagram (magnitude and angle) showing the source voltage and current, the voltage across the ac inductance and the

voltage at the ac side of the ac-dc converter.

8/18/2019 Assignment4-2015

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0

DA+

+ 

V d  c 

-

P2

DB-

Cf

1000uF

RLoad

50

+

 V s

 -

V1FREQ = 60

VAMPL = 169.7V

PHASE = 0

+

TB+

DB+

DA-

Ls

4mH+ 

V c onv 

-

P2

P1

P1

+

TA-

+

TB-

+ VLs -

+

TA+

---> Is