Download EE442 FE Spr 98-99 - faraday - Eastern Mediterranean University

Date
Duration
Eastern Mediterranean University
Department of Electrical and Electronic Engineering
EE 442 FINAL EXAM
: 23 / 6 / 1999
ANSWER ALL FOUR QUESTIONS
: 2 hrs.
EACH QUESTION IS 25 PTS.
1-) The three-phase fully-controlled midpoint converter shown below supplies power to a highly
inductive load with resistance RL = 10  . The converter is fed from a 380 V rms
( line-to-line ) three-phase source. Assume that the load current IL is constant .
(a) Derive an expression for the average load voltage Vdc in terms of the firing angle .
(b) For  =  / 3 find the average load current IL .
va
vb
vc
T1
va = Vm sin wt
vb = Vm sin (wt-2 /3)
vc = Vm sin (wt-4 / 3 )
T2
I
T3
L
Load
n
2-) In the resonant-pulse commutation circuit shown below, assume that the initial capacitor
voltage is Vo = Vs .
(a) The maximum load current to be commutated is Ia = 15 A. Find the maximum tq of
the main thyristor T1 .
(b) For Ia = 10 A, find the overvoltage on the capacitor after the commutation
interval.
D2
T1
+
Vs
_
L
C
+
-V
c
T2
Ia
D1
Load
Dm
Vs = 200 v , C = 0.5 F , L = 50 H
3-) The single-phase full-bridge inverter shown below is operated in the quasi-square-wave
( QSW ) mode ( phase displacement control ) at the frequency f = 100 Hz , with phase
shift  between half-bridge output voltages va and vb . The load is an R-L load with
R = 10  and L = 10 mH .
(a) For  = 2 / 3 sketch vo and find its total harmonic dostortion THD .
(b) For  = 2 / 3 find approximately the rms value of the load current i0 by
considering harmonics with order n  7.
+
Vs
va
= 200 V
+
io
vo
-
vb
load
-
4-) The three-phase half-bridge inverter shown below feeds a balanced Y-connected load , and is
operated in the square-wave mode ( pole voltages are square waves ) at frequency f s .
(a) Sketch the line-to-line voltage vab ( indicate all voltage levels ) and find its
fundamental amplitude.
(b) With a purely inductive load L per phase , find the peak value of phase A load
current ia . Show your derivation explicitly.
+
a
Vs
b
c
-
ia
n
USEFUL INFORMATION :
1-) THD of a periodic waveform x (t):
1/ 2
1   2
THD =
  Xn 
X1  n  2 
2-)
Xn = n’th harmonic amplitude
Fourier series of a quasi-square-wave
x
A

/2
-/2
/2
-A
-/2
t
x(t) =
4A  n 
sin  cos n t 
 2
n

n=1,3,5,..

3-) LC resonant circuits :
t=0
i
C
+
vc
L
vc (t) = Vo cos t
Vo = vc (0)
i(t) = -Ip sin t
Ip = Vo  C / L
_
L
+
Vs
_
-
C
+
vc
i
vc (t) = Vs + ( Io / C ) sin t
i (t) = Io cos t