Set A
Notation
: Lower case, such as ‘v’, represents instantaneous quantity and bold upper
case, such as ‘
V
’, represents phasor quantity.
1.
A 3phase balanced load is connected to a 3phase balanced power supply through
identical transformers of 1:1 turns ratio which are wye (Y)/delta connected as
shown in Fig. 1.
The load impedance is 
Z
=10 ohms. The source voltage 
E

(lineto ground) is 550 volt.
E1
E2
E3
S1
Z
Z
Z
I
L
i
La
i
Lb
i
Lc
i
a
i
b
i
c
i
A
i
B
i
C
B
C
A
b
c
a
Fig. 1
The switch S1 is closed,
(a) What are the linetoline voltages

V
ab

=

V
bc

=

V
ca

on the secondary sides of
the
transformers?
(b) What is the phase voltage (linetoneutral ),

V
ph

, across each load
Z
?
(c) What is the current

I
L

of each load
Z
?
(d) What are the magnitudes of

I
a

=

I
b

=

I
c

in the delta connection? (
Hint
: Draw
current phasors to represent i
La
=i
a
i
c
, i
Lb
=i
b
i
a
, and i
Lc
=i
c
i
b
).
(e) What are the magnitudes of

I
S

=

I
A

=

I
B

=

I
C

on the primary side?
(f)
What is

S
S

the complex power of the power source, 3
E
ph


I
S

, where

E
ph
=
E
1
=
E
2
=
E
3
?
(g) What is

S
Ts

the complex power of the secondary (load) side transformers, which
are delta connected?
From (f) and (g), it is clear that
the complex power is independent of whether the
transformers are connected in wye (Y) or delta.
2.
One of the transmission lines is lost. This is represented by opening the switch S1.
The current i
A
=0.
(a) What is the current i
a
?
The voltages with respect to ground across the primary transformers are v
A
, v
B
, v
C
.
The bphase is intact.
(b) What is the voltage v
bc
in terms of v
A
, v
B
, v
C
?
The cphase is intact.
(c) What is the voltage v
ba
in terms of v
A
, v
B
, v
C
?
Under balanced 3phase operating conditions, v
A
+v
B
+v
C
=0 so that v
A
= (v
B
+v
C
).
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