Power system, Symmetrical Components

1. Practice Questions for Unit II
Q1. Find the symmetrical component of line currents for an unbalanced load connected in
star across a balanced supply of 200V. Given: Zan = 20+j10 Ω, Zbn = 10+j5 Ω, Zcn =
5+j20 Ω.
Q2. What are the symmetrical components of the line voltages given below:
Vab = 200+j346 Volts; Vbc = 300-j346 Volts; Vca = -500 Volts. Draw the vector
diagram.
Q3. The line voltages of a balanced 10 ohms delta connected load are Vab = 100+j300
Volts, Vbc = 50 – j200 Volts, Vca = -150 – j100 Volts. Find the symmetrical
components of the phase currents.
Q4. Following are the line voltages (in volts) and the phase currents (in Amperes) for a
delta connected load : Vab = 10 + j0; Vbc = 5 – j10; Vca = -10 + j10; Iab = 4/100 ; Ibc =
6/ -800; Ica = 2/ 500 .Find the Active and reactive power of the circuit using
symmetrical component method.
Q5. Following are the phase voltages (in volts) and the phase currents (in Amperes) for a
delta connected load : Vab = 50 + j0; Vbc = 40 – j50; Vca = -50 + j50; (All in Volts)
Iab = 5 / 00 ; Ibc = 6 / -1000; Ica = 8/ 800 (All in Amperes)
Find the Active and reactive power of the circuit using symmetrical component
method.
Q6. For a 3 phase transformer which has Y(ungrounded neutral) on the HT side and ∆ on
the LT side, following are the symmetrical components :
LT side b phase positive sequence curren Ib1 = 0.4∟-200 pu
HT side A phase negative sequence current IA2 = 0.2∟450 pu
Vectorially build the line currents on both the sides of the transformer in per unit (pu).
Q7. A balanced delta connected load which has 10 Ω resistors across the phases, has 120V
balanced voltage across the lines. Line c fuse melts due to a fault. Find the line
currents and the symmetrical components of line currents before and after the fault.
Draw the vector diagram for the line currents.
Q8. Three resistances of 10, 15 and 20 ohms are connected in star across a three-phase
supply of 200V per phase as shown in the figure. The supply neutral is earthed while
the load neutral is isolated. Find the currents in each load branch and the voltage of
load neutral above earth.

2. Q9. Consider the circuit shown in the figure. Suppose Van=100(0◦), Vbn=60(60◦),
Vcn=60(120◦), Xs=12Ω and Xab=Xbc=Xca=5Ω.
a. Calculate Ia, Ib and Ic without using symmetrical components.
b. Calculate Ia, Ib and Ic using symmetrical components.
Q10. The voltages at the terminals of a balanced load consisting of three 10-Ώ resistors
connected in Y are Vab = 100∟0°, Vbc = 80.8∟-121.44°, and Vca = 90∟130° V.
Determine a general expression for the relation between the symmetrical components
of the line and the phase voltages, that is, between Vab1 and Van1 and between Vab2
and Van2. Assume that there is no connection of the neutral to the load. Find the line
currents from the symmetrical components of the given line voltages.
I
a
I
b
I
c
a
b
c
A
C
B
20
Ω
10
Ω
15
Ω
200V
+
Ib
Vbn
Xs
+
Ic
Vcn
Xs
+
Ia
Van
Xs
Xca
Xab
Xbc