EEL 3216 Introduction to Power Systems
Homework # 2
SOLUTIONS
1. A three phase wye-connected unbalanced load is supplied by a balanced three-phase
delta connected source. The source voltages and load impedances are:
Vab = 13.2 kV ∠90° Ian = 19.42 A ∠-33.1°
Vbc = 13.2 kV ∠210° Ibn = 16.34 A ∠189.3°
Vca = 13.2 kV ∠330°
a) Find the impedances Zan, Zbn, and Zcn.
b) Calculate the active, reactive, and apparent power delivered by the source.
c) Draw the phasor diagram of all voltages and currents
In = 0. (there is no return path to complete the current loop)
In = Ia + Ib + Ic
I c = −( I a + I b )
I c = −(19.42 Α ∠ − 33.1° + 16.34 Α ∠189.3°)
I c = 13.25 Α ∠90°
Vab
Van = ∠ + 30° = 7.62 KV ∠120°
3
Vbn = 7.62 KV ∠240°
Vcn = 7.62 KV ∠0°
Van 7.62 KV
Z an = = ∠120° + 33.1° = 392.4 Ω ∠153.1°
I an 19.42 A
Z bn = 466.3 Ω ∠50.7°
Z cn = 573.73 Ω ∠ − 90°
Power delivered:
S = Van I an
*
+ Vbn I bn
*
+ Vcn I cn* = Z an I an2 + Z bn I bn2 + Z cn I cn2
2. (Problem 2-2, p 79 in Textbook) The circuit below (Figure 2) shows a three-phase
power system with two loads. The ∆-connected generator is producing a line voltage of
480 V, and the line impedance is 0.09 + j0.16 Ω. Load 1 is Y-connected, with a phase
impedance of 2.5 ∠36.87° Ω and load 2 is ∆-connected, with a phase impedance of 5 ∠-
20° Ω.
a) What is the line voltage of the two loads?
b) What is the voltage drop on the transmission lines?
c) Find the real and reactive powers supplied to each load.
d) Find the real and reactive power losses in the transmission line.
e) Find the real power, reactive power, and power factor supplied by the generator
ATTEWNTION! The solution below is calculated with Va at zero degrees, while in fact
Va lies at –30 degrees considering the angle of Vab in the problem statement. However,
except for this –30 degrees overall phase shift in all voltage and current values the
solution process and the results (in magnitude of voltages and currents as well as powers)
are the same.
