Description
Question 1:
For the single-phase system in Figure 1, it is given that the load �!”#$ is consuming
16��� at a �� = 0.6 �������. The voltage across the load �!”#$ = 120∠0°
�(���).
The line impedance is �!&'( = 1 + �2Ω
Figure 1
(a) For the load impedance, �!”#$, draw the power triangle and find (include units for
each of the first three values): �!”#$; �!”#$; |�!”#$|; �!”#$ and the power factor
angle �)*
(b) Find the load impedance: �+”#$
(c) Find the power losses on the line impedance �+&'((�+&'()
Question 2:
Given the single-phase system in Figure 2, given that:
– �!”#$ = 13,800∠0°
�,-.
– Load 1: 60kW at 0.8 power factor lead;
– Load 2: 160 kVA at 0.5 power factor lag;
332:494/599 HW 1 2
Figure 2
(a) Find and draw the power triangle for load �!”#$/: what is the real power �!”#$/
and reactive power �!”#$/ consumed by load �!”#$/
(b) Find and draw the power triangle for load �!”#$0: what is the real power �!”#$0
and reactive power �!”#$0 consumed by load �!”#$0
(c) Find the power factor (pf) for the total load �!”#$_(2 = �!”#$/||�!”#$0 and the
total apparent power H�!”#$_(2H in Figure 3
Figure 3
(d) Find the line current phasor Iline
(e) A capacitor is added in parallel to ZLoad_eq (see figure 4). If the power grid
frequency is f=60Hz, calculate the size of the capacitor �3″-) required in order
to correct the power factor for the load to 0.95 lag
Figure 4
332:494/599 HW 1 3
Question 3:
A small manufacturing plant is located 3km down a transmission line, which has a series
reactance of j0.4 Ω/km. The line resistance is negligible. The plant is a three-phase load
with a line voltage of 690V (Assume a positive sequence and a phase voltage Van that
serves as reference with angle ∠0°). It consumes 200 kW at 0.85 power factor lagging.
(a) Determine the line voltage at the source
(b) Determine the 3-phase complex power generated by the source
Question4:
The following three-phase loads are connected in parallel across a 3,800 V (line-line;
(Assume a positive sequence and a phase voltage Van that serves as reference with angle
∠0°) balanced three-phase power network:
Load 1: 120 kVA at 0.9 power factor lag;
Load 2: 180 kW at 0.55 power factor lead;
Load 3: 30 kW at unity power factor.
(a) Find the total complex power of the three loads
(b) Find the overall power factor
(c) Find line current in the supply line
