Description
Question 1:
For the single-phase system in Figure 1, it is given that the load π!”#$ is consuming
16πππ΄ at a ππ = 0.6 πππππππ. The voltage across the load π½!”#$ = 120β 0Β°
π(πππ ).
The line impedance is π!&'( = 1 + π2Ξ©
Figure 1
(a) For the load impedance, π!”#$, draw the power triangle and find (include units for
each of the first three values): π!”#$; π!”#$; |π!”#$|; π!”#$ and the power factor
angle π)*
(b) Find the load impedance: π+”#$
(c) Find the power losses on the line impedance π+&'((π+&'()
Question 2:
Given the single-phase system in Figure 2, given that:
– π!”#$ = 13,800β 0Β°
π,-.
– 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 π!”#$/: what is the real power π!”#$/
and reactive power π!”#$/ consumed by load π!”#$/
(b) Find and draw the power triangle for load π!”#$0: what is the real power π!”#$0
and reactive power π!”#$0 consumed by load π!”#$0
(c) Find the power factor (pf) for the total load π!”#$_(2 = π!”#$/||π!”#$0 and the
total apparent power Hπ!”#$_(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 πΆ3″-) 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 Ξ©/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 β 0Β°). 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
β 0Β°) 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
