468 AC POWER SYSTEMScontrols. Pumped storage plants, which represent a large reserve that can be put into operation on
short notice, can help the situation.
The great blackout of 1965 had indeed been a sobering experience and possibly a needed
warning to reexamine some of our policies and plans. The warning will not have been wasted if
we learn from it how to build a more reliable grid to suppply all the power that is needed in the
years ahead. After all, our whole economy is almost completely dependent on electric power.Problems
10.2.1Two ideal voltage sources are connected to each
other through a feeder with impedanceZ ̄ =
1. 5 +j 6 , as shown in Figure P10.2.1. Let
E ̄ 1 = 120 0° V andE ̄ 2 = 110 45°.
(a) Determine the real power of each machine,
and state whether the machine is supplying
or absorbing real power.
(b) Compute the reactive power of each ma-
chine, and state whether each machine is
delivering or receiving reactive power.
(c) Find the real and reactive power associated
with the feeder impedance, and state whether
it is supplied or absorbed.*10.2.2If the impedance between the voltage sources in
Problem 10.2.1 is changed toZ ̄= 1. 5 −j 6 ,
redo parts (a) through (c) of Problem 10.2.1.
10.2.3A single-phase industrial plant consists of two
loads in parallel:
P 1 =48kW PF 1 = 0 .60 lagging
P 2 =24kW PF 2 = 0 .96 leading
It is operated from a 500-V, 60-Hz source. An
additional capacitorCis added in parallel to
improve the plant’s overall power factor to unity.
Determine the value ofCinμF. Also sketch the
power triangles before and after the addition of
C, and find the overall current drawn from the
supply.
10.2.4A 230-V, single-phase, 60-Hz source supplies
two loads in parallel. One draws 10 kVA at a
lagging power factor of 0.80 and the other draws
6 kW at a lagging power factor of 0.90. Compute
the source current.
10.2.5A three-phase power system consists of a wye-
connected ideal generator, supplying a wye-con-
nected balanced load through a three-phase
feeder. The load has Z ̄L = 20 30°/
phase, and the feeder has an impedanceZ ̄fdr=
1. 5 75°/phase. If the terminal voltage of the
load is 4.16 kV, determine:
(a) The terminal voltage of the generator.
(b) The line current supplied by the generator.
10.2.6A 345-kV, 60-Hz, three-phase transmission line
delivers 600 MVA at 0.866 power factor lagging
to a three-phase load connected to its receiving-
end terminals. Assuming that the voltage at the
receiving end is 345 kV and the load is wye-
connected, find the following:
(a) Complex load impedance per phaseZ ̄L/ph.
(b) Line and phase currents.
(c) Real and reactive powers per phase.
(d) Total three-phase real and reactive powers.
*10.2.7A three-phase load, connected to a 440-V bus,
draws 120 kW at a power factor of 0.85 lagging.
In parallel with this load is a three-phase capac-
itor bank that is rated 50 kVAR. Determine the
resultant line current and power factor.E 1 E 2I
−
+
−
+z Figure P10.2.1