PROBLEMS 46910.2.8A balanced three-phase, wye-connected, 2400-
V, 60-Hz source supplies two balanced wye-
connected loads in parallel. The first draws 15
kVA at 0.8 power factor lagging, and the second
needs 20 kW at 0.9 power factor leading. Com-
pute the following:
(a) Current supplied by the source.
(b) Total real and reactive power drawn by the
combined load.
(c) Overall power factor.
10.2.9A three-phase, 60-Hz substation bus supplies two
wye-connected loads that are connected in par-
allel through a three-phase feeder that has a per-
phase impedance of 0. 5 +j 2 . Load 1 draws
50 kW at 0.866 lagging PF, and load 2 draws 36
kVA at 0.9 leading PF. If the line-to-line voltage
at the load terminals is 460 V, find the following:
(a) Total line current flowing through the feeder.
(b) Per-phase impedance of each load.
(c) Line-to-line voltage at the substation bus.
(d) Total real and reactive power delivered by
the bus.10.2.10A balanced delta-connected load has a per-phase
impedance of 4560°. It is connected to a
three-phase, 208-V, 60-Hz supply by a three-
phase feeder that has a per-phase impedance of
- 2 +j 1. 6 .
(a) Determine the line-to-line voltage at the load
terminals.
(b) If a delta-connected capacitor bank, with a
per-phase reactance of 60, is connected in
parallel with the load at its terminals, com-
pute the resulting line-to-line voltage at the
load terminals.
*10.3.1Consider a lossless transmission line with only a
series reactanceX, as shown in Figure P10.3.1.
(a) Find an expression for the real power transfer
capacity of the transmission system.
(b) What isPmax(the theoretical steady-state
limit of a lossless line), which is the max-
imum power that the line can deliver?
(c) How could the same expressions be used for
a three-phase transmission line?
10.3.2A 20-km, 34.5-kV, 60-Hz, three-phase transmis-
sion line has a per-phase series impedance of
Z ̄= 0. 19 +j 0. 34 /km. The load at the receiv-
ing end absorbs 10 MVA at 33 kV. Calculate:
(a) The sending-end voltage for a load power
factor of 0.9 lagging.
(b) The sending-end voltage for a load power
factor of 0.9 leading.
(c) The transmission system efficiency for cases
(a) and (b).
(d) The transmission-line voltage regulation
(TLVR) for cases (a) and (b).
10.3.3It is sometimes convenient to represent a trans-
mission line by a two-port network, as shown in
Figure P10.3.3. The relations between sending-
end and receiving-end quantities are given by
V ̄S=A ̄V ̄R+B ̄I ̄RandI ̄S=C ̄V ̄R+D ̄I ̄R,
in which the generally complex parametersA ̄,
B ̄,C ̄, andD ̄ depend on the transmission-line
models. For the model that includes only the
series impedanceZ ̄of the transmission line, find
the parametersA ̄,B ̄,C ̄, andD ̄and specify their
units. Also evaluate(A ̄D ̄−B ̄C) ̄.
10.3.4For a transmission-line model that includes only
the series impedanceZ ̄, sketch phasor diagrams
for:
(a) Lagging power factor load.
(b) Leading power factor load.
10.3.5In terms of the parametersA ̄,B ̄,C ̄, andD ̄intro-
duced in Problem 10.3.3, find an expression for
V ̄Rat no load in terms ofV ̄Sand the parameters.
*10.3.6Consider an upgrade of a three-phase transmis-
sion system in which the operating line-to-line
voltage is doubled, and the phase or line currents
are reduced to one-half the previous value, for the
same level of apparent power transfer. Discuss
the consequent effects on the real and reactive
power losses, and on the voltage drop across the
series impedance of the transmission system.
10.3.7Justify the entries made in Tables 10.3.1, 10.3.2,
and 10.3.3 for load-bus data, transmission-line
data, and source-bus data, respectively, for the
example considered in the text.
10.3.8Justify the entries made in Table 10.3.4 for load-
bus data with power factor correction, and dis-
cuss the effects of power factor correction on
Ploss,Qloss, andVdropof the transmission line.
10.3.9Check the figures given in the text (for the ex-
ample considered) regarding the transmission-
system efficiencies and TLVR for the two cases,
with and without power factor correction.