PROBLEMS 219(a) The current taken from the supply and the
supply power factor.
(b) The total real power in kW supplied by the
source, if the supply voltage is 400 V.
4.2.12Two balanced, three-phase, wye-connected loads
are in parallel across a balanced, three-phase sup-
ply. Load 1 draws 15 kVA at 0.8 power factor
lagging, and load 2 draws 20 kVA at 0.6 power
factor leading. Determine:
(a) The total real power supplied in kW.
(b) The total kVA supplied.
(c) The overall power factor of the combined
load.*4.2.13Two balanced, wye-connected, three-phase loads
are in parallel across a balanced, three-phase 60-
Hz, 208-V supply. The first load takes 12 kW at 0.6
power factor lagging, and the second load takes 15
kVA at 0.8 power factor lagging.
(a) Draw the power triangle for each load and for
the combination.
(b) What is the total kVA supplied?
(c) Find the supply power factor, and specify
whether lagging or leading.
(d) Compute the magnitude of the current drawn
by each load and drawn from the supply.
(e) If wye-connected capacitors are placed in par-
allel with the two loads in order to improve
the supply power factor, determine the value
of capacitance in farads in each phase needed
to bring the overall power factor to unity.
4.2.14A three-phase balanced load draws 100 kW at
0.8 power factor lagging. In order to improve the
supply power factor to 0.95 leading, a synchronous
motor drawing 50 kW is connected in parallel with
the load. Compute the kVAR, kVA, and the power
factor of the motor (specify whether lagging or
leading).
4.2.15(a) A balanced wye-connected load with per-
phase impedance of 20+j 10 is connected to
a balanced 415-V, three-phase supply through
three conductors, each of which has a series
impedance of 2+j 4 . Find the line current,
the voltage across the load, the power deliv-
ered to the load, and the power lost in the line
conductors.
(b) Repeat the problem if the three per-phase
load impedances of part (a) were connected
in delta.
4.2.16A balanced electrical industrial plant load of 9.8
MW with 0.8 lagging power factor is supplied by
a three-phase 60-Hz system having a maximum
rating (load-carrying capacity) of 660 A at 11 kV
(line-to-line voltage).
(a) Determine the apparent power and the reactive
power drawn by the load.
(b) Additional equipment, consisting of a load
of 1.5 MW and 0.7 MVAR lagging, is to be
installed in the plant. Compute the minimum
rating in MVA of the power factor correction
capacitor that must be installed if the rating of
the line is not to be exceeded. Find the system
power factor.
(c) If the capacitor, consisting of three equal sec-
tions, is connected in delta across the supply
lines, calculate the capacitance required in
each section.
4.2.17Derive the relationships given in Figure 4.2.1 for
the wye–delta and the delta–wye transformations.
4.2.18Two three-phase generators are supplying to a
common balanced three-phase load of 30 kW at
0.8 power factor lagging. The per-phase imped-
ance of the lines connecting the generatorG 1 to
the load is 1. 4 +j 1. 6 , whereas that of the
lines connecting the generatorG 2 to the load is
0. 8 +j 1 . If the generatorG 1 , operating at a
terminal voltage of 800 V (line to line), supplies
15 kW at 0.8 power factor lagging, find the voltage
at the load terminals, the terminal voltage of the
generatorG 2 , and the real power, as well as the
reactive power output of the generatorG 2.
4.3.1Determine the wattmeter readings when the two-
wattmeter method is applied to Problem 4.2.4, and
check the total power obtained.
4.3.2When the two-wattmeter method for measuring
three-phase power is used on a certain balanced
load, readings of 1200 W and 400 W are obtained
(without any reversals). Determine the delta-
connected load impedances if the system voltage
is 440 V. With the information given, is it possible
to find whether the load impedance is capacitive
or inductive in nature?
4.3.3The two-wattmeter method for measuring three-
phase power is applied on a balanced wye-
connected load, as shown in Figure 4.3.2, and the
readings are given by
WC= 836 W and WA=224 W