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Power electronic control in electrical systems 377
connected)? (See Figures 2.3 and 9.3). Express the answer in ohms and also per
unit of X s (i.e. the ratio X L /X s ).
4. What value of capacitive reactance X C would be needed to raise the voltage by
3% in the power system of Question 1 (assuming that no other loads are
connected)? (See Figures 2.4 and 9.4). Express the answer in ohms and also per
unit of X s (i.e. the ratio X C /X s ).
5. In the symmetrical power system shown in Figure 2.5a, E s E r 6:35 kV and
X 2:52
. If the voltage-drop XI is 40% of E s , calculate the current I, the
power transmitted, the power factor at both ends of the line, and the load angle d
between E s and E r .
6. A three-phase delta-connected induction motor is fed from a supply of 440 V
line±line, and delivers 225 kW to a water pump. Calculate the line current,
assuming 90% for the efficiency and 85% for the power factor.
7. Each phase of a three-phase delta-connected load comprises a capacitor of 40 mF
in series with a resistor of 100
. This load is connected to a three-phase supply at
440 V and 50 Hz. Calculate (a) the rms phase current in the load; (b) the line
current; and (c) the total power taken from the supply.
8. The load of Question 7 is to be dismantled and shipped to a far-off country,
where the local power company has declared that all electrical goods of foreign
origin must be connected in star (i.e. wye). Calculate the new line currents and
the power taken from the supply, if the phases that were originally connected in delta
are reconnected in star. Comment on the result. The supply is still 440 V at 50 Hz.
9. Three impedances, each comprising a resistance of 40
in series with an induct-
ance of 95.5 mH, are connected in wye to a 400 V, 50 Hz, three-phase AC supply.
Calculate (a) the supply line current; and (b) the resistance R and inductance L
(in series) of a balanced delta-connected load that takes the same line current at
the same power factor.
10. Three identical inductive impedances are connected in delta to a 415 V, 50 Hz,
three-phase supply of sequence RYB. The current in the R line is 4.8 A and it
leads the voltage V YB by 53 . Determine (a) the rms phase current; and (b) the
resistance and inductance of each phase-impedance. (Do be careful with sub-
scripts, arrows, etc. in this one.)
11. Three single-phase loads are connected to a 250 V, three-phase, three-wire supply
of sequence RYB:
6 kW at unity PF between R and Y;
4 kW at 0.8 PF leading between Y and B;
2 kW at 0.5 PF lagging between B and R.
Taking V RY as reference phasor, calculate all three line-currents. (Hint: use S VI
and calculate the phase currents first. Watch the asterisks as well as the subscripts
and arrows.)
9.3.1 Answers to problems in Section 9.3
1. 2.52 kA; 2:52
.
2. R 26:643
or 0:238
; V 6:322 kV or 0.5979kV; X s I 0:5979 kV or 6:322 kV;
and d 5:403 or 84:597 .
