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378 Examples, problems and exercises
3. 81.48
; 32.33 p.u.
4. 86:52
; 34.33 p.u.
5. 1.008 kA; 6.271 MW; 0.980 lagging at the sending end (E s ); 0.980 leading at the
receiving end (E r ).
6. 386 A.
7. (a) I phase 3:44 A; (b) I line 5:96 A; (c) P 3:56 kW.
8. I line 1:99 A; P 1:19 kW (both reduced to one-third).
9. (a) 4.62 A; (b) 120
; 286 mH.
10. (a) 2.77 A; (b) 120
; 286 mH.
11. I R 16:0 j13:9A; I Y 21:6 j19:9A; I B 5:6 j33:7A.
9.4 Worked examples
1. An inductive three-phase wye-connected load is supplied at 4160 V and takes
1400 kW of real power and 700 kW of reactive power. The supply system imped-
ance is j0:9
/phase. Calculate
(i) the current;
(ii) the power factor;
(iii) the open-circuit voltage (i.e. the supply voltage E) if the load voltage
V 4160 V;
(iv) the ratio of the open-circuit voltage E to the load voltage V; and
(v) the load angle (i.e. the phase angle between E and V).
p
(i) P jQ 3V L I
L p
3
(ii) \I L (1400 j700) 10 /( 3 4160) 217:23e j26:56 A
X s Q X s P 0:9 700/3 0:9 1400/3
(iii) V j p j p
V V 4160/ 3 4160/ 3
87:435 j174:87 195:51e j63:43 V:
p
(iv) E (4160/ 3 j87:435) j174:87 2489:2 j174:87 2495:3e j4:02 V.
E 2495:3
(v) p 1:039
V 4160/ 3
2. For the system in Problem 1, use the equation V E(1 Q/S) to estimate the ratio
E/V, where S is the short-circuit level.
2
S 2495 /0:9 6917 kVA/phase, so
Q 700/3
V E 1 E 1 0:9663
S 6917
whence E/V 1/0:9663 1:035 (Unlike the result of Problem 1, this result is only
approximate).
3. For the system in Problem 1, find the capacitance/phase and the total reactive
power of a capacitor that will make E V 4160 V, if the load is constant at
1400 j700 kVA. The frequency is 50 Hz.