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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 ˆ 3:44 A; (b) I line ˆ 5:96 A; (c) P ˆ 3:56 kW.
                       8. I line ˆ 1:99 A; P ˆ 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 ˆ 16:0   j13:9A; I Y ˆ 21:6   j19:9A; I B ˆ 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 ˆ 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 ˆ  3V L I
                                          L         p
                                                  3
                                                      
                        (ii) \I L ˆ (1400 ‡ j700)   10 /( 3   4160) ˆ 217:23e j26:56   A
                                  X s Q  X s P  0:9   700/3  0:9   1400/3
                        (iii)  V ˆ    ‡ j    ˆ      p  ‡ j     p 
                                   V      V     4160/ 3      4160/ 3
                                ˆ 87:435 ‡ j174:87 ˆ 195:51e j63:43    V:
                                     p 
                        (iv) E ˆ (4160/ 3 ‡ j87:435) ‡ j174:87 ˆ 2489:2 ‡ j174:87 ˆ 2495:3e  j4:02    V.
                            E    2495:3
                        (v)   ˆ      p  ˆ 1:039
                            V   4160/ 3
                      2. For the system in Problem 1, use the equation V ˆ E(1 Q/S) to estimate the ratio
                        E/V, where S is the short-circuit level.
                                  2
                          S ˆ 2495 /0:9 ˆ 6917 kVA/phase, so
                                                  Q          700/3

                                       V ˆ E 1       ˆ E 1          ˆ 0:9663
                                                  S           6917
                        whence E/V ˆ 1/0:9663 ˆ 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 ˆ V ˆ 4160 V, if the load is constant at
                        1400 ‡ j700 kVA. The frequency is 50 Hz.
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