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//SYS21/F:/PEC/REVISES_10-11-01/075065126-CH009.3D ± 397 ± [373±406/34] 17.11.2001 10:33AM







                                                            Power electronic control in electrical systems 397

                            With three-wire connection, i a ‡ i b ‡ i c ˆ 0
                            \ p ˆ v a i a ‡ v b i b   v c (i a ‡ i b )

                                ˆ (v a   v c )i a ‡ (v b   v c )i b
                                ˆ v ab i a ‡ v bc i b
                         (iii) (a) I ˆ 115/(3 ‡ j14) ˆ 115/(14:318e j77:905   ) ˆ 8:032e  j77:905    A
                             (b) P ‡ jQ ˆ VI ˆ 115   8:032e  j77:905   ˆ 193:537 ‡ j903:171 VA

                             (c) Wattmeter voltage coil reads only 1/4 of the load voltage, so the reading is
                                W ˆ 193:537/4 ˆ 48:38 W.
                             (d) Wattmeter voltage coil voltage is
                                                  j6:429
                                          115             ˆ 24:097e  j77:904  V
                                                30   j6:429
                                Wattmeter coil current is 8:032e  j77:905    A.
                                \ Wattmeter reads Re fVI gˆ Ref24:097e  j77:904      8:032e j77:905   g

                                                      ˆ 193:55 W
                      24. (i) Draw the phasor diagram of induced voltages for a Yd11 transformer. Also
                             draw the configuration of the primary and secondary windings on a three-
                             limb core. Include all internal connections and correct terminal labels.
                         (ii) Draw the equivalent circuit for one phase of a three-phase transformer,
                            including the total series resistance R e and total series leakage reactance X e
                            referred to the primary, and the core-loss resistance R c and magnetizing
                            reactance X m , also referred to the primary.
                         (iii) A 400-MVA, 230/66-kV Yy6 transformer has series impedances of R e ˆ
                            2:0 
/phase, and shunt impedances of X e ˆ 20:0 
/phase, R c ˆ 13 000
                            
/phase and X m ˆ 6 500 
/phase, all referred to the high-voltage winding.
                            Calculate the three-phase power and reactive power supplied under the
                            following test conditions:

                                           Test       Condition
                                           Open circuit  HV winding open
                                                      25% voltage on LV winding
                                           Short circuit  LV winding shorted
                                                      2% voltage on HV winding


                         (i)











                      Fig. 9.19
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