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               390 Examples, problems and exercises

                        (ii) P 1 ˆ V RB I R cos (30   f) ˆ V LL I L ( cos 30 cos f ‡ sin 30 sin f)



                            P 2 ˆ V YB I Y cos (30 ‡ f) ˆ V LL I L (cos 30 cos f   sin 30 sin f)



                                                           p

                            P 1 ‡ P 2 ˆ V LL I L   2 cos 30 cos f ˆ  3V LL I L cos f ˆ P (total power)
                            P 1   P 2 ˆ V LL I L   2 sin 30 sin f ˆ V LL I L sin f

                           Hence
                                                        p P 1   P 2
                                                 tan f ˆ  3
                                                           P 1 ‡ P 2
                        (iii) P ˆ 9700/0:92 ˆ 10 543W ˆ P 1 ‡ P 2
                            tan f ˆ tan (arc cos (0:85)) ˆ 0:620
                                            p
                            \P 1   P 2 ˆ 0:620/ 3   10 543 ˆ 3:773W
                              P 1 ‡ P 2 ˆ 10 543W
                                  2P 1 ˆ 10 543 ‡ 3773 ˆ 14 316 so P 1 ˆ 7158W
                                  2P 2 ˆ 10 543   3773 ˆ 6770 so P 2 ˆ 3385W:

                      18. (i) State four distinct functions of power transformers.
                        (ii) Draw the equivalent circuit of one phase of a three-phase power transformer,
                            with all impedances referred to the HV (high-voltage) side.
                        (iii) A 250-kVA, 10-kV/400-V, three-phase Yy0 transformer gave the following
                            standard test data for the line±line voltage, line current, and total three-phase
                            input power:

                            Input to HV winding; LV short-circuited : V LL ˆ 1005 V, I L ˆ 14:4A,
                            P ˆ 2:49 kW.
                            Input to LV winding; HV open-circuited: V LL ˆ 400 V, I L ˆ 3:886 A,
                            P ˆ 2:50 kW.
                            Make a neat sketch of an approximate equivalent circuit for one phase
                            of this transformer, in which all the impedances R 1 , R ,jX L1 ,jX , R c and
                                                                                    0
                                                                           0
                                                                           2
                                                                                    L2
                            jX m are referred to the HV winding. Determine the values of these para-
                            meters.
                         (i)
                         . Transform voltage level for optimum transmission
                         . Transform current level for measurement (C.T.); or voltage (P.T. or V.T.)
                         . Isolate coupled circuits
                         . Impedance matching
                         . Introduce series impedance (to limit fault current)
                         . Create a neutral point (e.g. ground connection remote from power station)
                         . Suppress harmonics (especially triplen harmonics)
                         . Provide tappings for loads along a transmission line
                         . Produce phase shift or multiple phases (e.g. for multiple-pulse converters)
                         . Produce frequency-multiplication (saturated core)
                         . Constant-voltage reactive compensation (saturated core).
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