Question

(10 MARKS) (5 marks) PART-A: Fig. 1(a) shows a single-phase, fully-controlled rectifier and Fig. 1(b) represents its characteristic. The behavior of the controlled rectifier for a given firing angle, α, and battery current, Ibat is given in the characteristics. The dotted line, AB, represents the limiting case of the behavior on each angle, a. The rectifier is supplied from a 230 V, 50 Hz, source and used as a battery charger to control the battery current, lbat. E represents the equivalent of the number of series batteries, thus E is variable. Lac and Loc may be assumed to be ideal. The average output voltage of the rectifier, Vut is given by 2V cosa AC bat ; where XCC anda is fringangle And the equation of the curve-AB is given by: XAclb, Loc 2V a:0 Fig. 1. (a) Single phase rectifier circuit (b) characteristics

A battery with a terminal voltage of 145 V is charged by the rectifier in PART-A. The current is to be kept at 10 A. The rectifier parameters are: LDC= 1 mH, LAC = 10 mH

(a) Calculate the firing angle required.

(b) During the turn-off, the current Ibat is to be reduced at the fastest possible rate. Calculate the maximum decay rate possible when Ibat is at 10 A.

Answer 1

(a) Write the formula for the average output voltage of the single- phase fully controlled rectifier 2V V COS a ut 2X дс1ва 2V cOsa - 2(2T JLAC)I 2V cosa 2V cosa- 4 fL^C bat Substitute the values. 2x 230 2 145= cosa - 4 x 50 x 10 x103 x10 2x 2302 COS a 163 COs a 0.7968 a 37.17° (b) Consider the equation of the curve AB V Хдс1 bat out - 2VT Хдс1ра 2V V. bat 1 out 2 -Х,dI dV. out 4 AC AC C hat bat hat 4 x50x10 x 103 dI. dV 2dat out dI, bat 0.5 dV out