Question

Q3. (a) A star-connected, 3-phase, 10-MVA, 6·6 kV alternator has a per phase reactance of 10%. It is protected by Merz-Price circulating-current principle which is set to operate for fault currents not less than 175 A. Calculate the value of earthing resistance to be provided in order to ensure that only 10% of the alternator winding remains unprotected.

Answer 1

Let r_1 be earthing Resistance required to wave 10% of the winding unprotected V_ph = 6.6 kv/ squareroot of 3 = 3810 v full load current I_ful = 3/ squareroot of 3 times v_2 = 10 times 10^6/ squareroot of 3 times 6.6 times 10^3 I_fal = 875 A Reactance per phase be x_1 (r) 10 = squareroot of 3 times x_1 times 875/6600 times 100 x_1 = 6600 times 10/100 times squareroot of 3 times 875 = 0.436 Ohm Reactance of 10% winding = 0.436 times 0.1 x^1_1 = 0.0436 Ohm \r\n EMf at 10% = v_ph times 0.1 = 3810 times 0.1 = 381 v. impedance at fault z_f = squareroot of x^2_1 + r^2_1 = squareroot of 0.0436^2 + r^2_1 Earth fault current / squareroot of_ef = Enf/z_f = 381/ squareroot of 0.0436^2 + r^2_1 when fault occurs 175 175 = 381/ squareroot of 0.0436^2 + r^2_1