Power System Performance (Solved Numerical Problems)
A three phase 50 MVA, 11 kV generator is subjected to the various faults and the currents so obtained in each fault are: 2000 A for a three phase fault; 1800 A for a line-to-line fault and 2200 A for a line-to-ground fault. Find the sequence impedances of the generator. (AMIE Summer 2022, 10 marks) Case 1 Consider the conditions w.r.t. the three phase fault \(\begin{array}{l}{I_f} = {I_a} = {I_{a1}} = {E_{a1}}/{Z_1}\\2000 = 11000/(\sqrt 3 {Z_1})\\{Z_1} = 3.18\Omega \end{array}\) Case 2 Consider the conditions w.r.t. the LL fault \(\begin{array}{l}{I_{a1}} = [{E_{a1}}/({Z_1} + {Z_2})]\\{I_f} = {I_b} = - {I_c} = \sqrt 3 {I_{a1}}\\ = \sqrt 3 {E_{a1}}/({Z_1} + {Z_2})\,or\\({Z_1} + {Z_2}) = \sqrt 3 (11000/\sqrt 3 )/1800\\{Z_2} = 2.936\Omega \end{array}\) Case 3 Consider the conditions w.r.t. a LG fault \(\begin{array}{l}{I_{a1}} = \frac{{{E_{a1}}}}{{({Z_1} + {Z_2} + {Z_0})}}\\{I_f} = 3{I_{a1}} = 3\frac{{{E_{a1}}}}{{({Z_1} + {Z_2} + {Z_0})}}\\({Z_1} + {Z_2} + {Z_0}) = 3\frac{{{E_{a1}}}}...