Question

I want it step by step. Thank u.

2. A synchronous generator is used to supply a load drawing S-10 р.u. at a power factor of 0.85 lagging connected to the generator terminals. Assuming the terminal voltage is 1.05 p.u. (a) Determine Ea if the generator is a round rotor machine with synchronous reactance Xs 1.1 p.u. and stator resistance Ra-0.025pu. Sketch a per unit phasor diagram (b) Repeat parts (a) if the machine is supplying a unity power factor load (c) Repeat parts (a) if the machine is supplying a load with a power factor of 0.85 leading and S 1.0p.u. (d) Repeat parts (a) if the machine is operating as a synchronous condenser supplying S- 0 +j1.0pu

Answer 1

Given data: - Power (s) = 1.0 pu P.F (cos phi) = 0.85 lag: phi = cos^-1 [0.85] = 31.78 degrees sin phi = 0.5267 v_t = 1.05 pu X_s = 1.1 pu R_a = 0.025 pu E_a = squareroot (V cos phi + I_a r_a)^2 + (V sin phi plusminus I_a X_s)^2 P = V_t I_a cos phi 1.0/1.05 times 0.85 = I_a I_a = 1.12 pu a) E_a = squareroot (1.05 times 0.85 + 1.12 times 0.025)^2 + (1.05 times 0.5267 + 1.12 times 1.1)^2 = 2.00839 pa b) if cos phi = UPF, sin phi = 0 E_a = squareroot (1.05 times 1 + 0.9523 times 0.025)^2 + (0 + 0.9523 times 1.1)^2 = 1.5 pu c) If cos phi = 0.85 lead, sin phi = 0.5267 E_a = squareroot (1.05 times 0.85 + 1.12 times 0.025)^2 + (1.05 times 0.5267 - 1.12 times 1.1)^2 = 1.1438 pu d) Synchronous condenser given Q = j 1.0 pu