Question

Problem 3:A 480 V, 50 kW, 60 Hz, 3-φ synchronous motor has a synchronous reactance of Xs = 4.56 Ω and an armature-to-field mutual inductance, Laf = 150 mH. The motor is operating at rated speed and terminal voltage and at an output power of 35kW. Neglecting losses in the motor, calculate the magnitude and phase angle of the line-to-neutral generated voltage Eaf and field current I if the motor is operating at (a) 0.9 power factor lagging (b) unity power factor (c) 0.9 power factor leading. For each case draw the phasor diagram, calculate the apparent input power (volt-amperes) and reactive power.

Answer 1

(a) 0.9 power factor lagging: - E_a f^- = V_a^- - j X_S I_a^- ---(1) rightarrow line - t0o - natural voltage is, V_a^- = 480/squareroot 3 = 277.12 v rightarrow lagging p f of 0.9 so A = -Cos^-1 (0.9) = -25.85 degree I_A^- = P_in/3 V_a e^-j 25.84 degree = 50/KW/3 times 277.12 e^-j 25.84 degree I_a^- = 60.14 e^-j 25.84 degree rightarrow E_a f^- = 277.12 - j (4.56) (60.14 e^-j 25.84 degree) [from eq^n (1) = 217.12 - j (274.24) (Cos 25.84 degree - j sin 25.85 degree) = 277.12 - j (274.24) (0.9 - j (0.43)) = 277.12 - 246.81 j - 199.53 E_a f^- = 77.59 - 246.81 j = 258.72 < 287.45 degree E_a f^- = 258.72 e^-72.55 degree so, magnitude is 258.71 and phase angle is delta = -72.55 degree rightarrow field current I_f is I_f = squareroot 2 E_a f/w_e L_a f = squareroot 2 times 258.72 times e^72.55 degree/377 times 150 times 10^-3 = 6.47 e^-j 72.55 degree A