Question

A circuit of 500 V for single-phase asynchronous motor has synchronous impedance of 3.2 Ω. The armature resistance is 0.3 Ω. Determine the induced emf if the machine develops 31.3 kW and the mechanical losses equals 4 kW

Answer 1

$E= \sqrt{(V \cos \phi+IR)^2+(V \sin \phi+IX)^2}\\ E= \sqrt{(\frac{500}{\sqrt3}+IR)^2+(IX)^2}\\$

Input power

$4 kW +31.3 kW\\ 35.3kW$

$35.3kW= \sqrt3 VI \cos \phi\\ I= \frac{35.3*10^3}{\sqrt3 *500}*40.76A\\ \implies E_{phase}= 327.94 V$