# 3 Phase Synchronous Machine

## Homework Statement

A star-connected, 3-phase, 100kVA, 415V, 50Hz synchronous motor having a synchronous reactance of 1.2ohms and negligible resistance operates at its rated terminal voltage, rated current and per-phase field-induced emf of 228V. Determine the power factor.

The excitation is adjusted until the numerical value of the power factor is the same as initially but the sign of the reactive power is changed. Determine the new value of field induced emf.

## Homework Equations

Power = 3 Vp.Ip.PF.

Complex Power = Vl.Il/root3

V = Ef + jIaXs

Vl = Vp. root 3

Complex Power = S = P + jQ

## The Attempt at a Solution

I calculated the following(correctly, I think):

The synchronous angular velocity is 100.pi rad/s.

The line current is 46.37 Amps

IaXs = 55.65V

Phase Voltage = 239.6V

I can't seem to find the power factor though.

The answers are PF = 0.89, New value of field induced emf = 365V

As always any help would be greatly appreciated. Thank you