How Does Power Factor Change with Field Induced EMF in a Synchronous Motor?

AI Thread Summary
The discussion revolves around calculating the power factor of a synchronous motor with specified parameters, including a synchronous reactance of 1.2 ohms and a field-induced EMF of 228V. The initial power factor is determined to be 0.89, while the new field-induced EMF, after adjusting excitation to change the sign of reactive power, is found to be 365V. The calculations involve using equations related to complex power and synchronous motor operation. Participants express difficulty in reaching the solution and seek assistance to clarify the calculations. The thread emphasizes the importance of understanding the relationship between power factor and field-induced EMF in synchronous motors.
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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
 
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Hi Guys,

Been thinking about the problem a lot and I still can't figure out an answer to this problem.

If somebody could please help me with this I would be extremely grateful.

Thanks.
 

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