# Phasor Diagram for Synchronous Generator

A 60-Hz 24-kV 250-MVA Y-Connected salient-pole synchronous generator (Xd=1.75 per unit, Xq=1.40 per unit) is operating with a phase-A to a neutral voltage of 14 cos wt kV and a phase-A current of 5.75 cos wt kA; the currents and voltages are balanced at three-phase. The rotor angle is known to be wt+37 degrees.

a) Draw a phasor diagram for this condition indicating the terminal voltage, armature current, location of direct and quadrature axes.

b) Using the phasor diagram in part (a), calculate the magnitude of the direct-and quadrature-axis armature voltage and current.

I just need some direction.

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#### Solution Preview

Solution:

Given that the generator is 24kV and Y-connected, we have the rated voltage per phase U = 24/1.732 = 13.86 kV

Operating phase A to neutral voltage: U = 14 cos wt kVolts,

Operating phase A current: Ia = 5.75 cos wt kAmps

There is no phase shifting between the voltage and the current equations above, so the power factor is 1, i.e. cos? =1, ? =0°

The rotor angle ?= 37°

(a) The phasor ...

#### Solution Summary

The solution provides a phasor diagram, given the parameters of voltage, phase A current, and the three phase component. With the phasor diagram for the generator, the magnitude and current of the voltage is determined.