# Electrical Energy Conversion: Synchronous Generator

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Synchronous Generator

A 250 kVA, 280 V, three-phase, four-pole, 60 Hz, synchronous generator with a synchronous reactance of 0.99 ohms per phase is operating at rated conditions and a power factor of 0.832 lagging. The magnetization curve for the generator is shown in Figure 1.

a. Sketch a phasor diagram for the generator.

b. Name the 2 curves shown on the graph, and indicate briefly how they are found. Why is it that one is a straight line, but the other exhibits a curve?

c. Determine:

- the excitation voltage (magnitude and angle)

- the open-circuit phase voltage

- the voltage regulation

- the no-load voltage if the field current is reduced to 60% of its value at rated load.

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##### Solution Summary

This solution is attached in a Word document and includes a diagram for (a), calculations and explanations for each step. The method used in this assignment can be applied to any similar synchronous machines related questions.

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a. A phasor diagram for this generator

Where

- Power factor = 0.832 lagging, the corresponding angle phi = 37.4 degrees.

- Resistance of armature Ra is not given, so it is assumed that Ra = 0 Ohm

- Rated voltage line-to-line (vector): UL-L = 480 at 0 degrees Volts

U on the above vector diagram is rated voltage per phase. Assume the winding is wye connected, U = 277 Volts

- Rated current I:

Magnitude: I = S /(1.732*U) = (250*1000)/(1.732*480) = 300.7 Amps

Vector: I = 300.7 at -37.4 degrees Amps

- Synchronous reactance Xt = 0.99 Ohm

- E(delta) is the induced voltage at the air-gap or known as excitation voltage.

b. The two curves

- The curly curve is the ...

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