(a) What are the rated current and internal generated voltage of this generator? (b) What field current does this generator require to operate at the rated voltage, current, and power factor?

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(a) The rated line and armature current for this generator is

[latex]I_A=I_L=\frac{S}{\sqrt{3} V_T}=\frac{500 \ kVA }{\sqrt{3}(3200 \ V )}=90.2 \ A[/latex]

The power factor is 0.9 lagging, so [latex]\mathbf{I} _A=90.2 \angle-25.8^{\circ} A[/latex] . The rated phase voltage is [latex]V_\phi=3.2 \ k\ V / \sqrt{3}[/latex] = 1850 V. The saturated synchronous reactance at rated conditions was found to be 15.7 Ω in the previous problem. Therefore, the internal generated voltage is

[latex] \begin{aligned} & \mathbf{E} _A= V _\phi+R_A \mathbf{I} _A+j X_S \mathbf{I}_A \ & \mathbf{E} _A=1850 \angle 0^{\circ}+(0.7 \Omega)\left(90.2 \angle-25.8^{\circ} A ight)+j(15.7 \Omega)\left(90.2 \angle-25.8^{\circ} A ight) \ & \mathbf{E} _A=2814 \angle 26.3^{\circ} V \end{aligned} [/latex]

(b) This internal generated voltage corresponds to a no-load terminal voltage of [latex]\sqrt{3}(2814)[/latex] = 4874 V.
From the open-circuit characteristic, the required field current would be 3.2 A.

Question 4.17: (a) What are the rated current and internal generated voltag...

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