Question

A $3 \phi$, six-pole, $Y$-connected synchronous generator is rated at 550 volts and has a synchronous reactance of $X_d=2.0 \Omega$. If the generator supplies $50 \mathrm{kVA}$ at a rated voltage and a power factor of 0.95 lagging, find $\mathbf{I}_s$ and $\mathbf{E}_f$ and sketch the phasor diagram for $\mathbf{V}_s, \mathbf{I}_s$, and $\mathbf{E}_f$.

   A $3 \phi$, six-pole, $Y$-connected synchronous generator is rated at 550 volts and has a synchronous reactance of $X_d=2.0 \Omega$. If the generator supplies $50 \mathrm{kVA}$ at a rated voltage and a power factor of 0.95 lagging, find $\mathbf{I}_s$ and $\mathbf{E}_f$ and sketch the phasor diagram for $\mathbf{V}_s, \mathbf{I}_s$, and $\mathbf{E}_f$.

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Essentials of Electrical and Computer Engineering

Essentials of Electrical and Computer Engineering

David V. Kerns, Jr.,… 1st Edition

Chapter 16, Problem 24

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Step 1

The apparent power (\(S\)) is given by: \[ S = \sqrt{3} \cdot V_s \cdot I_s \] Where \(V_s\) is the line voltage. Rearranging the formula to find \(I_s\): \[ I_s = \frac{S}{\sqrt{3} \cdot V_s} \] Given \(S = 50 \, \text{kVA} = 50,000 \, \text{VA}\) and Show more…

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A $3 \phi$, six-pole, $Y$-connected synchronous generator is rated at 550 volts and has a synchronous reactance of $X_d=2.0 \Omega$. If the generator supplies $50 \mathrm{kVA}$ at a rated voltage and a power factor of 0.95 lagging, find $\mathbf{I}_s$ and $\mathbf{E}_f$ and sketch the phasor diagram for $\mathbf{V}_s, \mathbf{I}_s$, and $\mathbf{E}_f$.

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