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Question 7.7: A cylindrical-rotor machine is supplying a load of 0.8 PF la......

A cylindrical-rotor machine is supplying a load of 0.8 PF lagging at an infinite bus. The ratio of the excitation voltage to the infinite-bus voltage is found to be 1.25. Compute the power angle δ.

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For a power factor of 0.8, we have

{\frac{Q}{P}}=\tan\phi=0.75

Using the active and reactive power formulas, Eqs. (7.40) and (7.42), we have

P_{1}=P_{2}={\frac{E V}{X}}\sin\delta    (7.40)

Q_{2}={\frac{E V\cos\delta-V^{2}}{X}}       (7.42)

{\frac{Q}{P}}={\frac{\cos\delta-{\frac{V}{E}}}{\sin\delta}} \\ 0.75={\frac{\cos\delta-0.8}{\sin\delta}}

Cross multiplying, we have

0.8+0.75\sin\delta=\cos\delta

Using

\cos^{2}\delta=1-\sin^{2}\!\delta

We get

[(0.75)^{2}+1]\sin^{2}\delta+2(0.8)(0.75)\sin\delta+[(0.8)^{2}-1]=0

Consequently,

\sin\delta=0.23 \\ \delta=13.344{\mathrm{~deg}}

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