Question

The figure shows the single-line diagram of a synchronous generator delivering \(P=50\) MW of power at unity power factor to an infinite bus.

\(I_S\) denotes the stator current phasor. If the field excitation is increased, which one of the following options correctly describes its effect on the stator current, power factor, and load angle of the machine?

• A. Stator current increases, power factor becomes lagging, load angle remains the same
• B. Stator current decreases, power factor becomes leading, load angle remains the same
• C. Stator current increases, power factor becomes lagging, load angle decreases
• D. Stator current increases, power factor becomes leading, load angle increases

Hint:

Use P = (Ef V / Xs) sin(delta) with P held fixed to see that delta must fall as Ef rises, and recall that overexciting a generator moves it to the lagging side of its V-curve, away from the unity-PF minimum-current point.

Answer 1

The Correct Option is C

Another way to track this is through the phasor diagram of the generator, using the constant-power constraint directly.

With the bus voltage $V$ fixed as the reference phasor, the real power delivered is proportional to the component of $E_f$ that is in phase with $V$, scaled by $\sin\delta$. Holding $P$ (and hence $V$, $X_s$) fixed while raising $E_f$ forces $\sin\delta$, and hence $\delta$ itself, to shrink, since a larger $E_f$ needs a smaller angle to keep the product $E_f\sin\delta$ unchanged.

Geometrically, the stator current phasor $I_S$ is found from $E_f=V+jI_SX_s$, so $I_S=\dfrac{E_f-V}{jX_s}$. As $E_f$ grows in magnitude while its projection onto the $P$-axis stays fixed (constant $P$), the phasor difference $E_f-V$ grows, so $|I_S|$ grows too.

At the starting point, unity power factor means $I_S$ is exactly in phase with $V$. As $E_f$ increases beyond this point, the operating point moves into the region where $I_S$ lags $V$, which for a generator is defined as the LAGGING power factor region, corresponding to overexcitation and the generator supplying reactive power outward to the system.

So all three changes happen together: $|I_S|$ increases, the power factor shifts from unity to lagging, and $\delta$ shrinks.

\[ \boxed{\text{Stator current increases, power factor becomes lagging, load angle decreases}} \]