A 22 kV, 3-phase, star-connected turbo-alternator with a synchronous impedance of \text { j } 1.2 \Omega / \text { phase } is delivering 230 MW at UPF to 22 kV grid. With the turbine power remaining constant, the alternator excitation is increased by 30%. Determine machine current and power factor based upon linearity assumption.
At the new excitation, the turbine power is now increased till the machine delivers 275 MW. Calculate the new current and power factor
230 MW at UPF
I_{a}=\frac{230}{\sqrt{3} \times 22 \times 1}=6.04 kA , \bar{I}_{a}=6.04 \angle 0^{\circ} kA\bar{V}_{t}=(22 / \sqrt{3}) \angle 0^{\circ}=12.7 \angle 0^{\circ} kV
With reference to Fig. 8.112(a)
\bar{E}_{f}=12.7 \angle 0^{\circ}+j 1.2 \times 6.04 \angle 0^{\circ}=12.7+j 7.25Or E_{f}=14.62 kV
Excitation increased by 30%; turbine power input constant at 230 MW, refer Fig. 8.112(b)
E_{f}^{\prime}=14.62 \times 1.3=19 kV\frac{230}{3}=\frac{19 \times 12.7}{1.2} \sin \delta^{\prime}
Or \delta^{\prime}=22.4^{\circ}
\bar{I}_{a}^{\prime}=\frac{19 \angle 22.4^{\circ}-12.7 \angle 0^{\circ}}{j 1.2}=7.275 \angle-33.9^{\circ} kA
I_{a}=7.275 kA
p_{f}=\cos 33.9^{\circ}=0.83 lagging
Excitation constant at new value; turbine power increased to 275 MW
\frac{275}{3}=\frac{19 \times 12.7}{1.2} \sin \delta^{\prime \prime}Or \delta^{\prime \prime}=27.1^{\circ}
\bar{I}_{a}^{\prime \prime}=\frac{19 \angle 27.1-12.7 \angle 0^{\circ}}{j 1.2}=8.03 \angle-25.9^{\circ} kA
I_{a}=8.03 kA , pf =\cos 25.9^{\circ}=0.9 \text { lagging }
