0
\$\begingroup\$

Two identical three-phase, Y-connected, synchronous generators are connected in parallel to equally share a load of 900 kW at 11 kV and power factor 0.8 lagging. The synchronous impedance of each generator is 0.5 + jl0 R/phase. The field current of one generator is adjusted so that its armature current is 25 A at a lagging power factor. Determine (a) the armature current of the other generator, (b) the power factor of each generator, (c) the per-phase generated voltage, and (d) the power angle of each generator. What is the circulating current under no load?

My question is, how do I find the complex phasor angle of the phasor current with magnitude 25 A? I tried expressing the unknown current angle as theta and then I did a KCL to express the other generator current in terms of the 25 A phasor current and then 2 KVL equations involving the generator phasor voltages plus a power balance equation to complete the number of equations needed to solve all the unknowns. My reference phasor is the terminal voltage which is \$ \frac{11000}{\sqrt{3}}\small~\mathrm{V}\$.

\$\endgroup\$

1 Answer 1

0
\$\begingroup\$

a-) Each generator share the load equally. Each generator's load is 450 kW.

First of all, calculate the total load current:

$$I_{load} =\frac{900000}{\sqrt{3}\times11000\times 0.8}=59\ A $$ $$\vec{I_{load}}=59\ \angle{-36.87^\circ}\ A $$

If first generator's load is 450 kW, the power factor of this generator easily calculated as follow:

$$\cos \phi_1=\frac{450000}{\sqrt{3}\times11000\times25}=0.9447$$

and the angle of power is $$\phi_1=19.13^\circ$$

The total load current is the vectorel sum of two generator's current, i.e:

$$\vec{I_{load}}=\vec{I_1}+\vec{I_2}$$

So the current of second generator is

$$\vec{I_2}=\vec{I_{load}}-\vec{I_1}=59\ \angle{-36.87^\circ}-25\angle-19.13^\circ$$

$$\vec{I_2}=36\angle{-49^\circ}\ A$$

The remaining parts of question are easily solve from here.

\$\endgroup\$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.