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}\$.