A three-phase synchronous Y-connected generator has negligible armature resistance and synchronous reactance of 2 .

A three-phase synchronous Y-connected generator has negligible armature resistance and synchronous reactance of 2 Ω. The generator is connected to an infinite bus, where its terminal voltage remains fixed at 15 kV. The generator delivers 100 MVA at 0.8 power factor lagging. Mechanical losses and saturation effects can be ignored.(a) Find the line current of the machine, its internal generated voltage EA, and power angle δ.

(b) Recall that if Vφ is the phase terminal voltage, the active supplied by the generator to the system is P =(3 Vφ EA sin δ) / XS. Show that the reactive power supplied by the generator is Q =(3Vφ / XS)(EA cos δ − Vφ).

(c) If the field current is reduced by 10%, while the mechanical power input to the machine is maintained constant, determine the new value for the power angle and the reactive power delivered to the system.

(d) The prime mover is next adjusted without changing the excitation so that the machine delivers zero reactive power to the system. Find the new power angle and the real power being delivered to the system.

(e) What is the maximum reactive power that the machine can deliver if the level of excitation is maintained as in (b) and (c)?