Find the Machine Torque Angle

(a)  What are the four operating conditions that must be satisfied before a synchronous machine can be synchronised to an electrical grid?

(b)  A three phase Y-connected cylindrical rotor synchronous generator is operating into a grid at its rated l-l voltage of 6000V, with a rated stator current of 200A at a 0.8 lagging power factor. If the generator has a synchronous reactance of X_s = 10 Ω /phase and negligible stator winding resistance, find:

i.  The real and reactive power flow into the grid.

ii.  The internal back-emf E_o.

iii.  The machine torque angle δ (in electrical degrees).

(c)  Calculate the new torque angle, stator current and machine power factor if the field excitation is changed to reduce the generator internal back-emf to 1.2 pu. Is the generator supplying or sinking reactive power? Sketch a phasor diagram for this operating condition.

(d)  Sketch the capability diagram for this synchronous machine for 1 pu and 1.5 pu excitation levels, and show how the practical operating region can be identified on this diagram by considering various machine operating limits.