A 5KVA, 415V, 3-phase, 50Hz cylindrical-rotor synchronous machine is connected to a 415V infinite bus. It has a current rating of 6.95A and operates at a synchronous speed of 1500 rpm. The mechanical angle between the rotor shaft and the stator is set at -22.5 and a constant excitation current of 3A is supplied to the rotor. The open-circuit characteristic (OCC) and short-circuit characteristic (SCC) of the synchronous machine are shown in Figure 3.1. The armature resistance and power losses are assumed to be negligible. Open-circuit Voltage (V) 300 250 200 150 100 50 0 2 0 1.5 1 0.5 2 2.5 3 3.5 Field Excitation (A) Figure 3.1: Open-circuit characteristic (OCC) and short-circuit characteristic (SCC) 0 0.5 -0.5 -1 1 -1.5 1.5 -2 -2 What is the torque angle? Is the synchronous machine generating or motoring? Calculate the synchronous reactance per phase in ohms (2) and in per-unit of the synchronous machine. (Hint: S30,base = 5kVA and VLL,base = 415V) What is the field excitation voltage in volts (V) and in per-unit quantity? Calculate the armature current per phase in per-unit. (Hint: Draw a phasor diagram and use trigonometry to obtain the armature current) What is the active power, in per-unit being generated or consumed by the synchronous machine? -1.5 Calculate the reactive power in per-unit in the synchronous machine. What is the power factor? Is it leading or lagging? Draw the operating point of the synchronous machine and its capability diagram at the field excitation voltage obtained in part (d) along with its stability limit when generating and motoring. Label both axes and use per-unit values in the diagram. (Hint: The capability diagram has a radius of 1 p.u) -1 4 -0.5 OCC SCC 0 4.5 0.5 1 15 14 13 12 11 10 9 8 7 1.5 6 5 3 2 1 0 Short-circuit Armature Current (A)