EECE 370 Problems Synchronous Generators, Summer 2007

FBC July 2007 EECE370, ELECTRIC MACHINES and POWER FUNDAMENTALS PROBLEMS ON SYNCHRONOUS GENERATORS 1. A 5- KVA, 200- V, 4- pole 60- Hz Y- connected synchronous generator has negligible stator winding resistance and a synchronous reactance of 8 Ω per phase at rated voltage. This machine is operated in parallel with a phase 208 V, 60 Hz power supply. Determine the generator voltage and power angle when the machine is delivering rated KVA at 0.8 PF lagging. (206.7V, and 25.45o). 2. A Y- connected, 10- KVA, 230- V has a field winding resistance of 4.5Ω. At an operation of 0.85 lagging power factor, the excitation current is recorded at 10A, the core loss is 300W, and the mechanical loss is 200W. If the corresponding efficiency is 84.9%, calculate the per- phase armature winding resistance.(0.3 Ω) 3. A 3-phase synchronous generator delivers power to an electric at 13.8 KV. The generator reactance is 8 Ω / phase. Its resistance is negligible. The magnitude of the generator emf is 20 % higher than the machine’s terminal voltage. When the machine delivers 12 MW to the system, determine the power angle. 4. A 380- V, Y-connected synchronous generator supplies the rated voltage at 1800 rpm with a field current of 0.9A. If the speed of the prime mover, coupled to the rotor, falls to 1200 rpm, to what value should the field current be adjusted to maintain the same terminal voltage?(1.35A) 5. A 10- kW, 440- V, Δ- connected synchronous generator has a per phase armature resistance and synchronous reactance of 1Ω and 10Ω, respectively. Calculate the induced voltage when the generator is delivering the rated load at 0.8 lagging power factor. (509V) 6. A 2-MVA, 4400- V, Y- connected synchronous generator rated at 1200 rpm is tested as follows: The open- circuit voltage and short- circuit current are 5200V, and 260A, respectively, with the field current held at 20A. The generator is designed to have a resistive voltage drop of 2.5% of its line voltage. Determine: a. The armature resistance. b. The synchronous reactance. c. The induced voltage at unity power factor operation.( 3995V)