EE301 AC GENERATORS II

Transcription

1 Learning Objectives a. Use the power conversion diagram to describe power flow for a three phase generator b. Find line voltages and current for a Y-connected three phase generator Recall our power conversion diagram for the DC Motor, discussed a few weeks ago. We put electrical power in and got mechanical torque (a spinning rotor) out: For the AC Generator, we put mechanical torque (a spinning rotor) in, and we get three-phase electrical power out: Note that in the mechanical end of the AC generator, ω is the speed of the rotor, not the angular velocity of the AC current. where f (in Hz) is the frequency of the generated AC voltage and NP is the speed of the rotor (in RPM). So let s jump right in with an example! 1 11/30/2016

2 Example: Consider a 3-phase, 4 pole, 60Hz, 450 V synchronous generator rated to supply kva to a ship distribution system requiring a 0.8 lagging power factor. a. If this machine was operating at rated conditions, what would the real (P) and reactive (Q) power and the current being supplied? b. If the generator has an efficiency ( ) of 95%, what torque does the prime mover provide? c. What is the speed of the rotor (rpm)? Solution: 2 11/30/2016

3 Example: Consider that we have a 3-phase, 1800 rpm, 450V synchronous generator rated to supply 3.75 MVA apparent power to a ship distribution system requiring a 0.8 lagging power factor. a. If this machine were operating at rated conditions, what would be the real and reactive power and the current being supplied? b. If the generator has an efficiency of 98%, what torque does the prime mover provide? c. Sketch the power conversion diagram for this AC generator Solution: 3 11/30/2016

4 The AC Generator Single-Phase Equivalent Circuit Just as was the case for 3-phase loads, it is useful to look at just a single phase of the AC generator. In the above: EAN is the phase voltage of the a-phase Ia is the phase current for the a-phase Einduced is the induced armature voltage. RS is the resistance of the generator s stator coil. XS is the reactance of the stator coil. Thus, the equations for the AC power balance can be viewed as: 4 11/30/2016

5 The following template is useful for solving some AC generator problems: 1. Determine the rms value of the line current IL PL PL 3VLILcos IL (since FP cos ) 3VF 2. Determine phase angle of IL from the given power factor FP (using phase voltage as the reference) 1 cos FP I V L P 3. Determine the electrical losses (zero for a negligible stator resistance ). This is PER-PHASE, so you must multiply by 3 when adding this to other powers. P 3I R 2 ELEC LOSS L armature 4. Determine PIN P P P P IN OUT LOSS MECH ELEC LOSS 5. Determine torque supplied to the generator if needed. 2 rotor 2 f Poles PIN TIN rotor 5 11/30/2016

6 Example: A submarine has a 3-phase, Y-connected, 2-pole, 60Hz synchronous generator rated to deliver kva at a FP = 0.8 lagging with a line voltage of 450-V. The machine stator resistance RS = Ω. The synchronous reactance XS = 0.08 Ω. The actual system load on the machine draws 900 kw at FP = 0.6 lagging. Assume that a voltage regulator has automatically adjusted the field current so that the terminal voltage is its rated value. Mechanical losses are 100 kw. a. Determine the reactive and apparent power delivered by the generator. b. Find the current delivered by the generator c. What is the overall efficiency? Solution: 6 11/30/2016

7 Example: An Arleigh-Burke Class destroyer has a 3-phase, Y-connected, 4-pole, 60 Hz synchronous generator, rated to deliver 3.75 MVA with a 0.8 lagging power factor and a line voltage of 450 V. The machine stator resistance is negligible and the synchronous reactance is equal to The actual system load on the machine draws 2 MW at a 0.8 Fp lagging. Assume that a voltage regulator has automatically adjusted the field current so that the terminal voltage, VAN, is at its rated value. a. What is the rated speed? b. Determine the reactive and apparent power delivered by the generator. c. Find the current drawn from the generator using the terminal voltage, VAN, as the reference phasor. d. Determine the induced voltage, Einduced 7 11/30/2016