Lesson 34: AC Generators II

Learning Objectives Use the power conversion diagram to describe power flow for a three phase generator. Find line voltages and current for a Y-connected three phase generator.

Large AC Generator Unlike the generator model with a fixed magnetic field and rotating armature, it is more practical to fix the armature windings and rotate the magnetic field on large generators. Brushes and slip rings pass EXCITATION voltage to the field windings on the rotor to create the magnetic field. Minimizes current flow through brushes to rotor windings. 3

DC Generator Power Conversion Diagram Electrical Mechanical Electrical power in yields a mechanical torque out.

AC Generator Power Conversion Diagram Mechanical Electrical PIN = (T)rotor=746*hp POUT Pelectr-loss Pmech-loss Mechanical torque in yields a three-phase electrical output. NOTE: ω is the speed of the rotor, not the angular velocity of the AC current.

Single-Phase Equivalent Circuit Just like 3-phase loads, it is useful to look at just a single phase of the generator. Einduced + EAN - XS RS N A Ia  Single-phase equivalent 3-Phase Generator

Single-Phase Equivalent Circuit EAN is the phase voltage of the a-phase Ia is the line current. Einduced is the induced armature voltage. RS is the resistance of the generator’s stator coil. XS is the synchronous reactance of the stator coil. Einduced + EAN - XS RS N A Ia

AC Generator Power Balance Mechanical Input Power can be calculated: Electrical (Armature) Losses can be calculated (notice 3 sets of armature windings, so must multiply by 3) Electrical output power can be calculated The total overall power balance:

Solution Steps Determine the rms value of IL Determine phase angle of IL from the given power factor FP (using phase voltage as the reference)

Solution Steps Determine Electrical losses (zero for a “negligible stator resistance”). This is PER-PHASE, so must multiply by 3 when adding to other power. Determine PIN Determine torque supplied to the generator if needed

AC Generator Power Conversion Diagram Mechanical Electrical POUT PIN Pelectr loss Pmech-loss Mechanical torque in yields a three-phase electrical output. NOTE: ω is the speed of the rotor, not the angular velocity of the AC current.

Example Problem 1 Consider a 3-phase, 4 pole, 60Hz, 450V synchronous generator rated to supply 1687.5 kVA to a ship distribution system requiring a 0.8 lagging power factor. If this machine was operating at rated conditions, what is the real (P) power, reactive (Q) power and the current (I) being supplied to the load? When efficiency () is 95%, what torque does the prime mover provide? What is the speed of the rotor (N) in rpm?

QUESTIONS?