Page 236 - Fluid Power Engineering

Basics of Electricity and Generators 203

In summary, assuming 100% efficiency in conversion of mechanical
power from turbine rotor to electrical generator and direct connection
between the turbine rotor and generator rotor, when a steady mechan-
ical power of τ g ω is used to turn the generator, then electrical power of
an equal amount is produced when current flows through the circuit.

Synchronous Generator
Rotor of a synchronous generator is either permanent magnet or
DC-excited electromagnet. The simplest generator is a two-pole (one
north pole and one south pole) rotor with the stator connected to the
grid. The grid supplies the voltage and frequency, meaning the volt-
age and frequency of the stator circuit are fixed. The grid also supplies
the current to energize the stator. The stator produces a rotating mag-
netic field of angular speed ω, as described above. If a compass were
placed at the center, it would rotate with the magnetic field. Instead
of a compass, the rotor has a permanent or electro magnet that moves
with the stator magnetic field with angular speed ω. At zero load, the
speed of rotation of the rotor is the same (no relative speed between
rotor and stator) and the phase difference is zero (north pole of stator-
generated magnetic field is aligned with the south pole of the rotor).
There is zero torque in this scenario and, therefore, zero power.
From electric circuit standpoint, the grid supplies the terminal
voltage of V T to the stator and current i. The rotating magnetic field
of the rotor (which is synchronized with the rotating magnetic field
of the stator) cuts conductor in the stator and, therefore, induces EMF
in the stator coils; this generated EMF will be called E g . When the
stator and rotor poles are perfectly lined up, E g and V T are 180 apart.
◦
Perfect alignment of stator and rotor poles means that the angular
speed of stator’s magnetic field is the same as the angular speed of
rotation of the rotor and the opposite poles of stator and rotor face
each other (radial alignment). The magnitude of E g is determined by
the strength of the permanent magnet or the DC excitation current of
the electromagnet. Assuming zero resistance in stator coils, the only
load in the stator circuit is pure inductance. Therefore, current flowing
◦
through the stator coils is 90 from (V T − E g ).
Note that even when no power is delivered to the grid by the
generator, the grid is still supplying current to energize the magnetic
field of the stator. In this case, grid current drawn (by the stator of
the generator) is out of phase with grid voltage. Therefore, no “real”
power is drawn from the grid. However, the grid delivers “reactive”
power to the stator of the generator—power is delivered to the stator
from the grid during one-half of the cycle and power is returned to the
grid during the other half of the cycle. Therefore, over one complete
cycle, the net power delivered to or drawn from the grid is zero. For
60-Hz frequency, one cycle is 1/60 of second.