Environmental Engineering Reference
In-Depth Information
assuming a lossless environment with no friction and windage, the rotor will rotate at syn-
chronous speed with no requirement that any power is fed to it either mechanically from the
shaft or electrically from the power network to which the synchronous machine is connected.
The system is
idling
and can be thought as being suspended between motoring and
generating.
In the synchronous machine the speed of the locked magnet pair is fi xed because the infi nite
bus frequency and therefore the RMF speed is fi xed. However, the relative angular disposition
of the magnetic axes of the two locked pairs is not fi xed and is the mechanism that regulates
the direction of energy conversion. If an external braking torque
Q
t
is applied to the shaft the
rotor will keep rotating at the synchronous angular speed
s
, but its magnetic axis will fall
back or spatially lag the magnetic axis of the RMF. The tangential magnetic tension forces
caused by the misalignment of the magnet pair is at heart the mechanism of electromechanical
energy conversion. The mechanical power
P
m
given by
ω
P
mt
=
w
(4.5)
s
is extracted from the shaft; therefore an equal amount of electrical power must be supplied
from the electrical system to which the machine is connected if the conservation of energy
principle is to be satisfi ed. The synchronous machine is now motoring.
If the external torque is accelerating rather than decelerating the magnetic axis of the rotor
is advanced with respect to the RMF axis, mechanical power is now supplied to the shaft and
the energy conservation principle demands that an equal amount of power is fed into the
electrical grid system. The synchronous machine is now generating.
In renewable energy applications, a high number of pole pairs may be selected for the
generator as this requires a low rotational shaft speed to generate mains frequency voltages.
Hydro turbines and wind turbines are in this class. The multipole arrangement is particularly
desirable when a wind turbine is coupled directly to a synchronous machine without an
intervening gearbox. In such cases, if a frequency of 50 Hz is to be generated from a wind
turbine rotating at 15 rev/min, Table 4.1 indicates that two hundred pole pairs would be
necessary!
This power generation process will now be looked at from the perspective of the electrical
network to which the generator is connected.
4.2.4 The Synchronous Generator Equivalent Circuit
To analyse the power fl ows in electrical systems, component representations are required that
can be incorporated into network or circuit models. To use the available circuit analysis tools
described in Chapter 5, it is necessary to build up these representations from basic circuit
elements, namely: resistors, inductors, capacitors and voltage or current sources (Appendix
A). Electrical power engineers over the years have developed a range of what are known as
equivalent circuits
for network simulation of electrical generators.
Here, for an approximate steady state analysis of power fl ows a description is required of
a synchronous generator by the simplest possible equivalent circuit. The Thé venin principle
explained in Appendix A can be used, for example, to describe the behaviour of a DC battery
by a source voltage in series with a resistance. Amazingly, this principle can also be effec-
tively used to describe through a simple circuit, and to a good approximation, the behaviour
