Environmental Engineering Reference
In-Depth Information
P
Bmax
-P
B
δ
δ
= 90°
Figure 4.8
Power angle characteristic of an SG
4.2.8 Power - Load Angle Characteristic: Stability
Equation (4.8a) is plotted in Figure 4.8 to illustrate the dependence of the generated active
power on the load angle. Note that a synchronous generator (SG) connected to an infi nite bus
is capable of generating a maximum active power
P
Bmax
, at
= 90 ° . Any additional applied
mechanical torque will increase the load angle beyond 90 °, with a consequential decrease in
electrical power. Physically, the peripheral magnetic forces linking the two fi elds together is
insuffi cient to maintain the locking effect. The power balance between mechanical and elec-
trical powers has now been lost, the excess mechanical power accelerates the rotor beyond
synchronous speed and the synchronous generator has lost its ability to act as a stable power
converter. In this unstable regime the SG is described as having
lost synchronism
i.e. its rotor
generates an internal voltage
V
A
of a higher frequency than the infi nite bus voltage
V
B
. Opera-
tion under this condition, known as
pole slipping
, results in large overcurrents, is highly
undesirable and protection equipment will be brought into action to disconnect the synchro-
nous machine from the mains.
During system contingencies violent transient changes may take place that cause swings
in the load angles of synchronous generators. To ensure safe stability margins so that pole
slipping is prevented, the steady state load angles of SGs are kept well below 30 °. Power
system stability is a major topic in its own right involving the simultaneous solution of the
differential equations characterizing all the network components. This is beyond the scope
of this topic, but it is worth noting that connection of large RE sources on to the grid will
alter the system dynamics. Therefore studies may be required to assess the new system stabil-
ity margins.
δ
4.3 The Transformer
4.3.1 Transformer Basics
The transformer is an indispensable part of any power system operating at a range of voltages.
The transformer mode of operation is included here as it provides a useful aid to the under-
