Page 316 - Handbook of Electrical Engineering

302 HANDBOOK OF ELECTRICAL ENGINEERING

A more detailed treatment of this aspect is given in sub-section 3.5, however, (11.10) will be
used to illustrate the stability problem.

11.11.1.1 Steady state stability of a generator or motor

Equation (11.10) applies to any simple form of synchronous source and sink where E R and E S and
the voltages at either side of the linking reactance X. δ is the phase angle between E R and E S .For
the generator case, E R and E S may be replaced by V and E g and X by X sg . (For the synchronous
motor case E R and E S may be replaced by E m and V and X by X sm .)

Hence, for the generator:
VE g
P = sin δ g
X sg
Now V is usually kept close to the system rated voltage, i.e. 1.0pu ± 0.05 pu and X gs ,the
synchronous reactance of the generator may be assumed constant i.e. typically 1.8 pu to 2.9 pu
(depending on the generator rating).
E q is the internal emf produced by the field winding on the rotor. Hence, for any given
value of power P supplied by the generator there will be a wide range of E g and rotor angle δ g
values.

Example:

Let V = 1.0 pu,X sg = 2.5 pu and P = 1.0 pu (full load).
1.0E g sin δ g
P = 1.0 =
2.5
2.5
sin δ g = ≤ 1.0
E g

It can be seen that the larger the value of E g the smaller will be the value of δ g .
For full-load normal operation δ g is about 50 degrees, which would require E g to be 3.264 pu.
Suppose E g is reduced to 2.51 pu, then δ g would be 85 degrees.

If E g is reduced again, to 2.5 pu, then δ g wouldbe90degrees.
If E g is reduced below 2.5 pu then there is not a value of δ g to satisfy the equation and this
means that the power cannot be transferred if δ g is caused to exceed 90 degrees. The generator rotor
can no longer be kept in synchronism with the terminal voltage to which it is connected. δ g can
be caused to exceed 90 degrees by either reducing the field excitation, as described above, or by
allowing more power to be applied to the generator from its prime-mover, e.g. gas turbine. This can
happen at any level of power loading on the generator (above zero power). When the rotor angle
δ g exceeds 90 degrees, and the generator rotor pulls out of synchronism, the condition is unstable
which means the limit of steady state stability has been exceeded.