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 whereERandESand
the voltages at either side of the linking reactanceX.δis the phase angle betweenERandES.For
the generator case,ERandESmay be replaced byV andEgandXbyXsg. (For the synchronous
motor caseERandESmay be replaced byEmandVandXbyXsm.)

Hence, for the generator:

P=

VEg

Xsg

sinδg

NowV is usually kept close to the system rated voltage, i.e. 1.0pu± 0 .05 pu andXgs,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).

Eqis 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 ofEgand rotor angleδg
values.

Example:

Let V=1.0 pu,Xsg=2.5 pu andP=1.0 pu (full load).

P= 1. 0 =

1. 0 Egsinδg

2. 5

sinδg=

2. 5

Eg

≤ 1. 0

It can be seen that the larger the value ofEgthe smaller will be the value ofδg.

For full-load normal operationδgis about 50 degrees, which would requireEgto be 3.264 pu.

SupposeEgis reduced to 2.51 pu, thenδgwould be 85 degrees.

IfEgis reduced again, to 2.5 pu, thenδgwouldbe90degrees.

IfEgis reduced below 2.5 pu then there is not a value ofδgto satisfy the equation and this
means that the power cannot be transferred ifδgis caused to exceed 90 degrees. The generator rotor
can no longer be kept in synchronism with the terminal voltage to which it is connected.δgcan
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
δgexceeds 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.