### Abstract:

Power System transient stability study is a major component of the Power
System course offered in many undergraduate programmes in Electrical
Engineering " 'hen the transient stability of a power system is analysed, the
transient stability of the rotating synchronous machines connected to the
system should be analysed individually or in groups.
In transient stability analysis, a synchronous machine is described by a set of
differential equations. The type and the number of differential equations needed
to represent a single machine depend on the complexity of the model used. But
in any model, the swing equation (a second order differential equation) which
describes the motion of the rotor under transient conditions, is essentially
included. Therefore the simplest representation of a synchronous machine is
the swing equation of the machine. The solution of the swing equation of a
given machine provides basic information to determine the stability of the
machine under transient conditions.
The swing equation relating the relative motion of the rotor with time could
be solved using any method used for the solution of ordinary differential
equations. When the calculations are carried out on a digital computer,
modified Euler and fourth-order Runga-Kutta methods are commonly used.
But the point by point method developed by Dhal in 1938 is mostly used to
solve the swing equation in simple cases where hand calculations are involved.
When simple transient stability problems are solved in the classroom to
illustrate the behaviour of the machine, the point by point method is preferred
because of its simplicity. In this paper an important modification to improve
this method is discussed.