Continuation methods or branch tracing methods are used to trace a curve given an initial point on the curve. These are also called predictor-corrector methods since they involve the prediction of the next solution point and correcting the prediction to get the next point on the curve.
Consider a system of nonlinear equations
. By adding a
continuation parameter
and one more equation to the system,
can be traced by
varying
. The resulting system
has
dimensions. The additional
equation is a parameterized equation which identifies the location of the current solution
with respect to the previous or next solution.
The continuation process can be diagrammatically shown by (5.1).
| (5.1) |
where, represents the current solution at step
,
is the
predicted solution for the next step, and
is the next solution on the
curve.
Continuation methods are employed in power systems to determine steady state stability limits [22] in what is called a continuation power flow29 . The limit is determined from a nose curve where the nose represents the maximum power transfer that the system can handle given a power transfer schedule. To determine the steady state loading limit, the basic power flow equations
| (5.2) |
are restructured as
| (5.3) |
where and
is a vector of power transfer given by
| (5.4) |
The effects of the variation of loading or generation can be investigated using the
continuation method by composing the vector appropriately.