An extension of Newton–Raphson power flow problem

This paper explores an idea to extend Newton–Raphson power flow problem to handle power system transmission line
flow limits, by means of generation redispatch and phase shifters. We extend and reformulate the power flow so that it
includes a variety of flow limits (thermal, small-signal stability, voltage difference), generation redispatch, and phase shifters.
The novelty of the approach is three step procedure (in case any limit violations exist in the system): run ordinary
power flow (and identify flow limits violated), solve a set of linear equations using extended power flow Jacobian by adding
a new column and a new raw that characterize particular limit, and resolve ordinary power flow with initial solution
obtained after the correction made by solution of linear equations. The use of ordinary power flow Jacobian and minimal
extensions to it in the case of limits identified makes this approach an attractive alternative for practical use. A simple
numerical example and the examples using an approximate model of real-life European Interconnected Power System
are included in the paper to illustrate the concept.