Optimal power flow computations with constraints limiting the number of control actions

This paper focuses on optimal power flow (OPF) computations in which
no more than a pre-specified number of controls are allowed to move.
The benchmark formulation of this OPF problem constitutes a mixed integer
nonlinear programming (MINLP) problem. To avoid the prohibitive
computational time required by classical MINLP approaches to provide
a (potentially sub-optimal) solution, we propose instead two alternative
approaches. The first one consists in reformulating the MINLP problem
as a mathematical program with equilibrium constraints (MPEC).
The second approach includes in the classical OPF problem a nonlinear
constraint which approximates the integral constraint limiting the
number of control variables movement. Both approaches are solved by
an interior point algorithm (IPA), slightly adapted to
the particular characteristics of each approach.
We provide numerical results with the proposed approaches on two test systems
and for two practical problems: minimum cost to remove thermal
congestion, and minimum cost of load curtailment to restore a feasible
equilibrium point.