  The optimal operation of electrical energy systems by solving a security
constrained optimal power flow (SCOPF) problem is still a challenging research
aspect. Especially, for conventional optimization methods like sequential
quadratic constrained quadratic programming (SQCQP) the formulation of the
incremental control variables like in-phase and quadrature voltage controlled
transformers in a solver suitable way is complex. Compared to this, the
implementation of these control variables within heuristic approaches like the
particle swarm optimization (PSO) is simple but problem specific adaptations of
the classic PSO algorithm are necessary to avoid an unfortunate swarm behavior
and local convergence in bad results. The objective of this paper is to
introduce a SQCQP and a modified PSO approach in detail to solve the SCOPF
problem adequately under consideration of flexible incremental in-phase and
quadrature transformers tap sets and to compare and benchmark the results of
both approaches for an adapted IEEE 118-bus system. The casestudy shows that
both approaches lead to suitable results of the SCOPF with individual
advantages of the SQCQP concerning the quality and the reproducibility of the
results while the PSO lead to faster solutions when the complexity of the
investigation scenario increases.
