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The optimal operation of electrical energy systems by solving a securityconstrained optimal power flow (SCOPF) problem is still a challenging researchaspect. Especially, for conventional optimization methods like sequentialquadratic constrained quadratic programming (SQCQP) the formulation of theincremental control variables like in-phase and quadrature voltage controlledtransformers in a solver suitable way is complex. Compared to this, theimplementation of these control variables within heuristic approaches like theparticle swarm optimization (PSO) is simple but problem specific adaptations ofthe classic PSO algorithm are necessary to avoid an unfortunate swarm behaviorand local convergence in bad results. The objective of this paper is tointroduce a SQCQP and a modified PSO approach in detail to solve the SCOPFproblem adequately under consideration of flexible incremental in-phase andquadrature transformers tap sets and to compare and benchmark the results ofboth approaches for an adapted IEEE 118-bus system. The casestudy shows thatboth approaches lead to suitable results of the SCOPF with individualadvantages of the SQCQP concerning the quality and the reproducibility of theresults while the PSO lead to faster solutions when the complexity of theinvestigation scenario increases.

Comparison of Convexificated SQCQP and PSO for the Optimal Transmission  System Operation based on Incremental In-Phase and Quadrature Voltage  Controlled Transformers