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Many optimization problems in power transmission networks can be formulatedas polynomial problems with complex variables. A polynomial optimizationproblem with complex variables consists in optimizing a real-valued polynomialwhose variables and coefficients are complex numbers subject to some complexpolynomial equality or inequality constraints. These problems are usuallydirectly converted to real variables, either using the polar form or therectangular form. In this work, we propose a Julia module allowing therepresentation of polynomial problems in their original complex formulation.This module is applied to power systems optimization and its generic designenables the description of several variants of power system problems. Resultsfor the Optimal Power Flow in Alternating Current problem and for thePreventive-Security Constrained Optimal Power Flow problem are presented.

A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow