Quadratic Programming Problem in Power System Engineering Based on Projective Geometric Algebra

Abstract To find an optimal current in a three-phase four-wire power system we have to solve a quadratic programming problem with a positive definite quadratic form with an equality constraint. We offer an approach which solves this and similar problems using an apparatus of geometric algebras, namely Projective geometric algebra. We add dimensions to encode parts of a quadratic function and reformulate the problem to seeking an orthogonal projection of the origin to an intersection of hyperplanes.