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State-of-the-art techniques for modeling, analysis and control of three-phaseelectrical systems belong to the real-valued multi-input/multi-output (MIMO)domain, or to the complex-valued nonlinear single-input/single-output (SISO)domain. In order to complement both domains while simplifying complexity andoffering new analysis and design perspectives, this paper introduces theapplication of geometric algebra (GA) principles to the modeling, analysis andcontrol of three-phase electrical systems. The key contribution for themodeling part is the identification of the transformation that allowstransferring real-valued linear MIMO systems into GA-valued linear SISOrepresentations (with independence of having a balanced or unbalanced system).Closed-loop stability analysis in the new space is addressed by using intrinsicproperties of GA. In addition, a recipe for designing stabilizing anddecoupling GA-valued controllers is provided. Numerical examples illustrate keydevelopments and experiments corroborate the main findings.

Introducing Modelling, Analysis and Control of Three-Phase Electrical Systems Using Geometric Algebra