Geometric Algebra in Nonsinusoidal Power Systems: A Case of Study for Passive Compensation

Abstract

New-generation power networks, such as microgrids, are being affected by the proliferationof nonlinear electronic systems, resulting in harmonic disturbances both in voltage and current thataffect the symmetry of the system. This paper presents a method based on the application of geometricalgebra (GA) to the resolution of power flow in nonsinusoidal single-phase electrical systems for thecorrect determination of its components to achieve passive compensation of true quadrature current.It is demonstrated that traditional techniques based on the concepts of Budeanu, Fryze or IEEE1459fail to determine the interaction between voltage and current and therefore, are not suitable for beingused as a basis for the compensation of nonactive power components. An example is included thatdemonstrates the superiority of GA method and is compared to previous work where GA approachesand traditional methods have also been used.

Current survey of Clifford geometric algebra applications

“…Moreover, special treatment is devoted to compensations 44 in non-sinusoidal circuits, including passive compensation 45 and quadrature current compensation. 46 Applications of GA appear surprisingly even in optimal control of energy systems.…”

“…Moreover, special treatment is devoted to compensations 44 in non‐sinusoidal circuits, including passive compensation 45 and quadrature current compensation 46 …”

Formulating the geometric foundation of Clarke, Park, and FBD transformations by means of Clifford's geometric algebra

“…Note that this GA rotor has certain similarities to that derived in (30) for 3D case. The second GA rotor is R 2 4D = 0.9659 − 0.2588𝝁 34 (52) which encodes an angle of 15 • and represents a rotation of 30 • . It can be readily proved that…”

“…Once the geometric voltage and current are introduced, the geometric power [51][52][53] can be defined as their geometric product and the result is a multivector…”

“…Once the geometric voltage and current are introduced, the geometric power 51–53 can be defined as their geometric product and the result is a multivector …”