Power quality enhancement in single phase energy distribution systems using DQ optimal control

Arab, Naima; Kedjar, Bachir; Javadi, Alireza; Al‐Haddad, Kamal

doi:10.1109/ias.2017.8101769

Cited by 5 publications

(1 citation statement)

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“…From the pioneering work of Fortescue, 1 Park, 2 and Clarke, 3 a number of transformations have been proposed. [4][5][6] Initially, the main application was the analysis and modeling of electrical machines, but today, there is a wide range of applications such as active power filter, 7 power quality, 8 frequency estimation, 9 harmonic impedance measurement, 10 or multi-inverter control. 11 However, there is a central premise in the approach and derivation of these transformations regardless of the field used: geometrical meaning.…”

Section: Context and Previous Workmentioning

confidence: 99%

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

Montoya

Eid

2021

Math Methods in App Sciences

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Several of the most fundamental transformations widely used by the power engineering community are strongly based on geometrical considerations. Clifford's geometric algebra (GA) is the natural language for describing concepts in Euclidean geometry. In this work, we show how Clarke, Park, and Depenbrock's FBD transformations can be derived by imposing orthogonality on the voltage and current vectors defined in a Euclidean space by using GA. This paper presents these transformations as spatial‐like rotations and projections by means of the use of special algebraic objects named GA rotors. We prove that there is no need to use complex numbers nor matrices to perform the mentioned transformations and to provide geometrical intuition for electrical quantities and their transformations. Furthermore, power properties can be described using GA terminology by means of the proposed geometric power. The manipulation of the geometric power allows a useful current decomposition for a variety of applications such active filtering, frequency estimation, or electrical machinery. We provide in this paper an alternative approach focused on power systems under the paradigm of GA.

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