Study of symmetrical and related components through the theory of linear vector spaces

Rao, N.D.; Rao, H. N. Ramachandra

doi:10.1049/piee.1966.0171

Proc. Inst. Electr. Eng. UK

1966

DOI: 10.1049/piee.1966.0171

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Study of symmetrical and related components through the theory of linear vector spaces

N.D. Rao

H. N. Ramachandra Rao

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Cited by 4 publications

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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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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

View full text Add to dashboard Cite

show abstract

A digitally-controlled, real-time, analog power-system simulator for closed-loop protective relaying testing

Nimmersjo

Werner-Erichsen

Hillstrom

et al. 1988

IEEE Trans. Power Delivery

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Stability of Reluctance Synchronous Motor

Khanijo

Mohanty

1968

IEEE Trans. on Power Apparatus and Syst.

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Study of symmetrical and related components through the theory of linear vector spaces

Cited by 4 publications

References 5 publications

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

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

A digitally-controlled, real-time, analog power-system simulator for closed-loop protective relaying testing

Stability of Reluctance Synchronous Motor

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