Original Research

Orthogonal representation of power with the aid of quaternions

J. H. R. Enslin
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie | Vol 9, No 1 | a433 | DOI: https://doi.org/10.4102/satnt.v9i1.433 | © 1990 J. H. R. Enslin | This work is licensed under CC Attribution 4.0
Submitted: 05 July 1990 | Published: 05 July 1990

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J. H. R. Enslin,, South Africa

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The increased use of power control equipment resulted in the distortion of the excitation and response functions in power systems from simple sinusoids. These systems resulted in discrepancies in the general definition of power. This distortion has a negative effect on the accurate definition and representation of power in a contaminated power system. The mathe­matical representation of power with the aid of the theory of quaternions in vector calculus is investigated to obtain a generalized definition of power in all power systems, especially in power systems where the excitation and response functions show non-sinusoidal characteristics. The general description of power is illustrated with the aid of electrical power systems, but is however proposed to be beneficial in all power systems, being mechanical, thermal or chemical. Power is divided into different orthogonal components which describes the energy transfer through a system. The quaterni­on theory has orthogonal properties which can be used together with the Cauchy-Schwarz inequality to describe the power components using the excitation and respective response functions.


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