Abstract
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.
Highlights
The increased use o f power control equiptnent resulted in the distortion o f the excitation and response fu n ctio n s in power system s fr o m .simple sinusoids
IN L E ID IN G Oneffektiewe benutting van die infrastruktuur om drywing van een p u n t in 'n stelsel na ’nanderoor te d ra, is lank reeds bekend.^*’ D it is egter tans steeds ’n probleem om die drywingsvloei te analiseer en verder vir die oneffektiewe benutting te kom penseer, w anneer die verlope van die opwek- en responsiefunksies nie deur eenvoudige periodiese en sinusvormige funksies beskryf kan w ord nie.^‘‘-^ In dryw ingstelsels, veral in elektriese drywingstelsels, word vanaf die begin van die eeu fasors van die opwek- en responsiefunksies gebruik om drywingsvloei te beskryf
Die voo rw aard e geld n atuurlik dat sowel die opwek- as responsiefunksies sinusvorm i ge tydsverlope moet besit, wat fundamentele beperking in die gebruik van dié teorie in algem ene dryw ing stelsels impliseer
Summary
D. F. van der Merwe L aboratorium vir Energie, R andse Af'rikaanse U niversiteit, Posbus 524, Johannesburg 2000. Die wi.skundige voorstelling van drywing deur m iddel van die kwaternioonteorie word ondersoek am 'n algemene definisie van drywing daar te stel, vir ,'itelsels waar die opwek- en heladingsfunksies nie eenvoudige sinusvormige verlope hesit nie. Die algemene heskrywing van drywing word aan die hand van tipiese elektriese slelsels geiUustreer, maar word voorgestel in die algemene analise van alle ander drywingstelsels, lietsy meganies, termies o f chemies. D rywing word verdeel in kom ponente wat die netw erk h esk ry fa a n die hand van energie-oordrag en is onderling ortogonaal. Die kwaternioonteorie hesit ortogonale eienskappe wat, uitgaande vanaf die Cauchy-Schwarz-ongelykheid, die heladingsfunksie op die opwekfunksie b e sk ry f om sodoende drywing in drie dimensies voor te stel
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