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Depicting Electrical Systems Dynamics by Means of Various Cartesian Planes

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It is common knowledge that the assessment of dynamic performances of electrical systems is currently carried out by displaying diagrams depicting how certain characteristic quantities vary with time i.e. by employing Cartesian planes with the abscissa represented by the time variable only and the ordinate corresponding to each characteristic quantity. From the practical point of view, there is no reason why to perform the selection of only time value as the abscissa of the Cartesian planes utilised with the purpose of assessing the dynamic behaviour of an electrical system. Moreover, the system analysts are specifically interested of the critical values i.e. the relative extrema of the characteristic quantities, which are merely ordinates in the Cartesian planes endowed with time-axis, and in a very small extent of the stationary points that are conventionally recognized as time values. To better depict the dynamic behaviour of an electrical system, the treatment that assumes the time value as coordinate will be accompanied, in the present paper, by an approach that involves the employment of a class of auxiliary Cartesian planes with the coordinates represented only by pairs of characteristic quantities. The system subjected to dynamic assessment is typified by a salient-pole synchronous generator, with the damping cage taken into account by means of two differential equations.
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Electrical System; Dynamics; Differential Equations; Cartesian Plane; Dynamic Simulation

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