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Theory of Distributed-Parameter Circuits and Impedance/Admittance Formulas

Authored by: Akihiro Ametani , Naoto Nagaoka , Yoshihiro Baba , Teruo Ohno , Koichi Yamabuki

Power System Transients

Print publication date:  November  2016
Online publication date:  November  2016

Print ISBN: 9781498782371
eBook ISBN: 9781315366791
Adobe ISBN:

10.1201/9781315366791-2

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Abstract

When investigating transient and high-frequency steady-state phenomena, conductors such as a transmission line, a machine winding, and a measuring wire demonstrate a distributed-parameter nature. Well-known, lumped-parameter circuits are an approximation of a distributed-parameter circuit for describing a low-frequency, steady-state phenomenon of the conductor. That is, a current in a conductor, even a short conductor, needs time to travel from its sending end to its remote end because of its finite propagation velocity (300 m/µs in a free space). From this fact, it should be clear that a differential equation expressing the behavior of current and voltage along the conductor involves variables of distance x and time t or frequency f. Thus, it becomes a partial differential equation. However, a lumped-parameter circuit is expressed by an ordinary differential equation since no concept of the length or the traveling time exists. This is the most significant difference between the distributed-parameter circuit and the lumped-parameter circuit.

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