Analytical Expression for Resonances of an Inhomogeneous, Radial, Lossless LC Network

Mukherjee, Pritam and Satish, L (2019) Analytical Expression for Resonances of an Inhomogeneous, Radial, Lossless LC Network. In: IEEE TRANSACTIONS ON POWER DELIVERY, 34 (3). pp. 899-909.

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Abstract

This paper is a sequel to the authors' previous work wherein an analytical expression was derived for the harmonic sum of squares of natural frequencies of a lossless LC ladder network, which is a widely accepted means to model a single, isolated winding for analyzing impulse behavior. The present paper extends the previous result, so that it is applicable to multiple windings in actual transformers. The complexities of the previous work, viz., inhomogeneity and an exhaustive consideration of inductive coupling are retained, and additionally all possible capacitive couplings are now considered. Furthermore, the topology considered in this paper is generic enough to accommodate inductive branches emerging from any node. To the best of authors' knowledge, there exists no compact closed-form expression to relate the natural frequencies to the inductances and capacitances for a network having this extent of arbitrariness in topology. The success of this method can be ascribed to careful inspection of the inductance matrix to identify hidden pattern and/ or structure, followed by their deft manipulation guided by the basic law of mutual coupling between inductors. Interestingly, even a physical meaning can be assigned to each term of the derived expression, and this is done with the intention of assisting its use to conjure new applications.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON POWER DELIVERY
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	copyright for this article belongs to IEEE TRANSACTIONS ON POWER DELIVERY
Keywords:	Electric network; eigenvalue; frequency response; natural frequencies; resonance
Department/Centre:	Division of Electrical Sciences > Electrical Engineering Division of Electrical Sciences > High Voltage Engineering (merged with EE)
Date Deposited:	21 Jun 2019 12:17
Last Modified:	21 Jun 2019 12:17
URI:	http://eprints.iisc.ac.in/id/eprint/63043

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