Nonexistence of Symmetric Modes of Subharmonic Oscillations in Three-Phase Circuit--An Approach by Interval Computation

Takashi HISAKADO  Kohshi OKUMURA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.12   pp.3108-3115
Publication Date: 2001/12/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Circuit Theory
symmetry,  three-phase circuit,  subharmonic oscillation,  interval computation,  all solutions,  

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This paper describes how the symmetry of a three-phase circuit prevents the symmetric modes of several subharmonic oscillations. First, we make mathematically it clear that the generation of symmetrical 1/3l-subharmonic oscillations (l=1,2,) are impossible in the three-phase circuit. As far as 1/(3l+1)-subharmonic oscillations (l=1,2,) and 1/(3l+2)-subharmonic oscillations (l=0,1,) are concerned, the former in negative-phase sequence and the latter in positive-phase sequence are shown to be impossible. Further, in order to confirm the above results, we apply the method of interval analysis to the circuit equations and obtain all steady state solutions with unsymmetric modes.