Isolated ferroresonant solutions in transmission lines in the same right-of-way

This paper reports investigations carried out on isolated subharmonic ferroresonant oscillations in a transformer-terminated line due to an energised parallel line on the same right-of-way. The investigation is based on nonlinear dynamics. The motivation for investigating the isolated subharmonics is the reported case of “locking” into a subharmonic ferroresonance solution following a switching operation in the 525 kV system of Bonneville Power Administration (BPA), USA. The initial isolated subharmonic steady states are obtained by a class of temporal methods and it is referred to here as “temporal bifurcation diagram” approach. Starting with initial conditions provided by temporal bifurcation diagram, a continuation procedure predicts multiple subharmonic solutions. Analysis of isolated subharmonic solutions reveals that in general they form a closed loop. Further, odd symmetric subharmonic solutions give rise to supercritical and subcritical pitchfork bifurcations. The paper also reports the sensitivity of isolated subharmonics with respect to the length of de-energised line.