Investigation of subharmonic ferroresonant oscillations in power systems

Steady state bifurcation diagram based on continuation technique is a versatile tool for analyzing the behaviour of ferroresonance circuit, since it gives the visualization of multiple solutions. Stability analysis of the solutions obtained by steady state bifurcation diagram [K. Al-Anbarri, R. Ramanujam, T. Keerthiga, K. Kuppusamy, Analysis of non-linear phenomenon in MOV connected transformer, IEE Proc. Generation Transmission Distrib.148 (6) (2001) 562–566; K. Al-Anbarri, R. Ramanujam, R. Saravanaselvan, K. Kuppusamy, Effect of iron core loss nonlinearity on the chaotic ferroresonance in power transformers, Electric Power Syst. Res. 65 (2003) 1–12; K. Al-Anbarri, R. Ramanujam, Ch. Subba Rao, K. Kuppusamy, Effect of circuit configuration on chaotic ferroresonance in a power transformer, Electric Power Components Syst. 30 (2002) 1015–1031] demarcates stable fundamental ferroresonant solution, unstable fold and flip segments. Flip segment in steady state bifurcation diagram [K. Al-Anbarri, R. Ramanujam, T. Keerthiga, K. Kuppusamy, Analysis of nonlinear phenomenon in MOV connected transformer, IEE Proc. Generation Transmission Distrib.148 (6) (2001) 562–566; K. Al-Anbarri, R. Ramanujam, R. Saravanaselvan, K. Kuppusamy, Effect of iron core loss nonlinearity on the chaotic ferroresonance in power transformers, Electric Power Syst. Res. 65 (2003) 1–12; K. Al-Anbarri, R. Ramanujam, Ch. Subba Rao, K. Kuppusamy, Effect of circuit configuration on chaotic ferroresonance in a power transformer, Electric Power Components Syst. 30 (2002) 1015–1031] implies unstable fundamental solution, but does not reveal the range, order and stability of subharmonics. This paper proposes an approach to explore the unstable flip segment further and unearth the hidden subharmonics. As a consequence of this approach, continuum of stable solutions of well-defined domains can be identified. It is found that the existence of subharmonic solutions is sensitive to various factors such as transformer saturation index, non-linearity in the core loss and presence of an arrester. Exhaustive studies reveal that in the presence of an arrester, subharmonic mode exists for wider range of bifurcation parameter value at a high value of core saturation index, there by reducing the range of chaotic attractors.