Impact of Voltage Source and Initial Conditions on the Initiation of Ferroresonance KRUNO MILIEVI, IVAN RUTNIK - Faculty of Electrical Engineering, Osijek IGOR LUKAEVI - HEP-Transmission system operator Ltd, Osijek CROATIA http://www.etfos.hr; http://www.hep.hr Abstract: The impact of voltage source and initial conditions on the initiation of ferroresonance is investigated. The investigation is carried out by simulating the behaviour of the mathematical model of ferroresonant circuit realized in the laboratory. The initiation of ferroresonance is investigated by varying the values of phase shift and amplitude of voltage source in order to incite the ferroresonance. Thereby, the initial conditions are varied within a practically possible range of initial values of transformer voltage and transformer flux linkage. Key-Words: Ferroresonance, Iron-cored reactor, Bifurcation diagram, Chaos, Nonlinear circuits Corresponding author. K. Milicevic is with the Faculty of Electrical Engineering, Osijek, Croatia (e-mail: kruno.milicevic@etfos.hr). Tel: 00385912246021; Fax: 0038531224708. 1 Introduction The simple electrical circuit in which ferroresonant oscillation can occur is a circuit which comprises a linear capacitor in series with a nonlinear coil, driven by a sine-wave voltage source, Fig. 1. The nonlinearity of the coil comes from the nonlinear magnetization characteristic of the iron core. Fig. 1. Ferroresonant circuit The usual electrical model of the nonlinear coil is a nonlinear reactor described by i L (ϕ) characteristic in parallel with a nonlinear resistor described by i R (u L ) characteristic, Fig. 2. Fig. 2. Model of nonlinear coil The nonlinear coil is realized either as a winding of the unloaded iron-cored transformer or as a winding of the iron-cored reactor without air gap. The analyzed circuit is a laboratory model, but in praxis it is a simplest physical model of a large electrical power system for the ferroresonance case studies. An example of ferroresonance in three phase transmission system is shown on Fig. 3. Fig. 3. Ferroresonance in three phase system The nonlinear inductances represent iron core coils of unloaded three phase power transformer and the capacitance (C m , C Z ) represents capacitance of long transmission line (or HV underground cable). In this case, the ferroresonance occurs because of the malfunction of one pole of HV circuit breaker. The Fig. 1 shows the equivalent circuit where Z m Z m m C C C C C C u u u + = + + = 2 2 ) ( 3 2 (1) More practical examples are described in the literature [1]. Ferroresonant circuit is a nonlinear dynamical system and as such several steady-state responses of the circuit can be obtained: monoharmonic, odd WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS Kruno Milicevic, Ivan Rutnik and Igor Lukacevic ISSN: 1109-2734 800 Issue 8, Volume 7, August 2008