Flux reflection model of the ferroresonant circuit.(Research Article)(Report)

1. Introduction

A ferroresonant circuit is a circuit which comprises a linear capacitor in series with a nonlinear coil, driven by a sine-wave voltage. The ferroresonant circuit can exhibit several bifurcations and a chaotic steady state [1-5]. Common research procedures comprise the measurements of ferroresonant circuit and the computer simulation of the mathematical model based on state-equations of the circuit.

The nonlinearity of the model caused by the nonlinear magnetization characteristic of the coil is the driving force on the route to the chaotic steady state, which is marked by the bifurcations that are initiated by varying values of a circuit parameter. Complex models, that comprehend more nonlinear elements, are needed to match results of measurements and simulation completely [6, 7]. In order to obtain the complex behavior of the circuit, the nonlinear element that comprises the magnetization nonlinearity is only necessary. Therefore, the model comprises the magnetization nonlinearity [i.sub.L](([phi]), implying the core saturation of the coil. The winding resistance of the coil is neglected, and the resistor, that represents the core losses of the coil, is assumed to be linear. State equations of the ferroresonant circuit, Figure 1, are

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1.1)

[FIGURE 1 OMITTED]

The magnetization nonlinearity [i.sub.L](([phi]) is odd-symmetric and monotonically increasing. It can be presented in various forms, for example, in a polynomial form [8, 9] or piecewise linear form [10,11]. Thereby, the polynomial form is obtained often by an interpolation of a piecewise linear form. The magnetization nonlinearity is based on measurements carried out on a nonlinear coil regarding the above-mentioned assumptions made about properties of the coil. For example, one ought to rely on the results of standard measurements carried out on the nonlinear coil by the manufacturer [11,12]. Because of a limited thermal endurance of the coil, measurements cannot be carried out by applying the sine-wave voltage for the full range of flux and voltage peak values which occur in some operation modes of ferroresonant circuit. However, the importance of this problem is often ignored by a simple extrapolation of magnetization nonlinearity obtained by measurements.

Further problem of modeling based on standard measurements is that the parameters of model depend on the number of measurements, that is, on the number of measured values on U-I characteristic. Namely, a piecewise linear form of the magnetization nonlinearity, that is obtained by a small number of measurements, would not be as smooth as necessary; in the case of polynomial form of the magnetization nonlinearity, a small number of measurements could result with a significant interpolation error.

In the paper a novel kind of modeling the magnetization characteristic of the coil in the ferroresonant circuit is presented. The modeling will be based on a characteristic behavior that nonlinear coil exhibits in a ferroresonant circuit. The behavior will be identified from the flux waveforms obtained by measurements and by computer simulation.

The preliminary purpose of obtained novel model of the ferroresonant circuit is to enable a new comprehension of the circuit behavior and to simplify the modeling of nonlinear coil in the ferroresonant circuit by reducing the number of model parameters.

2. Measurements and Nonlinear Model

In order to notice the characteristic behavior of a coil in ferroresonant circuit, the ferroresonant steady states are obtained by measurements carried out on a ferroresonant circuit that is realized in laboratory and by computer simulation carried out on a typical nonlinear model of the ferroresonant circuit.

The ferroresonant circuit realized in the laboratory is composed of the capacitor C = 20 [mu]F and the primary winding of the toroidal iron-cored two-windings transformer used as a nonlinear coil. The transformer was designed for the nominal apparent power of 200 VA and for the nominal primary voltage of 30 V. The core is strip-wounded, made of Ni-Fe alloy (Trafoperm N3). The autotransformer of 10 kVA nominal apparent power is used as a variable voltage source in all experiments.

To simplify …