UBC Theses and Dissertations
Chaotic ferroresonance in power transformers Mozaffari, Said
Ferroresonance can be categorized as a nonlinear resonance which is unpredictable and whose occurrence can cause damage in power distribution and transmission systems. In most instances, ferroresonance occurs when one or two of the source phases are lost while the transformer is unloaded or lightly loaded. This can happen due to the clearing of single phase fusing, the operation of single phase reclosers or the performance of single phase switching procedures. In these cases, if one of the three switches was open, and only two phases of the transformer were energized, there would be a voltage induced in the "open" phase. This induced voltage will "backfeed" the distribution line, back to the open switch. Ferroresonance will occur if the distribution line is highly capacitive. This ferroresonance will involve the nonlinear magnetizing reactance of the transformer's open phase and the shunt capacitance of the distribution line. One of the fundamental properties of ferroresonance is the fact that several stable solutions can exist under steady-state conditions for a given circuit. The realization that ferroresonance is a nonlinear and sometimes chaotic process opens up many possibilities. The newly developed techniques for analysis of nonlinear dynamical systems and chaos should now be evaluated for use with ferroresonance. The method of Slowly Varying Amplitude is used to derive an analytical solution for the equivalent ferroresonant circuit. The solution of the nonlinear equation for a typical ferroresonant circuit containing a power transformer is shown to be dependent on the accurate description of the magnetization curve. A detailed analysis of many simulation results demonstrates that the probability of chaos increases as losses decrease and the nonlinearity of the transformer magnetization rises. The effect of varying the transformer core losses, the value of the source voltage and the length of the transmission line on the chaotic solution of the system has been studied. The concept of transient chaos as compared with steady-state chaos is also discussed. The solution of the ferroresonant circuit is shown to be dependent on the value of its initial conditions. It is shown that a small change in the initial conditions leads to a large difference in long-term behavior of the system, and this makes the future of the system unpredictable. With detailed analysis of many simulation results, the basins of attraction for different chaotic regions of the system have been obtained. It is shown that inclusion of series losses is not an important factor in studying ferroresonance as compared to core losses. The Electromagnetic Transient Program (EMTP) is used to simulate ferroresonance and to obtain Poincare maps and bifurcation diagrams. The appropriate representation of nonlinear elements in the EMTP when chaotic systems are to be simulated is shown to be very important. All the simulation results are tested using three different integration routines. In all the simulations the results of using different integration routines were the same. The result of the case study performed by using the EMTP showed the existence of chaos and bifurcation in a simple power system and the need to develop accurate ways to reliably identify chaotic behavior.
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