Ferroresonance and chaos: Observation and simulation of ferroresonance in a five-legged core distribution transformer.

摘要

Ferroresonance is a nonlinear LC resonance that can cause overvoltages, power quality problems, and damage in electrical distribution systems. Ferroresonance has been researched for over 80 years, but its complex behaviors are still not fully understood. Observation and categorization methods must be extended to increase existing knowledge of ferroresonance. Simulation methods must also be improved, mainly with respect to developing correct equivalent circuit models for transformers of various core designs. New theoretical developments in the area of nonlinear dynamics and chaos are identified as being applicable to the problem of ferroresonance.;Laboratory and simulation work is based on an actual five-legged core grounded-wye to grounded-wye distribution transformer, found in 80% of American distribution systems. Many ferroresonance problems are attributed to such transformers. Two new equivalent circuit models are derived--one based on Ampere's circuital law and the other on duality transformations. Graphical observation methods from nonlinear dynamic systems are used to observe and categorize ferroresonant behavior. Parameter values for the duality-derived equivalent circuit are obtained from laboratory measurements. The Alternative Transients Program (ATP) is used to simulate excitation, ferroresonance, Poincare sections and bifurcation. Several new means of comparing periodic and chaotic waveforms are proposed, investigated and then used to compare ATP simulation results to laboratory measurements.;Single phase open-circuit and short-circuit tests are sufficient to determine equivalent circuit parameters. Depending on capacitance and initial conditions, several different steady-state periodic and chaotic modes of ferroresonance are possible. Phase plane diagrams, invariant measure, Poincare sections and symmetrical dot patterns are found to be well-suited for observing and categorizing ferroresonant behavior. Fractal dimension lacks the precision needed to categorize similar chaotic modes of ferroresonance. Capacitive effects are found in some cases to have a greater effect on low-frequency transformer behavior than previously believed. Model performance is most sensitive to core parameters. Representing core losses with a linear resistance causes much larger errors when modeling a three phase transformer than a single phase transformer. The ATP model is capable of reproducing all of the nonlinear and chaotic behaviors observed in the laboratory.