A mathematical modeling of the number of short circuits withstood by transformer windings

Summary

Transformers are essential in power systems, but, as equipment, is susceptible to failures, that may cause losses of thousands of dollars and compromise the energy distribution. Therefore, transformers must be carefully designed to minimize the probability of failures occurrence. Transformer failures might have a mechanical origin, related to vibration and deformations caused by short circuit currents in the transformers windings. To evaluate the ability to withstand short circuits, computational simulations based methodologies, mathematical modeling and mechanical failure criteria can be used during the equipment design to provide a prediction of the windings behavior when they are submitted to short circuit currents, being possible to estimate the number of short circuits withstood by the windings and correlate them with the percentage of life reduction of the windings and the asymmetry factor of short circuit current. The correlation can be used to design the transformer to increase the safety margin for failure occurrence. Combining the safety margin with corrective, preventive and predictive actions, it is possible to raise the transformer lifespan. Aiming to purpose methods for increasing the lifespan of the transformer, computational simulations, based on Finite Element Method, and mechanical failure criteria were used to estimate the number of short circuits withstood by the transformers windings. The estimative was based on the use of Von Mises and Fatigue criteria. The behavior of the number of short circuits were analyzed plotting surfaces that correlate the number of short circuits withstood as a function of the percentage of life reduction of the windings and the asymmetry factor of short circuit current. With the surfaces, it was possible to determine, by Least Square Method, mathematical expressions that model the surfaces for different time duration of short circuit currents. Currently, there are no mathematical expressions that correlate the number of short circuits with the asymmetry factor of the short circuit current and the reduction of lifespan of the transformer. The goal of this paper is to propose the mathematical expressions to be used during the transformer design.

Additional informations

Authors

Da Costa, PISSOLATO FILHO, PAN, COLE

Keywords

Transformer Winding, Fatigue, Von Mises, Mathematical Expressions, Modeling, Short Circuit, Asymmetry Factor, Lifespan, Design, Mechanical Stress, Electromagnetic Force, Computational Simulation, Finite Element Method