A Damping-Free Method for Mitigation of Trapezoidal Rule Oscillations in Linear Systems

This paper presents a novel method for mitigating trapezoidal solver oscillations (trapezoidal ringing) by averaging them in real-time and without damping. The developed method represents a first-of-its-kind approach where efforts hitherto have focused on damping. Method derivation and conceptual development is given and illustrated with a simple circuit example. A diode benchmarking circuit is used for testing the developed method in comparison to typical damping methods with several damping factors against smaller solution time steps. Testing included an exact solution implementation of the developed method and an approximately exact implementation reserved for real-time applications. The results show superior performance compared to the typical damping methods where damping by its nature introduces amplitude and phase distortion. The method is applicable to linear or piecewise-linear systems and is hence applicable to a large variety of electromagnetic transient (EMT) problem cases.