Stability Evaluation of Interpolation, Extrapolation, and Numerical Oscillation Damping Methods Applied in EMT Simulation of Power Networks With Switching Transients

For Electro-Magnetic-Transient (EMT) simulations of power networks with switches, techniques such as linear interpolation and Critical Damping Adjustment (CDA) are widely used for improving numerical robustness. This paper analyzes the numerical stability of simulations with these techniques. Firstly, it is mathematically shown that the interpolation or CDA step is equivalent to the introduction of additional switching states. Subsequently, Common Quadratic Lyapunov Function (CQLF) theory is used to investigate the numerical stability of the whole simulation considering these new switching states. It is proved that the widely used strategies like linear interpolation and CDA always result a stable simulation if the original switched system is strictly passive in all switching states. Finally, it is shown that the developed approach can be used to determine the stability of other practical interpolation methods. Examples are provided to verify the proposed technique.