Suppression of numerical oscillations in the EMTP power systems

The integration scheme in the electromagnetic transients program EMTP has been modified to solve the problem of sustained numerical oscillations that occur when the trapezoidal rule has to act as a differentiator. These oscillations appear, for instance, on the voltage across an inductance after current interruption. The technique presented prevents these oscillations by providing critical damping of the discontinuity within one Δt of the simulation. The critical damping adjustment (CDA) is achieved by means of two Δt/2 integration steps using the backward Euler rule. With the CDA scheme the trapezoidal rule can still be used throughout the entire simulation without the problem at discontinuities. The effectiveness of the scheme is illustrated with simulation results