Suppression of Numerical Oscillations in the EMTP

When compared to other possible integration schemes for the EMTP, the trapezoidal rule of integration presents very good overall characteristics in terms of accuracy, efficiency, and run-off stability. During certain system conditions, however, the solution with trapezoidal may present sustained numerical oscillations (Fig. 1(a)). These oscillations are related to the behaviour of trapezoidal as a differentiator after a discontinuity is encountered (e.g., after a switching operation). To solve this problem, two kinds of approaches have been proposed in the past. One approach has been to add artificial damping to the system either through the integration rule itself, using for instance backward Euler instead of trapezoidal, or by adding external resistances to provide damping. The main drawback of this approach is that distortion through damping is introduced not only on the discontinuity but also on the rest of the simulation. The other approach has been to use interpolation to correct the initial conditions after the disturbance. These type of techniques, however, are relatively complicated to implement. The technique presented in this paper solves the problem of trapezoidal as a differentiator by neutralizing the overshoot at the discontinuity (for instance, in the voltage ¿ = L di/dt after switching) within one time step.