Electromagnetic transient simulation of power systems using root-matching techniques

For power system electromagnetic transient simulations, the method of substituting the trapezoidal integrator, developed by Dommel, is generally applied. The trapezoidal rule is based on a truncated Taylor series and therefore contains truncation errors. These truncation errors cause numerical oscillations when the time step is large relative to some of the time constants in the network. This leaves the user unsure whether observed oscillations are numerical or true artefacts of the system simulated. Various techniques have been developed to reduce the numerical oscillations, each with strengths and drawbacks. An exponential form of the difference equation is developed, using root-matching techniques and demonstrated on a simplified power system. This technique eliminates the truncation error and provides highly efficient and accurate time domain simulation regardless of the time step used. This exponential form of the difference equation generates a solution at each time point that is exact for the step response and a good approximation for an arbitrary forcing function