Comparison of root-matching techniques for electromagnetic transient simulation

Electromagnetic transient simulation has become a very important tool in the design of electrical power systems. Dommel's trapezoidal integrator substitution, the standard method for electromagnetic transient simulations, often causes numerical oscillations due to truncation errors, particularly if some small time constants exist in the network. An alternative exponential form of the difference equation has been developed and demonstrated, using root-matching techniques. This exponential form of difference equation results in highly efficient and accurate time domain simulation with no tendency for numerical oscillation regardless of the time step used. In applying the root-matching techniques, an assumption is made as to the variation of the input between time steps. This paper looks at the performance of the various exponential forms of difference equation.