Basics of Electromagnetic Transients: Underlying mathematics

Electromagnetic transient (EMT) simulation plays an important role is power system operation, control, and planning. Considering that the digital computer is unable to give a continuous history of transient phenomena, it is essential to solve the time response at discrete intervals reasonably. In the 1960s, Dommel first started an EMT solution by a nodal matrix method. To reduce solution time for nonlinear and time-varying components, Dommel proposed a compensation method and developed equivalent circuits for those components in 1971. To improve the calculation speed, Dommel introduced a new technique for solving EMTs with the implicit trapezoidal rule of integration in 1972. In 1986, Dommel published his EMT Program (EMTP) theory book, where all of the EMT component modeling and overall solution methods are detailed.