Frequency domain modeling of external systems in an Electro-Magnetic Transients Program

The standard EMTP (Electromagnetic Transients Program) is based on time domain calculations as these are eminently appropriate for simulation purposes. An approach to direct frequency-domain representation of an external system of any size or complexity is presented. The requirements for the external system are that it must be linear and time invariant, and it should include a transmission lines connecting it to the study zone and providing a travel delay τ. It is represented in the phase domain and does not have to be symmetrical. At the connecting bus between the study zone and the external system, Fourier transforms provide the conversion from the time domain to the frequency domain and vice versa. The accuracy and simplicity of direct frequency-domain modeling is preserved since no approximations or fitting are necessary, even for complex, three-phase frequency-dependent components