Computational efficiency improvement of the Universal Line Model by use of rational approximations with real poles

The Universal Line Model (ULM) is widely used for the simulation of electromagnetic transients in electrical power transmission systems. This paper proposes an improvement in the computational efficiency of the ULM by introducing a methodology for rational approximation of smooth frequency domain responses using real poles only through Vector Fitting (VF). The ULM uses a rational model formulation in pole-residue form, as obtained by VF. The models sometimes include several complex poles, leading to complex states that result in slower computations. Transformation into real states is possible but comes at the cost of more complicated expressions for the convolutions. A straightforward methodology is presented in which the complex poles are replaced with real poles based on the non-dominance property of the complex poles in smooth function approximations. This methodology is demonstrated in asymmetrical overhead line configurations, including single-circuit, double-circuit, and parallel lines. The examples show that replacement with real poles leads to negligible loss of accuracy in time domain simulations.