Time-delay estimation through all-pass functions for ULM line and cable models

• It establishes that the minimum RMS-error in the rational fit of power system EMT models does not guarantee minimum errors for the simulated transient responses. • It is demonstrated that time delays obtained from the minimum RMS error criterion can produce causality violations. • A new method based on all-pass functions is proposed. • The new method guarantees the causality and minimum-phase feature of the models synthesized with it. • The new method is faster than state-of-the art Brent´s method, it also offers similar accuracy and is free of causality violations. Traveling-wave line models, such as the ULM, are widely used in time-domain EMT simulations for power systems. These models require the rational approximation of both the characteristic admittance matrix Y c , and the propagation matrix H . Rational fitting of H is challenging due to the inclusion of a mix of modal delays in all its elements. These delays must therefore be identified and extracted before proceeding to calculate the rational approximation. This paper proposes a new iterative method to estimate time delays employing all-pass filters and delay equalizations. Unlike other currently used methods, the one proposed here ensures causality and minimum-phase features in the synthesized H model. Three test cases are included: 1) a synthetic transfer function, 2) a system of underground cables, and 3) the EMT response of an aerial line. The obtained results show that the proposed method maintains causality while achieving similar accuracies with fewer iterations compared to a state-of the art method based on rms-error minimization.