Investigation on the limitation of closed-form expressions for wideband modeling of overhead transmission lines

• Identification of passivity violations associated with image approximation for wideband line models.
• Identification of an unforeseen limitation regarding the use of image approximation.
• Passivity violations were small but led to unstable time-domain responses.
• Proposal of a mitigation technique allowing to maintain image approximations.
• Complex frequencies avoid small passivity violations associated with image approximations.

Power system throughout the world is facing new challenges that may involve a wideband accuracy modeling of transmission lines. As high frequency phenomena are involved, displacement currents in the ground cease to be negligible and should be considered in the calculations. This work shows that the use of the so-called image approximations for the evaluation of the per-unit-length line parameters in multiphase transmission lines leads to unexpected numerical stability problems due to small passivity violations above a few MHz when short line span lengths need to be considered.To illustrate that these violations are inherent to the image approximations, we considered three distinct line geometries commonly used in power systems involving different voltage levels. Several values for the ground parameters were also tested. The results indicate that passivity violations arise when image approximations are considered regardless of the line geometry. Furthermore, it was found that these passivity violations are related to the line length. In fact, there seems to be a minimal length suitable for the use of image approximations.Time-domain responses based on the Numerical Laplace Transform (NLT), and the travelling wave method are presented. The input voltage in both approaches is perturbed by a small amplitude high frequency component to excite the passivity violations. Mitigation techniques to avoid unstable time-domain responses are discussed.