**Computation of Transient Profiles along Nonuniform Transmission Lines Including Time-Varying and Nonlinear Elements Using the Numerical Laplace Transform** †

#### **Rodrigo Nuricumbo-Guillén 1,\*, Fermín P. Espino Cortés 1, Pablo Gómez 2 and Carlos Tejada Martínez 1**


Received: 30 June 2019; Accepted: 19 August 2019; Published: 21 August 2019

**Abstract:** Electromagnetic transients are responsible for overvoltages and overcurrents that can have a negative impact on the insulating elements of the electrical transmission system. In order to reduce the damage caused by these phenomena, it is essential to accurately simulate the effect of transients along transmission lines. Nonuniformities of transmission line parameters can affect the magnitude of voltage transients, thus it is important to include such nonuniformities correctly. In this paper, a frequency domain method to compute transient voltage and current profiles along nonuniform multiconductor transmission lines is described, including the effect of time-varying and nonlinear elements. The model described here utilizes the cascade connection of chain matrices in order to take into consideration the nonuniformities along the line. This technique incorporates the change of parameters along the line by subdividing the transmission line into several line segments, where each one can have different electrical parameters. The proposed method can include the effect of time-dependent elements by means of the principle of superposition. The numerical Laplace transform is applied to the frequency-domain solution in order to transform it to the corresponding time-domain response. The results obtained with the proposed method were validated by means of comparisons with results computed with ATP (Alternative Transients Program) simulations, presenting a high level of agreement.

**Keywords:** electromagnetic transients; nonuniform transmission line; numerical Laplace transform; time-dependent elements; transmission line modeling
