Evaluation of the extended modal-domain model in the calculation of lightning-induced voltages on parallel and double-circuit distribution line configurations

Highlights

• Lightning-induced voltages are calculated on parallel and double-circuit distribution lines with the extended modal-domain model.

• The influence of the frequency selected for calculating the transformation matrix is investigated.

• Best model accuracy is obtained with the use of complex poles in the fitting of the model parameters.

• Accurate results are obtained for most of the tested configurations.

Abstract

This paper evaluates the applicability of the extended modal-domain (EMD) model in the calculation of lightning-induced voltages on parallel and double-circuit distribution lines. The influence of a real and constant transformation matrix and of the fitting technique required in the model on the induced-voltage waveforms is also investigated. It is shown that the EMD model presents good accuracy in most of the tested configurations. Also, in most cases the influence of the frequency selected for the calculation of the transformation matrix required in the EMD model is minimal. On the other hand, the requirement of using strictly real poles and residues and the use of the built-in fitting tool available in the Alternative Transients Program (ATP) have both a detrimental influence on the accuracy of the EMD model, at least in the investigated cases.

Introduction

Lightning-induced voltage calculations on overhead distribution lines are mostly performed using transmission line theory, which is motivated by features like efficiency, accuracy, and possibility of implementation in electromagnetic transient (EMT) simulators [1], [2], [3]. Although the latter feature is of particular importance for the simulation of realistic networks including laterals, surge arresters, and transformers [4,5], it can actually be quite a demanding task because the user is expected to implement not only a code for the calculation of lightning electromagnetic fields and their coupling with the illuminated line, but also a lossy transmission line model for the calculation of the resulting transients [6]. In a recent paper, De Conti and Leal [6] proposed two models that make it possible to calculate lightning-induced voltages simply by adding independent current sources to both ends of lossy transmission line models that are already available in the libraries of EMT simulators. By using the proposed models, the user does not need to implement a dedicated transmission line model to solve the transients on the line, which greatly simplifies the process.

One of the models proposed in [6], called extended phase-domain (EPD) model, solves telegrapher's equations including the influence of external electromagnetic fields directly in the phase domain and is compatible with the universal line model (ULM) [7]. The EPD model can be used to calculate lightning-induced voltages on overhead distribution lines with arbitrary configuration even if the associated eigenvectors present a large variation with frequency, which is a characteristic commonly observed in lines with strongly asymmetric configuration and underground cables [6], [7], [8].

The other model proposed in [6], called extended modal-domain (EMD) model, uses modal decomposition techniques assuming a real and constant transformation matrix to solve telegrapher's equations including the influence of external electromagnetic fields. This model is compatible with Marti's model [9], which is expected to perform accurately as long as the line geometry is not strongly asymmetric. If this assumption is violated, the associated eigenvectors present a stronger variation with frequency and, consequently, the assumption of a real and constant transformation matrix may no longer hold. In practice, however, it is often difficult to characterize the line configuration simply in terms of its asymmetry. In fact, it was demonstrated in [10] that Marti's model can be used to simulate transients with accuracy at least comparable to ULM for a wide range of transmission line configurations. However, the analysis was restricted to switching transients on high-voltage lines. No similar study has been presented so far dealing with voltages induced by nearby lightning strikes on distribution lines.

In [6] and [11] it was shown that the EMD model predicts lightning-induced voltage waveforms in excellent agreement with the EPD model and the finite-difference time-domain (FDTD) method. However, the investigated cases were restricted to a single-circuit compact distribution line [11] and a typical medium-voltage (MV)/low-voltage (LV) line configuration [6]. It is still unclear whether the EMD model could be used to calculate lightning-induced voltages on double-circuit and parallel distribution line configurations with sufficient accuracy. Verifying this point is important because the calculation of the external current sources required in the EMD model is more efficient than in its phase-domain counterpart, the EPD model. It is also of great interest to identify in which cases the EMD model would ultimately fail to provide accurate lightning-induced voltage estimates, thus requiring the use of the EPD model.

In this paper, the use of the EMD model is investigated for different MV distribution lines used in Brazil, with focus on double-circuit and parallel line configurations. The idea of investigating such cases is to push the EMD model to critical conditions in which the assumption of a real and constant transformation matrix could possibly fail. It is also investigated how sensitive the model is to different fitting techniques, especially by the restriction imposed by Marti's model available in the Alternative Transients Program (ATP) regarding the use of strictly real poles and residues. This is important to delimit the model's ability to calculate lightning-induced voltages under different conditions in practical cases.

This paper is organized as follows. Section II describes the modeling details. Section III presents the tested configurations. In section IV, the results are presented and discussed. Finally, the conclusions are presented in section V.