A New Single-Logarithmic Approximation of Carson's Ground-Return Impedances-Part 1

초록

Distributed energy resources with unbalanced phases increase the power imbalance in a grid, and compensating for the imbalance requires accurate knowledge of the impedance of the transmission and distribution lines. To achieve such compensation, many studies have evaluated the series impedance of the lines. The previous studies can be classified into three categories: (a) studies that solved Carson's original equations (COEs), (b) those that approximated these equations by ignoring high-order terms, and (c) those that provided a closed-form solution for the equations. Solving the COEs requires the expansion of the improper integrals and infinite series. Therefore, the last approach is preferable for easier calculations and a small error. Thus, the objective of this study is to present a more accurate and robust closed-form solution. Toward this end, this study improves the single-logarithmic-approximation method by adding a fourth compensation term. That is, this study proposes the correction term (2x/(x + root 1 + x(2)) approximate to 1 - e(-2x) - (x(3)e(-2x))/3 + (x(5)e(-5x))/5). This study substitutes the correction term to the original derivatives and finds their correct integrations to improve a single-logarithmic-approximation solution. The proposed solution was verified through case studies, and it showed fewer errors than the previous solutions. Additionally, the proposed solution can be also used to estimate the expected value of the self- and mutual impedance of overhead lines via stochastic simulations (e.g., Monte Carlo simulations), which will be presented in the second paper of this study.

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