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• Comprehensive physics-based analytical model for HIF location. • Statistical behavior of estimates is analyzed to identify the faulted section. • One-ended data based frequency domain measurement model. This paper presents a physics-based analytical model for high impedance fault location in power distribution systems. The presented analytical solution is composed by two interdependent processes. First, fault distance is estimated through a Weighted Least Square approach applied to solve an overdetermined and nonlinear algebraic system of equations. Second, an analytical method based on the statistical behavior of the estimates obtained from the frequency domain system model solution is presented to address the multiple estimates problem, identifying the faulted section. The presented fault location physics-based analytical model considers the capacitive effect of distribution lines. Furthermore, voltages and currents measured from only one terminal are used. The formulation is evaluated using the IEEE 13-bus and a modified version of the IEEE 34-bus test feeders. Comparative analysis with state-of-the-art methods is presented. Average errors of 1.95% are obtained. Easy to implement analytical model, without hard to derive parameters, built on the weighted least squares state estimator, highlight potential aspects for real-life applications. [ABSTRACT FROM AUTHOR]