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This paper presents a novel method to optimize the settings of the resistive and reactive reaches of the zones of the distance relays. The method considers the probabilistic behavior of the variables that affect the apparent impedance seen by relays: prefault load flow, fault type, faulted line, distance up to the fault, fault resistance, and measurement errors. The optimization has been conceptually formulated as a multiobjective problem, with two objective functions: 1) minimize the probability of loss of sensitivity and 2) minimize the probability of loss of selectivity. To solve this problem, a preference function is defined, which is equal to the weighted sum of the two objective functions. A factor of weight represents the relative importance of selectivity regarding the sensitivity, and it is selected for each zone. This method was applied to a system with 7 busbars (3 of them with generation), where there are 18 distance relays with quadrilateral characteristic, and with an independent setting of the reactive and resistive reaches for the phase distance function and the ground distance function. The results obtained are compared with the results of other methods of adjustment.

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