When addressing the problem of calculating the settings for directional overcurrent elements, the focus is usually the determination of the pickup, time dial and operating characteristic, in order to ensure proper selectivity with adjacent protection elements, thus limiting the problem related to the settings calculation of the direction determination characteristic to the application of typical settings and general guidelines, which cannot provide a reliable measure of the suitability of such settings. The present article describes in detail an alternative methodology for determining these settings, based on a characterization of the power system where the directional protection is to be applied, through the performance of a detailed short-circuit sensitivity analysis. From this, an optimization problem is formulated and solved to obtain the main settings shaping the direction determination characteristic, and then, a series of variables are used to measure the performance of the obtained settings, and even to improve it. The obtained results show the advantages of the application of the proposed methodology over the traditional methodology, based on typical settings and general guidelines, pointing out the risks of using the later.

Protection of mutually coupled transmission lines poses special challenges to protection engineers, since the general principles outlining the expected performance of the protection elements are based on simplified versions of the issues affecting them.  Distance protection elements are among the most commonly accepted methods for protecting mutually coupled transmission lines, however, the calculation of settings and the validation of their performance is a complex task, involving lots of simulations and analysis of results to come up with an acceptable solution.  Though various methods have been proposed to deal with the problem of calculating the optimal settings of distance protection elements, there is still room for improvement, since these methods have been formulated for the general case considering simple transmission lines.  In this paper, a variation of one of these methods is introduced to enhance the computing times and reliability of the solutions for the specific application of quadrilateral distance protection to mutually coupled transmission lines, through the characterization of the expected performance of the operating characteristic, and the formulation of the optimization problem and the solution method.  The obtained results show the improvements in computing times and quality of the solution provided by the proposed algorithm.