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Contemporary methods of providing specially shaped relay characteristics, i.e. other than the familiar circular and straight-line types, are assessed, particularly from the point of view of relay performance and complexity. A new method of shaping is established in which the phase-angle criterion of the block-average type of comparator is a function of the primary system quantities and is therefore continuously variable between well defined limits around the characteristic boundary. This method of shaping affords precise design, which is confirmed by comparisons of experimental and theoretical results. The applications described are limited to providing a characteristic with optimum fault coverage but which has increased immunity from extreme balanced system conditions such as heavy loads and power swings. Further applications, to provide characteristics that will accommodate high fault resistances, will be considered in a later paper.