A novel analysis of offset mho characteristic of memory-polarized and cross-polarized distance functions

This article shows a novel and detailed description of the offset mho characteristic of memory-polarized and cross-polarized distance functions. The exact expressions for offset impedances are found, analyzing by symmetrical components a power system taken as an example. The power system model is general, and it includes the effect of additional interconnections between both line ends. Single line-to-ground faults, line-to-line faults, and double-line-to-ground faults are rigorously analyzed. Memory-polarized and cross-polarized distance functions have variable characteristics in the R-X plane (i.e., offset values change, depending on power system conditions), and these variations are shown for the analyzed example. Under some circumstances, the directionality of these distance functions is not evident, and the possible use of an additional directionality restraint is analyzed.