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Phase portraits are a powerful mathematical model for describing oriented textures. An isotangent-based approach in a phase portrait is introduced to discriminate between internal and external faults. The scheme described is new and is a different approach to the problem of relaying ground faults on transmission lines. The geometrical theory of differential equations is used to drive a symbol set on the basis of the visual appearance of phase portraits. The dasiaphase portraitdasia of the instantaneous rate of change of current against voltage gives valuable information on the transient and stability characteristics of system configuration with high fault resistance and shunt susceptance of the transmission lines. Hundred percent of the protected zone is successfully discriminated rather than the external zone. An additional parameter that is considered, which is sometimes neglected in protection studies, is the shunt susceptance of the transmission lines.