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This paper presents a relaying technique for detection and categorization of various types of faults such as intermittent faults (IFs), bus faults (BFs), and multi-position faults (MPFs) in transmission lines with TCSC-compensation including faults under variation in the degree of series compensation. The SMMBG (simplified mathematical morphological beucher gradient) is utilized for the removal of characteristics from the fault currents to detect and categorize various fault types. The three-phase fault currents are measured at B-1 of the line to extort the beucher gradients of SMMBG from the three-phase fault currents and zero-sequence component of fault current after fault inception followed by the modeling and simulation of TCSC-compensated transmission line (TCTL) in MATLAB software. The performance of presented relaying technique is evaluated for a TCTL connecting together two power plants of 400-kV and also, the technique is tested under unexpected load switching events (SEs) and various fault situations. The response of the SMMBG-based technique is found perfect and rapid independent of type of fault, resistance of fault, position of fault, degree of series compensation, and time at which the fault is incepted.