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This study proposes a new concept of transmission line differential protection based on an alternative alpha plane of incremental complex power, where the restraint characteristic is simply defined as its left‐half‐plane, so that no settings are required to define it. As the incremental complex power is evaluated per phase, the proposed algorithm is inherently phase segregated, not requiring additional faulted phase selection logics. A simple harmonic restraint strategy along with an external fault detection logic provides security for external faults with current transformer saturation. Aiming to evaluate the performance of the proposed algorithm, a wide variety of fault scenarios are simulated for a 500 kV transmission line 200 km long using the Alternative Transients Program. The obtained results reveal the proposed algorithm provides a fast and reliable line protection, being robust against variations in fault parameters, sources strength and loading conditions, as well as power swing situations and line energisation manoeuvres. Accordingly, one can suppose the proposed algorithm might be successfully used in numerical transmission line relaying. [ABSTRACT FROM AUTHOR]