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Currently, an issue of relay protection (RP) settings determination that ensures its correct operation in electric power systems (EPSs) has not been resolved completely. The main reason for this is the lack of methods and tools for adequate consideration of transients during a fault existence for RP settings calculation. In this study, a novel approach for RP settings determination is presented. Its main feature is the application of detailed mathematical models reproducing simultaneously processes in the entire set of elements in the RP scheme, including instrumental transformers, and in large-scale EPS mathematical model as a whole. This key feature can be achieved via the hybrid power system simulator -- hybrid real-time power system simulator -- implementing a methodically accurate analogue--digital solution of the EPS mathematical model. The numerical transformer differential protection (NTDP) based on this approach was set up via the standard dual-slope tripping characteristic. Also, a novel approach to the formation of the tripping characteristic is proposed. The key feature of this approach is applying a flexible curve that enveloping all fault characteristics Idiff = f(Irest) of those modes in which the NTDP should not trip. [ABSTRACT FROM AUTHOR]