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This paper presents injection‐shift‐factor‐based linear modelling for various types of series flexible ac transmission system (FACTS) devices within the DC power flow framework. The presented models allow FACTS devices to be properly integrated in current operation and planning software tools, which is key to harnessing the power flow capabilities provided by FACTS technology. Although recent literature has attempted to develop linear models for FACTS devices, the existing models do not accurately reflect the actual operating range for many FACTS devices. Compared to the existing models, the modelling approach presented here reflects the principle of operation of each type of series FACTS device in adjusting transmission line reactance. Through mathematical derivation, linear constraints for FACTS operation are formulated, which are used to formulate power system operation models. The formulated problems are then analysed through simulation studies on various test systems. The results highlight the significant computational efficiency improvements provided by linear FACTS modelling in DC‐based operation models. [ABSTRACT FROM AUTHOR]