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In this study, a transient stability constrained‐optimal power flow (TSC‐OPF) model is proposed and applied to a real case in the currently interconnected Balearic Islands‐Iberian Peninsula system. The TSC‐OPF retains the dynamics of all generators in the islands with fourth degree transient synchronous generator models and includes a representation of a high‐voltage direct current (HVDC) link on the inverter side. The proposed large‐scale non‐linear optimisation problem, programmed in GAMS and solved using the CONOPT tool, is used to assess the economic impact of the HVDC on the Balearic Islands generation cost under different circumstances, using TSC‐OPF and traditional OPF on the dispatch. Different recovery patterns of the HVDC link after a severe fault in the transmission grid are evaluated from the viewpoint of the cost and stability of power generation. [ABSTRACT FROM AUTHOR]