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Multi-Contingency Transient Stability Constrained Optimal Power Flow (MC-TSCOPF) models optimize the economic dispatch of power systems while ensuring their stability after a series of reference incidents. This paper proposes a MC-TSCOPF model that represents the power balance at each node of the system and at each sample time. The proposed model includes non-linear loads, synchronous generators, a windfarm, and a Flywheel Energy Storage system (FESS). The model is written on GAMS and solved using a standard Interior Point algorithm. This study focuses on the Fuerteventura-Lanzarote insular grid in Spain, where stability problems and load shedding cause high additional costs due to the low inertia of the system. A FESS has been recently installed in the system to improve its stability, taking advantage of its high-power capacity and rapid response. The proposed TSCOPF model has been applied to optimize the operation of the FESS to support stability in the event of a contingency. The results of the study show that 1) a proper model of non-linear loads is essential in TSCOPF studies; 2) the proposed MC-TSCOPF provides a tool for minimizing the generation costs while ensuring transient and frequency stability; and 3) it is possible to further reduce the generation costs by using the proposed model to calculate an optimal dynamic response of the FESS.
Energy storage; Insular grid; Nonlinear programming; Optimal power flow; Power system transient stability