Abstract-This paper proposes an efficient solution approach based on Benders' decomposition to solve a network-constrained ac unit commitment problem under uncertainty. The wind power production is the only source of uncertainty considered in this paper, which is modeled through a suitable set of scenarios. The proposed model is formulated as a two-stage stochastic programming problem, whose first-stage refers to the day-ahead market, and whose second-stage represents real-time operation. The proposed Benders' approach allows decomposing the original problem, which is mixed-integer nonlinear and generally intractable, into a mixed-integer linear master problem and a set of nonlinear, but continuous subproblems, one per scenario. In addition, to temporally decompose the proposed ac unit commitment problem, a heuristic technique is used to relax the inter-temporal ramping constraints of the generating units. Numerical results from a case study based on the IEEE one-area reliability test system (RTS) demonstrate the usefulness of the proposed approach.

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Abstract-Trajectory sensitivity analysis (TSA) is used as analysis tool for suitable placement of shunt compensators in the power system. The goal is to maximize the benefit of these devices in order to enhance the transient stability of the system. For this purpose, the trajectory sensitivities of the rotor angles of generators with respect to the reactive power injected into different nodes of the system are calculated in the presence of most probable severe faults. Based on the obtained trajectory sensitivities, a method is proposed to determine how effective the shunt compensation in each node is for improving the transient stability. This method is applied to the IEEE 3-machine 9-bus to find the priorities of system's nodes for installation of shunt compensators. Simulation with industrial software shows the validity and efficiency of the proposed method.