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We consider the operation of a power system with high renewable penetration and minimal network bottlenecks and provide a technique to determine the appropriate level of reserve to enforce. Within a daily scheduling framework, we model the production uncertainty of renewable units via scenarios and include security constraints per scenario to ensure an uneventful operation in case of failure of key thermal units. The rarely constraining network is modeled via areas with limited capacity at their interfaces. The considered decision-making framework results in a two-stage stochastic programming problem whose first stage decides on the commitment of thermal units and whose second stage reproduces, per scenario, the operation of the system with and without the failure of key thermal units. The optimal unit scheduling obtained from the proposed model implicitly identifies a generating reserve pattern that we compare with common rules used in industry for reserve identification, such as 20% or 30% of the demand. We use the Illinois 200-bus system to illustrate and computationally characterize the methodology proposed. • An economically efficient yet secure reserve determination procedure. • Renewable uncertainty is modeled via scenarios. • Security regarding unit failures is ensured via security constraints. • The resulting optimization model is tractable and does not need decomposition. • The reserve determined is superior to setting a percentage of the load as reserve. [ABSTRACT FROM AUTHOR]

• Propose a solution approach for the AC network-constrained unit commitment problem. • The proposed approach relies on convex (continuous and mixed-integer) programming. • An active set strategy is used to speed up the solution time of the proposed approach. • An AC feasible solution is recovered using a sequence of convex optimization problems. • Demonstrate the effectiveness of the proposed approach using the IEEE 24-bus test system and an Illinois 200-bus system. To address the AC network-constrained unit commitment problem, we propose an effective three-step solution approach. We first solve a DC (mixed-integer linear) approximation of the original problem to identify an initial solution and the set of transmission lines likely to be congested. Secondly, with the linear solution as a starting point, we solve a mixed-integer second-order conic relaxation of the original problem using an active set strategy regarding transmission constraints. Finally, using the solution of the relaxed problem as a starting point, we solve a set of increasingly accurate continuous convex optimization problems to ensure full AC feasibility. We show the effectiveness of the proposed approach using the IEEE 24-bus test system and an Illinois 200-bus system with 49 generators and 245 lines. [ABSTRACT FROM AUTHOR]