Two-stage robust unit commitment (RUC) models have been widely used for day-ahead energy and reserve scheduling under high renewable integration. The current state of the art relies on budget-constrained polyhedral uncertainty sets to control the conservativeness of the solutions. The associated lack of interpretability and parameter specification procedures, as well as the high computational burden exhibited by available exact solution techniques call for new approaches. In this work, we use an alternative scenario-based framework whereby uncertain renewable generation is characterized by a polyhedral uncertainty set relying on the direct specification of its vertexes. Moreover, we present a simple, yet efficient, adaptive data-driven procedure to dynamically update the uncertainty set vertexes with observed daily renewable-output profiles. Within this setting, the proposed data-driven RUC ensures protection against the convex hull of realistic scenarios empirically capturing the complex and timevarying intra-day spatial and temporal interdependences among renewable units. The resulting counterpart features advantageous properties from a computational perspective and can be effectively solved by the column-and-constraint generation algorithm until -global optimality. Out-of-sample experiments reveal that the proposed approach is capable of attaining efficient solutions in terms of cost and robustness while keeping the model tractable and scalable.Index Terms-Adaptive data-driven approach, energy and reserve scheduling, renewable integration, robust optimization, scenario-based uncertainty set, unit commitment.

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The security-constrained optimal power flow (SCOPF) is fundamental in power systems and connects the automatic primary response (APR) of synchronized generators with the short-term schedule. Every day, the SCOPF problem is repeatedly solved for various inputs to determine robust schedules given a set of contingencies. Unfortunately, the modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs, which are hard to solve. To address this challenge, leveraging the wealth of available historical data, this paper proposes a novel approach that combines deep learning and robust optimization techniques. Unlike recent machine-learning applications where the aim is to mitigate the computational burden of exact solvers, the proposed method predicts directly the SCOPF implementable solution. Feasibility is enforced in two steps. First, during training, a Lagrangian dual method penalizes violations of physical and operations constraints, which are iteratively added as necessary to the machine-learning model by a Column-and-Constraint-Generation Algorithm (CCGA). Second, another different CCGA restores feasibility by finding the closest feasible solution to the prediction. Experiments on large test cases show that the method results in significant time reduction for obtaining feasible solutions with an optimality gap below 0.1%.

We present a distributionally robust optimization (DRO) approach for the transmission expansion planning problem, considering both long-and short-term uncertainties on the system demand and renewable generation. On the longterm level, as it is customary in industry applications, the deep uncertainties arising from social and economic transformations, political and environmental issues, and technology disruptions are addressed by long-term scenarios devised by experts. The system planner is then allowed to consider exogenous long-term scenarios containing partial information about the random parameters, namely, the average and the support set. For each constructed long-term scenario, a conditional ambiguity set is used to model the incomplete knowledge about the probability distribution of the uncertain parameters in the short-term. Consequently, the mathematical problem is formulated as a DRO model with multiple conditional ambiguity sets. The resulting infinite-dimensional problem is recast as an exact, although very large, finite-deterministic mixedinteger linear programming problem. To circumvent scalability issues, we propose a new enhanced-column-and-constraintgeneration (ECCG) decomposition approach with an additional Dantzig-Wolfe procedure. In comparison to existing methods, ECCG leads to a better representation of the recourse function and, consequently, tighter bounds. Numerical experiments based on the benchmark IEEE 118-bus system are reported to corroborate the effectiveness of the method.

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