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We propose an approach to solving the AC network-constrained unit commitment problem (AC-NCUC) of large-scale power systems. This approach relies on solving convex (continuous and mixed-integer) optimization problems. First, we formulate a second-order conic relaxation of the original optimization problem, which renders a mixed-integer second-order conic optimization problem. To solve this problem, we use Benders’ decomposition, which decomposes it into a master problem, which is mixed-integer linear, and a subproblem, which is continuous and second-order conic. To improve the convergence of the Benders’ algorithm, we add several linear feasibility constraints to the master problem. Since the second-order relaxation of the original problem cannot guarantee AC feasibility of the solution found, we ensure such feasibility by solving a sequence of continuous convex optimization problems. We numerically validate the proposed approach using a Texas 2000-bus system. [ABSTRACT FROM AUTHOR]

Capacity expansion planning (CEP) of power systems determines the optimal future generation mix and/or transmission lines. Due to the increasing penetration of renewables, CEP has to capture the hourly variations of renewable generator outputs and load demand. Since CEP problems typically involve planning horizons of several years, solving the fullspace models where the operating decisions corresponding to all the days is intractable. Therefore, some "representative days" are selected as a surrogate to the fullspace model. We present an input-based and a cost-based approach in combination with the k -means and the k -medoids clustering algorithms for representative day selection. The mathematical properties of the proposed algorithms are analyzed, including an approach to calculate the "optimality gap" of the investment decisions obtained from the representative day model to the fullspace model, and the relationship between the clustering error and the optimality gap. To capture the extreme operating conditions, two novel approaches, i.e., a "load shedding cost" approach and a "highest cost" approach, are proposed to identify the "extreme days". We conclude with a case study based on the Electric Reliability Council of Texas (ERCOT) region, which compares the different approaches and the effects of adding the extreme days. • Representative days are used for capacity expansion planning. • We present an input-based and a cost-based methods for representative day selection. • The theoretical properties of both methods, including the optimality gap, are analyzed. • Computational studies are performed for the Texas region. [ABSTRACT FROM AUTHOR]