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Distributionally robust optimization is a popular modeling paradigm in which the underlying distribution of the random parameters in a stochastic optimization model is unknown. Therefore, hedging against a range of distributions, properly characterized in an ambiguity set, is of interest. We study two-stage stochastic programs with linear recourse in the context of distributional ambiguity, and formulate several distributionally robust models that vary in how the ambiguity set is built. We focus on the Wasserstein distance under a p-norm, and an extension, an optimal quadratic transport distance, as mechanisms to construct the set of probability distributions, allowing the support of the random variables to be a continuous space. We study both unbounded and bounded support sets, and provide guidance regarding which models are meaningful in the sense of yielding robust first-stage decisions. We develop cutting-plane algorithms to solve two classes of problems, and test them on a supply-allocation problem. Our numerical experiments provide further evidence as to what type of problems benefit the most from a distributionally robust solution. [ABSTRACT FROM AUTHOR]

This paper introduces a two-stage stochastic program for transmission planning. The model has two dependent random variables, namely, total electric load and available wind power. Given univariate marginal distributions for these two random variables and their correlation coefficient, the joint distribution is modeled using a Gaussian copula. The optimal power flow (OPF) problem is solved based on the linearized direct current (DC) power flow. The Electric Reliability Council of Texas (ERCOT) network model and its load and wind data are used for a test case. A 95% confidence interval is formed on the optimality gap of candidate solutions obtained using a sample average approximation with 200 and 300 samples from the joint distribution of load and wind. [ABSTRACT FROM PUBLISHER]