As renewable energy increasingly penetrates into power grid systems, new challenges arise for system operators to keep the systems reliable under uncertain circumstances, while ensuring high utilization of renewable energy. With the naturally intermittent renewable energy, such as wind energy, playing more important roles, system robustness becomes a must. In this paper, we propose a robust optimization approach to accommodate wind output uncertainty, with the objective of providing a robust unit commitment schedule for the thermal generators in the day-ahead market that minimizes the total cost under the worst wind power output scenario. Robust optimization models the randomness using an uncertainty set which includes the worst-case scenario, and protects this scenario under the minimal increment of costs. In our approach, the power system will be more reliable because the worst-case scenario has been considered. In addition, we introduce a variable to control the conservatism of our model, by which we can avoid over-protection. By considering pumped-storage units, the total cost is reduced significantly.

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In this paper, we study data-driven chance constrained stochastic programs, or more specifically, stochastic programs with distributionally robust chance constraints (DCCs) in a data-driven setting to provide robust solutions for the classical chance constrained stochastic program facing ambiguous probability distributions of random parameters. We consider a family of density-based confidence sets based on a general φ-divergence measure, and formulate DCC from the perspective of robust feasibility by allowing the ambiguous distribution to run adversely within its confidence set. We derive an equivalent reformulation for DCC and show that it is equivalent to a classical chance constraint with a perturbed risk level. We also show how to evaluate the perturbed risk level by using a bisection line search algorithm for general φ-divergence measures. In several special cases, our results can be strengthened such that we can derive closed-form expressions for the perturbed risk levels. In addition, we show that the conservatism of DCC vanishes as the size of historical data goes to infinity. Furthermore, we analyze the relationship between the conservatism of DCC An early version of this paper is available online at and the size of historical data, which can help indicate the value of data. Finally, we conduct extensive computational experiments to test the performance of the proposed DCC model and compare various φ-divergence measures based on a capacitated lotsizing problem with a quality-of-service requirement.

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