Publications

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Stochastic versions of the unit commitment problem have been advocated for addressing the uncertainty presented by high levels of wind power penetration. However, little work has been done to study trade-offs between computational complexity and the quality of solutions obtained as the number of probabilistic scenarios is varied. Here, we describe extensive experiments using real publicly available wind power data from the Bonneville Power Administration. Solution quality is measured by re-enacting day-ahead reliability unit commitment (which selects the thermal units that will be used each hour of the next day) and real-time economic dispatch (which determines generation levels) for an enhanced WECC-240 test system in the context of a production cost model simulator; outputs from the simulation, including cost, reliability, and computational performance metrics, are then analyzed. Unsurprisingly, we find that both solution quality and computational difficulty increase with the number of probabilistic scenarios considered. However, we find unexpected transitions in computational difficulty at a specific threshold in the number of scenarios, and report on key trends in solution performance characteristics. Our findings are novel in that we examine these tradeoffs using real-world wind power data in the context of an out-of-sample production cost model simulation, and are relevant for both practitioners interested in deploying and researchers interested in developing scalable solvers for stochastic unit commitment.

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We describe experiments concerning enhancing a simple, yet effective method to compute high-accuracy prediction intervals (PIs) for day-ahead wide area wind power forecasts. The resulting PIs are useful for operators and traders, to improve reliability, anticipate threats, and increase situational awareness. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94-AL85000. This work was funded by the Bonneville Power Administration (BPA).

Optimizing thermal generation commitments and dispatch in the presence of high penetrations of renewable resources such as solar energy requires a characterization of their stochastic properties. In this paper, we describe novel methods designed to create day-ahead, wide-area probabilistic solar power scenarios based only on historical forecasts and associated observations of solar power production. Each scenario represents a possible trajectory for solar power in next-day operations with an associated probability computed by algorithms that use historical forecast errors. Scenarios are created by segmentation of historic data, fitting non-parametric error distributions using epi-splines, and then computing specific quantiles from these distributions. Additionally, we address the challenge of establishing an upper bound on solar power output. Our specific application driver is for use in stochastic variants of core power systems operations optimization problems, e.g., unit commitment and economic dispatch. These problems require as input a range of possible future realizations of renewables production. However, the utility of such probabilistic scenarios extends to other contexts, e.g., operator and trader situational awareness. We compare the performance of our approach to a recently proposed method based on quantile regression, and demonstrate that our method performs comparably to this approach in terms of two widely used methods for assessing the quality of probabilistic scenarios: the Energy score and the Variogram score.

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Progressive hedging, though an effective heuristic for solving stochastic mixed integer programs (SMIPs), is not guaranteed to converge in this case. Here, we describe BBPH, a branch and bound algorithm that uses PH at each node in the search tree such that, given sufficient time, it will always converge to a globally optimal solution. In addition to providing a theoretically convergent “wrapper” for PH applied to SMIPs, computational results demonstrate that for some difficult problem instances branch and bound can find improved solutions after exploring only a few nodes.

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