Many predictive control problems can be solved at lower cost if the practitioner is able to make use of a high-dimensional forecast of exogenous uncertain quantities. For example, power system operators must accommodate significant short-term uncertainty in renewable energy infeeds. These are predicted using sophisticated numerical weather models, which produce an ensemble of scenarios for the evolution of atmospheric conditions. We describe a means of incorporating such forecasts into a multistage optimization framework able to make use of spatial and temporal correlation information. We derive an optimal procedure for reducing the size of the look-ahead problem by generating a low-dimensional representation of the uncertainty, while still retaining as much information as possible from the raw forecast data. We then demonstrate application of this technique to a model of the Great Britain grid in 2030, driven by the raw output of a real-world high-dimensional weather forecast from the U.K. Met Office. We also discuss applications of the approach beyond power systems.
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