Parametric Cost Function Approximations for Robust Energy Systems Planning

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The transition to a grid where an increasing portion of our energy comes from wind and solar energy is requiring that the grid operators develop a planning process that can handle a much higher level of uncertainty than is encountered today. Current tools have been criticized as ad-hoc procedures that consist of optimizing around a deterministic forecast, leaving the grid vulnerable to unexpected variations. Proposed "stochastic models" are much harder to solve, and grid operators still struggle to solve their existing deterministic models. Existing industry practice, while ad-hoc, actually represents a simple example of a powerful class of policies called "parametric cost function approximations." that has received virtually no attention from the academic literature. This research builds on the core strategy in use today, but blends the capabilities of existing commercial optimization solvers for deterministic models with the power of machine learning algorithms. The work will formalize existing industry practice, providing an implementable path to handling uncertainty which will provide a way for grid operators to naturally handle the steady increase in energy from wind and solar.The research proposes an algorithmic strategy that represents a fundamental departure from the field of stochastic programming, which handles uncertainty through the solution of stochastic look-ahead policies where the future is represented using a set of sampled realizations (scenarios). This research introduces a new class of policies called parametric cost function approximations. These are parametrically modified deterministic optimization problems which are optimized to minimize cost and risk, just as any machine learning model is optimized to fit data. This strategy blends the power of high-dimensional statistical learning with math programming and stochastic gradient methods, which form the basis of a feedback learning algorithm for identifying the best objective function to achieve the objectives of the ISO. Both offline and online versions of the algorithm will be developed, so policies can be tuned in a simulator (offline) but then continually adapted in production (online).