Applying Robust Design Optimization to Large Systems

While Robust Optimization has been utilized for a variety of design problems, application of Robust Design to the control of large-scale systems presents unique challenges to assure rapid convergence of the solution. Specifically, the need to account for uncertainty in the optimization loop can lead to a prohibitively expensive optimization using existing methods when using robust optimization for control. In this work, a robust optimization framework suitable for operational control of large scale systems is presented. To enable this framework, robust optimization uses a utility function for the objective, dimension reduction in the uncertainty space, and a new algorithm for evaluating probabilistic constraints. The proposed solution accepts the basis in utility theory, where the goal is to maximize expected utility. This allows analytic gradient and Hessian calculations to be derived to reduce the number of iterations required. Dimension reduction reduces uncertain functions to low dimensional parametric uncertainty while the new algorithm for evaluating probabilistic constraints is specifically formulated to reuse information previously generated to estimate the robust objective. These processes reduce the computational expense to enable robust optimization to be used for operational control of a large-scale system. The framework is applied to a multiple-dam hydropower revenue optimization problem, then the solution is compared with the solution given by a non-probabilistic safety factor approach. The solution given by the framework is shown to dominate the other solution by improving upon the expected objective as well as the joint failure probability.