Robust metamodel-based simulation-optimization approaches for designing hybrid renewable energy systems

We propose two robust metamodel-based approaches for designing stand-alone hybrid renewable energy systems that combine conventional and renewable energy generators with battery storage. Since the cost and reliability functions of the stochastic system do not have closed-form expressions, they can only be estimated via simulation. In the response surface methodology, the simulation input/output data is used first to locally fit first-degree surrogate functions for each supply scenario to perform a stochastic gradient descent, before a second-degree function is fitted and optimized when the gradient becomes small. In contrast, the global response surface technique globally fits a convex quadratic surrogate function on the simulation input/output data, then uses its minimizer to iteratively refine the search space. To account for estimation errors, a distributional ambiguity set based on a linear ϕ-divergence function is constructed around the nominal probability distribution of supply scenarios, and the expected reliability-adjusted cost of the system is computed using the worst-case distribution in this set. The validity of the proposed approaches and the value of considering distributional ambiguity are demonstrated through a realistic case study of a remote community in Northern Ontario.