A ROBUST SIMULATION-OPTIMIZATION APPROACH FOR DESIGNING HYBRID RENEWABLE ENERGY SYSTEMS

Abstract

Stand-alone hybrid renewable energy systems (HRES) provide a viable alternative to satisfy the energy demand of remote and isolated communities. We consider a PV/Wind/Diesel/Battery HRES and propose a design approach that minimizes the total setup and operations cost and maximizes the supply reliability. A finite number of supply scenarios, extracted from a limited sample of data points through clustering, are first used under the assumption that their probabilities are known with certainty to solve the nominal problem. Next, the robust problem is considered by constructing an ambiguity set, based on the Variation Distance phi-divergence, around the nominal probability distribution and minimizing the expected cost, where the expectation is taken with respect to the worst distribution in the ambiguity set. Since the cost and the reliability functions cannot be evaluated explicitly, they are estimated through simulation based on certain operational rules and using solar and wind supply scenarios drawn at random according to the considered probability distribution (nominal or worst-case). To solve the problem, two novel robust simulation-optimization approaches that estimate a surrogate objective function through a classical Response Surface Methodology (RSM) and a Global Response Surface Technique (GRST) are proposed. The classical RSM approach uses a three-level (R-III) fractional factorial design to estimate the steepest descent direction and perform a gradient search, before using a Central Composite Design (CCD) to estimate a local quadratic approximation and find the optimum solution when the gradient becomes sufficiently small. The GRST, on the other hand, approximates the response function over the entire search space using a convex quadratic function and finds the optimizer of the surrogate function, before restricting the search space around it to obtain a better quadratic approximation and repeat the process. The results obtained from implementing the proposed approaches on a hypothetical case study confirm their applicability and show that the robust solutions outperform those obtained from classical risk-neutral methods when applied with external data samples.