Multistage Distributionally Robust Design of a Renewable Source Processing Network under Uncertainty

Integration of renewable sources into chemical and power production is one of the crucial pathways toward an effective, affordable, and deep decarbonization of the world economy in line with carbon neutrality and sustainable development. The present work concentrates on the robust design of the process network for multiproduct and power production with renewable sources under uncertainty. We propose a multistage distributionally robust optimization model to hedge against uncertain chemical product demand and feedstock availability. 1-norm Wasserstein metric is employed to construct the ambiguity set with limited uncertain data. We derive an equivalent robust counterpart of the multistage distributionally robust optimization based on the reformulations of the worst-case expectation term of each stage by taking advantage of a complete recourse, which remedies the computational issues. Computational results, including one base case and four correlated cases with different capacities, demonstrate that the optimal solutions from the proposed multistage distributionally robust optimization with the Wasserstein ambiguity set achieve better out-of-sample performance than the conventional multistage stochastic programming. Obviously, this is because distributionally robust optimization incorporates the worst-case probability distribution, while the multistage stochastic programming only considers empirical distribution.