Comparing stochastic programming with posteriori approach for multi-objective optimization of distributed energy systems under uncertainty

Uncertainty complicates the optimization model of distributed energy systems, it is a challenge to address the fragility of optimal solutions, which calls for an effective but convenient approach to introduce uncertainties into multi-objective optimization. This study proposes and compares the priori and the posteriori modeling approaches for optimizing the design of distributed energy systems under uncertainty. The posteriori approach is developed as a Monte Carlo simulation combined with the deterministic programming model, while the priori approach is formulated as a two-stage stochastic programming model. Both approaches consider economic and environmental objectives and use the same set of uncertainty parameters based on a case study in Shanghai. The results show that, compared with the priori-approach model, the posteriori-approach model leads to an underestimation of the total annual cost, but their total annual carbon emission approximates. Besides, the Pareto frontier cliques from the posteriori approach demonstrate the distributions of system performance, whereas the priori approach can capture the uncertainties at the substantially higher computational cost. Finally, the tradeoff between model complexity and computational cost is discussed to generate more insights on the optimal design, i.e., configuration and dispatch, of distributed energy systems.