Finding better alternatives: Shadow prices of near-optimal solutions in energy system optimization modeling

Energy System Optimization Models are applied to inform decision making processes and therefore must account for the uncertainty as it exists in the real world. In the recent decade, Modeling to Generate Alternatives gained popularity for considering structural uncertainty in Energy System Optimization Models. Modeling to Generate Alternatives finds numerous near-optimal alternatives, which could give the impression that all alternatives are comparably good. However, if one could compare near-optimal shadow prices of energy demand, certain alternatives would be superior to other solutions. Nevertheless, shadow prices of near-optimal solutions reflect the effort of being different and no approach to calculate expedient shadow prices of near-optimal solutions (comparable to the optimal one) has been presented. A simple approach is suggested and discussed with its implications, using an example scenario. The obtained shadow prices further differentiate the quality of solutions in the near-optimal solution space. Deeper analysis reveals regional or temporal bottlenecks of solutions and can help identify better search directions for alternative solutions. To some extent, the shadow prices highlight effects of parametric uncertainty, even though the proposed method cannot counteract this uncertainty.