Two-Stage Distributionally Robust Optimization for Energy Hub Systems

Energy hub system (EHS) incorporating multiple energy carriers, storage, and renewables can efficiently coordinate various energy resources to optimally satisfy energy demand. However, the intermittency of renewable generation poses great challenges on optimal EHS operation. This article proposes an innovative distributionally robust optimization model to operate EHS with an energy storage system (ESS), considering the multimodal forecast errors of photovoltaic (PV) power. Both battery and heat storage are utilized to smooth PV output fluctuation and improve the energy efficiency of EHS. This article proposes a novel multimodal ambiguity set to capture the stochastic characteristics of PV multimodality. A two-stage scheme is adopted, where 1) the first stage optimizes EHS operation cost, and 2) the second stage implements real-time dispatch after the realization of PV output uncertainty. The aim is to overcome the conservatism of multimodal distribution uncertainties modeled by typical ambiguity sets and reduce the operation cost of EHS. The presented model is reformulated as a tractable semidefinite programming problem and solved by a constraint generation algorithm. Its performance is extensively compared with widely used normal and unimodal ambiguity sets. The results from this article justify the effectiveness and performance of the proposed method compared to conventional models, which can help EHS operators to economically consume energy and use ESS wisely through the optimal coordination of multienergy carriers.