Hybrid Stochastic–Information Gap Decision Theory Method for Robust Operation of Water–Energy Nexus Considering Leakage

The water–energy nexus (WEN) is of great significance due to the strong interdependence between the energy and water sectors. Nevertheless, water leakage in water distribution networks (WDNs), which is often ignored in existing WEN operation models, causes notable water and energy losses. In this research, a cooperative operation model for WEN considering WDN water leakage is put forward. A hybrid stochastic–information gap decision theory (IGDT) method was tailored in this study to properly manage the probabilistic uncertainties associated with renewable generation, electrical and water demand in the WEN, and water leakage with limited information to enhance the robustness of the operation strategies of the WEN under complex operational conditions. The proposed model and method were validated on a modified IEEE 33-bus system integrated with a 15-node commercial WDN. The co-optimization model reduced the operational cost by 23.01% compared to the independent operation model. When considering water leakage, the joint optimization resolved the water supply shortage issue caused by ignoring leakage and reduced the water purchase volume by 94.44 cubic meters through coordinated optimization. These quantitative results strongly demonstrate the effectiveness of the proposed framework.