Combined Electrical and Heat Load Restoration Based on Bi-Objective Distributionally Robust Optimization

As extreme events such as natural disasters and cyberattacks become more frequent, the resilience of energy systems has become increasingly important. However, due to the growing interdependence between natural gas, district heating, and power systems, the resilience of energy systems is becoming more and more complicated. Typical challenges include conflicts in the restoration of heterogeneous energy systems due to infrastructure limitations and multiple uncertainties, such as renewable energy and outdoor temperature, during the system restoration. To address these challenges, we propose a novel combined electrical and heat load restoration (CEHLR) model for the heat and electricity-integrated energy systems. The CEHLR model is formulated as a bi-objective distributionally robust chance-constrained programming, which can coordinate the electrical and heat load recovery process and has strong robustness to uncertainties from renewable energy and outdoor temperature. Then, we convert the CEHLR model into an equivalent bi-objective mixed-integer second-order conic programming problem. Finally, we use a tailored normalized normal constraint method to obtain an evenly distributed Pareto frontier to facilitate the decision selection. Case studies demonstrate the effectiveness of the proposed method, which also reveals the significant impact of the coupling between electricity and heat on the load recovery process.