A multi-objective mixed integer linear programming approach for simultaneous optimization of cost and resilience of power distribution networks

In recent years, customers have experienced a significant increase in weather-related power outages. The power distribution network (PDN), a subset of the power system, in particular is more susceptible to extreme events. Therefore, ensuring the resilient and cost-effective operation of PDNs following extreme weather conditions poses a significant challenge for distribution network operators. This paper presents an approach for simultaneously optimizing the cost and load restoration for resilience enhancement of power distribution networks while determining the optimal positioning and generation levels of mobile emergency generators. The proposed method, in addition, employs a distribution network reconfiguration to improve the load restoration process, by optimally determining the status of switches. The multi-objective formulation involves the minimization of load shedding to increase the resilience of the system, while the other objective is formulated to minimize the cost of load restoration. A weighted sum method is employed to address the multi-objective mixed-integer linear programming (MILP) model. A set of non-dominated solutions determined using the proposed formulation provides opportunities to the distribution system operator in choosing a resilience improvement strategy according to the availability of the operational budget. The proposed model is implemented on 33-bus distribution system to validate the efficacy of the proposed model.