Two-stage distributionally robust optimization for port integrated energy system with berth allocation under uncertainties

The interactive impact between energy system and logistics system in port area is becoming increasingly prominent, and the operation of both systems can be greatly affected by random weather or unforeseen events. On this basis, this paper studies the optimization problem of port integrated energy system (PIES) coupled with berth allocation system (BAS) under dual uncertainty, which includes wind power output within PIES and ship arrival times within BAS. The problem is constructed as a two-stage distributionally robust optimization (DRO) model. In the first stage, a collaborative model between PIES and BAS is established under the uncertainties of forecast, in which the dissatisfaction of shipowners is introduced to represent the service level of port. The second stage is constructed as an adjustment minimization problem under the worst-case distribution within ambiguity set. The flexible resources in PIES and BAS are fully exploited to hedge against the uncertainties. Moreover, the proposed two-stage DRO model is transformed into a tractable mixed-integer linear programming framework using linear decision rule and strong dual theory. Simulation results evaluate the economic and environmental benefits of the proposed model while resisting the risk of uncertainties.