Collaborative scheduling of seaport integrated energy, logistics, and vessels: A bi-level nash-stackelberg-nash game approach

The application of multi-energy logistic equipment has facilitated the collaboration of seaport integrated energy systems (SIESs) and seaport logistics systems (SLSs). This paper proposes a bi-level Nash-Stackelberg-Nash (N-S-N) game framework for the collaborative scheduling of SIESs, SLSs, and multi-energy vessels. First, a multi-energy SIES model is proposed to realize the coordinated operation of electric, heating, cooling, natural gas, hydrogen, and water, along with the cascaded utilization of liquid natural gas cold energy. Then, a bi-level N-S-N game framework is established to represent the game relationship among the SIES, SLS, and multi-energy vessels, where both cooperative and noncooperative strategies of the SIES and SLS are considered. Finally, the Karush-Kuhn-Tucker condition is applied to reformulate the bi-level N-S-N game model into a tractable single-level model. In addition, the operation model of the individual SIES and SLS under the noncooperative strategy is solved using the Gauss-Seidel iterative algorithm. The numerical results demonstrate the improved energy efficiency of the multi-energy coordinated operation and the computational effectiveness of the Gauss-Seidel iterative algorithm. Moreover, the scheduling results obtained under cooperative and noncooperative operation strategies are analyzed to provide a practical reference for seaport operations.