Integrated equilibrium model for electrified logistics and power systems

Rui Yao, Xuhang Liu, Anna Scaglione, Shlomo Bekhor, Kenan Zhang

Abstract: This paper proposes an integrated equilibrium model to characterize the complex interactions between electrified logistics systems and electric power delivery systems. The model consists of two major players: an electrified logistics operator (ELO) and a power system operator (PSO). The ELO aims to maximize its profit by strategically scheduling and routing its electric delivery vehicles (e-trucks) for deliveries and charging, in response to the locational marginal price (LMP) set by the PSO. The routing, delivery, and charging behaviors of e-trucks are modeled by a perturbed utility Markov decision process (PU-MDP) while their collective operations are optimized to achieve the ELO's objective by designing rewards in the PU-MDP. On the other hand, PSO optimizes the energy price by considering both the spatiotemporal e-truck charging demand and the base electricity load. The equilibrium of the integrated system is formulated as a fixed point, proved to exist under mild assumptions, and solved for a case study on the Hawaii network via Anderson's fixed-point acceleration algorithm. Along with these numerical results, this paper provides both theoretical insights and practical guidelines to achieve sustainable and efficient operations in modern electrified logistics and power systems.