Braess' Paradoxes in Coupled Power and Transportation Systems

Transportation electrification introduces strong coupling between the power and transportation systems. In this paper, we generalize the classical notion of Braess' paradox to coupled power and transportation systems, and examine how the cross-system coupling induces new types of Braess' paradoxes. To this end, we model the power and transportation networks as graphs, coupled with charging points connecting to nodes in both graphs. The power system operation is characterized by the economic dispatch optimization, while the transportation system user equilibrium models travelers' route and charging choices. By analyzing simple coupled systems, we demonstrate that capacity expansion in either transportation or power system can deteriorate the performance of both systems, and uncover the fundamental mechanisms for such new Braess' paradoxes to occur. We also provide necessary and sufficient conditions of the occurrences of Braess' paradoxes for general coupled systems, leading to managerial insights for infrastructure planners. For general networks, through characterizing the generalized user equilibrium of the coupled systems, we develop efficient algorithms to detect Braess' paradoxes and novel charging pricing policies to mitigate them.