Unsupervised learning for efficiently distributing EVs charging loads and traffic flows in coupled power and transportation systems

With the escalating adoption of electric vehicles (EVs), the intricate interplay between power and traffic systems becomes increasingly pronounced. Understanding the distribution of charging loads and traffic flows are paramount for effective coordination. Traditionally, the distribution of EVs charging loads and traffic flows are obtained via solving the EVs traffic assignment problem with User Equilibrium (TAP-UE). Despite the general convexity of TAP-UE, the iterative nature of the prevailing solution process and the nonlinear objective function pose challenges, leading to prolonged solution times. This paper introduces a novel unsupervised learning-based framework aimed at efficiently distributing EVs charging loads and traffic flows without off- the-shelf solvers or a large dataset. Firstly, feasible paths are identified for each OD pair, eliminating the need for iterative procedures. Subsequently, the convexity-preserving reformulation of TAP-UE converts it into an unconstrained nonlinear optimization problem, leading to a properly designed loss function to guide neural networks in directly learning a legitimate OD demands-EVs loads-traffic flows mapping which satisfies the UE conditions. The incorporation of the Hessian matrix into the gradient update of network parameters, facilitated by the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, enhances the convergence speed of the unsupervised learning process. Case studies are conducted to demonstrate the efficacy of the proposed framework.