Model-based variable speed limit control on wireless charging lanes: Formulation and algorithm

This paper addresses the variable speed limit (VSL) control problem on wireless charging lanes (WCLs). We first introduce a predictive model to describe the evolution of both traffic flow and the state of charge of electric vehicles, considering the impact of VSL control. The model is formulated as a piecewise affine system through various linearization techniques. Subsequently, we propose a control model that accounts for both traffic and charging efficiencies. By employing a hybrid model predictive control approach, the control problem at each stage is cast as a mixed-integer linear programming (MILP) problem. To expedite the MILP problem, we propose an innovative learning-based algorithm, termed Learning from K-nearest Neighbors Mode Sequences (LKNMS). The algorithm identifies and eliminates predicted inactive system states (each represented by a binary variable) by leveraging historical solutions of the binary configuration. It thereby significantly reduces the size of the resulting MILP problem. We conduct a series of numerical examples on a 10.7 km WCL to test the proposed control model and algorithm. Our simulation results reveal that VSL control can significantly affect the charging efficiency of WCLs, particularly under light traffic conditions. Moreover, an inherent conflict between traffic efficiency and charging efficiency consistently arises on WCLs. The proposed algorithm significantly reduces the computational time of the MILP problem from 46 % of the 60s control cycle to 5∼12%, without compromising closed-loop performance, which implies strong potential for real-time implementation. We further test the proposed algorithm on a 26.75 km WCL to confirm its robust scalability to large-scale networks.