A robust approach to integrated wireless charging infrastructure design and bus fleet size optimization

Due to the advantage of low emissions, electric buses are an appealing option for public bus systems. However, the driving range restriction and long charging time requirement of electric bus systems limit their development in practice. Wireless power transfer (WPT) is able to charge buses en route and makes electric bus systems more flexible. We consider a multiline transit system in which each bus line is associated with a given number of trips. We propose a new WPT location problem incorporating operational-level information, such as the number of trips for each line. The WPT location is restricted to bus stops that have a less negative impact on normal traffic and are good candidates for WPT installation. The problem is formulated as mixed integer programming (MIP). It simultaneously determines the WPT location, the length of the charging lane, the number and line assignment of buses and battery size. In addition, due to widespread uncertainty in energy consumption and charging, we propose a robust model, which can be reformulated into a tractable deterministic equivalent MIP model so that reliable bus operation can be obtained. Numerical experiments are conducted with two real bus systems. The solutions of the robust model indicate high robustness against uncertainty.