Infrastructure Planning for Inductive Charging in Electrified Shuttle Systems

TL;DR

This paper tackles infrastructure planning for mixed stationary and dynamic inductive charging for electric shuttles operating on fixed stop sequences but allowing detours. It develops a microscopic, graph-based, cost-minimization model and solves it with an Iterated Local Search (ILS) framework, using a per-vehicle dynamic-programming subproblem solved by a bidirectional label-setting algorithm with lazy dominance. Empirical results show the approach outperforms a warm-started commercial solver by up to $60\%$ in solution quality on artificial and real-world Hof instances, and reveal that dynamic charging is not yet cost-competitive under base costs; however, permitting detours can reduce total costs by up to $3.5\%$ and decentralized PV storage can yield more than $20\%$ additional savings. The work delivers a scalable planning framework that integrates variable energy pricing and renewable-energy storage into charging infrastructure decisions, with clear implications for urban transit electrification strategy.

Abstract

In response to climate goals, growing environmental awareness, and financial incentives, municipalities increasingly seek to electrify public transportation networks. We study the problem of locating stationary and dynamic inductive charging stations for electric vehicles (EVs), allowing detours from fixed transit routes and schedules. Dynamic charging, which enables energy transfer while driving, reduces space usage in dense urban areas and lowers vehicle idle times. We formulate a cost-minimization problem that considers both infrastructure and operational costs and propose an Iterated Local Search (ILS) algorithm to solve instances of realistic size. Each configuration requires solving a decomposed subproblem comprising multiple resource-constrained shortest-path problems. For this, we employ a bi-directional label-setting algorithm with lazy dominance checks based on local bounds. On adapted benchmark instances, our approach outperforms a commercial solver by up to 60% in solution quality. We further apply our method to a real-world case study in Hof, Germany. Results indicate that, under current cost structures calibrated from a test track in Bad Staffelstein, dynamic inductive charging is not yet cost-competitive with stationary alternatives. We quantify the value of allowing detours at up to 3.5% of the total system cost and show that integrating photovoltaics with decentralized energy storage can yield savings exceeding 20%.

Figures (11)

• Figure 1: Inductive charging of autonomous passenger vehicles
• Figure 2: Exemplary setting with two dynamic charging stations (displayed in green and blue) consisting of multiple segments.
• Figure 3: Illustrative example with $|\mathcal{K}|=1$. Solution $1$ routes the vehicle to a stationary charging station before servicing the first stop. Subsequently the vehicle traverses a dynamic charging station before servicing the next stop and returning to the depot at time $15$ with an of $25$. The alternative solution $2$ services the stops first and only visits a stationary charging station before returning to the depot. Note that the departure time and profile for this solution are not displayed.
• Figure 4: Illustrative example with depot and two stops on the corners of an equilateral triangle with side length one, one stationary charger in the center of the triangle, and a dynamic charging station on the side between $s_1$ and $s_2$. The vehicle travels with speed $1$, we consider a time discretization of $\delta=1$, and all stations charge with $h_{f}=1$. We assume that service time windows are such that the vehicle can charge a maximum of three time steps between servicing the two stops and similarly at other points of the route. Every arc is associated with a tuple reflecting time and net energy balance where a positive value encodes a situation in which charging replenishes more energy than the vehicle consumes.
• Figure 5: Left: Illustration of potential charging infrastructure in a selected scenario in Hof, Germany. Icons encode stationary charging stations and dynamic charging segments are highlighted in red. Right: Vehicle routes.

Theorems & Definitions (2)

• Definition 3.1: Forward Domination
• Definition 3.2: Backward Domination