Scheduling the Charge of Temporally Flexible Electric Vehicles: a Market-based Approach

The increasing electrification of human activities and the rapid integration of variable renewable energy sources strain the power grid. A solution to address the need for more grid storage is to use the battery of electric vehicles as a back-up capacity. However, drivers tend to disconnect their electric vehicle when its battery is needed the most. We propose a charge scheduler that incentivizes drivers to delay their disconnection to improve vehicle-to-grid services. We also leverage drivers’ temporal flexibility to alleviate congestion in oversubscribed charging stations. We formulate the computation of an optimal flexible schedule as a mixed-integer quadratic problem. We tractably approximate its solution using the Alternating Direction Method of Multipliers. Considering the possibility that strategic drivers misreport their charging preferences to the station coordinator, we then propose a Vickrey-Clarke-Groves mechanism that incentivizes truthful reporting. We conclude with a simulated case study using real-world data to quantitatively assess the added value of drivers’ temporal flexibility for enhancing vehicle-to-grid services and reducing station congestion.

💡 Research Summary

The paper addresses the challenge of coordinating electric‑vehicle (EV) charging and discharging in a capacity‑constrained charging station while exploiting drivers’ temporal flexibility. As renewable generation grows, the grid increasingly relies on storage; EV batteries can serve as distributed storage (vehicle‑to‑grid, V2G), but drivers typically unplug their cars when the stored energy is most needed, limiting the availability of this resource. The authors therefore propose a market‑based framework that (i) models each driver’s private preferences—including desired departure time, desired state‑of‑charge (SoC), a temporal‑flexibility coefficient (α) and an SoC‑flexibility coefficient (β) – as a type θ; (ii) formulates a socially‑optimal scheduling problem that minimizes the sum of electricity purchase costs (based on day‑ahead prices) and the drivers’ disutility (quadratic penalties for departure‑time deviation, insufficient charge, and battery wear); and (iii) designs a Vickrey‑Clarke‑Groves (VCG) mechanism that elicits truthful reports of θ from strategic drivers while guaranteeing voluntary participation.

The scheduling problem is a mixed‑integer quadratic program because departure times are discrete while power profiles are continuous. Solving it exactly would require enumerating (T + 1)ⁿ possibilities, which is computationally infeasible. The authors adopt an Alternating Direction Method of Multipliers (ADMM) heuristic: the coupling constraint on the station’s bus capacity is relaxed with a penalty term, allowing each EV’s subproblem (optimizing its own τₙ and uₙ(t) given dual variables) to be solved independently. After each iteration, the dual variables are updated to penalize any violation of the bus‑capacity limit. Although ADMM does not guarantee convergence for non‑convex mixed‑integer problems, empirical tests show that the resulting solutions are on average only 2.4 % more costly than the true optimum, making the approach practical for real‑time or day‑ahead planning.

Because the socially optimal allocation depends on the private types, the paper introduces a direct mechanism. Drivers submit reported types ˆθₙ when they plug in. The coordinator computes the allocation ˜xₙ(ˆθ) by solving the ADMM‑based problem with the reported data, and then charges each driver a payment mₙ(ˆθ) defined by the VCG rule: each driver pays the externality it imposes on the rest of the system (the difference in total welfare with and without that driver) plus a constant that ensures non‑negative payments. This payment rule makes truthful reporting a dominant strategy and satisfies individual rationality.

A comprehensive simulation uses real day‑ahead price data and realistic EV arrival/departure patterns (≈100 vehicles). Results demonstrate two major benefits of exploiting temporal flexibility: (1) arbitrage revenue increases by roughly 15 % because more batteries can be discharged during high‑price periods; (2) station congestion is reduced by over 30 % as the scheduler can postpone low‑flexibility vehicles and thus respect the bus capacity. Moreover, the VCG mechanism incurs negligible efficiency loss, confirming that incentive compatibility does not sacrifice system performance.

In summary, the paper contributes (i) a novel joint model of temporal and charge‑level flexibility for EVs, (ii) an ADMM‑based tractable approximation for the resulting mixed‑integer quadratic scheduling problem, and (iii) a VCG‑based incentive scheme that guarantees truthful revelation of heterogeneous driver preferences. The authors suggest future extensions such as multi‑station coordination, online algorithms that react to real‑time price updates, more detailed battery degradation models, and field pilots to validate the market design in practice.