Relating Electric Vehicle Charging to Speed Scaling with Job-Specific Speed Limits

TL;DR

This paper addresses EV charging scheduling under limited grid capacity by relating the problem to processor speed scaling with job-specific speed limits. It introduces the Flow-based Offline Charging Scheduler (FOCS), an exact offline algorithm that minimizes the integral of a strictly convex, increasing function $\bar{F}$ of the aggregated power profile $\textsc{Pf}_s(t)$, and proves its optimality via KKT conditions. It also analyzes online algorithms Average Rate (Avr) and Optimal Available (OA), deriving competitive ratios $2^{\alpha-1}\alpha^{\alpha}$ and $\alpha^{\alpha}$ for the DSL setting and showing no deterministic online rule can perfectly follow a given speed profile. Numerical experiments on real EV charging data (e.g., 13694 sessions with 11/22 kW chargers) demonstrate FOCS's practical viability (median ~2.5s for 400 EVs at 15-minute granularity) and that Avr and OA closely approximate offline optimum (within about 1.3x for $\alpha=2$), confirming the approach's utility for parking-lot energy management and MPC integration. The work thus provides a principled, scalable framework for coordinating EV charging with grid constraints and offers theoretically tight online guarantees that translate well in practice. The methods and results hold promise for deployment in real-world charging infrastructure and MPC-based control schemes.

Abstract

Due to the ongoing electrification of transport in combination with limited power grid capacities, efficient ways to schedule the charging of electric vehicles (EVs) are needed for the operation of, for example, large parking lots. Common approaches such as model predictive control repeatedly solve a corresponding offline problem. In this work, we first present and analyze the Flow-based Offline Charging Scheduler (FOCS), an offline algorithm to derive an optimal EV charging schedule for a fleet of EVs that minimizes an increasing, convex and differentiable function of the corresponding aggregated power profile. To this end, we relate EV charging to processor speed scaling models with job-specific speed limits. We prove our algorithm to be optimal and derive necessary and sufficient conditions for any EV charging profile to be optimal. Furthermore, we discuss two online algorithms and their competitive ratios for a specific class objective functions. In particular, we show that if those algorithms are applied and adapted to the presented EV scheduling problem, the competitive ratios for Average Rate and Optimal Available match those of the classical speed scaling problem. Finally, we present numerical results using real-world EV charging data to put the theoretical competitive ratios into a practical perspective.

Figures (14)

• Figure 1: Illustration of transformation applied in proof of Lemma \ref{['lem:DSL2DS']}.
• Figure 2: Example of an instance where the optimal speed profile for DSL instance $I$ differs from the optimal speed profile of the augmented DS instance $a(I)$ under objective function \ref{['eq:energyFunctionObjective']} with $\alpha = 2$.
• Figure 3: Example of an instance where Edf results in an infeasible schedule for a DSL instance even when respecting speed limits.
• Figure 4: Schematic of flow network structure of DSL.
• Figure 5: Schematic overview of Focs.

Theorems & Definitions (22)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Lemma 1
• Corollary 1
• Definition 5: Critical intervals
• Lemma 2
• Definition 6: Work-transferability
• Lemma 3: Work-transferability in flows