[Paper Review] Clustering Consumption in Queues: A Scalable Model for Electric Vehicle Scheduling

Mahnoosh Alizadeh, George Kesidis+1 more|arXiv (Cornell University)|Apr 24, 2013

Electric Vehicles and Infrastructure10 references4 citations

TL;DR

This paper proposes a scalable clustering-based model for electric vehicle (EV) load scheduling that groups EV charging demands into finite clusters based on consumption patterns, enabling efficient real-time load following. Using a model predictive control (MPC) scheduler and a heuristic method, the approach achieves near-zero deviation from ISO dispatch signals while maintaining hard QoS guarantees, with the heuristic offering near-optimal performance in under a minute despite lower computational cost.

ABSTRACT

In this paper, we introduce a scalable model for the aggregate electricity demand of a fleet of electric vehicles, which can provide the right balance between model simplicity and accuracy. The model is based on classification of tasks with similar energy consumption characteristics into a finite number of clusters. The aggregator responsible for scheduling the charge of the vehicles has two goals: 1) to provide a hard QoS guarantee to the vehicles at the lowest possible cost; 2) to offer load or generation following services to the wholesale market. In order to achieve these goals, we combine the scalable demand model we propose with two scheduling mechanisms, a near-optimal and a heuristic technique. The performance of the two mechanisms is compared under a realistic setting in our numerical experiments.

Motivation & Objective

• To develop a scalable, accurate model for aggregate EV electricity demand that balances simplicity and fidelity.
• To enable real-time scheduling of EV fleets to follow intra-hour load-following signals from the Independent System Operator (ISO) while maintaining hard quality of service (QoS) guarantees.
• To minimize market costs by purchasing exactly enough bulk power in advance, aligned with predicted demand.
• To evaluate the performance of both optimal (MPC) and heuristic scheduling techniques under realistic conditions.
• To demonstrate that coarse clustering of EV charging behavior enables effective system-level control without requiring full controllability of individual charging rates.

Proposed method

• The model classifies EV charging tasks into clusters based on energy consumption profiles, using quantization and classification to approximate aggregate load behavior.
• Each cluster is assigned a representative charge profile (code), enabling scalable multiple-description modeling of EV load dynamics.
• A model predictive control (MPC) scheduler solves an integer program to minimize deviation from the target load profile $P^{(k)}(t) + a(t)$, with penalties weighted 10× higher for intra-hour deviations.
• A heuristic scheduler is designed for low computational cost, using a greedy selection of cluster assignments to minimize deviation.
• The performance of both schedulers is evaluated using a 12-hour simulation of 1,000 EVs with realistic charging profiles and wind forecast errors.
• Wind following signals are derived from real-world data (Bonneville Power Administration), normalized to a 60 kWs capacity, and applied over the first 9 hours.

Experimental results

Research questions

• RQ1 Can clustering EV charging demand into a finite number of behavior types enable scalable and accurate load modeling for real-time scheduling?
• RQ2 How well can a heuristic scheduling method approximate the performance of a model predictive control (MPC) scheduler in terms of load-following accuracy and computational cost?
• RQ3 What is the impact of using a fixed bulk purchase (P^{(0)}(t)) versus an updated one (P^{(k)}(t)) on heuristic scheduler performance?
• RQ4 To what extent does the clustering approach maintain QoS guarantees while enabling load following in the presence of real-time market signals?
• RQ5 How does the system perform under realistic wind forecast errors and variable EV arrival/departure patterns?

Key findings

• The MPC scheduler achieved near-zero deviation from the target load profile $P^{(k)}(t) + a(t)$, with only 0.03 kWhs of total deviation over the 12-hour night period.
• The heuristic scheduler achieved comparable performance to MPC with a total deviation of 13 kWhs, despite running in under one minute compared to over an hour for MPC.
• When using a fixed bulk purchase $P^{(0)}(t)$, the heuristic method performed poorly in the final two hours, indicating the importance of adaptive bulk purchase updates.
• When updated with adaptive bulk purchases $P^{(k)}(t)$, the heuristic method successfully followed the target profile $P^{(k)}(t) + a(t)$, demonstrating strong performance under realistic conditions.
• The clustering model effectively reduced complexity while preserving accuracy, enabling scalable real-time scheduling without requiring full control over individual EV charging rates.
• The model is robust to uncertainties such as early departures, inexact cluster estimates, and variable arrival processes, as supported by related work cited in the paper.