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An Integer Clustering Approach for Modeling Large-Scale EV Fleets with Guaranteed Performance

Sijia Geng, Thomas Lee, Dharik Mallapragada, Audun Botterud

TL;DR

This paper tackles the computational challenge of planning and operating large-scale EV fleets by introducing an integer-clustering framework that aggregates vehicles and chargers by type while preserving the ability to dispatch individual vehicles. A two-stage disaggregation procedure (disaggregation to recover feasible individual operations) provides guaranteed performance through theoretical lower and upper bounds that relate the clustered model to the true individual formulation. The approach is validated on a Boston MBTA case study, showing substantial computational speedups (up to ~2000x) with minimal loss in solution quality (often within 0.5%). The method integrates fleet-level charging with a simplified energy system model and supports both planning and operational decision-making, offering a practical tool for designing and running electrified urban fleets.

Abstract

Large-scale integration of electric vehicles (EVs) leads to a tighter integration between transportation and electric energy systems. In this paper, we develop a novel integer-clustering approach to model a large number of EVs that manages vehicle charging and energy at the fleet level yet maintain individual trip dispatch. The model is then used to develop a spatially and temporally-resolved decision-making tool for optimally planning and/or operating EV fleets and charging infrastructure. The tool comprises a two-stage framework where a tractable disaggregation step follows the integer-clustering problem to recover an individually feasible solution. Mathematical relationships between the integer clustering, disaggregation, and individual formulations are analyzed. We establish theoretical lower and upper bounds on the true individual formulation which underpins a guaranteed performance of the proposed method. The optimality accuracy and computational efficiency of the integer-clustering formulation are also numerically validated on a real-world case study of Boston's public transit network under extensive test instances. Substantial speedups with minimal loss in solution quality are demonstrated.

An Integer Clustering Approach for Modeling Large-Scale EV Fleets with Guaranteed Performance

TL;DR

This paper tackles the computational challenge of planning and operating large-scale EV fleets by introducing an integer-clustering framework that aggregates vehicles and chargers by type while preserving the ability to dispatch individual vehicles. A two-stage disaggregation procedure (disaggregation to recover feasible individual operations) provides guaranteed performance through theoretical lower and upper bounds that relate the clustered model to the true individual formulation. The approach is validated on a Boston MBTA case study, showing substantial computational speedups (up to ~2000x) with minimal loss in solution quality (often within 0.5%). The method integrates fleet-level charging with a simplified energy system model and supports both planning and operational decision-making, offering a practical tool for designing and running electrified urban fleets.

Abstract

Large-scale integration of electric vehicles (EVs) leads to a tighter integration between transportation and electric energy systems. In this paper, we develop a novel integer-clustering approach to model a large number of EVs that manages vehicle charging and energy at the fleet level yet maintain individual trip dispatch. The model is then used to develop a spatially and temporally-resolved decision-making tool for optimally planning and/or operating EV fleets and charging infrastructure. The tool comprises a two-stage framework where a tractable disaggregation step follows the integer-clustering problem to recover an individually feasible solution. Mathematical relationships between the integer clustering, disaggregation, and individual formulations are analyzed. We establish theoretical lower and upper bounds on the true individual formulation which underpins a guaranteed performance of the proposed method. The optimality accuracy and computational efficiency of the integer-clustering formulation are also numerically validated on a real-world case study of Boston's public transit network under extensive test instances. Substantial speedups with minimal loss in solution quality are demonstrated.
Paper Structure (21 sections, 1 theorem, 25 equations, 4 figures, 4 tables)

This paper contains 21 sections, 1 theorem, 25 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Integer-Clustering Fleet Formulation
  3. Individual Vehicles Formulation
  4. Fleet-Individuals Operational Matching
  5. Energy System Model
  6. Optimization Formulation
  7. Planning Problem
  8. Integer-clustering formulation
  9. Individual formulation
  10. Operation Problem
  11. Theoretical Bounds on Performance
  12. Case Study and Numerical Results
  13. Fleet Data: MBTA Transit Schedule
  14. Parameters for EV, Charger, and Energy System
  15. Experimental Setup
  16. ...and 6 more sections

Key Result

Theorem 1

Let $\underline{J}_1^*$ and $\overline{J}_1^*$ be the optimal values of problem $\mathcal{P}_1$ with constraint eq_lower and eq_upper, respectively. Let $\underline{J}_2^*$ and $\overline{J}_2^*$ be the optimal values of problem $\mathcal{P}_2$ with constraints eq_lower,eq_lower_disag and eq_upper,e

Figures (4)

  • Figure 1: (a) Conventional formulation: Track charging and state-of-energy for individual vehicles and chargers. (b) Integer-clustering formulation: Group vehicles and chargers by type, and manage charging and SOE at the group level.
  • Figure 2: (a) Routes supported by the Cabot bus depot. (b) Block schedules for the Cabot bus depot on a representative weekday in the Fall season.
  • Figure 3: Empirical accuracy: Relative gap of the integer-clustering optimal value $J_1^*$ compared to the true individual optimal value $J_2^*$. If $\mathcal{P}_2$ did not solve within the set 1-hour time limit, the relative gap of $J_4^*$ (which is a valid upper bound) versus $J_1^*$ is reported instead. (Showing cases when surplus energy is allowed.) An outlier of 0.5% at $K=137$ is omitted. Note that 8 of the $\mathcal{P}_4$ cases were infeasible; but these were solved after allowing an $N^\text{c}$ slack $\leq$ 1.
  • Figure 4: Computational efficiency: Model solution time and speedup factors $T_{\mathcal{P}_2} / (T_{\mathcal{P}_1} + T_{\mathcal{P}_4})$. $\mathcal{P}_2$ models were not reliably solved within the 1-hour time limit at cases larger than $K\sim 100$, and speedup factors are not reported for these cases.

Theorems & Definitions (6)

  • Remark 1
  • Definition 1
  • Remark 2
  • Remark 3
  • Theorem 1
  • proof