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Multi-objective Optimal Trade-off Between V2G Activities and Battery Degradation in Electric Mobility-as-a-Service Systems

Fabio Paparella, Pim Labee, Steven Wilkins, Theo Hofman, Soora Rasouli, Mauro Salazar

TL;DR

The paper addresses optimizing a fleet of electric MaaS vehicles that can service travel requests while engaging in charging and V2G, explicitly accounting for battery degradation. It proposes a linearized MILP framework that couples routing, energy exchanges, and aging through a DAG-based routing representation and decision tensors, yielding a tractable optimization problem with $J = J_{trav} + J_{elec} + J_{batt}$. A key contribution is the linearized degradation term, enabling global-optimality guarantees within MILP formulations, demonstrated via a case study for Eindhoven where V2G revenue does not affect service levels but degradation costs can negate gains. The results emphasize that battery aging costs can outweigh energy trading revenues, highlighting the importance of incorporating degradation in planning and motivating online extensions via stochastic model predictive control to handle uncertainty.

Abstract

This paper presents optimization models for electric Mobility-as-a-Service systems, whereby electric vehicles not only provide on-demand mobility, but also perform charging and Vehicle-to-Grid (V2G) operations to enhance the fleet operator profitability. Specifically, we formulate the optimal fleet operation problem as a mixed-integer linear program, with the objective combining of operational costs and revenues generated from servicing requests and grid electricity sales. Our cost function explicitly captures battery price and degradation, reflecting their impact on the fleet total cost of ownership due to additional charging and discharging activities. Simulation results for Eindhoven, The Netherlands, show that integrating V2G activities does not compromise the number of travel requests being served. Moreover, we emphasize the significance of accounting for battery degradation, as the costs associated with it can potentially outweigh the revenues stemming from V2G operations.

Multi-objective Optimal Trade-off Between V2G Activities and Battery Degradation in Electric Mobility-as-a-Service Systems

TL;DR

The paper addresses optimizing a fleet of electric MaaS vehicles that can service travel requests while engaging in charging and V2G, explicitly accounting for battery degradation. It proposes a linearized MILP framework that couples routing, energy exchanges, and aging through a DAG-based routing representation and decision tensors, yielding a tractable optimization problem with . A key contribution is the linearized degradation term, enabling global-optimality guarantees within MILP formulations, demonstrated via a case study for Eindhoven where V2G revenue does not affect service levels but degradation costs can negate gains. The results emphasize that battery aging costs can outweigh energy trading revenues, highlighting the importance of incorporating degradation in planning and motivating online extensions via stochastic model predictive control to handle uncertainty.

Abstract

This paper presents optimization models for electric Mobility-as-a-Service systems, whereby electric vehicles not only provide on-demand mobility, but also perform charging and Vehicle-to-Grid (V2G) operations to enhance the fleet operator profitability. Specifically, we formulate the optimal fleet operation problem as a mixed-integer linear program, with the objective combining of operational costs and revenues generated from servicing requests and grid electricity sales. Our cost function explicitly captures battery price and degradation, reflecting their impact on the fleet total cost of ownership due to additional charging and discharging activities. Simulation results for Eindhoven, The Netherlands, show that integrating V2G activities does not compromise the number of travel requests being served. Moreover, we emphasize the significance of accounting for battery degradation, as the costs associated with it can potentially outweigh the revenues stemming from V2G operations.
Paper Structure (9 sections, 20 equations, 6 figures, 3 tables)

This paper contains 9 sections, 20 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Optimization Framework
  3. Objective
  4. Battery Degradation
  5. Problem Definition
  6. Discussion
  7. Results
  8. Case Study of Eindhoven, The Netherlands
  9. Conclusions

Figures (6)

  • Figure 1: Schematic representation of the decision tree of one vehicle. At every step, each electric vehicle can either serve a travel requests, charge or discharge the battery.
  • Figure 2: Directed Acyclic Graph (DAG) representation showing the operation of one vehicle. Figure taken from PaparellaHofmanEtAl2024.
  • Figure 3: Normalized battery degradation model and linearized version as a function of the overall energy flown through a $\unit[40]{kWh}$ battery.
  • Figure 4: The figure shows the number of demands during a day, and the recorded energy price in the Netherlands during November 1st, 2023 (courtesy of nordpoolgroup.com).
  • Figure 5: Charging, discharging activities and net energy withdrawn from the grid during the day. In the top figure the fleet is not allowed to perform V2G, while in the bottom figure the fleet can perform V2G. Fleet composed of $70$ Nissan Leaf. Power of the chargers of $\unit[22]{kW}$.
  • ...and 1 more figures