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Designing a Robust and Cost-Efficient Electrified Bus Network with Sparse Energy Consumption Data

Sara Momen, Yousef Maknoon, Bart van Arem, Shadi Sharif Azadeh

TL;DR

This work tackles charging infrastructure design for Battery Electric Buses under sparse energy consumption data. It introduces two robust formulations: BoU-CID, which treats energy use with a box uncertainty and a conservatism budget, and DRCC-CID, a data-driven distributionally robust chance-constrained approach that uses sparse observations within a Wasserstein ambiguity set to protect feasibility. Through synthetic grid tests and a Rotterdam case study, the authors show that ignoring energy variability yields high infeasibility, while worst-case designs (BoU) can be prohibitively costly; the data-driven DRCC-CID achieves substantial cost reductions (relative to BoU) while maintaining high reliability, especially when extreme energy values are rare. The results underscore the value of incorporating sparse data into robust CID and highlight DRCC-CID as a practical, scalable framework for resilient, cost-efficient BEB electrification in real-world urban networks.

Abstract

This paper addresses the challenges of charging infrastructure design (CID) for electrified public transport networks using Battery Electric Buses (BEBs) under conditions of sparse energy consumption data. Accurate energy consumption estimation is critical for cost-effective and reliable electrification but often requires costly field experiments, resulting in limited data. To address this issue, we propose two mathematical models designed to handle uncertainty and data sparsity in energy consumption. The first is a robust optimization model with box uncertainty, addressing variability in energy consumption. The second is a data-driven distributionally robust optimization model that leverages observed data to provide more flexible and informed solutions. To evaluate these models, we apply them to the Rotterdam bus network. Our analysis reveals three key insights: (1) Ignoring variations in energy consumption can result in operational unreliability, with up to 55\% of scenarios leading to infeasible trips. (2) Designing infrastructure based on worst-case energy consumption increases costs by 67\% compared to using average estimates. (3) The data-driven distributionally robust optimization model reduces costs by 28\% compared to the box uncertainty model while maintaining reliability, especially in scenarios where extreme energy consumption values are rare and data exhibit skewness. In addition to cost savings, this approach provides robust protection against uncertainty, ensuring reliable operation under diverse conditions.

Designing a Robust and Cost-Efficient Electrified Bus Network with Sparse Energy Consumption Data

TL;DR

This work tackles charging infrastructure design for Battery Electric Buses under sparse energy consumption data. It introduces two robust formulations: BoU-CID, which treats energy use with a box uncertainty and a conservatism budget, and DRCC-CID, a data-driven distributionally robust chance-constrained approach that uses sparse observations within a Wasserstein ambiguity set to protect feasibility. Through synthetic grid tests and a Rotterdam case study, the authors show that ignoring energy variability yields high infeasibility, while worst-case designs (BoU) can be prohibitively costly; the data-driven DRCC-CID achieves substantial cost reductions (relative to BoU) while maintaining high reliability, especially when extreme energy values are rare. The results underscore the value of incorporating sparse data into robust CID and highlight DRCC-CID as a practical, scalable framework for resilient, cost-efficient BEB electrification in real-world urban networks.

Abstract

This paper addresses the challenges of charging infrastructure design (CID) for electrified public transport networks using Battery Electric Buses (BEBs) under conditions of sparse energy consumption data. Accurate energy consumption estimation is critical for cost-effective and reliable electrification but often requires costly field experiments, resulting in limited data. To address this issue, we propose two mathematical models designed to handle uncertainty and data sparsity in energy consumption. The first is a robust optimization model with box uncertainty, addressing variability in energy consumption. The second is a data-driven distributionally robust optimization model that leverages observed data to provide more flexible and informed solutions. To evaluate these models, we apply them to the Rotterdam bus network. Our analysis reveals three key insights: (1) Ignoring variations in energy consumption can result in operational unreliability, with up to 55\% of scenarios leading to infeasible trips. (2) Designing infrastructure based on worst-case energy consumption increases costs by 67\% compared to using average estimates. (3) The data-driven distributionally robust optimization model reduces costs by 28\% compared to the box uncertainty model while maintaining reliability, especially in scenarios where extreme energy consumption values are rare and data exhibit skewness. In addition to cost savings, this approach provides robust protection against uncertainty, ensuring reliable operation under diverse conditions.
Paper Structure (20 sections, 20 equations, 4 figures, 13 tables, 1 algorithm)

This paper contains 20 sections, 20 equations, 4 figures, 13 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Model Formulation
  4. Formulation Using Mean Energy Consumption Estimates
  5. Formulation based on uncertainty range
  6. Empirical Data-Driven Uncertainty Modeling
  7. Computational results
  8. Data Structure
  9. Hypothetical grid network
  10. Deterministic and robust solutions on Rotterdam bus lines
  11. Monte Carlo simulation: Feasibility analysis of the results of the three models
  12. Effect of data quantity on data-driven distributionally robust optimization solutions
  13. Sensitivity analysis in charging infrastructure design
  14. Economic factor sensitivity
  15. Fleet size sensitivity
  16. ...and 5 more sections

Figures (4)

  • Figure 1: Rotterdam bus lines depicted on the map
  • Figure 2: Impact of sample size on feasibility and computational time of the DRCC-CID model
  • Figure 3: The impact of charging station costs on total battery capacity of robust models
  • Figure A.4: Diverse network configuration scenarios in hypothetic grid network with varying level of inter-connectivity