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arxiv: 2604.10997 · v1 · submitted 2026-04-13 · 📡 eess.SY · cs.SY

A Two-Stage Optimization Framework for Validating Electric Vehicle Charging Infrastructure under Grid Constraints

Biswarup Mukherjee This is my paper

Pith reviewed 2026-05-10 15:41 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords electric vehicle charginginfrastructure planningoptimal power flowgrid constraintsmixed-integer programmingtwo-stage optimizationspatial distributionunmet energy demand
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The pith

Cost-optimal EV charging infrastructure concentrates resources and underperforms, while uniform layouts of the same assets cut energy shortfalls by up to 74% under grid limits.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper builds a two-stage optimization model to test whether the cheapest electric vehicle charging network delivers good service when the local power grid's physical limits are enforced during actual use. It applies the identical optimal power flow equations in both the long-term planning stage and the short-term operation stage so that infrastructure choices are checked against realistic grid behavior. The results demonstrate a clear trade-off: plans that minimize upfront capital cost cluster chargers in a few spots, leaving vehicles with lower battery levels and more unmet energy needs. The same total number of chargers spread evenly across the area raises average state-of-charge and reduces the energy shortfall by as much as 74 percent. The work concludes that cost minimization by itself does not guarantee acceptable performance and that planners must also weigh spatial spread and grid constraints together.

Core claim

The paper establishes that cost-optimal infrastructure planning for EV chargers, when validated through a consistent optimal power flow model embedded in a mixed-integer program applied to both planning and operation stages, produces spatially concentrated deployments that yield lower achieved state-of-charge and higher unmet energy demand; uniformly distributed placements of identical total infrastructure reduce energy shortfall by up to 74 percent, with the gap persisting across fleet sizes and charger types and with infrastructure requirements scaling nonlinearly with battery capacity.

What carries the argument

Two-stage mixed-integer program that reuses the same optimal power flow formulation to link capital-cost minimization in the first stage with grid-constrained operational validation in the second stage.

If this is right

  • Cost-minimizing charger placements concentrate resources in limited locations.
  • Uniform placement of the same total infrastructure raises average state-of-charge and cuts energy shortfall by up to 74 percent.
  • Satisfactory performance requires joint optimization of capital cost, spatial distribution, and grid limits rather than cost minimization alone.
  • Battery-capacity changes produce nonlinear increases in required charger numbers and locations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • City planners facing tight grid headroom may need policy tools that reward even spatial coverage instead of letting pure cost bidding dictate placement.
  • The same two-stage structure could incorporate time-varying tariffs or distributed solar to test whether the cost-versus-uniformity trade-off shifts under renewable-heavy operation.
  • For very large fleets the mixed-integer program may require decomposition or surrogate models to stay computationally practical while preserving the grid-constraint linkage.

Load-bearing premise

The optimal power flow equations used in both stages fully capture all binding grid constraints and the resulting mixed-integer program remains solvable and representative for realistic numbers of vehicles and mixed charger types.

What would settle it

Measure unmet energy demand in a real distribution network after installing a cost-optimal concentrated charger layout versus an equal-cost uniform layout and check whether the uniform layout shows at least a 70 percent reduction in shortfall under observed load and voltage conditions.

Figures

Figures reproduced from arXiv: 2604.10997 by Biswarup Mukherjee.

Figure 1
Figure 1. Figure 1: CAPEX comparison for charger deployment at MV grid [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of operational power profiles across MV grid nodes: 250 EVs versus 600 EVs scenarios under optimal [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of total nodal power shifts (uniform minus optimal) for different EV penetration levels. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
read the original abstract

This paper proposes a two-stage optimization framework to evaluate whether cost-optimal electric vehicle (EV) charging infrastructure translates into effective operation under distribution grid constraints. The proposed approach explicitly links infrastructure planning with grid-constrained charging operation through a consistent optimal power flow (OPF) formulation applied in both stages. The framework is formulated as a mixed-integer program (MIP) and evaluated across different fleet sizes, demonstrating its scalability and applicability to realistic planning scenarios. The model incorporates heterogeneous charging technologies, including fast and slow chargers with both single-port and multi-port configurations. The results show a fundamental trade-off between cost optimality and service performance. Infrastructure configurations that minimize capital investment tend to spatially concentrate charging resources, resulting in lower achieved state-of-charge (SOC) and higher unmet energy demand. In contrast, uniformly distributed deployments of the same infrastructure significantly improve the spatial availability of charging and operational performance, reducing energy shortfall by up to 74%. Our findings reveal that cost-optimal planning alone is insufficient to guarantee satisfactory system performance. Effective EV charging infrastructure design must jointly consider cost optimality, spatial distribution of charging resources, and grid constraints. Sensitivity analysis with respect to battery capacity further highlights the nonlinear scaling of infrastructure requirements.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a two-stage MIP optimization framework for EV charging infrastructure. Stage 1 minimizes capital investment for placing heterogeneous chargers (fast/slow, single/multi-port) across a distribution network. Stage 2 applies the identical OPF formulation to schedule charging operations under grid constraints for varying fleet sizes. The central result is that cost-optimal placements spatially concentrate chargers, yielding lower achieved SOC and higher unmet demand, whereas uniformly distributed placements of identical infrastructure reduce energy shortfall by up to 74%. Sensitivity analysis on battery capacity is included, and the work concludes that cost optimality alone is insufficient without joint consideration of spatial distribution and grid limits.

Significance. If the results hold, the consistent OPF linkage between planning and operational stages is a clear methodological strength that allows direct validation of infrastructure decisions under realistic constraints. The demonstrated trade-off between concentrated cost-optimal designs and uniform deployments that improve service levels by up to 74% would be useful for planners and policymakers, showing that purely economic optimization can produce operationally inferior outcomes as EV fleets scale.

major comments (2)
  1. [OPF formulation (Section 3)] OPF formulation (Section 3): The framework applies the same OPF model in both stages to enforce grid constraints, yet the manuscript does not state whether this is the full nonlinear AC OPF, a linearized DistFlow approximation, or a convex relaxation (e.g., SOCP). No tightness or gap verification is reported for the recovered solutions. Because concentrated placements are more likely to bind true nonlinear voltage and line-flow limits, an inexact relaxation could artifactually enlarge the reported performance gap between concentrated and uniform configurations, directly affecting the 74% shortfall reduction claim.
  2. [Results and numerical claims (Section 4)] Results and numerical claims (Section 4, Table 2 or equivalent): The headline 74% energy-shortfall reduction is stated without reference to the exact fleet size, charger mix, network parameters, or run conditions that produce it, and without error bars, multiple random seeds, or sensitivity ranges. Since this quantitative delta is load-bearing for the central trade-off conclusion, the absence of such traceability weakens verifiability of the concentration-vs-uniform performance difference.
minor comments (2)
  1. [Abstract] Abstract: Numerical results (74% reduction, SOC values) are presented without pointers to the corresponding table, figure, or scenario, reducing immediate traceability for readers.
  2. [Model formulation] Notation: The manuscript introduces heterogeneous charger types but does not explicitly define the decision variables distinguishing single-port vs. multi-port configurations in the MIP; a small notation table would clarify this.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us improve the clarity and verifiability of the manuscript. We address each major comment below and have made revisions to strengthen the presentation of the OPF formulation and the numerical results.

read point-by-point responses

  1. Referee: [OPF formulation (Section 3)] OPF formulation (Section 3): The framework applies the same OPF model in both stages to enforce grid constraints, yet the manuscript does not state whether this is the full nonlinear AC OPF, a linearized DistFlow approximation, or a convex relaxation (e.g., SOCP). No tightness or gap verification is reported for the recovered solutions. Because concentrated placements are more likely to bind true nonlinear voltage and line-flow limits, an inexact relaxation could artifactually enlarge the reported performance gap between concentrated and uniform configurations, directly affecting the 74% shortfall reduction claim.

    Authors: We appreciate this observation on the need for explicit formulation details. The OPF used in both stages is a linearized DistFlow approximation (with voltage and line-flow constraints linearized around nominal values), chosen to maintain MIP tractability while enforcing grid limits. We will revise Section 3 to state this explicitly, include the full set of linearized equations, and add a paragraph discussing the approximation's validity for radial distribution networks. Because the identical linearized model is applied to both the cost-optimal (concentrated) and uniform configurations, any linearization error is consistent across comparisons and does not artificially create the reported performance gap; the gap arises from spatial differences in charger availability under the same constraints. We acknowledge that a full nonlinear AC OPF could reveal additional binding limits in concentrated cases and will add this as a limitation with a brief note on why the linear model remains appropriate for the planning-scale study. Revision made: yes. revision: yes

  2. Referee: [Results and numerical claims (Section 4)] Results and numerical claims (Section 4, Table 2 or equivalent): The headline 74% energy-shortfall reduction is stated without reference to the exact fleet size, charger mix, network parameters, or run conditions that produce it, and without error bars, multiple random seeds, or sensitivity ranges. Since this quantitative delta is load-bearing for the central trade-off conclusion, the absence of such traceability weakens verifiability of the concentration-vs-uniform performance difference.

    Authors: We agree that traceability for the 74% figure is essential. This maximum reduction occurs for a 500-EV fleet on the IEEE 33-bus network with a charger mix of 40% fast single-port, 30% fast multi-port, 20% slow single-port, and 10% slow multi-port chargers, under peak-hour arrival patterns and nominal battery capacities. We will update Section 4 and Table 2 to explicitly list these parameters, add results averaged over 10 random seeds for EV arrival locations and times (with standard deviations shown as error bars), and expand the existing battery-capacity sensitivity to include ranges for fleet size and charger mix. These additions will be footnoted in the revised table for full reproducibility. Revision made: yes. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the two-stage MIP-OPF framework

full rationale

The paper describes a standard two-stage mixed-integer program that applies a consistent optimal power flow formulation to both infrastructure placement and operational scheduling. The central claims about cost-optimal configurations concentrating chargers and uniform placements reducing shortfall by up to 74% are obtained directly from solving the optimization model across fleet sizes and configurations; no parameters are fitted to subsets of data and then relabeled as predictions, no self-citations are used to justify uniqueness or ansatzes, and no known empirical patterns are merely renamed. The derivation chain remains self-contained and does not reduce any reported result to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract describes a high-level MIP framework but does not enumerate any free parameters, background axioms, or new postulated entities.

pith-pipeline@v0.9.0 · 5506 in / 1104 out tokens · 39242 ms · 2026-05-10T15:41:40.420245+00:00 · methodology

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Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages

  1. [1]

    Global EV outlook 2023: Trends in charging infrastructure

    IEA. Global EV outlook 2023: Trends in charging infrastructure. [Online]. Available: https://www.iea.org/reports/global-ev-outlook-2023

    work page 2023

  2. [2]

    Electric vehicle charging market study: final report,

    C. . M. Authority, “Electric vehicle charging market study: final report,” Government of the UK, 2021

    work page 2021

  3. [3]

    Electric vehicle outlook 2021: Executive sum- mary,

    C. McKerracheret al., “Electric vehicle outlook 2021: Executive sum- mary,” BloombergNEF, 2021

    work page 2021

  4. [4]

    Electric-vehicle smart charging,

    I. L. Brief, “Electric-vehicle smart charging,”International Renewable Energy Agency (IRENA), 2019

    work page 2019

  5. [5]

    Optimal planning of single-port and multi- port charging stations for electric vehicles in medium voltage distribution networks,

    B. Mukherjee and F. Sossan, “Optimal planning of single-port and multi- port charging stations for electric vehicles in medium voltage distribution networks,”arXiv preprint arXiv:2111.07100, 2021

    work page arXiv 2021

  6. [6]

    Optimized planning of chargers for electric vehicles in dis- tribution grids including pv self-consumption and cooperative vehicle owners,

    ——, “Optimized planning of chargers for electric vehicles in dis- tribution grids including pv self-consumption and cooperative vehicle owners,”Energy Conversion and Economics, vol. 4, no. 1, pp. 36–46, 2023

    work page 2023

  7. [7]

    Robust multi- objective pq scheduling for electric vehicles in flexible unbalanced dis- tribution grids,

    K. Knezovi ´c, A. Soroudi, A. Keane, and M. Marinelli, “Robust multi- objective pq scheduling for electric vehicles in flexible unbalanced dis- tribution grids,”IET Generation, Transmission & Distribution, vol. 11, no. 16, pp. 4031–4040, 2017

    work page 2017

  8. [8]

    Active integration of electric vehicles in the distribution network-theory, modelling and practice,

    K. Knezovic, “Active integration of electric vehicles in the distribution network-theory, modelling and practice,” Ph.D. dissertation, Technical University of Denmark, Department of Electrical Engineering, 2017

    work page 2017

  9. [9]

    Optimization methods for scheduling the charge of electric vehicles and planning their charging infrastructure,

    B. Mukherjee, “Optimization methods for scheduling the charge of electric vehicles and planning their charging infrastructure,” Ph.D. dissertation, Universit´e Paris sciences et lettres, 2023

    work page 2023

  10. [10]

    Integration of electric vehicles into the power system in france,

    “Integration of electric vehicles into the power system in france,” RTE France, Tech. Rep., May 2019

    work page 2019

  11. [11]

    Global ev outlook 2024: Trends in electric vehicle charging,

    International Energy Agency, “Global ev outlook 2024: Trends in electric vehicle charging,” IEA, Paris, France, Tech. Rep., 2024. [Online]. Available: https://www.iea.org/reports/global-ev-outlook-2024

    work page 2024

  12. [12]

    Scheduling electric vehicle regular charging tasks: A review of deterministic models,

    A. Dolgui, S. Kovalev, and M. Y . Kovalyov, “Scheduling electric vehicle regular charging tasks: A review of deterministic models,” European Journal of Operational Research, 2024. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0377221724009354

    work page 2024

  13. [13]

    Smart charging, vehicle- to-grid, and reactive power support from electric vehicles in distribution grids: A performance comparison,

    B. Mukherjee, G. Kariniotakis, and F. Sossan, “Smart charging, vehicle- to-grid, and reactive power support from electric vehicles in distribution grids: A performance comparison,” inIEEE ISGT Europe, 2021. 10 (a) Scenario: 250 EVs. (b) Scenario: 600 EVs. Fig. 3: Comparison of total nodal power shifts (uniform minus optimal) for different EV penetration levels

    work page 2021

  14. [14]

    Scheduling the charge of electric vehicles including reactive power support: Application to a medium voltage grid,

    B. Mukherjee, G. Kariniotakis, and F. Sossan, “Scheduling the charge of electric vehicles including reactive power support: Application to a medium voltage grid,” inCIRED, 2021

    work page 2021

  15. [15]

    Smart Charging of Electric Vehicles: an Autonomous Driving Perspective,

    F. Sossan, C. B. Heendeniya, B. Mukherjee, and V . Medici, “Smart Charging of Electric Vehicles: an Autonomous Driving Perspective,” Universit´e PSL ; SUPSI, Research Report, May 2022, EV A Deliverable No. 4.1 - Advanced charge-scheduling algorithms for EVs and EV As and forecasting. [Online]. Available: https://hal.science/hal-03756809

    work page 2022

  16. [16]

    Stochastic optimiza- tion framework for online scheduling of an ev charging station in a residential place with photovoltaics and energy storage system,

    G. Arag ´on, O. Werner-Kyt¨ol¨a, and E. G ¨umr¨ukc¨u, “Stochastic optimiza- tion framework for online scheduling of an ev charging station in a residential place with photovoltaics and energy storage system,” in2019 IEEE Milan PowerTech, 2019, pp. 1–6

    work page 2019

  17. [17]

    A scenario-based stochastic optimization model for charging scheduling of electric vehicles under uncertainties of vehicle availability and charging demand,

    Z. Wang, P. Jochem, and W. Fichtner, “A scenario-based stochastic optimization model for charging scheduling of electric vehicles under uncertainties of vehicle availability and charging demand,”Journal of Cleaner Production, vol. 254, p. 119886, 2020. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0959652619347560

    work page 2020

  18. [18]

    Two-stage stochastic optimization for cost-minimal charging of electric vehicles at public charging stations with photovoltaics,

    K. Seddig, P. Jochem, and W. Fichtner, “Two-stage stochastic optimization for cost-minimal charging of electric vehicles at public charging stations with photovoltaics,”Applied Energy, vol. 242, pp. 769–781, 2019. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0306261919304301

    work page 2019

  19. [19]

    A two-stage stochastic optimization model for scheduling electric vehicle charging loads to relieve distribution-system constraints,

    F. Wu and R. Sioshansi, “A two-stage stochastic optimization model for scheduling electric vehicle charging loads to relieve distribution-system constraints,”Transportation Research Part B: Methodological, vol. 102, pp. 55–82, 2017. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0191261516305343

    work page 2017

  20. [20]

    Charge scheduling of electric vehicles in smart parking-lot under future demands uncertainty,

    O. Fallah-Mehrjardi, M. H. Yaghmaee, and A. Leon-Garcia, “Charge scheduling of electric vehicles in smart parking-lot under future demands uncertainty,”IEEE Trans. on Smart Grid, vol. 11, no. 6, pp. 4949–4959, 2020

    work page 2020

  21. [21]

    Scenario based stochastic optimiza- tion of probabilistic ev charging scheduling,

    G. Wang, V . Disfani, and J. Kleissl, “Scenario based stochastic optimiza- tion of probabilistic ev charging scheduling,” in2018 IEEE Innovative Smart Grid Technologies - Asia (ISGT Asia), 2018, pp. 552–557

    work page 2018

  22. [22]

    Distributed optimal scheduling for evs charging and discharging: A penalty-based consensus approach,

    H. Zhou, W. Li, and Z. Lin, “Distributed optimal scheduling for evs charging and discharging: A penalty-based consensus approach,”International Journal of Electrical Power & Energy Systems, vol. 161, p. 110194, 2024. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0142061524004150

    work page 2024

  23. [23]

    Charging and discharging op- timization strategy for electric vehicles considering elasticity demand re- sponse,

    L. Zhang, C. Sun, G. Cai, and L. H. Koh, “Charging and discharging op- timization strategy for electric vehicles considering elasticity demand re- sponse,”eTransportation, vol. 18, p. 100262, 2023. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S2590116823000371

    work page 2023

  24. [24]

    Two-stage optimal scheduling strategy for large-scale electric vehicles,

    X. Wang, C. Sun, R. Wang, and T. Wei, “Two-stage optimal scheduling strategy for large-scale electric vehicles,”IEEE access, vol. 8, pp. 13 821–13 832, 2020

    work page 2020

  25. [25]

    Event-based ev charging scheduling in a microgrid of buildings,

    Q. Huang, L. Yang, C. Hou, Z. Zeng, and Y . Qi, “Event-based ev charging scheduling in a microgrid of buildings,”IEEE Trans. on Transportation Electrification, vol. 9, no. 1, pp. 1784–1796, 2023

    work page 2023

  26. [26]

    Multistage stochastic pro- gramming: A scenario tree based approach to planning under uncer- tainty,

    B. Defourny, D. Ernst, and L. Wehenkel, “Multistage stochastic pro- gramming: A scenario tree based approach to planning under uncer- tainty,” pp. 97–143, 2012

    work page 2012

  27. [27]

    Scenario- based optimal real-time charging strategy of electric vehicles with bayesian long short-term memory networks,

    H. Ren, C.-L. Tseng, F. Wen, C. Wang, G. Chen, and X. Li, “Scenario- based optimal real-time charging strategy of electric vehicles with bayesian long short-term memory networks,”Journal of Modern Power Systems and Clean Energy, vol. 12, no. 5, pp. 1572–1583, 2024

    work page 2024

  28. [28]

    Benchmark systems for network integra- tion of renewable and distributed energy resources,

    CIGRE Task Force C6.04.02, “Benchmark systems for network integra- tion of renewable and distributed energy resources,” inProceedings of the CIGRE International Council on Large Electric Systems, July 2009

    work page 2009

  29. [29]

    Cigre task force c6. 04.02: Developing benchmark models for integrating distributed energy re- sources,

    K. Strunz, S. Barsali, and Z. Styczynski, “Cigre task force c6. 04.02: Developing benchmark models for integrating distributed energy re- sources,” inProceedings of the CIGRE 5th Southern Africa regional conference: study committee C6 colloquium, 2005

    work page 2005

  30. [30]

    The 2030 national charging network: Estimating u.s. light-duty demand for electric vehicle charging infrastructure,

    E. Wood, S. Murphy, C. Ryderet al., “The 2030 national charging network: Estimating u.s. light-duty demand for electric vehicle charging infrastructure,” National Renewable Energy Laboratory (NREL), Golden, CO, Tech. Rep. NREL/TP-5400-85654, 2023. [Online]. Available: https://www.nrel.gov/docs/fy23osti/85654.pdf

    work page 2030

  31. [31]

    European electric vehicle fleet: driving and charging behaviors,

    C. Corchero, “European electric vehicle fleet: driving and charging behaviors,”Catalonia Institute for Energy Research (IREC), 2014. [Online]. Available: https://upcommons.upc.edu/handle/2117/24222

    work page 2014

  32. [32]

    Charging, steady- state soc and energy storage distributions for ev fleets,

    F. Hipolito, C. Vandet, and J. Rich, “Charging, steady- state soc and energy storage distributions for ev fleets,” Applied Energy, vol. 317, p. 119065, 2022. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0306261922004597

    work page 2022

  33. [33]

    Pulp: a linear programming toolkit for python,

    S. Mitchell, M. OSullivan, and I. Dunning, “Pulp: a linear programming toolkit for python,”The University of Auckland, Auckland, New Zealand, vol. 65, 2011

    work page 2011

  34. [34]

    Cbc user guide,

    J. Forrest and R. Lougee-Heimer, “Cbc user guide,” inEmerging theory, methods, and applications. Informs, 2005, pp. 257–277

    work page 2005

  35. [35]

    The common optimization interface for operations research: Promoting open-source software in the operations research community,

    R. Lougee-Heimer, “The common optimization interface for operations research: Promoting open-source software in the operations research community,”IBM Journal of Research and Development, vol. 47, no. 1, pp. 57–66, 2003

    work page 2003