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arxiv: 2605.16765 · v1 · pith:CKBUSWQ2new · submitted 2026-05-16 · 📡 eess.SY · cs.SY

A Coupled V2G Equilibrium Model of Electric Vehicle and Power System Interactions

Jiaxin Hou , Yujia Li , Jong-Shi Pang This is my paper

Pith reviewed 2026-05-19 21:33 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords vehicle-to-gridequilibrium modelvariational inequalityelectric vehiclespower systemsdistribution system operatorload sheddingEV routing
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The pith

A variational inequality model couples EV routing and power grid decisions to show that incentivized V2G eliminates load shedding and lowers prices under stress.

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

This paper develops a multi-player coupled equilibrium framework for vehicle-to-grid technology that captures bidirectional interactions between electric vehicle routing and power system operations. It formulates the joint problem as a variational inequality that integrates the optimization choices of the distribution system operator, charging network operator, load serving entities, and EV drivers. Energy prices arise endogenously from market clearing, while EV charging and discharging options enter through a preprocessed feasible path generation step. Numerical tests under increased household load and power line outage scenarios demonstrate that reduced generalized path costs for EVs enable V2G to remove load shedding and cut distribution locational marginal prices. The same incentives produce divergence in EV route and charging behavior between normal and scarcity conditions while improving overall trip economics.

Core claim

The paper claims that a coupled equilibrium model expressed as a variational inequality unites the decision-making of the Distribution System Operator, Charging Network Operator, Load Serving Entities, and EV drivers, with energy prices determined endogenously by market clearance and EV choices incorporated via preprocessed feasible paths; numerical validation under increased household load and power line outage scenarios shows that incentivized V2G participation eliminates load shedding, reduces distribution locational marginal electricity prices, leads to divergence in EV behavior between normal and scarcity conditions, and alters route choices while improving overall trip economic.

What carries the argument

A variational inequality formulation that unites the optimization problems of the Distribution System Operator, Charging Network Operator, Load Serving Entities, and EV drivers, with endogenous prices from market clearance and EV charging/discharging choices captured by a preprocessed feasible path generation procedure.

If this is right

  • When EVs respond to reduced generalized path costs, V2G participation eliminates load shedding under both increased household load and power line outage conditions.
  • V2G lowers distribution locational marginal electricity prices during the same stress scenarios.
  • EV drivers display divergent route and charging behavior between normal operating conditions and scarcity conditions.
  • V2G incentives change EV route choices yet raise overall trip economic value for drivers.

Where Pith is reading between the lines

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

  • The equilibrium framework could support design of dynamic incentive schemes that align EV owner costs with grid relief needs.
  • Scaling the variational inequality to larger networks would test whether the observed price reductions and behavioral shifts persist at regional scale.
  • Connecting this model to renewable integration studies could examine V2G's role in balancing variable generation alongside the stress scenarios already considered.

Load-bearing premise

The model assumes that a preprocessed feasible path generation procedure can accurately incorporate all charging and discharging choices for EV drivers and that energy prices are fully determined by internal market clearance conditions.

What would settle it

A simulation or real-network test that supplies actual EV routing data and line-outage events, applies the model's endogenous prices and path costs, and checks whether load shedding is eliminated and distribution locational marginal prices fall as predicted.

Figures

Figures reproduced from arXiv: 2605.16765 by Jiaxin Hou, Jong-Shi Pang, Yujia Li.

Figure 1
Figure 1. Figure 1: Original and Expanded Transportation Networks [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Player interactions and shared variables in the integrated power-transportation system. Orange ellipses represent shared [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Power network: IEEE-123 feeder [19] [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Transportation network: Sioux Falls [20] [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Scarcity quantity and price tail $36.4 (Stress) and $528.7 (Island) down to approximately $14.7. Even for less severely impacted routes like OD 14 and OD 17, V2G energy revenues effectively offset time costs, yielding net savings (nonnegative) in all evaluated scenarios. Ultimately, these reduced path costs provide a compelling economic incentive for EVs to voluntarily reroute their trips and actively part… view at source ↗
Figure 8
Figure 8. Figure 8: Generalized path cost consistent. The numerical results demonstrate that V2G has minimal impact under normal operating conditions but becomes critically important under stressed and contingency scenarios. In particular, when the power system experiences high demand or network dis￾ruptions, V2G-enabled EVs provide localized energy support that mitigates scarcity, stabilizes DLMPs, and prevents load shedding… view at source ↗
Figure 7
Figure 7. Figure 7: EV charging and discharging profile systems under V2G integration. By explicitly capturing the decision￾making processes of CNO, EV users, DSO, and LSEs, the proposed model characterizes how system-wide outcomes emerge endoge￾nously through market-clearing mechanisms and price signals. The resulting VI formulation admits a solution, provide the constraints of the players’ decision problems and the market-c… view at source ↗
Figure 10
Figure 10. Figure 10: Analysis of total system social costs Reports, vol. 15, p. 16202, 2025. [10] S. Zhan, Y. Zhou, D. Feng, C. Fang, H. Wang, S. Dou, and L. Chen, “V2G-enhanced operation optimization strategy for EV charging station with photovoltaic and energy storage integration,” Applied Energy, vol. 171, p. 111002, 2025. [11] Y. Xiao, J. Tang, X. Lin, X. Feng, B. Qian, and F. Zhang, “Reinforcement-learning-based V2G sche… view at source ↗
Figure 9
Figure 9. Figure 9: Longer routes, lower cost: V2G-Driven detour behavior. [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
read the original abstract

Vehicle-to-grid (V2G) technology empowers electric vehicles (EVs) to act as mobile energy resources, providing critical support to power systems, especially under stressed conditions. To understand the economic mechanism driving V2G participation and its benefits to power grid, this paper proposes a multi-player coupled equilibrium framework that models the bidirectional interactions between power grid operations and EV routing, incorporating charging and discharging choice in a preprocessed feasible path generation procedure. Energy prices are endogenously determined by market clearance conditions. We formulate the overall problem as a Variational Inequality that unite the decision-making of Distribution System Operator, Charging Network Operator, Load Serving Entities, and EV drivers. Numerical studies validate the framework under two stress scenarios: increased household load and power line outages. Results show that when EVs are incentivized by reduced generalized path costs, V2G is particularly effective in eliminating load shedding and reducing distribution locational marginal electricity prices. On the transportation side, V2G can lead to divergence in EV behavior between normal and scarcity conditions, and alter route choices yet improve overall trip economic.

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

1 major / 2 minor

Summary. The paper proposes a multi-player coupled equilibrium model for V2G interactions between electric vehicles and the power system. It formulates the problem as a single variational inequality (VI) that integrates the optimization problems of the Distribution System Operator (DSO), Charging Network Operator (CNO), Load Serving Entities (LSE), and EV drivers, with energy prices cleared endogenously by market conditions. EV routing and bidirectional charging/discharging decisions are incorporated via a preprocessed feasible path generation step. Numerical studies examine two stress scenarios (increased household load and power line outages) and report that V2G incentives reduce load shedding, lower distribution locational marginal prices, and alter EV route choices.

Significance. If the VI formulation is internally consistent and the preprocessing step does not introduce artifacts under endogenous prices and outages, the framework could offer a useful unified approach for analyzing economic incentives and equilibrium outcomes in coupled transportation-energy systems under stress. The endogenous price clearing and explicit multi-player structure are strengths; however, the absence of detailed quantitative results, data sources, or solver information in the abstract limits evaluation of practical significance and reproducibility.

major comments (1)
  1. The central modeling choice of a preprocessed feasible path set for EV routing and V2G choices (described in the abstract and used to define the EV decision variables in the VI) assumes that the generated paths remain feasible and optimal once prices and line statuses are solved endogenously. In the power line outage scenario, changes in grid topology or capacity could render some preprocessed paths infeasible or suboptimal, which would invalidate the VI equilibrium and make the reported reductions in load shedding and price divergence artifacts of the preprocessing rather than genuine market outcomes. This assumption is load-bearing for the stress-test claims and requires either dynamic path regeneration, explicit feasibility constraints inside the VI, or post-solution validation against the solved prices and outages.
minor comments (2)
  1. Abstract, sentence 3: 'that unite the decision-making' should read 'that unites the decision-making' for grammatical agreement.
  2. Abstract, final sentence: 'improve overall trip economic' is unclear; consider 'improve overall trip economics' or 'improve the economic efficiency of trips'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed and constructive review of our manuscript. The major comment raises an important point about the preprocessing of feasible paths, which we address directly below. We outline revisions that will strengthen the presentation of our modeling assumptions and results while preserving the core contributions of the coupled VI framework.

read point-by-point responses

  1. Referee: The central modeling choice of a preprocessed feasible path set for EV routing and V2G choices (described in the abstract and used to define the EV decision variables in the VI) assumes that the generated paths remain feasible and optimal once prices and line statuses are solved endogenously. In the power line outage scenario, changes in grid topology or capacity could render some preprocessed paths infeasible or suboptimal, which would invalidate the VI equilibrium and make the reported reductions in load shedding and price divergence artifacts of the preprocessing rather than genuine market outcomes. This assumption is load-bearing for the stress-test claims and requires either dynamic path regeneration, explicit feasibility constraints inside the VI, or post-solution validation against the solved prices and outages.

    Authors: We appreciate the referee's identification of this modeling assumption. The feasible path set is generated in a preprocessing step from the transportation network and charging station locations to maintain tractability of the single variational inequality that couples the DSO, CNO, LSE, and EV driver problems. Grid outages are modeled endogenously through modified line capacities and power flow constraints inside the DSO's optimization, which in turn affect the cleared prices and load-shedding variables. We selected the numerical outage scenarios such that the preprocessed paths remain physically accessible and the V2G decisions adjust via price signals rather than through direct disconnection of stations. Nevertheless, we acknowledge that a more severe outage could render certain paths suboptimal. In the revised manuscript we will add (i) an explicit discussion of the preprocessing assumptions in the model section, (ii) a post-solution validation procedure that checks equilibrium path flows against the solved line statuses and station availability, and (iii) a limitations paragraph noting that dynamic path regeneration could be explored in future extensions. These changes directly respond to the referee's suggestions without requiring reformulation of the core VI. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the VI formulation or preprocessing step

full rationale

The paper formulates the coupled equilibrium as a Variational Inequality integrating independent decisions from DSO, CNO, LSE, and EV drivers, with prices cleared endogenously via market conditions. The preprocessed feasible path generation is presented as an explicit input procedure to incorporate EV charging/discharging choices into the model, rather than being derived from or equivalent to the solved equilibrium by construction. No load-bearing steps reduce to self-definitions, fitted parameters renamed as predictions, or self-citation chains. Numerical validation under stress scenarios supplies independent content against external benchmarks, rendering the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review limited to abstract; no explicit free parameters, axioms, or invented entities can be identified beyond the stated modeling assumptions.

axioms (1)
  • domain assumption Energy prices are endogenously determined by market clearance conditions.
    Explicitly stated as part of the model setup in the abstract.

pith-pipeline@v0.9.0 · 5722 in / 1122 out tokens · 41305 ms · 2026-05-19T21:33:18.833815+00:00 · methodology

discussion (0)

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Reference graph

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