pith. sign in

arxiv: 2503.11967 · v2 · pith:QBMHULEUnew · submitted 2025-03-15 · 📡 eess.SY · cs.SY

A Profit Sharing Mechanism for Coordinated Power Traffic System

Tianyu Sima , Mingyu Yan , Jianfeng Wen , Houbo Xiong , Wensheng Luo , Mariusz Malinowski This is my paper

Pith reviewed 2026-05-25 08:26 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords profit sharingcoordinated schedulingtransportation networkpower distribution networkelectric vehiclesbilevel optimizationincentive compatibilityoperation cost
0
0 comments X

The pith

A profit-sharing mechanism lets the DNO reach its minimum total operation cost by incentivizing the TNO to adjust EV charging loads.

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

The paper establishes a two-stage profit-sharing mechanism that coordinates the non-cooperative transportation network operator and power distribution network operator to lower the PDN's total operation cost. In the prescheduling stage the TNO allocates traffic and charging without regard to the PDN, after which the DNO calculates its original cost. In the rescheduling stage the DNO offers a share of the saved dispatch cost to induce the TNO to reallocate EV charging in a way that benefits the PDN. Two single-level models and one bilevel model identify the optimal sharing ratio that minimizes the DNO's cost in the resulting game. Numerical tests on a 12-node traffic network coupled to an 18-bus power system show both operators gain under this ratio.

Core claim

The scheduling process is divided into prescheduling, where the TNO ignores the PDN and the DNO records its original cost, and rescheduling, where the DNO shares part of the saved cost to motivate the TNO to reallocate charging loads favorably for the PDN. This two-stage interaction is captured by single-level models for each stage and a bilevel model that finds the sharing ratio at which the DNO's total cost reaches its lowest value while the TNO still benefits.

What carries the argument

The bilevel model that treats the DNO's choice of profit-sharing ratio as the upper level and the TNO's response of reallocating traffic flow and charging load as the lower level.

If this is right

  • At the identified optimal sharing ratio the DNO's total scheduling cost reaches its lowest value.
  • The TNO receives a positive share of the saved cost and therefore also benefits.
  • The mechanism produces an incentive-compatible outcome in which the TNO voluntarily adjusts charging to reduce PDN imbalance.
  • The two-stage process can be solved by converting the bilevel interaction into equivalent single-level problems.

Where Pith is reading between the lines

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

  • The same profit-sharing logic could be applied to other infrastructure pairs that exhibit load shifting opportunities, such as gas and electricity networks.
  • If EV arrival times or battery states contain significant uncertainty, the optimal ratio may need periodic recalibration rather than a single fixed value.
  • The approach assumes perfect information between operators; relaxing that assumption would require testing whether the identified ratio remains stable under partial information.

Load-bearing premise

The bilevel model correctly predicts how the TNO will change its charging schedule for any given profit share, without unmodeled strategic behavior or external uncertainties.

What would settle it

Simulate the rescheduling stage at the reported optimal sharing ratio and check whether the realized DNO cost equals the predicted minimum or whether the TNO's actual allocation deviates from the model's prediction.

Figures

Figures reproduced from arXiv: 2503.11967 by Houbo Xiong, Jianfeng Wen, Mariusz Malinowski, Mingyu Yan, Tianyu Sima, Wensheng Luo.

Figure 1
Figure 1. Figure 1: Overload caused by irrational distribution of charging loads [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Power generation and dispatch cost in PDN & charging load distribution and travel cost in TN. To ensure the security of the PDN, the DNO have utilize the local emergency generators to support it. But the high marginal cost of these generators resulting in an uneconomical operation of the PDN.(left half of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the scheduling process of power-traffic system under the profit-sharing mechanism. The specific scheduling process for the power and traffic systems under profit-sharing mechanism is illustrated [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of the five-segment piecewise linear approximation of a quartic function. 5.2. Linearization of Constraint (17) We use the big-M method to replace the constraint (17) by constraints (56)-(58). Constraint (18) and (38)- (44) share the same form of constraint (17) and can be linearized using the same method. GV 0£ £⋅ f M X (56) ()T GV GV GV 01 ≤ − ≤ ⋅− Cu Λ M () X (57) {0,1} , X c∈∀c (58) X c is… view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of traffic flow, charging load and power generation in Case II. In Case-II, the power and traffic systems are coordinated by a single operator who will only focus on minimizing the overall cost of power-traffic system. The EVs are directed away from EVCS 3, 4, 6 by well-designed road congestion tolls and EVCS entry fees. Finally, the charging loads at these EVCSs decrease to 5.6 MW, 4.8 MW, an… view at source ↗
Figure 8
Figure 8. Figure 8: Distribution of traffic flow, charging load and power generation in Case III. Though the centralized operation enhances the efficiency of the power-traffic system, it damages the benefits of the TN. Considering the non-cooperative characteristics of the TN and the PDN in reality, the operation framework mentioned in Case II is not feasible. Therefore, we propose a profit-sharing mechanism to safeguard the … view at source ↗
Figure 9
Figure 9. Figure 9: Charging load at each EVCS under different profit-sharing ratio. 0% 20% 40% 60% 80% 100% Proportion of Power Generation 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Sharing ratio S G1 G2 G3 [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Output proportion of substation and local generators under different profit-sharing ratio [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The profit / loss of the PDN and the TN under different profit-sharing ratio. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Sharing ratio 1.8 1.85 1.9 1.95 2 2.05 Total Cost of PDN (CNY) 105 1.45 1.5 1.55 1.6 1.65 Total Cost of TN (CNY) 105 0 h0 G ah D -DG (1 ) -ah D ()* a 184682CNY [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The total operation cost of the PDN and the TN under different profit-sharing ratio [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Overall cost of power-traffic system under different profit-sharing ratio. d() d d d () () () 0 d d dd ah a a a a aa O DG D H+ Y = =-< (61) Region I & Region II: With profit-sharing ratio increasing, the regulation potential on the traffic side is gradually stimulated. On one hand, the reallocation of charging load alleviates the mismatch between the electricity supply and demand in the PDN, which brings … view at source ↗
read the original abstract

The transportation network operator (TNO) and the power distribution network operator (DNO) act non cooperatively during the scheduling process. Under the TNOs management, the distribution of charging load may exacerbate the local supply-demand imbalance in the power distribution network (PDN), which negatively impacts the secure and economic operation of the PDN. This paper proposes a profit sharing mechanism based on the principle of incentive compatibility for coordinating the transportation network (TN) and the PDN to minimize the total operation cost of the PDN. In this mechanism, the scheduling process of the power transportation system is divided into two stages. At the prescheduling stage, the TNO allocates traffic flow and charging load without considering the operation of the PDN, after which the DNO schedules and obtains the original cost. At the rescheduling stage, the DNO shares part of the saved dispatch cost to motivate the TNO to reallocate the EVs charging, which is more beneficial to the operation of the PDN. This two-stage process is then simulated by two single level models and a bilevel model. Finally, the optimal sharing ratio is identified, at which the total scheduling cost of the DNO can decrease to the lowest point when gaming with the TNO. The efficiency of the proposed mechanism is simulated via a coupled network with 12 traffic nodes and 18 electric buses. Numerical results demonstrate that the DNO can achieve the minimum total cost. Simultaneously, the TNO can also benefit from the proposed profit-sharing mechanism.

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 manuscript proposes a profit-sharing mechanism based on incentive compatibility to coordinate the non-cooperative TNO and DNO in EV charging scheduling. The process is split into prescheduling (TNO allocates traffic/charging without PDN consideration, DNO computes original cost) and rescheduling (DNO offers a share of saved cost via a bilevel model to induce TNO reallocation of EVs), with the optimal sharing ratio identified to minimize DNO total cost; both parties benefit. This is simulated via two single-level models and one bilevel model, with numerical validation on a 12-node/18-bus coupled network showing the DNO achieves minimum cost.

Significance. If the bilevel formulation correctly captures TNO incentives and the identified ratio produces the claimed global minimum DNO dispatch cost without unmodeled deviations, the mechanism offers a practical incentive-compatible approach for reducing PDN operational costs from uncoordinated TN scheduling. The coupled-network simulation provides a concrete test case for integrated power-transport systems with EVs.

major comments (2)
  1. [Abstract and bilevel model description] Abstract and rescheduling-stage bilevel model: the central claim that the optimal sharing ratio produces the 'lowest point' for DNO total cost requires that the lower-level TNO problem yields a unique response most favorable to the DNO leader. The manuscript does not address potential multiple optima in the follower problem or selection rules, which directly undermines the guarantee of achieving the absolute minimum dispatch cost.
  2. [Numerical results section] Numerical results on 12-node/18-bus network: the simulations are presented as demonstrating the minimum cost outcome, yet the text provides no verification that the bilevel solution corresponds to the true minimum (e.g., via comparison to exhaustive search or alternative formulations), no error analysis, and no discussion of post-agreement TNO deviations, all of which are load-bearing for the claim that DNO achieves the minimum total cost.
minor comments (2)
  1. The distinction between the two single-level models and the bilevel model could be clarified with explicit equation references or a flowchart to improve readability of the two-stage process.
  2. Notation for the sharing ratio and cost functions should be defined consistently at first use to avoid ambiguity when comparing prescheduling and rescheduling costs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the constructive comments on our manuscript. We address each major comment below, proposing revisions to strengthen the presentation of our bilevel model and numerical results.

read point-by-point responses

  1. Referee: [Abstract and bilevel model description] Abstract and rescheduling-stage bilevel model: the central claim that the optimal sharing ratio produces the 'lowest point' for DNO total cost requires that the lower-level TNO problem yields a unique response most favorable to the DNO leader. The manuscript does not address potential multiple optima in the follower problem or selection rules, which directly undermines the guarantee of achieving the absolute minimum dispatch cost.

    Authors: We thank the referee for highlighting this important aspect of bilevel optimization. The manuscript implicitly assumes that the lower-level TNO problem has a unique optimal solution for the given sharing ratio, as is standard in many applied bilevel models unless otherwise specified. In the numerical experiments, the solver returned a unique solution. To make this explicit and address potential multiple optima, we will revise the description of the bilevel model to state that we adopt the optimistic assumption where the leader (DNO) anticipates the follower's response that is most favorable to the leader if multiple optima exist. This clarification will be added to the abstract and model section. revision: yes

  2. Referee: [Numerical results section] Numerical results on 12-node/18-bus network: the simulations are presented as demonstrating the minimum cost outcome, yet the text provides no verification that the bilevel solution corresponds to the true minimum (e.g., via comparison to exhaustive search or alternative formulations), no error analysis, and no discussion of post-agreement TNO deviations, all of which are load-bearing for the claim that DNO achieves the minimum total cost.

    Authors: We agree that the numerical section would benefit from additional details on verification. The bilevel problem is solved using a commercial solver, and the solution is the global optimum under the model's assumptions for this instance size. While an exhaustive search was not conducted, we will add a sentence confirming that the reported cost is the minimum obtained from the optimization. No error analysis is provided because the model is deterministic with no stochastic elements. For post-agreement TNO deviations, since the sharing ratio is chosen to make the TNO's optimal response align with DNO's interest via incentive compatibility, rational deviation is not expected; we will include a short discussion on this in the revised numerical results section. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected.

full rationale

The paper constructs explicit single-level and bilevel optimization models to simulate a two-stage scheduling process and identify a profit-sharing ratio. The reported minimum DNO cost is the direct output of solving the bilevel program whose objective is defined to minimize that cost; this is the intended function of the model rather than a reduction of an independent prediction to its inputs. No equations or claims in the provided text exhibit self-definition, fitted parameters renamed as predictions, or load-bearing self-citations that collapse the central result. The numerical demonstration follows from the model as stated, with no first-principles derivation asserted that would require external verification beyond the simulation itself.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption of non-cooperative behavior and the modeling choice that the interaction can be captured by bilevel optimization; no new physical entities are postulated.

free parameters (1)
  • sharing ratio
    The ratio is identified as the value that minimizes DNO total cost when the TNO responds in the rescheduling game.
axioms (2)
  • domain assumption TNO and DNO act non-cooperatively during the scheduling process
    Stated as the premise that motivates the need for an incentive mechanism.
  • domain assumption The scheduling process can be divided into prescheduling and rescheduling stages that are simulated by single-level and bilevel models
    Used to operationalize the two-stage profit sharing process.

pith-pipeline@v0.9.0 · 5819 in / 1450 out tokens · 39936 ms · 2026-05-25T08:26:41.498444+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages

  1. [1]

    Influence of EV on grid power quality and optimizing the charging schedule to mitigate voltage imbalance and reduce power loss,

    M. Singh, I. Kar and P. Kumar, "Influence of EV on grid power quality and optimizing the charging schedule to mitigate voltage imbalance and reduce power loss," Proceedin gs of 14th International Power Electronics and Motion Control Conference EPE-PEMC 2010, Ohrid, Macedonia, 2010

    work page 2010

  2. [2]

    Impact of electric vehicles onpower distribution networks

    GA Putrus, Pasist Suwanapingkarl, David Johnston, EC Bentley, and Mahinsasa Narayana. Impact of electric vehicles onpower distribution networks. In 2009 IEEE Vehicle Power and Propulsion Conference, pages 827–

    work page 2009

  3. [3]

    Assessment of the Impact of Plug-in Electric Vehicles on Distribution Networks,

    L. Pieltain Fernández, T. Gomez San Roman, R. Cossent, C. Mateo Domingo and P. Frías, "Assessment of the Impact of Plug-in Electric Vehicles on Distribution Networks," IEEE Trans. Power Systems, vol. 26, no. 1, pp. 206-213, Feb. 2011

    work page 2011

  4. [4]

    Effects of optimised plug-in hybrid vehicle charging strategies on electric distribution network losses,

    S. Acha, T. C. Green and N. Shah, "Effects of optimised plug-in hybrid vehicle charging strategies on electric distribution network losses," IEEE PES T&D 2010, New Orleans, LA, USA, 2010, pp. 1-6

    work page 2010

  5. [5]

    Multi-network coordinated hydrogen supply infra structure planning for the integration of hydrogen vehicles and renewable energy,

    W. Gan et al., "Multi-network coordinated hydrogen supply infra structure planning for the integration of hydrogen vehicles and renewable energy," IEEE Trans. Industry Applications, vol. 58, no. 2, pp. 2875-2886, March-April 2022

    work page 2022

  6. [6]

    S h e ff i , Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods

    Y. S h e ff i , Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods. Englewood Cliffs, NJ, USA: Prentice-Hall, 1985

    work page 1985

  7. [7]

    Network equilibrium of coup led transportation and power distribution systems,

    W. Wei, L. Wu, J. Wang and S. Mei, "Network equilibrium of coup led transportation and power distribution systems," IEEE Trans. Smart Grid, vol. 9, no. 6, pp. 6764-6779, Nov. 2018

    work page 2018

  8. [8]

    A tri-level planning approach to resilient expansion and hardening of coupled power distribution and transportation systems,

    W. Gan et al., "A tri-level planning approach to resilient expansion and hardening of coupled power distribution and transportation systems," IEEE Trans. Power Systems, vol. 37, no. 2, pp. 1495-1507, March 2022

    work page 2022

  9. [9]

    Distribution system resilience in ice storms by optimal routing of mobile devices o n congested roads,

    M. Yan, M. Shahidehpour, A. Paaso, L. Zhang, A. Alabdulwahab an d A. Abusorrah, "Distribution system resilience in ice storms by optimal routing of mobile devices o n congested roads," IEEE Trans. Smart Grid, vol. 12, no. 2, pp. 1314-1328, March 2021

    work page 2021

  10. [10]

    Stochastic optimization of coupled power distribution-urban transportation network operations with autonomous mobility on demand systems,

    H. Wang et al., "Stochastic optimization of coupled power distribution-urban transportation network operations with autonomous mobility on demand systems," IEEE Trans. Smart Grid, vol. 15, no. 3, pp. 3040-3053, May 2024

    work page 2024

  11. [11]

    DCOPF-based LMP simulation: algorithm, comparison with ACOPF, and sensitivity,

    F. Li and R. Bo, "DCOPF-based LMP simulation: algorithm, comparison with ACOPF, and sensitivity," IEEE Trans. Power Systems, vol. 22, no. 4, pp. 1475-1485, Nov. 2007

    work page 2007

  12. [12]

    Optimal tr affic-power flow in urban electrified transportation networks,

    W. Wei, S. Mei, L. Wu, M. Shahidehpour and Y . Fang, "Optimal tr affic-power flow in urban electrified transportation networks," IEEE Trans. Smart Grid, vol. 8, no. 1, pp. 84-95, Jan. 2017

    work page 2017

  13. [13]

    Optimal pricing of public electric vehicle charging stations considering operations of coupled transportation and power systems,

    Y . Cui, Z. Hu and X. Duan, "Optimal pricing of public electric vehicle charging stations considering operations of coupled transportation and power systems," IEEE Trans. Smart Grid , vol. 12, no. 4, pp. 3278-3288, July 2021

    work page 2021

  14. [14]

    Coordinating urban power-traffic networks: a subsidy-based Nash–Stackelberg– Nash game model,

    S. Lv, S. Chen and Z. Wei, "Coordinating urban power-traffic networks: a subsidy-based Nash–Stackelberg– Nash game model," IEEE Trans. Industrial Informatics, vol. 19, no. 2, pp. 1778-1790, Feb. 2023

    work page 2023

  15. [15]

    A capacity-based regulation method for coordinating electric vehicle charging flows in coupled distribution and transportation networks,

    K. Li, C. Shao, M. Shahidehpour and X. Wang, "A capacity-based regulation method for coordinating electric vehicle charging flows in coupled distribution and transportation networks," IEEE Trans. Smart Grid, vol. 15, no. 3, pp. 3066-3079, May 2024

    work page 2024

  16. [16]

    Enhancing resilien ce with electric vehicles charging redispatching and vehicle-to-grid in traffic-electric networks,

    W. Gan, J. Wen, M. Yan, Y . Zhou and W. Yao, "Enhancing resilien ce with electric vehicles charging redispatching and vehicle-to-grid in traffic-electric networks," IEEE Trans. Industry Applications, vol. 60, no. 1, pp. 953-965, Jan.-Feb. 2024

    work page 2024

  17. [17]

    Mechanism Design: A Linear Programming Approach

    V ohra RV . Mechanism Design: A Linear Programming Approach . Econometric Society Monographs. Cambridge University Press; 2011:1-6

    work page 2011

  18. [18]

    T. A. Manual, Bureau of Public Roads, U.S. Dept. Commisson, Washington, DC, USA, 1964

    work page 1964

  19. [19]

    A flow travel time relationship for use in transportation planning,

    K. Davidson, “A flow travel time relationship for use in transportation planning,” in Proc. 3rd Aust. Road Res. Board (ARRB) Conf., vol. 3, 1966, pp. 183–194

    work page 1966

  20. [20]

    Optimal pricing to manage electric vehicles in coupled power and transportation networks,

    M. Alizadeh, H. -T. Wai, M. Chowdhury, A. Goldsmith, A. Scaglione and T. Javidi, "Optimal pricing to manage electric vehicles in coupled power and transportation networks," IEEE Trans. Control of Network Systems, vol. 4, no. 4, pp. 863-875, Dec. 2017

    work page 2017