pith. sign in

arxiv: 2602.17352 · v2 · submitted 2026-02-19 · 📡 eess.SY · cs.SY

Herd Behavior in Decentralized Balancing Models: A Case Study in Belgium

Max Bruninx , Seyed Soroush Karimi Madahi , Timothy Verstraeten , Jan Decuyper , Chris Develder , Jan Helsen This is my paper

Pith reviewed 2026-05-15 21:15 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords decentralized balancingimplicit balancingBalance Responsible Partiesbattery assetsovershoot riskBelgiummarket simulatorbalancing costs
0
0 comments X

The pith

Implicit balancing by Belgian BRPs cuts TSO costs at moderate battery capacities but produces overshoots that raise costs again at higher levels, while BRPs continue to profit.

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

The paper tests how Balance Responsible Parties react to real-time price signals in Belgium's decentralized balancing model by deviating battery schedules to help restore grid balance. A market simulator generates minute-level prices from 2023 Belgian data and models the responses of battery assets under different risk profiles and three candidate price formulas. Moderate implicit reactions reduce the TSO's balancing costs, yet the study shows that larger total reaction capacity creates overshoots that require extra explicit activations and ultimately increase costs. BRPs still record net savings even after the TSO's costs begin to rise. These results matter because they quantify the practical limit at which encouraging flexible assets through price signals stops helping the system and starts creating new imbalances.

Core claim

The central claim is that implicit balancing via price signals produces a significant initial reduction in balancing costs, but the risk of overshoots outweighs the benefits once the aggregate capacity of implicit reactions grows too large; even in that regime, BRPs continue to benefit financially from participating.

What carries the argument

The market simulator that generates minute-level price signals and models the implicit reactions of battery assets under varying risk profiles.

If this is right

  • Moderate growth in implicit balancing capacity lowers the TSO's explicit activation costs.
  • Beyond a capacity threshold, implicit reactions create overshoots that increase total balancing costs.
  • BRPs record financial gains from implicit balancing even after TSO costs start rising.
  • Alternative price formulas can be ranked by their ability to delay the onset of overshoots.

Where Pith is reading between the lines

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

  • TSOs may need dynamic caps or adjusted price formulas to prevent aggregate implicit capacity from crossing the overshoot threshold.
  • The same capacity limit could apply when designing decentralized balancing rules in other European markets.
  • Battery operators could select risk profiles that maximize their gains while staying below the system-wide overshoot point.
  • Real-time monitoring of aggregate implicit reaction volume would allow the TSO to switch price signals before costs rise.

Load-bearing premise

The market simulator and assumed risk profiles of battery assets accurately reflect how real Balance Responsible Parties would react to the tested price signals in live operation.

What would settle it

Compare actual BRP schedule deviations and resulting balancing costs in the Belgian market during periods of rapidly growing battery capacity against the simulator outputs for the same price signals.

Figures

Figures reproduced from arXiv: 2602.17352 by Chris Develder, Jan Decuyper, Jan Helsen, Max Bruninx, Seyed Soroush Karimi Madahi, Timothy Verstraeten.

Figure 1
Figure 1. Figure 1: High-level overview of the simulation environment [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Boxplots of the RMSE of the minute-level imbalance [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Distribution of the absolute system imbalance (1- [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Profit per imbalance settlement period normalized by [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Balancing cost per imbalance settlement period for the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 8
Figure 8. Figure 8: Profit per imbalance settlement period normalized by [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 6
Figure 6. Figure 6: Boxplots of the RMSE of the minute-level imbalance [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: Distribution of the absolute system imbalance (1- [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Boxplots of the RMSE of the minute-level imbalance [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 13
Figure 13. Figure 13: Distribution of the absolute system imbalance (1- [PITH_FULL_IMAGE:figures/full_fig_p009_13.png] view at source ↗
Figure 12
Figure 12. Figure 12: Profit per imbalance settlement period normalized by [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
read the original abstract

In a decentralized balancing model, Balance Responsible Parties (BRPs) are encouraged by the Transmission System Operator (TSO) to deviate from their schedule to help the system restore balance, also referred to as implicit balancing. This could reduce balancing costs for the grid operator and lower the entry barrier for flexible assets compared to explicit balancing services. However, these implicit reactions may overshoot when their total capacity is high, potentially requiring more explicit activations. This study analyses the effect of increased participation in the decentralized balancing model in Belgium. To this end, we develop a market simulator that produces price signals on minute-level and simulate the implicit reactions for battery assets with different risk profiles. Besides the current price formula, we also study two potential candidates for the near-term presented by the TSO. A simulation study is conducted using Belgian market data for the year 2023. The findings indicate that, while having a significant positive effect on the balancing costs at first, the risk of overshoots can outweigh the potential benefits when the total capacity of the implicit reactions becomes too large. Furthermore, even when the balancing costs start to increase for the TSO, BRPs were still found to benefit from implicit balancing.

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

3 major / 2 minor

Summary. The paper develops a minute-level market simulator for Belgium's decentralized balancing model and uses 2023 market data to examine how increasing implicit balancing participation by battery assets affects TSO balancing costs and BRP profits. It tests the current imbalance price formula plus two TSO-proposed alternatives, models battery reactions under different risk profiles, and concludes that implicit balancing initially lowers TSO costs but produces net cost increases once total implicit capacity exceeds a threshold due to overshoots, while BRPs continue to benefit even after that point.

Significance. If the simulator's price-response loop and battery reaction rules are faithful, the work supplies a concrete, data-driven illustration of herd-behavior limits in implicit balancing and quantifies a capacity threshold beyond which additional implicit participation becomes counterproductive for the TSO. The use of real 2023 Belgian data and the comparison of three price formulas are strengths that make the results policy-relevant for TSOs considering expanded implicit mechanisms.

major comments (3)
  1. [Section 3] Section 3 (Market Simulator) and the price-formula description: it is not stated whether the imbalance volume fed into the minute-level price calculation is updated by the sum of all implicit BRP actions within the same minute. If prices are generated from an exogenous forecast rather than the closed-loop net imbalance, the simulated price spikes that trigger further reactions are too mild, which would make the reported capacity threshold at which TSO costs begin to rise artificially high and directly undermine the headline overshoot claim.
  2. [Section 5] Section 5 (Simulation Results) and abstract: no validation against observed 2023 balancing costs, no error bars on the reported cost curves, and no calibration details for the battery risk profiles are provided. Because the quantitative claims rest entirely on forward simulation with free parameters (risk profiles and participation capacities), the absence of any grounding against real outcomes leaves the magnitude and location of the overshoot threshold weakly supported.
  3. [Section 4.2] Section 4.2 (BRP profit calculation): the statement that BRPs still benefit even after TSO costs rise is load-bearing for the policy conclusion, yet the paper does not show how BRP revenues are computed once explicit activations increase or whether those revenues remain positive under the alternative price formulas.
minor comments (2)
  1. [Figures 4-5] Figure 4 and 5: axis labels and legend entries are too small to read at standard print size; add explicit units (MW, €/MWh) and a note on whether shaded regions represent min/max or standard deviation across risk profiles.
  2. [Section 3] Notation: the symbol for imbalance price is used interchangeably with the imbalance volume in several equations; introduce distinct symbols and a nomenclature table.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below, providing clarifications on the simulator mechanics and committing to revisions that strengthen the presentation of methods, results, and robustness checks.

read point-by-point responses

  1. Referee: [Section 3] Section 3 (Market Simulator) and the price-formula description: it is not stated whether the imbalance volume fed into the minute-level price calculation is updated by the sum of all implicit BRP actions within the same minute. If prices are generated from an exogenous forecast rather than the closed-loop net imbalance, the simulated price spikes that trigger further reactions are too mild, which would make the reported capacity threshold at which TSO costs begin to rise artificially high and directly undermine the headline overshoot claim.

    Authors: The simulator implements a closed-loop update: for each minute, the net imbalance volume is first computed from the exogenous forecast and then adjusted by subtracting the aggregate volume of all implicit BRP actions (battery deviations) occurring in that same minute. The resulting net volume is fed directly into the imbalance price formula. This feedback is essential to the herd-behavior dynamics we study. We will revise Section 3 to state this explicitly, add a flowchart of the minute-level loop, and include pseudocode showing the update step before price calculation. revision: yes

  2. Referee: [Section 5] Section 5 (Simulation Results) and abstract: no validation against observed 2023 balancing costs, no error bars on the reported cost curves, and no calibration details for the battery risk profiles are provided. Because the quantitative claims rest entirely on forward simulation with free parameters (risk profiles and participation capacities), the absence of any grounding against real outcomes leaves the magnitude and location of the overshoot threshold weakly supported.

    Authors: We acknowledge the value of additional grounding. The model is driven by real 2023 Belgian imbalance volumes and prices, but granular minute-level records of actual explicit activations are not publicly available for direct validation. Risk-profile parameters are drawn from typical battery operator risk tolerances reported in the literature; we will add an appendix with the exact parameter values, a sensitivity analysis across plausible ranges, and error bands on the cost curves obtained from repeated simulations. These additions will better support the location of the overshoot threshold. revision: partial

  3. Referee: [Section 4.2] Section 4.2 (BRP profit calculation): the statement that BRPs still benefit even after TSO costs rise is load-bearing for the policy conclusion, yet the paper does not show how BRP revenues are computed once explicit activations increase or whether those revenues remain positive under the alternative price formulas.

    Authors: BRP profit for each minute is the product of the realized imbalance price and the BRP’s net deviation volume (including its implicit balancing action). Explicit activations are settled separately by the TSO and do not alter the imbalance price applied to BRP deviations in our model. We will expand Section 4.2 with the explicit profit formula, apply it to all three price formulas, and add a supplementary figure confirming that BRP profits remain positive beyond the TSO-cost overshoot threshold under each formula. revision: yes

standing simulated objections not resolved
  • Direct validation of simulated TSO balancing costs against observed 2023 minute-level explicit activation data, which is not publicly available at the required granularity.

Circularity Check

0 steps flagged

No circularity: forward simulation on external data

full rationale

The paper reports outcomes from a market simulator run on 2023 Belgian market data. Price signals are generated and battery reactions are simulated for different risk profiles and capacity levels; results on balancing costs and overshoot thresholds are produced by executing the model rather than by fitting parameters to those same outcomes or by reducing equations to self-definitions. No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work appear in the derivation chain. The central findings are therefore independent empirical outputs of the simulation and receive score 0.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim depends on behavioral assumptions about risk-averse BRPs and the fidelity of the minute-level price simulator; no new entities are postulated.

free parameters (2)
  • battery risk profiles
    Different risk tolerances are simulated to generate reactions; exact parameter values not specified in abstract.
  • participation capacity levels
    Varied across scenarios to identify overshoot threshold.
axioms (1)
  • domain assumption BRPs make rational adjustments to their schedules based on observed price signals and their risk profiles
    Core modeling choice for implicit reactions.

pith-pipeline@v0.9.0 · 5533 in / 1098 out tokens · 23013 ms · 2026-05-15T21:15:42.769070+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

25 extracted references · 25 canonical work pages

  1. [1]

    [Online]

    IEA,Global energy review 2025, Licence: CC BY 4.0, Paris, 2025. [Online]. Available: https://www.iea.org/ reports/global-energy-review-2025

    work page 2025

  2. [2]

    Harmonisation of imbalance settlement,

    A. for the Cooperation of Energy Regulators (ACER). “Harmonisation of imbalance settlement,” Accessed: Oct. 16, 2024. [Online]. Available: https://www.acer. europa.eu/electricity/market-rules/electricity-balancing/ harmonisation-of-imbalance-settlement

    work page 2024

  3. [3]

    Harnessing Flexibility in the Energy Transition,

    Elia Transmission Belgium SA. “Harnessing Flexibility in the Energy Transition,” Accessed: Oct. 30, 2025. [Online]. Available: https://issuu.com/eliagroup/docs/ harnessing flexibility in the energy transistion ? fr = sZjZlOTg0NTQ2NDY

    work page 2025

  4. [4]

    Strategic implicit balancing with energy storage systems via stochastic model predictive control,

    R. Smets, K. Bruninx, J. Bottieau, J.-F. Toubeau, and E. Delarue, “Strategic implicit balancing with energy storage systems via stochastic model predictive control,” IEEE Transactions on Energy Markets, Policy and Reg- ulation, vol. 1, no. 4, pp. 373–385, 2023

    work page 2023

  5. [5]

    Risk-aware par- ticipation in day-ahead and real-time balancing markets for energy storage systems,

    E. Wessel, R. Smets, and E. Delarue, “Risk-aware par- ticipation in day-ahead and real-time balancing markets for energy storage systems,”Electric Power Systems Research, vol. 235, p. 110 741, 2024

    work page 2024

  6. [6]

    Safe reinforcement learning for battery energy storage partic- ipation in the imbalance settlement,

    C. Rasic, P. Favaro, Y . Wang, and J.-F. Toubeau, “Safe reinforcement learning for battery energy storage partic- ipation in the imbalance settlement,”IEEE Transactions on Energy Markets, Policy and Regulation, 2025

    work page 2025

  7. [7]

    Model predictive control-guided reinforce- ment learning for implicit balancing,

    S. S. Karimi Madahi, K. Bruninx, B. Claessens, and C. Develder, “Model predictive control-guided reinforce- ment learning for implicit balancing,”arXiv preprint arXiv:2510.04868, 2025

    work page arXiv 2025

  8. [8]

    Gaming strategies in european imbalance settlement mechanisms,

    S. S. Karimi Madahi, K. Bruninx, B. Claessens, and C. Develder, “Gaming strategies in european imbalance settlement mechanisms,” in2025 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT Europe), IEEE, 2025, pp. 1–5

    work page 2025

  9. [9]

    Public consultation on the “real-time price

    Elia Transmission Belgium SA. “Public consultation on the “real-time price” design note II focused on the imbalance price formula evolutions,” Accessed: Sep. 23,

    work page

  10. [10]

    Available: https : / / www

    [Online]. Available: https : / / www. elia . be / en / public-consultation/20250404 public-consultation-on- the-real-time-price-design-note-ii

    work page arXiv

  11. [11]

    Day-ahead bidding strategies for wind farm operators under a one-price balancing scheme,

    M. Bruninx, T. Verstraeten, J. Kazempour, and J. Helsen, “Day-ahead bidding strategies for wind farm operators under a one-price balancing scheme,” inPro- ceedings of the 16th ACM International Conference on Future and Sustainable Energy Systems, 2025, pp. 719– 726

    work page 2025

  12. [12]

    Adequacy and flexibil- ity study for belgium 2026–2036

    Elia Transmission Belgium SA. “Adequacy and flexibil- ity study for belgium 2026–2036. ”[Online]. Available: https : / / issuu . com / eliagroup / docs / adequacy and flexibility study for belgium 2026-2

    work page 2026

  13. [13]

    Elia open data plat- form,

    Elia Transmission Belgium SA. “Elia open data plat- form,” Accessed: Jul. 1, 2025. [Online]. Available: https://opendata.elia.be/

    work page 2025

  14. [14]

    Platform for the Interna- tional Coordination of Automated Frequency Restora- tion and Stable System Operation (PICASSO),

    European Network of Transmission System Operators for Electricity (ENTSO-E). “Platform for the Interna- tional Coordination of Automated Frequency Restora- tion and Stable System Operation (PICASSO),” Ac- cessed: May 7, 2025. [Online]. Available: https://www. entsoe.eu/network codes/eb/picasso/

    work page 2025

  15. [15]

    Manual activation of re- serves initiative,

    European Network of Transmission System Operators for Electricity (ENTSO-E). “Manual activation of re- serves initiative,” Accessed: May 7, 2025. [Online]. Available: https://www.entsoe.eu/network codes/eb/ mari/

    work page 2025

  16. [16]

    Classification of balanc- ing markets based on different activation philosophies: Proactive and reactive designs,

    M. H ˚aberg and G. Doorman, “Classification of balanc- ing markets based on different activation philosophies: Proactive and reactive designs,” inIn proceedings of the 13th International Conference on the European Energy Market (EEM), IEEE, 2016, pp. 1–5

    work page 2016

  17. [17]

    A forecast-driven stochastic optimization method for proactive activation of manual reserves,

    J. Allard, A. Arrigo, J. Bottieau, G. Bertrand, Z. De Gr`eve, and F. Vall ´ee, “A forecast-driven stochastic optimization method for proactive activation of manual reserves,”Electric Power Systems Research, vol. 235, p. 110 804, 2024

    work page 2024

  18. [18]

    Terms and Conditions for Balance Responsible Parties (BRPs),

    Elia Transmission Belgium SA. “Terms and Conditions for Balance Responsible Parties (BRPs),” Accessed: Sep. 23, 2025. [Online]. Available: https://www.elia. be/ - /media / project / elia / elia - site / electricity - market - and- system--- document- library/balance- responsible- party- and- system- imbalance/2025/tc- brp- en-- as- of- 010625.pdf APPENDIX...

    work page 2025

  19. [19]

    aFRR component:The aFRR component is given by the weighted average price of all aFRR activations (in both directions): λaFRR = X t∈Q,t≤T P a+∈aFRR+ µa+ ba+ t +P a−∈aFRR− µa− ba− tP a+∈aFRR+ ba+ t +P a−∈aFRR− ba− t . (5) Note that in case there are no aFRR activations, this price is set equal to the average of the value of additional activation (V oAA)4 in...

    work page

  20. [20]

    mFRR component:The mFRR component is given by the marginal price of all mFRR activations: λmFRR = ( maxt∈Q,t≤T λmFRR+ t SI≤0 mint∈Q,t≤T λmFRR− t SI >0 .(6) Note that the mFRR component does not exist in case there are no mFRR activations

    work page

  21. [21]

    Spot price component:The spot price component is given by average between the value of additional activation (V oAA) in the upward and downward direction: λspot = V oAA+ +V oAA− 2 .(7) Note that in the current price calculation Elia refers to this component as the deadband value

    work page

  22. [22]

    withclip(x) = min (1,max(0, x))a function which clips the values between 0 and 1

    Alpha component:The alpha component is a correction to low imbalance prices for large system imbalances (with an absolute value larger than 150 MW) and is given by: α= a+ b 1 +e c−x d cp,(8) witha= 0, b= 200, c= 450, d= 65, x=average between the system imbalance during the current ISP and the system imbalance during the previous ISP andcpdefined as: cp= ...

    work page

  23. [23]

    Note that here we exclude the floor and the cap components since they are introduced to mitigate certain effects related to European balancing platforms (PICASSO/MAARI)

    Current formula:The current balancing price formula (as described in [17]) is given by: λB =    λspot SI∈[−25,25] max (λaFRR, λmFRR)SI <−25 min (λaFRR, λmFRR)SI >25, (11) When the system imbalance is small, the balancing price should not incentivize BRPs to react and therefore it is set equal to the spot price component between -25 MW and 25 MW. Note...

    work page

  24. [24]

    (14) The advantage of this approach is that it results in a smooth transition between the spot price component and the aFRR/mFRR component rather than jumps at the boundary values

    Max/min with smoothed deadband:In the first propo- sition by Elia to calculate the balancing price, a continuous weight (as a function of system imbalance) is attributed to the spot price component rather than a fixed deadband: λB =w spot λspot + (1−w spot)λ FRR (12) with: wspot =e −( SI 25 )4 ,(13) λFRR = ( max (λaFRR, λmFRR)SI≤0 min (λaFRR, λmFRR)SI >0....

    work page

  25. [25]

    Weighted average with dynamic weights:In the second proposition, the balancing price consists of the weighted average of the aFRR and mFRR price components rather than a max/min approach. λB =w aFRRλaFRR + (1−w aFRR)λmFRR (15) with: waFRR = X t∈Q,t≤T P a+∈aFRR+ ba+ t +P a−∈aFRR− ba− tP r∈R br t .(16) APPENDIXB SENSITIVITY STUDY In this section we provide ...

    work page