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REVIEW 4 major objections 5 minor 19 references

BESS Participation Planning for Provision of Grid Services in Energy and Regulation Markets

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper presents a stochastic optimization model that decides, for every hour, which Nordic grid-service market a battery should bid into in order to maximize expected profit, including the effects of penalties and battery degradation.

desk verdict FCR-N charging is forbidden at high frequencies, the objective has undefined variables, and the missing figures make the headline results unverifiable — the formulation needs a major rewrite. read the letter →

arxiv 2506.08472 v1 pith:RK65DNX4 submitted 2025-06-10 math.OC

Zeenat Hameed , Chresten Traeholt This is my paper · ORCID
classification math.OC MSC 90C1590C11
keywords batteryenergystoragestochasticoptimizationelectricitymarketsregulationpricescenariosdegradationcostsmarketparticipationNordicpowersystem
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper is trying to establish that a battery storage system's market participation can be planned hour by hour with a stochastic optimization model that accounts for real bid submission rules, pricing mechanisms, penalty payments, and degradation costs. If the model is right, a battery owner can calculate the business value of single versus multi-market services and see which combination of markets yields the highest profit under different price conditions. The key output is the percentage of hours each market service should be targeted, a number that directly guides bidding strategy. This matters because prior work mostly treated batteries as controllers, not as businesses facing market-specific rules.

What carries the argument

The central object is a mixed-integer linear program that makes three binary decisions per hour and scenario: whether to submit a bid, whether the bid is accepted, and whether the battery fulfills its energy promise. Droop-control curves translate grid-frequency samples into per-minute energy requirements, and Big-M linearization converts the nonlinear revenue and penalty terms into linear constraints. This machinery converts market rules and battery physics into an objective function that maximizes total expected revenue minus degradation costs, subject to state-of-charge and bid constraints.

What would settle it

Run the same optimization with bid power and energy as decision variables instead of fixed values; if the resulting optimal bid sizes differ materially from 0.9 MW and 0.4 MWh, the paper's recommended percentage-of-hours allocations are not robust to bid sizing. Alternatively, compare the model's recommended hour-level market choices against the profit-maximizing choices observed from a real BESS operating in the Nordic markets over a full year; a systematic mismatch would indicate the model's assumptions about prices or penalties are off.

Watch

Extended reading notes

Core claim

The central claim is that modelling price uncertainty with market price scenarios and representative days allows the optimizer to output the percentage of hours each market service (FCR-N, FCR-D, spot discharge, spot charge) can be targeted to maximize expected profit. The model compares single-market and multi-market participation, and shows that including degradation costs changes the choice of markets and reduces bid-submission hours, but that profit does not fall proportionally. For the test week studied, frequency markets are shown to be more attractive than spot markets, and FCR-D becomes preferable over FCR-N when degradation is accounted for.

Load-bearing premise

The battery is assumed to always bid a fixed 0.9 MW in frequency markets and a fixed 0.4 MWh in spot markets, rather than optimizing its bid size; if real bids are sized differently, the recommended market shares, revenues, and penalties would change.

Editorial extensions

If this is right

  • Battery owners can use the model's percentage-of-hours output as a bidding calendar: in hours where a market's share is zero, the battery should stay idle or switch to a more profitable service.
  • Including degradation costs makes the optimizer favour low-energy-demand markets like FCR-D over high-energy-demand markets like FCR-N, so ignoring battery wear overstates the value of FCR-N.
  • Limiting bid-submission hours is a viable lever: the model shows profit falls far less than bid hours when degradation is included, because penalty-heavy high-degradation hours are avoided.
  • The model's structure is general enough that the same formulations can be applied to other zonal or pay-for-availability markets beyond the Nordic system.
  • Because the model returns a recommended market mix for each price scenario, it can be re-run whenever price forecasts change, giving a rolling participation plan.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension is to make bid size an optimization variable instead of a fixed input; the paper fixes 0.9 MW for frequency bids and 0.4 MWh for spot, so the current results are conditional on those sizes.
  • The percentage-of-hours recommendation could be turned into a real-time switching policy by coupling the stochastic plan with a lower-level controller, linking the business layer to operational dispatch.
  • The model could be tested against a year of historical market data to see whether the recommended hour-by-hour market choices would have beaten a fixed 'always FCR-N' strategy in realized revenue.
  • For other regions, the penalty terms and pricing mechanisms would need to be re-parameterised, but the optimisation skeleton and the degradation-avoidance insight likely carry over.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a stochastic mixed-integer optimization model for planning BESS participation in Nordic spot, FCR-N, FCR-D, and related regulation markets. The model is intended to capture droop-based energy requests, bid submission and acceptance, availability and spot payments, penalties for non-fulfillment, and degradation costs, and to output the percentage of hours each market service should be targeted in order to maximize expected profit. The manuscript reports single-market and multi-market participation percentages from one representative week of 2024 data. The central claim is that the model quantifies business value and recommends hour-level market participation for BESSs.

Significance. The planning problem addressed here is relevant: translating market rules, penalty structures, and degradation costs into an optimization model for BESS revenue is a useful step beyond pure controller-design studies. The scenario-based MILP structure is a reasonable vehicle for the intended analysis. However, as printed the central model is not internally consistent: key constraints contradict the droop requirement, the objective references undefined variables, the penalty construction applies both imbalance prices regardless of the accepted spot side, and the numerical results rely on missing figures. Because the claimed hour-level participation percentages are derived from this model, the central claim is not supported by the written manuscript. If the formulation and results were corrected, the general idea could be of interest to the ancillary-services and energy-storage communities, but the current text does not provide a verified basis for its conclusions.

major comments (4)
  1. [III-F] The constraint block in Section III-F imposes zch_stm=0 for every (s,t,m) with Pm2 < f_m_st. For FCR-N, Pm2=50.0 Hz, while the droop equation (2) requires Ech_stm>0 exactly when 50.0 < f_m_st <= 50.1 Hz. Thus the model forbids the charging action that FCR-N downward regulation requires. Consequently, for an accepted FCR-N bid in any hour containing a minute above 50.0 Hz, the balance equation zch_stm+sch_stm=Ech_stm xbid,acc_shm forces the slack sch_stm to be positive, and the penalty-coupling constraint sum_{t:ht=h}(sdch_stm+sch_stm) <= M(1-wok_sh) then forces wok_sh=0. The optimizer must either refuse the bid or incur the full penalty, so the downward-regulation service that is half of FCR-N's value is absent from the written model. The participation percentages in Section IV are therefore not supported by the formulation as presented.
  2. [III-F, Eq. (20)] The objective function in Eq. (20) uses variables wwon,s-dch_sh, wlost_sh, wlost,s-dch_sh, wlost,s-ch_sh, and wenergy_sh, but none of these is defined or constrained in Section III-E. The variables actually defined there are wwon,avail_sh, wlost,avail_sh, wwon,spot,dch_sh, wlost,spot,dch_sh, and wlost,spot,ch_sh. With undefined variables in the objective, the optimization problem is not a well-defined mathematical program, and the reported optimal revenues and hour percentages cannot be reproduced or interpreted.
  3. [III-E] The penalty expression for wok_sh=0 subtracts wavail_sh + C_up_sh Espot + C_down_sh Espot regardless of which spot bid was accepted. If the accepted spot bid is S-DCH, the down-regulation imbalance price C_down_sh should not apply; if the accepted bid is S-CH, the up-regulation price C_up_sh should not apply. As printed, a failed spot discharge is penalized by both the up and down imbalance prices, which overstates penalties and distorts the model's choice among S-DCH, S-CH, FCR-N, and FCR-D. The numerical results in Section IV inherit this distortion.
  4. [IV] The results section is not checkable because the supporting figures are missing. The text refers to 'Fig. ??' twice in Section IV-A, and the subsequent figures (Figs. 3-8 in the reference list of figures) are placeholders or absent from the submitted text. Without these figures or a table of numerical values, the claimed percentages (e.g., 92%, 79%, 100%, 54%, 12%) and the profit comparisons cannot be verified against the model.
minor comments (5)
  1. [III-A] The line defining the droop control points is duplicated immediately before equations (1) and (2); one copy should be removed.
  2. [III-C/III-D] The model fixes the frequency-market bid at Pmax=0.9 MW and the spot bid at Espot=0.4 MWh rather than optimizing bid sizes. The reported hour-level recommendations are conditional on these arbitrary values, and no sensitivity analysis is provided to indicate how the results would change for other bid sizes.
  3. [III-F, Eq. (20)] The degradation term C_degradation_shtm xbid,acc_shm in Eq. (20) sums over t and m, but the acceptance variable xbid,acc_shm is indexed by hour h, not by minute t. The indices should be aligned so that the degradation cost is charged for the correct time resolution.
  4. [III-F] The constraint involving Pmax_shm is not clearly defined: Pmax_shm appears as a parameter in the bid-acceptance constraints, but no definition or source for this scenario-hour-market-specific parameter is given in Section III.
  5. [II] The market description for FCR-N states symmetrical response at f <= 49.9 Hz or f >= 50.1 Hz, while the droop model in Section III-A uses 50.0 Hz as the deadband boundary; the manuscript should reconcile these threshold descriptions.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the reported market-share percentages are optimization decision variables under stated constraints, not fitted quantities, and the self-citations are background only.

full rationale

The paper is a planning model rather than an empirical prediction. It takes market price scenarios and frequency traces as inputs, maps them to per-minute energy requirements through the droop equations (1)-(2), and optimizes binary bid, acceptance, and fulfillment decisions. The reported 'percentage of hours' values are the optimal outcomes of xbid and xbid,acc, not fitted parameters renamed as predictions. The fixed bid size assumptions (Pmax = 0.9 MW, Espot = 0.4 MWh) are stated simplifications, not calibration targets. The self-citations (e.g., refs. [13], [16], [17]) support background statements about Nordic market mechanisms, but the central optimization does not reduce to any self-cited theorem or prior fitted result. There are internal correctness concerns, such as the constraint zch_stm = 0 for f > 50.0 conflicting with the FCR-N downward requirement from Eq. (2), and the objective function (20) referencing variables not defined in the printed formulation; however, these are completeness or consistency defects, not circular reductions. No equation or output is equivalent to an input by construction, so no significant circularity is present.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The model relies on several user-specified parameters (bid sizes, capacity, degradation cost, Big-M) and on structural assumptions about Nordic market rules and droop behavior. The fixed bid sizes and unstated degradation cost function are the most consequential because they directly shape the reported profit percentages.

free parameters (6)
  • Pmax = 0.9 MW
    Assumed fixed bid power for FCR-N and FCR-D markets (Section III-C). The choice is arbitrary and not optimized; profit results depend on it.
  • Espot = 0.4 MWh
    Assumed fixed bid energy for spot market charge/discharge (Section III-D).
  • Degradation cost parameters = Not specified
    The objective includes C_degradation_shtm but the cost function and its coefficients are never defined in the text.
  • Battery capacity bounds (Emin, Emax) and initial SOC (M0) = Not specified
    State-of-charge constraints require these values but they are not given.
  • Big-M constant = Not specified
    Used in all linearizations; typically large but must be tuned; not specified.
  • Bid price limits (Bidmin, Bidmax) = Not specified
    Constraints on bid price xprice_h require these bounds.
assumptions (5)
  • domain assumption Nordic market rules as summarized in Section II: zonal pricing, pay-as-bid for FCR availability, pay-as-clear for spot, penalties for non-delivery.
    The model takes these market mechanisms as given inputs.
  • domain assumption Linear droop control relationship between grid frequency and BESS activation (Eqs. 1-2).
    Used to compute per-minute energy requirements from frequency data.
  • domain assumption Each day of the representative week is an equally likely scenario for prices and frequency.
    The scenario set and probabilities are assumed; no statistical justification.
  • ad hoc to paper Battery degradation cost can be represented as a separable cost per market activation (C_degradation_shtm).
    The specific degradation model is not defined, so it is an unverified modeling choice.
  • standard math Big-M reformulation of products of binary and continuous variables is valid.
    Standard technique; requires a finite upper bound M.

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Pith. "Pith review of BESS Participation Planning for Provision of Grid Services in Energy and Regulation Markets." pith.science (2026). https://pith.science/paper/RK65DNX4

@misc{pith2026250608472,
  author       = {Pith},
  title        = {Pith review of: BESS Participation Planning for Provision of Grid Services in Energy and Regulation Markets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RK65DNX4}},
  note         = {Machine review of arXiv:2506.08472}
}
read the original abstract

This paper presents a stochastic optimization model for planning the participation of battery energy storage systems (BESSs) in energy and regulation markets. The proposed model quantifies and compares the business value of single and multi-market BESS services by accounting for their bid submission and acceptance procedures, pricing mechanisms and revenue streams, and penalty payments and degradation costs. By modelling the price uncertainties using market price scenarios (MPSs) and considering representative days for different price seasonalities, the model outputs the percentage of hours each market service can be targeted to maximize profits. This helps in quantifying the impact of operational and market requirements of different services on choice of markets for BESSs. It also helps in determining the approximate costs and revenues that may be accrued by the BESS owners by choosing combinations of available services under different price conditions. The model thus overcomes the key limitations of previous studies that were mainly conducted from a controller design viewpoint and were thus more focused on the operational control of BESSs. The proposed model is generalizable and extendable to BESS service provision in multiple markets of different regions.

Figures

Figures reproduced from arXiv: 2506.08472 by the authors.

Figure 1
Figure 1. Nordic markets arXiv:2506.08472v1 [math.OC] 10 Jun 2025 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Binary decisions B. Binary Decisions At each hour h ∈ H, for each market m ∈ M and scenario s ∈ S, the optimizer makes three binary decisions ( [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Bid submitted and accepted hours for single-market services (scenario [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Costs and earnings for single-market participation (scenario [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: Costs and earnings for single-market participation [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: Charge/Discharge profile of BESS in multiple markets no-DC [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: Charge/Discharge profile of BESS in multiple markets DC [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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