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Day-Ahead Bidding Strategies for Wind Farm Operators under a One-Price Balancing Scheme

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Pith's one-line read Under a one-price balancing scheme, the expected-profit-maximizing day-ahead bid for a wind farm is all-or-nothing; adding a risk constraint on balancing positions makes the optimal bid the point forecast shifted by sqrt(alpha…

desk verdict A clean analytical bidding rule undermined by an empirical counterfactual that double-counts the wind farm's open position; the paper deserves a referee but not publication as is. read the letter →

arxiv 2505.05153 v3 pith:RMWG5J2X submitted 2025-05-08 eess.SY cs.SY

Max Bruninx , Timothy Verstraeten , Jalal Kazempour , Jan Helsen This is my paper · ORCID
classification eess.SYcs.SY
keywords day-aheadbiddingone-pricebalancingschemewindfarmstochasticoptimizationriskcertificatepriceimpactoffshore
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The pith

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

The reading

This paper tries to establish what a wind-farm operator should bid in the day-ahead market when imbalance settlement uses a one-price scheme, the common European rule in which an open position that helps the system is rewarded and one that hurts it is penalized. It shows that the expected-profit-maximizing bid is an all-or-nothing choice, zero or the installed capacity, because the objective is linear in the bid. Since that extreme strategy is risky when balancing prices are hard to forecast and large open positions can flip the sign of the system imbalance, the paper adds a risk certificate limiting the expected squared open position and derives a closed-form optimum: the point forecast shifted by $\sqrt{\alpha-\mathrm{Var}(E_t)}$, capped at zero and capacity. Using Belgian market data and an offshore wind farm, it then shows that the all-or-nothing strategy loses money in the long run once its price impact on the balancing market is modeled, while the risk-constrained strategy still beats point-forecast bidding. If right, the paper gives operators a transparent, analytically solved bidding rule and a warning that backtests ignoring price impact overstate returns and understate risk.

What carries the argument

The load-bearing object is the linearized profit expression in Eq. (6): $\mathbb{E}[\Lambda_t^{\mathrm{DA}} y_t + \Lambda_t^{\mathrm{B}}(E_t-y_t)] = (\mathbb{E}[\Lambda_t^{\mathrm{DA}}]-\mathbb{E}[\Lambda_t^{\mathrm{B}}]) y_t + \mathbb{E}[\Lambda_t^{\mathrm{B}} E_t]$, which turns bidding into a sign test on the price gap. The risk certificate $\alpha$ constrains the expected squared open position and, through the variance decomposition $\mathrm{Var}(X)=\mathbb{E}[X^2]-\mathbb{E}[X]^2$, becomes a symmetric interval $\pm\sqrt{\alpha-\mathrm{Var}(E_t)}$ around the point forecast. The ex-post price-impact analysis uses the counterfactual system imbalance $\psi_t^\alpha=\psi_t+4(E_t-y_t)$ (the factor 4 converts MWh over a 15-minute window to MW) plus the merit-order curve built from historical balancing volume bids to recompute balancing prices.

What would settle it

Compare Eq. (11)'s counterfactual prices with an alternative shift that subtracts the farm's historical position, e.g. $\psi_t+4(y_t^{\mathrm{hist}}-y_t)$, on the same Belgian data; if the all-or-nothing strategy's long-run loss disappears or reverses, the price-impact result depends on double counting the farm's imbalance. A second check: rerun the evaluation on a smaller farm whose open positions are negligible relative to system imbalance, where the paper's own prediction is that the no-price-impact and price-impact profit curves should nearly coincide.

Watch

Extended reading notes

Core claim

The paper's central discovery is that, under a one-price balancing scheme, the day-ahead bidding problem has a boundary solution unless risk is constrained explicitly. Rewriting expected profit as $\left(\mathbb{E}[\Lambda_t^{\mathrm{DA}}] - \mathbb{E}[\Lambda_t^{\mathrm{B}}]\right) y_t + \mathrm{const}$ makes the objective linear in $y_t$, so the optimizer bids $\beta$ when $\mathbb{E}[\Lambda_t^{\mathrm{DA}}] > \mathbb{E}[\Lambda_t^{\mathrm{B}}]$ and $0$ otherwise. With the risk constraint $\mathbb{E}[(E_t-y_t)^2]\le\alpha$, variance decomposition bounds the feasible bid by $E[E_t]\pm\sqrt{\alpha-\mathrm{Var}(E_t)}$, and the same price comparison picks the upper or lower endpoint: $y_t^*=\min\{E[E_t]+\Delta_t;\beta\}$ or $y_t^*=\max\{E[E_t]-\Delta_t;0\}$ where $\Delta_t=\sqrt{\alpha-\mathrm{Var}(E_t)}$. The paper further claims that when the bid is large enough to alter the system imbalance's direction, the all-or-nothing strategy incurs long-term losses, whereas a moderate risk certificate still improves operational profit over point-forecast bidding.

Load-bearing premise

The load-bearing assumption is that the historical system imbalance data does not already include the wind farm's own past deviations; if it does, the balancing-price impact and the reported losses change.

Editorial extensions

If this is right

  • A risk certificate set to $\alpha=\mathrm{Var}(E_t)$ reduces the rule exactly to point-forecast bidding, while a sufficiently large $\alpha$ makes the constraint non-binding and recovers the all-or-nothing strategy.
  • Any moderate $\alpha$ between those extremes yields the binary rule $\min\{E[E_t]+\Delta_t;\beta\}$ or $\max\{E[E_t]-\Delta_t;0\}$ for each hour, so the operator's decision reduces to a price-gap forecast plus forecasts of the mean and variance of production.
  • If the price-impact model is right, backtesting a large offshore wind farm's bidding strategies on historical balancing prices without counterfactual price shifts will overstate cumulative profit and understate left-tail losses.
  • Across the first half of 2024 in Belgium, the all-or-nothing strategy turns from the most profitable to a long-term loss once price impact is included, while a moderate risk certificate remains superior to point-forecast bidding.

Reading between the lines

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

  • Beyond the paper: the all-or-nothing result is purely a consequence of linearity, so it likely extends to any price-taker whose balancing-market reward has the same sign structure, such as storage or flexible demand, whenever they can bid at a price of zero.
  • Beyond the paper: the expression $\Delta_t=\sqrt{\alpha-\mathrm{Var}(E_t)}$ says better production forecasts (lower variance) allow larger profitable open positions under the same risk budget, suggesting a direct economic value-of-forecasts calculation that the paper does not perform.
  • Beyond the paper: the paper notes that price impact makes the optimization bilevel; a testable extension is to learn the optimal bid directly from market data, treating the balancing-price response as an unknown function, and compare with the closed-form rule on the same Belgian dataset.
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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

2 major / 4 minor

Summary. The paper studies day-ahead bidding for a wind farm under a one-price balancing market. It first shows that, without risk constraints, the optimal bid is an all-or-nothing strategy: bid the full installed capacity when the expected day-ahead price exceeds the expected balancing price, and bid zero otherwise. To control the risk of large open positions, the authors add a constraint on the expected squared deviation between production and bid, governed by a risk certificate α, and derive in Section III the analytical solution in Eq. (10): the optimal bid is the upper or lower endpoint of a prediction interval around the point forecast, capped by capacity, depending on the sign of the expected price difference. The proposal is evaluated on Belgian market data and an offshore wind farm for the first half of 2024, comparing a no-price-impact evaluation using historical balancing prices with a price-impact evaluation that recalculates balancing prices from a shifted system imbalance (Eq. (11)) and a merit-order curve built from historical balancing volume bids. Under the price-impact evaluation, the all-or-nothing strategy yields long-term losses, while a risk-constrained strategy with α̃=25% still outperforms point-forecast bidding. The paper also compares profit distributions to show that ignoring price impact underestimates risk.

Significance. The analytical derivation is clean and correct under the stated assumptions, and the risk-constrained closed form is a useful, interpretable extension of the point-forecast baseline. The empirical price-impact framework is a valuable step toward realistic backtesting, and the use of real Belgian market data together with an offshore wind farm adds practical relevance. The paper is generally transparent about its assumptions and provides an appendix for the unequal-resolution case. However, the central empirical claims—that the all-or-nothing strategy produces long-term losses and that the α̃=25% strategy remains profitable under price impact—depend critically on the counterfactual system imbalance in Eq. (11), which appears to double-count the wind farm's historical open position. Until this is resolved, these conclusions are not supported.

major comments (2)
  1. [Section IV-B, Eq. (11)] The counterfactual system imbalance ψ_t^α = ψ_t + 4(E_t − y_t) appears to double-count the wind farm's historical open position. If ψ_t is the total system imbalance reported by the TSO, it already contains the wind farm's actual imbalance, which in the same units is 4(E_t − y_t^hist), where y_t^hist is the farm's historical day-ahead volume. Replacing the historical bid by the strategy bid y_t should change the total imbalance by 4(y_t^hist − y_t), not by 4(E_t − y_t). The paper never defines y_t^hist or demonstrates that ψ_t excludes this farm's imbalance. Because Eq. (11) drives the recalculation of balancing prices in Figs. 3b and 4, the claims that the all-or-nothing strategy causes long-term losses and that the α̃=25% strategy remains profitable under price impact are not supported without either a justification that ψ_t excludes the farm's own deviation or a re-evaluation using the corrected formula. This is a load-bearing issue for the paper's main empirical conclusions.
  2. [Section IV-A and IV-B] The evaluation does not report the historical day-ahead contracted volume y_t^hist of the wind farm, which is needed both to assess the magnitude of the double-counting in Eq. (11) and to reproduce the price-impact results. Please provide this data or explicitly state the assumption that the historical system imbalance excludes the farm's open position; without this, the empirical claims cannot be independently verified.
minor comments (4)
  1. [Section IV-A] The normalization of the risk certificate α̃ is not defined precisely; please specify the exact mapping between α and α̃ (e.g., α̃ = (α − Var(E_t))/(α_all − Var(E_t))) so that the reported values can be translated back to constraint (1b).
  2. [Figure 4] The y-axis label 'Frequency [.]' is uninformative; if these are probability densities or relative frequencies, please state the estimator and label the axis accordingly.
  3. [Section IV-B] The merit-order price calculation is described only in words; please add a step-by-step algorithm that explains how the balancing price is selected from the sorted bids, including the treatment of ties and the simultaneous activation of aFRR and mFRR volumes.
  4. [Throughout] The currency symbol appears as 'C/MWh' in several places, which is likely a rendering error; if the intended unit is euros, please use '€/MWh' consistently.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the optimal bid is derived from the stated optimization problem, and the empirical evaluation uses external historical market data.

full rationale

The paper's central analytical results, Eq. (7) and Eq. (10), are derived directly from the stated stochastic optimization problem (1). The objective is linear in the bid y_t, and the risk constraint is rewritten using the variance decomposition (9), yielding an explicit interval for y_t that depends only on E[E_t], Var(E_t), and the exogenous risk certificate α. No fitted parameter is renamed as a prediction: α is an input parameter, and the values α̃ = 0% to 100% are presented as a sensitivity sweep, not as an estimated quantity. The all-or-nothing result is a property of the linear objective, not an imported conclusion from a prior citation; prior work such as [2] and [16] is cited for context and comparison, not as the load-bearing source of the derivation. The only self-citation visible in the reference list, [10] which includes author Kazempour, appears in the literature review and does not support any central claim. The ex-post price-impact evaluation uses external data from Elia and a described merit-order construction, and the profit computations are explicitly labeled as a theoretical upper bound because observed prices are used instead of forecasts. The only notable concern is the counterfactual system imbalance in Eq. (11), where the paper assumes the historical system imbalance ψ_t does not already include the wind farm's own open position; if it does, the correct displacement would be 4(y_hist_t - y_t) rather than 4(E_t - y_t). This is a potential identifiability or modeling-error issue, not a circularity, because it does not make the paper's conclusions equivalent to its inputs by construction. Overall, the derivation chain is self-contained and the findings are not forced by self-citation or by defining a quantity in terms of the result it is used to predict.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The main burden is a set of market-structure assumptions plus one unverified counterfactual imbalance shift that drives the price-impact experiment.

free parameters (1)
  • risk certificate α (normalised as α̃) = α̃=25% highlighted as the preferred strategy in the experiments; part of a sweep from 0% to 100%
    The risk certificate sets the allowed deviation from the point forecast. It is an input chosen by the operator, not estimated from data, but the paper's claim that the risk-constrained strategy improves profit relies on selecting a favourable value after seeing the sweep.
assumptions (5)
  • domain assumption The wind farm is a price-taker in the optimisation problem
    Section II-C states this; it keeps the objective linear and makes Eq. (7) valid. Price impact is only added ex-post.
  • domain assumption Day-ahead offers at zero marginal cost are always accepted in the market clearing
    Section II-C, Assumption 2; required for the bid quantity y_t to be the cleared quantity.
  • domain assumption No curtailment or storage is available, so each tradable contract is independent
    Section II-C, Assumption 3; independence is used to solve each contract separately.
  • domain assumption The balancing price is derived from the historical merit-order of balancing volume bids with simplifications, including no cross-border sharing, no imbalance netting, and no Elia correction factor
    Section IV-B; needed to compute counterfactual balancing prices.
  • ad hoc to paper The counterfactual system imbalance is ψ_t + 4(E_t - y_t), i.e. the historical system imbalance does not already contain the wind farm's historical open position
    Eq. (11) in Section IV-B; this is load-bearing for the price-impact results and is not justified in the text.

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Cite this review

Pith. "Pith review of Day-Ahead Bidding Strategies for Wind Farm Operators under a One-Price Balancing Scheme." pith.science (2026). https://pith.science/paper/RMWG5J2X

@misc{pith2026250505153,
  author       = {Pith},
  title        = {Pith review of: Day-Ahead Bidding Strategies for Wind Farm Operators under a One-Price Balancing Scheme},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RMWG5J2X}},
  note         = {Machine review of arXiv:2505.05153}
}
read the original abstract

We study day-ahead bidding strategies for wind farm operators under a one-price balancing scheme, prevalent in European electricity markets. In this setting, the profit-maximising strategy becomes an all-or-nothing strategy, aiming to take advantage of open positions in the balancing market. However, balancing prices are difficult, if not impossible, to forecast in the day-ahead stage and large open positions can affect the balancing price by changing the direction of the system imbalance. This paper addresses day-ahead bidding as a decision-making problem under uncertainty, with the objective of maximising the expected profit while reducing the imbalance risk related to the strategy. To this end, we develop a stochastic optimisation problem with explicit constraints on the positions in the balancing market, providing risk certificates, and derive an analytical solution to this problem. Moreover, we show how the price-impact of the trading strategy on the balancing market can be included in the ex-post evaluation. Using real data from the Belgian electricity market and an offshore wind farm in the North Sea, we demonstrate that the all-or-nothing strategy negatively impacts the balancing price, resulting in long-term losses for the wind farm. Our risk-constrained strategy, however, can still significantly enhance operational profit compared to traditional point-forecast bidding.

Figures

Figures reproduced from arXiv: 2505.05153 by the authors.

Figure 1
Figure 1. Illustrative example of optimal day-ahead bidding [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. A simplified example of the merit-order curve and [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Cumulative profit of different trading strategies defined based on the risk certificate [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Comparison of the profit distributions of the trading strategies between the case where the price-impact is not considered [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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Reference graph

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Reviewed August 15, 2026 · model on record in the stance chip above.