Refinement of Reliability Grid Codes in the Provision of Ancillary Services

Jalal Kazempour; Lesia Mitridati; Steven A. Gabriel; Torine R. Herstad

Refinement of Reliability Grid Codes in the Provision of Ancillary Services

T0 review · 1 major / 0 minor · reviewed 2026-07-03 · grok-4.3

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Pith's one-line read A bilevel optimization model shows the cost-optimal reliability threshold for stochastic reserve providers lies below the conventional P90 level.

desk verdict The paper endogenizes the reliability threshold in a bilevel model and reports up to 14.5% cost savings versus fixed P90 in the Nordic FCR-D market, but the closed-form chance constraints rest on an unvalidated Weibull assumption. read the letter →

arxiv 2607.02319 v1 pith:TGV2I7HQ submitted 2026-07-02 eess.SY cs.SYmath.OC

Torine R. Herstad , Jalal Kazempour , Lesia Mitridati , Steven A. Gabriel This is my paper · ORCID

classification eess.SYcs.SYmath.OC

keywords ancillaryservicesreliabilitythresholdsstochasticresourcesbileveloptimizationchanceconstraintsFCR-DmarketWeibulldistributionreserveprocurement

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 establishes a framework for treating the minimum reliability threshold imposed on stochastic providers in ancillary service markets as an endogenous design variable rather than a fixed regulatory constant. It builds a bilevel model in which the transmission system operator chooses the threshold to minimize total procurement costs while providers optimize their bids subject to the resulting chance constraints. These constraints are reformulated exactly using a Weibull tail model of delivery uncertainty. When tested on the Nordic FCR-D market, the optimized threshold produces procurement cost reductions of up to 14.5 percent relative to the P90 standard, with an additional 2.4 percent saving available from allowing the threshold to vary by hour.

What carries the argument

Bilevel optimization framework in which the TSO sets the reliability threshold in the upper level and stochastic providers respond with reliability-constrained bids in the lower level, using analytical reformulation of chance constraints via Weibull tail distribution.

What would settle it

Implement the model's cost-optimal threshold in the actual Nordic FCR-D market clearing and measure whether realized procurement costs fall by approximately 14.5 percent while accepted bids continue to meet the chosen reliability level.

Watch

Extended reading notes

Core claim

The central claim is that endogenizing the reliability threshold via bilevel optimization, with chance constraints reformulated analytically from a Weibull tail distribution on delivery uncertainty, yields a cost-optimal threshold below P90 that reduces total procurement costs by as much as 14.5 percent in the studied Nordic FCR-D cases, while dynamic hourly thresholds provide further reductions up to 2.4 percent.

Load-bearing premise

Delivery uncertainty of stochastic providers follows a Weibull tail distribution that permits exact analytical reformulation of the chance constraints.

Editorial extensions

If this is right

Total reserve procurement costs fall when the TSO selects a threshold below the current P90 standard.
Stochastic providers submit larger accepted bids at the optimized threshold without violating reliability requirements.
Allowing the threshold to adjust each hour produces additional cost savings beyond a static threshold.
The same bilevel structure can be applied to other ancillary service products that admit stochastic participation.

Reading between the lines

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

In markets with greater diversity of stochastic resources the value of hourly threshold adjustment would likely increase.
Regulatory bodies could replace fixed probability thresholds with a periodic optimization process that updates the requirement based on observed bid distributions.
The framework could be extended to joint procurement across multiple ancillary services to capture cross-product reliability interactions.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The core result is that treating the minimum reliability threshold as a decision variable rather than a fixed regulatory number like P90 can lower total procurement costs, with the model finding an optimum below P90 and further gains from hourly variation.

What is new is the bilevel structure: the TSO in the upper level chooses the threshold to minimize system cost, while providers in the lower level submit bids subject to chance constraints on delivery. The authors obtain an analytical reformulation by assuming Weibull tails on the uncertainty, which avoids sampling and keeps the problem tractable. They apply the framework to actual Nordic FCR-D market data and show concrete cost reductions.

This is a practical step. Regulators currently pick thresholds by convention; the paper gives them a way to quantify the cost-reliability trade-off and test whether the current rule is efficient. The case study numbers are tied to a real market, which makes the claim testable in principle.

The soft spot is the distributional assumption. The analytical reformulation works only because of the Weibull tail; the abstract gives no evidence of a Kolmogorov-Smirnov test or tail fit on actual FCR-D delivery traces, nor any sensitivity run with an empirical quantile or alternative distribution. If the real tails are heavier or lighter, both the feasible set and the reported 14.5% savings shift. That modeling choice carries the central numerical claim.

The paper is for researchers working on ancillary service market design and stochastic optimization in power systems. A reader focused on regulatory mechanisms for reserves will see a structured way to revisit fixed rules.

It deserves peer review. The question is real, the modeling approach is coherent, and the Nordic application gives referees something concrete to check even if validation and robustness need work.

Referee Report

1 major / 0 minor

Summary. The manuscript develops a bilevel optimization framework in which the TSO endogenously sets a reliability threshold for stochastic reserve providers while lower-level providers optimize bids subject to chance constraints that are analytically reformulated under a Weibull tail assumption on delivery uncertainty. Applied to the Nordic FCR-D market, the cost-optimal threshold lies below the conventional P90 level, producing cost reductions of up to 14.5% relative to the fixed standard, with dynamic hourly thresholds yielding an additional 2.4% reduction.

Significance. If the distributional assumption holds, the work supplies a quantitative method for treating reliability thresholds as design variables rather than regulatory constants, which could improve efficiency in ancillary-service markets with growing stochastic participation. The closed-form chance-constraint reformulation is a methodological contribution that enables tractable optimization; the numerical results on threshold location and savings are the primary empirical claim.

major comments (1)

[chance-constraint reformulation (abstract and modeling sections)] The headline claims (optimal threshold below P90 and up to 14.5% cost reduction) rest on the Weibull tail assumption that permits exact analytical reformulation of the chance constraints. The abstract states this reformulation but the provided text contains no Kolmogorov-Smirnov test, tail-index estimation, or other goodness-of-fit evidence on actual Nordic FCR-D delivery traces, nor any sensitivity replacing Weibull with an empirical quantile or alternative distribution. Because the feasible set and objective are defined by this choice, the quantitative results cannot be assessed for robustness without such validation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment on the robustness of our distributional assumptions. We address the point directly below and will revise the manuscript accordingly to strengthen the empirical support for the reported results.

read point-by-point responses

Referee: The headline claims (optimal threshold below P90 and up to 14.5% cost reduction) rest on the Weibull tail assumption that permits exact analytical reformulation of the chance constraints. The abstract states this reformulation but the provided text contains no Kolmogorov-Smirnov test, tail-index estimation, or other goodness-of-fit evidence on actual Nordic FCR-D delivery traces, nor any sensitivity replacing Weibull with an empirical quantile or alternative distribution. Because the feasible set and objective are defined by this choice, the quantitative results cannot be assessed for robustness without such validation.

Authors: We agree that explicit validation of the Weibull assumption on Nordic FCR-D data is necessary for assessing robustness of the quantitative claims. The Weibull tail was selected because it yields a closed-form reformulation of the chance constraints (detailed in the modeling section), which is the methodological contribution enabling the bilevel optimization. In the revised manuscript we will add: (i) Kolmogorov-Smirnov goodness-of-fit tests and maximum-likelihood tail-index estimates on historical Nordic delivery traces; (ii) sensitivity runs replacing the parametric assumption with empirical quantiles and with alternative distributions (lognormal, gamma). These additions will qualify the 14.5 % cost-reduction figure and the location of the optimal threshold without altering the core bilevel framework or the analytical reformulation itself. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: bilevel optimization derives threshold endogenously from market data and Weibull reformulation

full rationale

The derivation optimizes the reliability threshold as an upper-level decision variable in a bilevel program whose lower level produces reliability-constrained bids; the chance-constraint reformulation is obtained directly from the explicit Weibull tail assumption rather than from any fitted parameter or self-citation. The reported cost savings and optimal threshold below P90 are therefore computed outputs of the model applied to Nordic FCR-D data, not quantities that reduce to the inputs by construction. No self-citation load-bearing steps, uniqueness theorems, or renaming of known results appear in the provided text.

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

The central claim rests on the bilevel market model and the Weibull distributional assumption for tractable chance constraints; limited information is available from the abstract alone.

free parameters (1)

Weibull shape and scale parameters
Parameters of the tail distribution used to reformulate chance constraints; likely estimated from data though not detailed in abstract.

assumptions (1)

domain assumption Delivery uncertainty of stochastic providers admits an exact analytical reformulation via Weibull tail probabilities
Invoked to convert probabilistic bidding constraints into deterministic equivalents inside the bilevel program.

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Cite this review

Pith. "Pith review of Refinement of Reliability Grid Codes in the Provision of Ancillary Services." pith.science (2026). https://pith.science/paper/TGV2I7HQ

@misc{pith2026260702319,
  author       = {Pith},
  title        = {Pith review of: Refinement of Reliability Grid Codes in the Provision of Ancillary Services},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TGV2I7HQ}},
  note         = {Machine review of arXiv:2607.02319}
}

read the original abstract

Stochastic resources such as wind farms, electric vehicle aggregators, and demand-side assets are increasingly participating as reserve providers in ancillary service markets. To manage delivery uncertainty, system operators impose minimum reliability thresholds on such providers. Energinet, the Danish transmission system operator (TSO), has pioneered this approach through the P90 requirement, requiring stochastic providers to make accepted reserve capacity bids available with at least 90% probability. Yet this threshold is set by regulatory convention, not optimization: no existing framework treats it as a design variable or characterizes the cost-reliability trade-off it governs. This paper closes that gap. We develop a bilevel optimization framework in which the TSO in the upper level sets the reliability threshold endogenously while providers in the lower levels respond through reliability-constrained bidding, with chance constraints reformulated analytically using a Weibull tail distribution. Applied to the Nordic frequency containment reserve for disturbances (FCR-D) market, the cost-optimal threshold lies below P90 in the studied cases, with cost reductions by up to 14.5% relative to the fixed standard. Dynamic hourly thresholds yield a further reduction of up to 2.4%, suggesting efficiency gains may increase in larger and more diverse reserve markets.

Figures

Figures reproduced from arXiv: 2607.02319 by the authors.

**Figure 1.** Information exchange in the bilevel optimization formulation. In the upper level, the TSO sets the reliability threshold 1 − εt, optimized hourly in the dynamic case and reduced to a single value 1 − ε in the static case, to minimize total reserve-related costs, including reserve procurement and expected shortfall penalties. In the lower level, a representative EV aggregator and a representative wind farm receive th… view at source ↗

**Figure 2.** Illustration of how the reliability threshold affects the wind farm’s reserve bid and the resulting reserve merit order for a representative hour. The left plot shows the cumulative distribution function (CDF) of the wind power forecast, where the x-axis represents the reserve bid size (MW) and the y-axis represents the shortfall probability εt. Three reliability thresholds are illustrated using dashed arrows: 1−εt… view at source ↗

**Figure 3.** Cumulative histogram of empirical samples below the 20th percentile with fitted Weibull cumulative distribution function and associated p-values following [24] of wind forecast with p = 0.62 (left) and EV flexibility with p = 0.99 (right) for hour 1. The pvalues indicate that these are sufficient fits to represent the tails of the sample pool. The inflection point indicates where the distribution changes from conve… view at source ↗

Figures from the paper (2 more)

**Figure 5.** Figure 5: Total stacked reserve provision mix as a function of the reliability threshold 1 − ε, with the associated total shortfall cost shown in red. these savings are expected to scale with the number of market participants, the volume of procured reserves, and the degree of t…

**Figure 7.** Figure 7: Cost versus reliability for (7) (circles) and (12) (diamonds). The McCormick relaxation consistently yields lower costs at comparable reliability levels, reflecting the optimistic bias introduced by replacing bilinear terms with their convex envelope approximations. G…

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Reference graph

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Pith tools

Reviewed July 3, 2026 · model on record in the stance chip above.

[1] [1]

A. J. Wood, B. F. Wollenberg, and G. B. Sheblé,Power Generation, Operation, and Control. John Wiley & Sons, 3 ed., 2013

work page 2013

[2] [2]

Optimizing the flexibility of a portfolio of generating plants to deal with wind generation,

D. S. Kirschen, J. Ma, V . Silva, and R. Belhomme, “Optimizing the flexibility of a portfolio of generating plants to deal with wind generation,” in2011 IEEE Power and Energy Society General Meeting, pp. 1–7, 2011

work page 2011

[3] [3]

Classification and quantifi- cation of reserve requirements for balancing,

J. Frunt, W. Kling, and P. van den Bosch, “Classification and quantifi- cation of reserve requirements for balancing,”Electric Power Systems Research, vol. 80, no. 12, pp. 1528–1534, 2010

work page 2010

[4] [4]

Estimation of regulation reserve re- quirement based on control performance standard,

G. Zhang and J. D. McCalley, “Estimation of regulation reserve re- quirement based on control performance standard,”IEEE Transactions on Power Systems, vol. 33, no. 2, pp. 1173–1183, 2018

work page 2018

[5] [5]

Estimating the spinning reserve requirements in systems with significant wind power generation penetration,

M. A. Ortega-Vazquez and D. S. Kirschen, “Estimating the spinning reserve requirements in systems with significant wind power generation penetration,”IEEE Transactions on Power Systems, vol. 24, no. 1, pp. 114–124, 2009

work page 2009

[6] [6]

Wind gener- ation as a reserve provider,

Y . Dvorkin, M. A. Ortega-Vazuqez, and D. S. Kirschen, “Wind gener- ation as a reserve provider,”IET Generation, Transmission & Distribu- tion, vol. 9, no. 8, pp. 779–787, 2015

work page 2015

[7] [7]

Electric vehicle aggregator as an automatic reserves provider under uncertain balancing energy procurement,

I. Pavi ´c, H. Pandži ´c, and T. Capuder, “Electric vehicle aggregator as an automatic reserves provider under uncertain balancing energy procurement,”IEEE Transactions on Power Systems, vol. 38, no. 1, pp. 396–410, 2023

work page 2023

[8] [8]

A packetized energy management macromodel with quality of service guarantees for demand- side resources,

L. A. Duffaut Espinosa and M. Almassalkhi, “A packetized energy management macromodel with quality of service guarantees for demand- side resources,”IEEE Transactions on Power Systems, vol. 35, no. 5, pp. 3660–3670, 2020

work page 2020