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arxiv: 1907.07736 · v1 · pith:23QDOFQPnew · submitted 2019-07-17 · 📡 eess.SY · cs.SY

Assessment of the Value of Frequency Response Times in Power Systems

Yifu Ding , Roberto Moreira , Dagoberto Cedillos This is my paper

Pith reviewed 2026-05-24 20:02 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords frequency responseunit commitmentrenewable integrationsystem inertiaenhanced frequency responseMILP optimizationUK electricity marketbalancing services
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The pith

Faster frequency response products can cost-effectively meet UK power system balancing needs with rising renewables.

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

The paper develops a mixed integer linear programming unit commitment model that schedules inertial response, mandatory frequency response, and sub-second enhanced frequency response together. It quantifies how faster products reduce total system costs relative to slower alternatives across several future UK energy scenarios. A sympathetic reader would care because declining inertia from renewables raises the volume and speed of balancing services required, and the model isolates the economic advantage of sub-second response under those conditions.

Core claim

The paper claims that its MILP unit commitment model, which simultaneously optimizes inertial response, mandatory FR, and EFR, demonstrates that faster reacting FR products meet system balancing requirements at lower cost than typical slower products when evaluated in projected UK market and system conditions.

What carries the argument

A mixed integer linear programming (MILP) unit commitment model that co-optimizes inertial response, mandatory frequency response, and enhanced frequency response (EFR) to compare value across response times.

If this is right

  • Faster FR products mitigate the balancing impact of reduced system inertia from renewables.
  • Including sub-second EFR in the schedule lowers overall system operating costs.
  • The value of EFR varies with the specific future energy mix and demand profile.
  • Mandatory FR and inertial response alone become insufficient or more expensive without faster options.

Where Pith is reading between the lines

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

  • Market designs that procure response by speed rather than by product type could capture similar savings.
  • The same scheduling logic could be tested on systems outside the UK with comparable inertia decline.
  • If EFR procurement volumes increase, the model implies a shift in the mix of conventional plant needed for other services.

Load-bearing premise

The chosen future energy scenarios and the MILP formulation's representation of costs, constraints, and response dynamics accurately reflect real UK market and system conditions.

What would settle it

Compare the model's predicted cost savings from EFR against actual UK balancing services market outcomes or real frequency event data under comparable renewable penetration levels.

Figures

Figures reproduced from arXiv: 1907.07736 by Dagoberto Cedillos, Roberto Moreira, Yifu Ding.

Figure 2
Figure 2. Figure 2: Bilinear constraint linearization P req t + E ≤ P max l − D · dt · fmax (15) Ht fo · (E + P req t Tp ) ≤ P req t ·P req t 4(fo−fmax) (16) S req t + E ≤ P max l − D · dt · fss (17) For a thermal power plant, FR provision are achieved by the governor control system. According to [11], the provision characteristics can be captured by (18) and (19). (20) defines the maximum PFR and SFR provision levels from st… view at source ↗
Figure 1
Figure 1. Figure 1: The frequency evolution in the power system after a contingency [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 4
Figure 4. Figure 4: Hourly EFR effectiveness regarding annual system inertia and demand [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: System operation cost abatements after deploying the EFR under [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The economic benefits of EFR (thousand £/MW) in ’Steady State’ and ’Two Degrees’ scenarios [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
read the original abstract

Given the increasing penetration in renewable generation, the UK power system is experiencing a decline in system inertia and an increase in frequency response (FR) requirements. Faster FR products are a mitigating solution that can cost-effectively meet the system balancing requirements. Thus, this paper proposes a mixed integer linear programming (MILP) unit commitment model which can simultaneously schedule inertial response, mandatory FR, as well as a sub-second FR product - enhanced frequency response (EFR). The model quantifies the value of providing faster reacting FR products in comparison with other response times from typical FR products. The performance and value of EFR are determined in a series of future energy scenarios with respect to the UK market and system conditions.

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 / 1 minor

Summary. The paper proposes a mixed-integer linear programming (MILP) unit commitment model that co-optimizes inertial response, mandatory frequency response, and sub-second enhanced frequency response (EFR) to quantify the cost savings from faster FR products relative to conventional ones. The model is applied to future UK energy scenarios with declining inertia due to renewables, with the central claim that EFR can cost-effectively meet balancing requirements.

Significance. If the MILP formulation and its linearization of response dynamics are shown to be accurate, the results would provide a quantitative basis for valuing faster FR products in low-inertia systems and could inform UK market design for frequency services. The use of external scenarios and standard costs avoids obvious circularity.

major comments (2)
  1. [Abstract, model formulation (likely §3)] The central claim (abstract) that EFR reduces total balancing costs requires that the MILP correctly couples sub-second EFR provision to frequency metrics (ROCOF, nadir) via inertia and response constraints. The manuscript must specify the time resolution of the unit-commitment problem and the exact linearization used for EFR dynamics; standard 30-min or hourly resolutions without explicit differential-equation validation risk misstating the attributed savings.
  2. [Scenario description and results sections] The performance claims rest on the chosen future energy scenarios and cost parameters accurately reflecting UK conditions. The paper should report sensitivity of the EFR value to variations in these inputs (e.g., inertia levels, reserve requirements) to demonstrate robustness of the cost-effectiveness conclusion.
minor comments (1)
  1. [Abstract] The abstract states the model purpose but supplies no equations or numerical results; the main text should include at least one key constraint or objective term illustrating how EFR response time enters the optimization.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and have revised the manuscript to provide additional clarification and analysis.

read point-by-point responses

  1. Referee: [Abstract, model formulation (likely §3)] The central claim (abstract) that EFR reduces total balancing costs requires that the MILP correctly couples sub-second EFR provision to frequency metrics (ROCOF, nadir) via inertia and response constraints. The manuscript must specify the time resolution of the unit-commitment problem and the exact linearization used for EFR dynamics; standard 30-min or hourly resolutions without explicit differential-equation validation risk misstating the attributed savings.

    Authors: The model employs a standard hourly time resolution for the unit commitment decisions. Frequency metrics (ROCOF and nadir) are enforced via linearized constraints derived from the swing equation that explicitly incorporate the sub-second response time of EFR. We will revise §3 to state the time resolution explicitly and to provide the precise linearization formulas together with the underlying differential-equation approximations and any validation steps performed. These additions will remove ambiguity about how the cost savings are attributed. revision: yes

  2. Referee: [Scenario description and results sections] The performance claims rest on the chosen future energy scenarios and cost parameters accurately reflecting UK conditions. The paper should report sensitivity of the EFR value to variations in these inputs (e.g., inertia levels, reserve requirements) to demonstrate robustness of the cost-effectiveness conclusion.

    Authors: We agree that robustness checks strengthen the conclusions. The scenarios are taken from established UK projections, but we will add a dedicated sensitivity subsection that varies inertia levels and reserve requirements over plausible ranges and reports the resulting changes in EFR value. This will confirm that the cost-effectiveness finding is not an artifact of the base-case inputs. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model uses external scenarios and standard costs

full rationale

The paper formulates a MILP unit commitment model to schedule inertial response, mandatory FR, and EFR, then evaluates it against external future UK energy scenarios and market conditions. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the cost savings attributed to faster EFR emerge from the optimization constraints and input data rather than being presupposed. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions about power-system modeling rather than new free parameters or invented entities.

axioms (2)
  • domain assumption The MILP formulation accurately captures the technical and economic constraints of frequency response products and system inertia.
    Invoked when the model is used to quantify value (abstract, paragraph 2).
  • domain assumption The selected future energy scenarios represent plausible UK market and system conditions.
    Required for the performance and value assessment (abstract, paragraph 3).

pith-pipeline@v0.9.0 · 5644 in / 1169 out tokens · 34904 ms · 2026-05-24T20:02:58.973350+00:00 · methodology

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Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages

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