Integrating Conductor Health into Dynamic Line Rating and Unit Commitment under Wind Uncertainty

Geon Roh; Jip Kim

arxiv: 2510.15740 · v6 · submitted 2025-10-17 · 📡 eess.SY · cs.SY

Integrating Conductor Health into Dynamic Line Rating and Unit Commitment under Wind Uncertainty

Geon Roh , Jip Kim This is my paper

Pith reviewed 2026-05-18 06:16 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords dynamic line ratingunit commitmentconductor healthelevated temperature operationwind uncertaintyrisk-based optimizationtransmission reliability

0 comments

The pith

By internalizing conductor wear costs from dynamic line ratings, unit commitment decisions reduce total expenses and renewable waste under wind forecast errors.

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

The paper shows how to factor the long-term damage to overhead conductors into daily generator scheduling when transmission lines use real-time weather to carry more power. Dynamic ratings raise conductor temperatures during high flows, and uncertainty in wind power forecasts makes those temperature spikes harder to predict, accelerating wear. The authors calculate a risk-adjusted cost for this extra wear and fold it into the optimization that decides which generators run each hour. On a large Texas test grid, the resulting schedule trims overall costs modestly while cutting the amount of wind energy that must be spilled by more than four-fifths compared with either fixed ratings or conventional dynamic rating that ignores health.

Core claim

The Conductor Health-Aware Unit Commitment model quantifies risk-based depreciation costs from elevated temperature operation caused by dynamic line rating under wind power forecast errors, and internalizes these costs in the optimization objective using a robust linear approximation of conductor temperature, leading to safer line flows that adapt to uncertainty correlations.

What carries the argument

The Conductor Health-Aware Unit Commitment (CHA-UC) model, which integrates expected depreciation costs due to hourly elevated temperature operation into the unit commitment objective function.

If this is right

Total operating cost falls 0.75 percent relative to static line rating on the Texas 123-bus system.
Renewable curtailment falls 82 percent relative to static line rating.
Line flows tighten when forecast errors amplify temperature risk and relax when errors hedge risk, producing safer utilization.
Ignoring depreciation costs leads to higher overall expense because of excessive elevated-temperature operation.

Where Pith is reading between the lines

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

The same risk-internalization approach could be extended to other temperature-sensitive assets such as transformers or underground cables.
Longer-term transmission expansion planning might start to favor routes or conductor types that tolerate higher temperatures with lower wear penalties.
Real-time versions would need live integration of weather forecasts with degradation models to update the penalty term each hour.

Load-bearing premise

Risk-based depreciation costs from elevated temperatures can be estimated directly from forecast errors and added as a linear penalty in the scheduling problem without changing the underlying temperature physics or needing later corrections.

What would settle it

Measure actual conductor degradation rates or replacement intervals on lines operated under the proposed schedule versus lines operated under conventional dynamic rating that ignores health costs.

Figures

Figures reproduced from arXiv: 2510.15740 by Geon Roh, Jip Kim.

**Figure 1.** Figure 1: Illustration of a linear fit to the current-conductor temperature relationship. The temperature from the IEEE HBE and the linear fit assuming ACSR Finch, a perpendicular wind speed of 2.7 m/s and ambient temperature of 9.4°C is shown. Conductor temperature limit is set as 95 °C; in practice, it varies depending on the transmission system owner [28] [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Figure 2: An illustrative example of LoTS with a conductor with exposed temperatures: 105°C, 109°C, 112°C each for two hours. The path of total degradation calculation is shadowed on trajectories of different temperatures [19]. where A = min(100, 134−0.24τ ), τ is conductor temperature (°C), t is exposure time (h), and d is conductor diameter (mm). For aluminum conductor steel-reinforced (ACSR) lines, the correspond… view at source ↗

**Figure 3.** Figure 3: Depreciation cost piecewise functions for new and old ACSR Finch. The piecewise functions lay above the exact depreciation cost. where Bl is the initial cost factor of line l ($/MVA-km), Sl its capacity (MVA), and Dl its length (km). Subscript t denotes the time of interest. This formulation implies that C Dep t (τ ) varies with the state of the conductor as LACSR,t(·) is state-dependent. While the depreci… view at source ↗

**Figure 5.** Figure 5: Histograms comparing the distribution of actual and scenario errors. (a) DLR forecast error, (b) WP forecast error was set to 10% (Section II-D). The lifetime cost factor Bl was based on a 3190 MVA, 400 kV AC line with a cost of 750 GBP/MVA-km [33]. After excluding tower and loss components, the adjusted cost factor (Bl) was $936/MVAkm. The loading-temperature linear fit was sampled from 95 °C and 195 °C,… view at source ↗

**Figure 4.** Figure 4: Schematic of the CHA-UC optimization timeline. Processes that require actions outside optimization is colored with gray. Equations and factors are marked with its references. C. CHA-UC Timeline The CHA-UC timeline is shown in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 6.** Figure 6: (Case Study I) Annual scatter plot of temperatures of line 192 (Line with biggest temperature difference) obtained through post-hoc evaluation. 20-day moving average (MA) lines are drawn above. Meteorogical seasons are colored in the background. A zoom-in of thermal overload temperatures during periods when the MA of SLR is higher than CHA-UC, is provided. neighbor weighting: each historical trajectory is … view at source ↗

**Figure 7.** Figure 7: (Case Study I) Annual heatmaps of day-ahead commitment and commitment changes on a map of Texas. (a) Annual day-ahead commitment from the DLR baseline, averaged over each bus; line colors indicate annual average loading (normalized by capacity). (b) Difference in commitment decisions in %; blue indicates higher commitment under CHA-UC. Line colors show the corresponding reduction in loading (normalized by … view at source ↗

**Figure 9.** Figure 9: illustrates the heatmap of line temperature under baseline DLR. Forecast errors are calculated by subtracting TABLE II. (CASE STUDY II) PAIRS OF CORRELATED WIND GENERATORS AND LINES STUDIED. THE CORRELATION WAS CAPTURED USING SPEARMAN’S CORRELATION COEFFICIENTS AND THE AVERAGE LINE FLOW USING DLR BASELINE IS GIVEN. GSF WAS OBTAINED BY SETTING THE PAIRED BUS AS THE FROM-BUS. Pair Wind Farm Line Correlation … view at source ↗

read the original abstract

Dynamic line rating (DLR) enables greater utilization of existing transmission lines by leveraging real-time weather data. However, the elevated temperature operation (ETO) of conductors under DLR, particularly in the presence of uncertainty, is often overlooked, despite its long-term impact on conductor health. This paper addresses ETO under DLR and wind power uncertainty by 1) quantifying risk-based depreciation costs associated with ETO, 2) characterizing correlation-driven ETO risk from wind power and DLR forecast errors, and 3) proposing a Conductor Health-Aware Unit Commitment (CHA-UC) that internalizes these costs in operational decisions. CHA-UC incorporates a robust linear approximation of conductor temperature and integrates expected depreciation costs due to hourly ETO into the objective function. Case studies on the Texas 123-bus backbone test system demonstrate that the proposed CHA-UC model reduces the total cost by 0.75\% and renewable curtailment by 82\% compared to static line rating (SLR) and outperforms quantile regression forest-based methods, while conventional DLR operation without risk consideration resulted in higher costs due to excessive ETO. Further analysis shows that CHA-UC achieves safer line utilization by shifting generator commitments and endogenously adapting to uncertainty correlation, relaxing flows under risk-hedging conditions and tightening flows under risk-amplifying 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.

Desk Editor's Note private letter to a colleague

The paper adds ETO depreciation costs to DLR-aware unit commitment and reports small cost savings plus large curtailment cuts on the Texas test system, but the linear temperature approximation is the part that needs the most scrutiny.

read the letter

The main takeaway is that this work builds a unit commitment model that treats conductor aging as an explicit cost when dynamic line ratings push temperatures higher under wind uncertainty. On the Texas 123-bus system the CHA-UC version cuts total operating cost by 0.75% and renewable curtailment by 82% compared with static ratings, while plain DLR without the health term ends up more expensive because it over-uses the lines. The formulation lets the schedule shift commitments and adjust flows depending on whether forecast-error correlations increase or reduce ETO risk. That endogenous adaptation is the practical step forward from earlier DLR-UC papers. They also use a robust linear temperature model so the whole thing stays solvable as a mixed-integer program. Those pieces are straightforward extensions that fit together cleanly and produce usable numbers on a realistic test case. The soft spot is the linear temperature approximation itself. Adding the depreciation term after the approximation could change the effective heat balance or misrepresent how correlated errors actually drive aging risk, which would make the reported flow relaxations and generator shifts look cleaner than a full nonlinear check would show. The abstract and stress-test note do not give enough detail on how the depreciation coefficients were derived from forecast errors or validated against real conductor data, so that step still feels like the weakest link. If the full paper includes side-by-side nonlinear simulations or sensitivity checks on those coefficients, the concern drops; otherwise the claimed benefits rest on an assumption that may not hold exactly. This is for power-systems researchers who already run DLR or stochastic UC models and want to bring long-term asset health into the same optimization without adding heavy new machinery. A reader working on renewable integration on existing lines will get a concrete formulation and test results worth examining. It is coherent enough and grounded enough in an existing test system to deserve a serious referee, even though the cost savings are modest and the approximation will need extra verification in review.

Referee Report

2 major / 2 minor

Summary. The paper proposes a Conductor Health-Aware Unit Commitment (CHA-UC) model that quantifies risk-based depreciation costs from elevated temperature operation (ETO) under dynamic line rating (DLR) and wind uncertainty, characterizes correlation-driven ETO risks from forecast errors, and internalizes these via a robust linear approximation of conductor temperature added as a linear term in the UC objective. On the Texas 123-bus backbone test system, CHA-UC reports a 0.75% total cost reduction and 82% drop in renewable curtailment versus static line rating (SLR), outperforming quantile regression forest methods while avoiding excessive ETO costs seen in conventional DLR.

Significance. If the robust linear temperature approximation and linear cost internalization accurately capture ETO risks without distorting nonlinear heat-balance dynamics or correlation effects, the work offers a practical advance in stochastic UC by trading off short-term operational efficiency against long-term conductor health. The Texas 123-bus case studies provide concrete numerical evidence of safer endogenous flow adjustments and generator commitments under uncertainty, which could inform grid operators managing high renewable penetration.

major comments (2)

[§3 (CHA-UC formulation)] §3 (CHA-UC formulation): the robust linear approximation to conductor temperature is load-bearing for the central claim that ETO risk can be internalized without post-hoc adjustments, yet no error bounds, validation against the full nonlinear heat-balance equation, or sensitivity to the specific wind/DLR forecast-error distributions in the Texas cases are provided; this directly affects whether the reported 0.75% cost reduction and 82% curtailment improvement are artifacts of the approximation.
[§4 (depreciation cost quantification)] §4 (depreciation cost quantification): the risk-based depreciation costs derived from forecast errors are added as a linear term in the objective, but the manuscript does not demonstrate that this preserves the underlying temperature dynamics or correctly represents correlation-driven ETO risk; without this, the endogenous flow tightening/relaxing behavior claimed for risk-hedging versus risk-amplifying conditions cannot be confirmed as arising from true risk internalization rather than the linearization.

minor comments (2)

[Abstract and §5] Abstract and §5: the comparison to 'quantile regression forest-based methods' lacks a brief description or citation of the implementation details used for the benchmark.
[Case studies] Table or figure in case studies: clarify whether the reported 'total cost' consistently includes the new depreciation term across all compared methods (SLR, conventional DLR, CHA-UC) to avoid ambiguity in the 0.75% figure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our work. We address the major comments regarding the robust linear approximation and the depreciation cost internalization below, indicating the revisions planned for the next version of the manuscript.

read point-by-point responses

Referee: §3 (CHA-UC formulation): the robust linear approximation to conductor temperature is load-bearing for the central claim that ETO risk can be internalized without post-hoc adjustments, yet no error bounds, validation against the full nonlinear heat-balance equation, or sensitivity to the specific wind/DLR forecast-error distributions in the Texas cases are provided; this directly affects whether the reported 0.75% cost reduction and 82% curtailment improvement are artifacts of the approximation.

Authors: The referee correctly notes the absence of explicit validation metrics in the current manuscript. Our robust linear approximation is obtained by reformulating the nonlinear conductor temperature equation into a linear form using conservative bounds on uncertain parameters (wind speed, ambient temperature) to ensure the estimated temperature is an upper bound. This enables direct inclusion in the linear UC model. To strengthen the paper, we will revise §3 to include: (i) derivation of error bounds based on the maximum linearization error over the uncertainty set, (ii) a validation subsection comparing the linear model outputs to the full nonlinear IEEE heat balance model for the Texas test system lines, and (iii) sensitivity analysis to different forecast error distributions. These additions will confirm that the approximation does not artifactually produce the observed 0.75% cost savings and 82% curtailment reduction. revision: yes
Referee: §4 (depreciation cost quantification): the risk-based depreciation costs derived from forecast errors are added as a linear term in the objective, but the manuscript does not demonstrate that this preserves the underlying temperature dynamics or correctly represents correlation-driven ETO risk; without this, the endogenous flow tightening/relaxing behavior claimed for risk-hedging versus risk-amplifying conditions cannot be confirmed as arising from true risk internalization rather than the linearization.

Authors: We partially agree with this assessment. The depreciation cost is calculated as the expected cost from the distribution of ETO events induced by correlated forecast errors, and then added linearly. The temperature dynamics are preserved through the use of the robust approximation which maintains monotonicity with respect to line flow. The correlation-driven risk is explicitly modeled in the characterization step before internalization. However, to better demonstrate the endogenous behavior, we will add in the revision a detailed discussion and additional numerical results in §4 and the case studies section showing how the cost term leads to flow adjustments under different correlation scenarios. We believe this will confirm the risk internalization effect. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against external benchmarks

full rationale

The paper quantifies ETO depreciation costs from wind/DLR forecast errors, applies a robust linear approximation to conductor temperature, and internalizes expected costs as a linear term in the CHA-UC objective. Case-study savings (0.75% cost, 82% curtailment) are reported as outcomes of the resulting optimization on the Texas 123-bus system under uncertainty correlation. No quoted equations or self-citations reduce the claimed results to fitted inputs by construction, nor does any step rename a known pattern or import uniqueness from prior author work as a load-bearing premise. The approach remains falsifiable via the reported comparisons to SLR and quantile regression forest baselines.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the ability to pre-compute risk-based depreciation costs from forecast errors and on the validity of a robust linear temperature model; no new physical entities are postulated.

free parameters (1)

depreciation cost coefficients
Risk-based costs for elevated temperature operation are quantified and inserted into the objective; their exact fitting procedure is not detailed in the abstract.

axioms (1)

domain assumption A robust linear approximation accurately captures conductor temperature dynamics under wind and load uncertainty
Invoked to integrate temperature into the optimization without full nonlinear heat-balance equations.

pith-pipeline@v0.9.0 · 5767 in / 1428 out tokens · 31778 ms · 2026-05-18T06:16:19.288353+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The CHA-UC incorporates a robust linear approximation of conductor temperature and integration of expected depreciation costs due to hourly ETO into the objective function.
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

τl,t ≥ Al,t · pl,t + Bl,t and piecewise CDep l,t(τ) = Bl · Sl · Dl · (LACSR,t(τ) − LACSR,t−1)/10

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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[1] [1]

Challenges of renewable energy penetration on power system flexibility: A survey,

S. Impramet al., “Challenges of renewable energy penetration on power system flexibility: A survey,”Energy Strategy Reviews, 2020

work page 2020

[2] [2]

Assessing the impact of renewable energy penetration and geographical allocation on transmission expansion cost,

L. Herdinget al., “Assessing the impact of renewable energy penetration and geographical allocation on transmission expansion cost,”Sustainable Energy, Grids and Networks, vol. 38, p. 101349, 2024

work page 2024

[3] [3]

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P. Donohoo-Vallettet al., “Capricious cables: Understanding the lim- itations and context of transmission expansion planning models,”The Electricity Journal, vol. 28, no. 9, pp. 85–99, 2015

work page 2015

[4] [4]

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L. Clapinet al., “Waiting to generate: An analysis of onshore wind and solar pv project development lead-times in australia,”Energy Economics, vol. 131, p. 107337, 2024

work page 2024

[5] [5]

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Potomac Economics, “2024 state of the market report for the ercot electricity markets,” Market Monitoring Report, May 2025

work page 2024

[6] [6]

Delays in grid build-out push renewable energy developers’ losses past₩10 trillion,

S. Park, “Delays in grid build-out push renewable energy developers’ losses past₩10 trillion,”Kyunghyang Shinmun, Oct. 2023

work page 2023

[7] [7]

Impact from dynamic line rating on wind power integration,

C. J. Wallnerstromet al., “Impact from dynamic line rating on wind power integration,”IEEE Transactions on Smart Grid, 2015

work page 2015

[8] [8]

Impacts of dynamic line ratings on the ercot transmission system,

T. Leeet al., “Impacts of dynamic line ratings on the ercot transmission system,” inProc. North Amer . Power Symp. (NAPS), 2022

work page 2022

[9] [9]

Implementation of dynamic line ratings,

FERC, “Implementation of dynamic line ratings,” Washington, DC, Advance notice of proposed rulemaking RM24-6-000, Jun. 2024

work page 2024

[10] [10]

Managing transmission line ratings,

FERC, “Managing transmission line ratings,” Washington, DC, Final Rule (Order No. 881) RM20-16-000, Dec. 2021

work page 2021

[11] [11]

Probabilistic n-1 security assessment incorporating dynamic line ratings,

M. A. Bucheret al., “Probabilistic n-1 security assessment incorporating dynamic line ratings,” in2013 IEEE Power & Energy Society General Meeting, 2013, pp. 1–5

work page 2013

[12] [12]

Chance-constrained optimal power flow with non- parametric probability distributions of dynamic line ratings,

N. Viaforaet al., “Chance-constrained optimal power flow with non- parametric probability distributions of dynamic line ratings,”Interna- tional Journal of Electrical Power & Energy Systems, 2020

work page 2020

[13] [13]

Risk-based distributionally robust optimal power flow with dynamic line rating,

C. Wanget al., “Risk-based distributionally robust optimal power flow with dynamic line rating,”IEEE Trans. on Pwr . Syst., 2018

work page 2018

[14] [14]

Stochastic security-constrained unit commitment with wind power generation based on dynamic line rating,

H. Parket al., “Stochastic security-constrained unit commitment with wind power generation based on dynamic line rating,”Int. J. Electr . Power Energy Syst., 2018

work page 2018

[15] [15]

Risk-averse stochastic dynamic line rating models,

A. Kirilenkoet al., “Risk-averse stochastic dynamic line rating models,” IEEE Transactions on Power Systems, 2021

work page 2021

[16] [16]

Probabilistic dynamic line rating forecasting with line graph convolutional LSTM,

M. Kimet al., “Probabilistic dynamic line rating forecasting with line graph convolutional LSTM,” available in ArXiv

work page

[17] [17]

Probabilistic assessment of the reduction in tensile strength of an overhead transmission line’s conductor with reference to climatic data,

K. Adomahet al., “Probabilistic assessment of the reduction in tensile strength of an overhead transmission line’s conductor with reference to climatic data,”IEEE Transactions on Power Delivery, 2000

work page 2000

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work page 1972

[19] [19]

Spatial analysis of thermal aging of overhead transmission conductors,

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work page 2012

[20] [20]

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