arxiv: 2604.04116 · v1 · submitted 2026-04-05 · 📡 eess.SY · cs.SY

Recognition: 2 theorem links

· Lean Theorem

Assessing Maintenance of Medium Voltage Cable Networks Under Time-Varying Loading

Jochen Lorenz Cremer

Authors on Pith no claims yet

Pith reviewed 2026-05-13 16:55 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords medium voltage cablestime-varying loadingWeibull failure ratesthermal ageingmaintenance assessmentenergy transitionPILC cablescable networks

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The pith

A time-varying Weibull approximation from thermal models shows maintenance needs may rise 10-300 times under variable loading for mixed MV cable networks.

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

This paper develops a shortcut method to derive time-varying Weibull failure rates from thermal ageing models, allowing quantification of maintenance impacts for heterogeneous medium voltage cable populations under fluctuating loads. The approach matters because electrification is increasing load variability beyond the constant low levels networks were designed for, potentially accelerating ageing and failures. Case studies on Danish and German datasets show that 25 percent of older low-quality cables cause 82 percent of failures, while only 1.4 percent of time at peak loads drives 46 percent of ageing. Under future energy transition conditions, maintenance requirements could increase by factors of 10 to 300, especially in networks with older PILC cables. The method gives operators a practical tool to evaluate how close to ampacity limits they can operate while controlling failures.

Core claim

The paper introduces a novel approach that derives a time-varying Weibull approximation of failure rates using thermal models and provides a shortcut method to quantify maintenance implications under time-varying loading for heterogeneous MV cable populations. The case studies investigate datasets from Denmark and the Oberrhein MV system in Germany, showing that a small fraction of 25 percent of old, low-quality cables leads to 82 percent of failures, 1.4 percent of the time of highest loading can cause 46 percent of cable ageing, and maintenance needs may be between 10-300 times higher under future loading conditions, particularly in networks with older PILC cables.

What carries the argument

The time-varying Weibull approximation of failure rates derived from thermal ageing models, which aggregates cumulative damage over variable load profiles to estimate evolving failure probabilities and maintenance needs for mixed cable populations.

Load-bearing premise

Standard thermal ageing models remain accurate predictors of failure rates when loads vary rapidly over time, without significant additional effects from mechanical stress, moisture, or installation-specific factors.

What would settle it

Collecting measured time-varying load profiles and actual failure counts over several years from an MV network with known cable mix, then checking whether observed failure rates match the model's time-varying Weibull predictions within acceptable bounds.

Figures

Figures reproduced from arXiv: 2604.04116 by Jochen Lorenz Cremer.

**Figure 2.** Figure 2: The annual cable utilisation for three energy scenarios (applied from [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Oberrhein MV network with PILC and XLPE cables. Using (32) and assuming maintenance strategy is not changed ( |Ω R| dt = 0), an estimate of the cables requiring replacement is N(t1) = ηˆ0 ηˆ1 β F(t0) + |Ω R| (44) or the maintenance increase is N(t1) N(t0) = ηˆ0 ηˆ1 β F(t0) + |Ω R| F(t0) + |ΩR| (45) that can also be expressed in terms of r1 and r0. B. Considering individual asset data We consider a DS… view at source ↗

**Figure 5.** Figure 5: Life expectancy and conductor temperature as functions of conductor current for XLPE and PILC cables. (a) Life expectancy of XLPE cables. (b) Life expectancy of PILC cables. (c) Conductor temperature of XLPE cables. (d) Conductor temperature of PILC cables. MV grid in 2023 [8]. At the simulation time t = 0 years, the ages for PILC cables were assumed as a skewed normal distribution with µ = 58, σ = 21 and … view at source ↗

**Figure 7.** Figure 7: Temperature distributions and their contribution to effective ageing for the loading scenarios in [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 6.** Figure 6: Accelerated ageing under time-varying conductor currents. (a) Normalised current profiles Ic/Iz. (b) Ageing acceleration factor r(T(t)). (c) Effective age A(10, t) of a cable with service age a = 10 years. ageing. The ’area under the curve’ is the cumulative contribution of the times that the cable is operated above the ampacity, i.e. applying (15). In the PV-dominated case, the 1.4% share of operating a… view at source ↗

**Figure 8.** Figure 8: (a) Time-varying ageing acceleration factor r(t) for PV- and winddominated scenarios. (b) Effective age A(a, t) of cables with service ages a = 5 years and a = 10 years under the same scenarios. 0 10 20 30 40 50 0 200 400 600 Age a (years) lim t→±∞ A(a, t) A0(a, t) A1(a, t), PV A1(a, t), Wind [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

**Figure 9.** Figure 9: The effective age for different cable ages [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗

**Figure 11.** Figure 11: The age distributions of XLPE and PILC. 0.8 0.9 1 1.1 1.2 10−6 10−3 100 103 106 Ic/Iz Failure rate F |ΩC | XLPE PILC [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗

**Figure 12.** Figure 12: Failures increase with Ic applied to XLPE and PILC cables. maintenance increase N(t1) N(t0) from before to after the energy transition. Table II shows the maintenance increase when applying the three strategies (applying equations (36), (40), and (45), respectively). For PILC cables, we observe around 250−300 times increase in maintenance in the PV-Dominated and around times 45 − 55 increase in the Wind-D… view at source ↗

**Figure 14.** Figure 14: Replace-all strategy applied to the Oberrhein system. (a) Histogram of the cable age distribution at t = 0, t = 25, and t = 50 years. (b) Annual number of replacements N(t). 2.8 2.9 3 3.1 3.2 200 400 β N(t1) N(t0) PV-dominated Wind-dominated [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗

**Figure 15.** Figure 15: Sensitivity of PILC results to the selection of [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗

read the original abstract

The electrification and ongoing energy transition lead to systematic changes in electricity loading and variability in power systems. Distribution systems were designed for regular operating patterns, assuming constant low loading. Now, operators need to assess whether their assets can withstand more, as well as time-varying loading. Operating the system at or near its ampacity potentially accelerates thermal ageing, so the question arises: 'how much can one operate at the limits while keeping maintenance and failures low?' This paper introduces a novel approach that derives a time-varying Weibull approximation of failure rates using thermal models and provides a shortcut method to quantify maintenance implications under time-varying loading for heterogeneous MV cable populations. The case studies investigate a dataset from Denmark and the Oberrhein Medium Voltage (MV) system in Germany, studying ageing assets and the interplay with loading, and replacement paradigms of two different cable insulation types. The studies demonstrate that a small fraction of 25% of old, low-quality cables leads to 82% of failures, and 1.4% of the time of highest loading can cause 46% of cable ageing. The case studies also demonstrate that maintenance needs may be between 10-300 times higher under future loading conditions associated with the energy transition, specifically in networks that have older PILC cables. This paper provides a new tool for operators to plan maintenance under more realistic, future operating 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 turns thermal ageing equations into a time-varying Weibull failure model and gives operators a shortcut to estimate maintenance multipliers for mixed MV cable fleets under variable future loads.

read the letter

The core contribution is the explicit mapping from time-varying temperature histories to a Weibull failure rate, plus a simple aggregation trick for heterogeneous cable populations. That is not a standard extension of the steady-state reliability literature, and the Danish and Oberrhein case studies make the practical payoff clear: 25 % of the oldest cables drive 82 % of failures, and 1.4 % of high-load hours produce 46 % of total ageing. The reported 10–300× maintenance increase under energy-transition loading patterns is the kind of number planners can actually use when deciding replacement schedules for PILC cables. The work is grounded in established thermal models and applies them to real loading profiles, which is the right direction for distribution asset management. The main limitation is that the abstract and available description give no derivation steps, error propagation, or sensitivity checks on how the Weibull shape and scale parameters are obtained from the thermal equations. Without those, it is difficult to judge how robust the shortcut remains when loads swing on hourly scales or when installation-specific factors (moisture, mechanical cycling) start to matter. The case-study multipliers are presented as demonstrations rather than validated predictions, so a referee would want to see direct comparison against observed failures during documented high-variability periods. This is written for utility engineers and network planners who need quantitative tools for maintenance under non-stationary loads. It is not a foundational theoretical advance, but the framing and numbers are concrete enough that a serious editor should send it to review rather than desk-reject it.

Referee Report

3 major / 2 minor

Summary. The paper claims to introduce a novel method deriving a time-varying Weibull approximation of MV cable failure rates directly from standard thermal ageing models, then using it as a shortcut to quantify maintenance needs under time-varying loading for heterogeneous cable populations. Case studies on Danish and Oberrhein networks report that 25% of old low-quality cables cause 82% of failures, 1.4% of highest-load time causes 46% of ageing, and future loading may require 10-300x higher maintenance, especially for PILC cables.

Significance. If the thermal-to-Weibull mapping holds and is validated, the work supplies operators with a practical planning tool for asset management under electrification-driven load variability, emphasizing disproportionate impacts from small asset subsets and peak periods.

major comments (3)

[Abstract / Methods] Abstract and methods section: the claimed derivation of the time-varying Weibull failure-rate approximation from thermal models lacks explicit equations or steps showing how temperature history maps to Weibull parameters (shape/scale), including any integration over cumulative damage; this step is load-bearing for the novelty claim.
[Case Studies] Case-study results: the reported multipliers (25% cables → 82% failures; 1.4% time → 46% ageing; 10-300× maintenance) are presented without visible error propagation, sensitivity analysis to loading-profile assumptions, or parameter uncertainty, weakening the quantified implications.
[Case Studies / Discussion] Validation: no comparison of model-predicted versus observed failures is shown for periods of documented high load variability, leaving the assumption that thermal history alone suffices (without mechanical/moisture effects) untested.

minor comments (2)

[Methods] Clarify notation for time-varying Weibull parameters and their relation to Arrhenius constants in the methods.
[Figures] Add loading-profile details and axis labels to figures illustrating the 1.4% high-load periods.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We have revised the manuscript to address the points raised, adding explicit derivation steps, sensitivity analyses, and expanded discussion of limitations.

read point-by-point responses

Referee: [Abstract / Methods] Abstract and methods section: the claimed derivation of the time-varying Weibull failure-rate approximation from thermal models lacks explicit equations or steps showing how temperature history maps to Weibull parameters (shape/scale), including any integration over cumulative damage; this step is load-bearing for the novelty claim.

Authors: We appreciate the referee pointing this out. The Methods section derives the time-varying Weibull parameters from the thermal ageing model via cumulative damage integration, but the presentation was not sufficiently step-by-step. We have added a dedicated subsection with the full set of equations, explicitly showing the mapping from temperature history to the Weibull shape and scale parameters, including the integration over cumulative damage. revision: yes
Referee: [Case Studies] Case-study results: the reported multipliers (25% cables → 82% failures; 1.4% time → 46% ageing; 10-300× maintenance) are presented without visible error propagation, sensitivity analysis to loading-profile assumptions, or parameter uncertainty, weakening the quantified implications.

Authors: We agree that the quantified multipliers would benefit from uncertainty quantification. We have performed additional sensitivity analyses on loading-profile assumptions and parameter uncertainty, incorporated error propagation, and added confidence intervals and sensitivity ranges to the reported multipliers in the revised Case Studies section. revision: yes
Referee: [Case Studies / Discussion] Validation: no comparison of model-predicted versus observed failures is shown for periods of documented high load variability, leaving the assumption that thermal history alone suffices (without mechanical/moisture effects) untested.

Authors: This is a fair observation. The model focuses on thermal ageing as the primary mechanism for the cable populations studied, but we acknowledge that mechanical and moisture effects are not explicitly modeled. We have added a paragraph in the Discussion section addressing these assumptions and their potential limitations, and note that the available datasets do not contain periods of documented high load variability suitable for direct predicted-versus-observed validation. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation applies standard thermal models to new profiles

full rationale

The paper's central step derives a time-varying Weibull failure-rate approximation from established thermal ageing models (Arrhenius-type) and applies it to time-varying loading data. This is a forward application rather than a self-definitional loop, fitted-parameter renaming, or load-bearing self-citation chain. Case-study multipliers are computed outputs from the model on external datasets (Denmark, Oberrhein), not re-expressions of inputs already embedded by construction. No uniqueness theorems or ansatzes are smuggled via self-citation in the abstract or described method. The derivation remains self-contained against external thermal benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of existing thermal ageing equations to time-varying loads and on the Weibull distribution remaining a valid failure-rate model once the time-varying hazard is inserted; no new physical entities are postulated.

free parameters (1)

Weibull shape and scale parameters
Shape and scale are adjusted to match thermal ageing under varying load profiles; exact fitting procedure not visible in abstract.

axioms (1)

domain assumption Thermal models from prior literature accurately map load history to insulation ageing rate
Invoked to derive the time-varying failure rate approximation.

pith-pipeline@v0.9.0 · 5538 in / 1239 out tokens · 27484 ms · 2026-05-13T16:55:27.230990+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

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

We consider ... the effective age A(a,t) = ∫ r(T(τ)) dτ ... λ(a,t) = (β/η̂r) (A(a,t)/η̂r)^{β-1} r(t) (Eqs. 6,8,12,14)
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean costAlphaLog_high_calibrated_iff unclear

?

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

Montsinger ... r(T) = 2^{(T-Tr)/ΔT}; Arrhenius r(T) = exp(B(1/Tr-1/T))

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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