⚡ electrical engineering

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

This paper introduces a novel time-varying Weibull-based approach to quantify the accelerated thermal ageing and significantly increased maintenance requirements of medium voltage cable networks under the dynamic loading conditions driven by the energy transition, revealing that a small fraction of aging assets and peak loading periods disproportionately drive system failures.

Original authors: Jochen Lorenz Cremer

Published 2026-04-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jochen Lorenz Cremer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: The "Heavy Truck" Problem

Imagine our electrical grid (the network of wires that brings power to your home) is like a highway system.

For decades, this highway was built for a specific type of traffic: small, steady cars driving at a constant speed. The engineers designed the road to handle this perfectly. They knew exactly how much wear and tear the asphalt would take, so they planned maintenance (repaving) based on that steady, predictable traffic.

But now, the energy transition is happening.
We are adding electric cars, solar panels, and wind turbines. This changes the traffic pattern. Instead of steady cars, we now have:

Heavy Trucks: Massive surges of power when the sun is shining or the wind is blowing hard.
Stop-and-Go Traffic: The power load fluctuates wildly throughout the day.

The problem? The "asphalt" (our old power cables) wasn't built for these heavy trucks. If we keep driving them at the same speed, the road will crumble much faster than the engineers predicted.

The Core Question

The paper asks a critical question: "How much can we push these old cables to their limits before they break, and how much more maintenance will we need to fix them?"

The authors found that if we don't adjust our plans, we are in for a shock. We might think our cables will last 50 years, but with this new "heavy truck" traffic, they might only last 10.

The Two Types of Cables (The "Old vs. New" Shoes)

The study looks at two main types of cables in the ground:

PILC (The Old Leather Boots): These are the older cables (often over 50 years old). They are tough but brittle. They are like old leather boots that have been worn for decades. If you walk a little bit, they are fine. But if you suddenly run a marathon in them, they will fall apart immediately.
XLPE (The Modern Sneakers): These are newer, more flexible cables. They can handle a bit more stress, but even they have limits.

The Shocking Discovery:
The study found that in a mixed network, only 25% of the cables are the "Old Leather Boots" (PILC). However, these few old cables are responsible for 82% of all the failures.
Analogy: It's like having a fleet of delivery trucks where only a quarter are old, rusted models. Yet, those old models break down so often that they cause 8 out of every 10 delivery delays.

The "1.4% Rule" (The Danger of Peak Moments)

One of the most fascinating findings is about when the damage happens.

You might think that if a cable is overloaded for 50% of the time, it will age 50% faster. Wrong.
The study found that the top 1.4% of the time when the load is highest (the absolute peak moments) causes 46% of the total aging damage.

Analogy: Imagine you are a marathon runner.

Running a slow jog for 23 hours a day is fine.
But sprinting at your maximum speed for just 20 minutes a day will destroy your knees faster than the slow jogging will save them.
The "sprinting" moments (peak electricity demand) do the most damage in the shortest amount of time.

The Maintenance Nightmare

The paper calculates what happens to maintenance costs when we switch to this new, high-energy world.

For the Old Cables (PILC): The maintenance needs could jump 10 to 300 times higher.
- Analogy: If you used to change the oil in your car once a year, you might now need to change it every week.
For the New Cables (XLPE): If we push them too hard, the failure rate could jump by a million times (mathematically speaking, because the failure rate grows exponentially).

The Three Strategies (How to Fix It)

The paper tests three ways utility companies can handle this:

Run-to-Failure (The "Wait and See" Approach):
- Strategy: Don't do anything until the cable breaks, then fix it.
- Result: Disaster. With the new traffic, the cables break so fast that the cost to fix them becomes astronomical.
Replace-All (The "Scorched Earth" Approach):
- Strategy: Replace every cable every 50 years, no matter what.
- Result: This is expensive and wasteful. You are throwing away cables that might still be working, but it prevents sudden blackouts.
Preventive Maintenance (The "Smart Doctor" Approach):
- Strategy: Check the health of every cable regularly. If a cable looks tired, fix it before it breaks.
- Result: This is the most efficient, but it requires smart sensors and data to know which cables are actually in trouble.

The Bottom Line

The energy transition is great for the planet, but it puts a massive, unexpected strain on our old electrical infrastructure.

The Warning: We cannot use old maps to navigate new territory. The old rules for how long cables last are wrong because the "traffic" has changed.
The Risk: If we don't update our maintenance plans, we will face a huge financial burden and frequent power outages.
The Solution: We need to stop assuming the load is steady. We need to recognize that those few moments of "peak stress" are doing the most damage, and we need to treat our old cables with extreme care or replace them before they snap.

In short: We are driving a Ferrari engine in a Model T chassis. If we don't upgrade the chassis (the cables) and change how we drive (the maintenance), the car is going to break down.

1. Problem Statement

The global energy transition, driven by the electrification of transport and industry and the integration of Distributed Energy Resources (DERs), is fundamentally altering the loading profiles of Medium Voltage (MV) distribution networks.

The Core Issue: Traditional MV networks were designed for constant, low-loading patterns. The new paradigm introduces time-varying loading with frequent peaks that may exceed rated ampacities.
The Risk: Operating cables near or above their thermal limits accelerates thermal ageing, potentially drastically shortening asset lifespans.
The Gap: Existing reliability models typically assume stationary loading conditions (constant stress over time). They fail to account for the non-stationary nature of future loading, leading to an overestimation of cable lifespan and a severe underestimation of future maintenance needs and failure rates. This creates a risk of unexpected asset failures and massive financial burdens for Distribution System Operators (DSOs).

2. Methodology

The paper proposes a novel framework that links thermal ageing physics with non-stationary reliability theory to model failure rates under evolving loading conditions.

A. Thermal Ageing Models

The authors model the conductor temperature $T$ based on current loading $I_c$ and ambient temperature. They apply two distinct ageing acceleration models depending on the insulation type:

XLPE Cables: Use the Arrhenius model, where the ageing acceleration factor $r(T)$ is exponential with respect to temperature.
PILC (Paper Insulated Lead Covered) Cables: Use the Montsinger approach, where the ageing rate doubles for every fixed temperature increment ( $\Delta T$ ).

B. Effective Age and Time-Varying Loading

Instead of treating age as simple calendar time, the paper introduces the concept of Effective Age ( $A(a, t)$ ).

Cumulative Damage: Similar to Miner's rule, the model integrates the ageing acceleration factor $r(T)$ over time.
Time-Varying Distribution: The loading is modeled as a probability density function $\rho_T(T, t)$ that changes over time (e.g., transitioning from a "Without DER" state to a "PV-dominated" or "Wind-dominated" state).
Logistic Transition: The shift in loading regimes is modeled using a logistic function to simulate the gradual integration of DERs over decades.

C. Reliability Modeling

The failure rate is derived using a Weibull distribution where the shape parameter $\beta$ and scale parameter are functions of the effective age rather than just service time.

Failure Rate Equation: $\lambda(a, t) = \frac{\beta}{\hat{\eta}_r} \left( \frac{A(a, t)}{\hat{\eta}_r} \right)^{\beta-1} r(t)$
This formulation allows for the analytical estimation of population-level failure evolution under non-stationary stress.

D. Maintenance Strategy Assessment

The paper develops "shortcut methods" to quantify the increase in maintenance requirements ( $N(t_1)/N(t_0)$ ) for three strategies:

Run-to-Failure: Replacing cables only after failure.
Replace-all: Replacing cables at a fixed age threshold ( $a_R$ ).
Preventive Maintenance: Replacing/maintaining based on health indices.

3. Key Contributions

Novel Analytical Framework: A method to derive a time-varying Weibull approximation of failure rates that explicitly incorporates the history of thermal stress (effective age) rather than just calendar age.
Shortcut Methods: Analytical formulas to rapidly estimate the multiplier of maintenance needs when loading conditions shift from steady-state to time-varying regimes, applicable to heterogeneous cable populations.
Quantification of "Peak" Impact: Demonstrating that a small fraction of time spent at high loading levels disproportionately drives the majority of ageing.
Case Study Validation: Application of the model to real-world data from Danish distribution grids and the Oberrhein MV system in Germany, comparing PILC and XLPE cable behaviors.

4. Key Results

The case studies yielded several critical findings:

Disproportionate Impact of High Loading:
- In a PV-dominated scenario, cables operate above their rated temperature for only 1.4% of the time. However, this small fraction accounts for 46% of the total thermal ageing.
- This confirms a non-linear amplification effect where peak loads drive degradation much faster than average loads.
Cable Type Sensitivity:
- PILC Cables: Highly sensitive to loading changes. The studies show that 25% of the network consisting of old, low-quality PILC cables contributes to 82% of total failures.
- Maintenance Surge: Under future energy transition scenarios, maintenance needs for networks with PILC cables could increase by 10 to 300 times compared to current levels.
- XLPE Cables: While more robust, they are not immune. Under "Run-to-Failure" strategies, maintenance needs could theoretically increase by factors of 100,000+ if loading approaches ampacity limits, due to the high exponent ( $\beta \approx 3.4$ ) in the Weibull model.
Maintenance Strategy Efficiency:
- Replace-all strategies showed a 10-fold increase in maintenance for PV scenarios but were inefficient for aging assets (replacing healthy cables).
- Preventive Maintenance was shown to be the most stable strategy, mitigating the massive spikes in failure rates seen in "Run-to-Failure" approaches.
Sensitivity Analysis: The results are highly sensitive to the Weibull shape parameter ( $\beta$ ). Small variations in $\beta$ lead to exponential changes in predicted maintenance increases, highlighting the need for accurate empirical data.

5. Significance and Implications

Operational Planning: The paper provides DSOs with a critical tool to move beyond static reliability models. It demonstrates that assuming constant loading leads to dangerous underestimations of asset failure risks in the era of electrification.
Asset Management: It highlights the urgent need to prioritize the replacement of aging PILC cables, as they are the primary bottleneck for reliability under time-varying loads.
Economic Impact: The findings suggest that failing to adapt maintenance strategies to time-varying loading could lead to catastrophic financial burdens due to mass asset failures and emergency replacements.
Policy & Transition: The research underscores that the energy transition requires not just new generation assets, but a fundamental re-evaluation of the resilience and maintenance of the existing distribution infrastructure.

In conclusion, the paper argues that time-varying loading fundamentally changes the physics of cable ageing, and operators must adopt dynamic, physics-based reliability models to ensure grid stability and cost-efficiency during the energy transition.