Calculation of Aging Coefficient for Establishing Aging Condition Index of Thermoplastic Insulated Power Cables

Abstract

The growing demand for direct current transmission emphasizes the need for advanced insulation suitable for high-capacity, long-distance applications. Thermoplastics, especially polypropylene, offer several advantages over conventional materials like XLPE (cross-linked polyethylene) and EPR (ethylene propylene rubber), including higher thermal stability, recyclability, and reduced space charge accumulation. However, due to the inherent rigidity and limited flexibility of PP, its mechanical aging becomes a critical factor in assessing its long-term reliability as a cable insulation. In this study, mechanical aging characteristics, specifically declines in tensile strength and elongation, were selected as key indicators of insulation aging. Accelerated aging tests were conducted at 90 °C, 110 °C, and 130 °C for up to 5000 h. The experimental data were fitted to exponential models to derive aging coefficients, which formed the basis for the proposed aging model and the ACI (aging condition index). The ACI enables quantitative assessment of the current insulation condition and estimation of the remaining lifetime until a predefined threshold (e.g., ACI = 0.5) is reached. These findings contribute to the development of condition-based maintenance strategies and long-term asset management for power cables, offering practical insights for improving the reliability of future power grid systems.

1. Introduction

The rapid growth in DC (direct current) transmission has intensified the need for advanced insulation materials that can meet the demands of high-capacity power systems and long-distance transmission networks. In this context, thermoplastic insulation materials have emerged as promising alternatives to conventional materials like XLPE (cross-linked polyethylene) and EPR (ethylene propylene rubber) [1,2,3]. These materials not only exhibit higher melting points and superior thermal stability but also offer environmental benefits such as recyclability and reduced space charge accumulation, which in turn help minimize electric field distortions [4,5,6].

Compared to conventional insulation materials, namely, XLPE, EPR, HEPR (highly cross-linked ethylene propylene rubber), HDPE (high-density polyethylene), and LDPE (low-density polyethylene), thermoplastic insulation materials offer notable advantages in thermal and environmental performance. Their higher melting points and thermal stability support increased current capacity and improved transmission efficiency under elevated temperatures. Additionally, the absence of crosslinking enhances recyclability and lowers the risk of degradation from space charge accumulation. However, polypropylene (PP), a representative thermoplastic, is inherently rigid and lacks flexibility, which presents mechanical challenges during cable bending, laying, and installation [7,8]. Consequently, mechanical properties are not only a limitation but also a key indicator of insulation reliability. In particular, degradation in tensile strength and elongation under thermal aging critically reflects the material’s performance decline.

While aging diagnostics and health indices have been widely investigated for conventional AC cables using materials like XLPE and EPR, very limited research has addressed aging evaluation methods for DC-specific thermoplastic-insulated cables, especially those based on polypropylene. Given the unique mechanical rigidity of PP, which significantly affects installation and operational durability, mechanical degradation must be prioritized when evaluating its insulation performance. This study, therefore, introduces a novel framework that emphasizes mechanical behavior as the primary degradation indicator. By focusing on tensile strength and elongation, a customized Aging Condition Index (ACI) is proposed for PP-based insulation, filling a gap in the existing literature and providing a new direction for condition assessment in DC cable systems.

The successful implementation of thermoplastic insulation in practical power cable systems necessitates reliable methods for evaluating long-term aging behavior. Accurate assessment of cable aging is crucial for effective asset management and reliability evaluation, where indices such as the aging index, aging condition index, and health index serve as essential metrics [9,10,11]. A key element in these evaluations is the determination of the aging coefficient, which serves as the foundation for establishing the aging model. Based on this model, the ACI can be defined, enabling the estimation of the remaining lifetime of the cables.

This study introduces a systematic approach to calculate the aging coefficient for thermoplastic-insulated power cables. Accelerated aging experiments were conducted at controlled temperatures of 90 °C, 110 °C, and 130 °C for durations up to 5000 h. During these tests, critical mechanical properties, specifically tensile strength and elongation at break, were continuously monitored. The resulting experimental data were then fitted to an exponential model to extract the aging coefficient, providing a quantitative measure of performance degradation. The aging coefficient was utilized to establish the aging model, based on which a systematic process was proposed for calculating the ACI and estimating the remaining life.

By establishing a robust methodology for calculating the aging coefficient, this study not only advances the quantification of insulation aging but also develops a comprehensive aging condition index and a technique for estimating the remaining lifetime. Ultimately, the findings enhance capabilities for reliability assessment, maintenance planning, and long-term asset management of power cables for efficient and sustainable power transmission systems.

2. Literature Review and Background

2.1. Comparison of Conventional Materials and Thermoplastic Materials for Cable Insulation

Polypropylene (PP), a representative thermoplastic material, is valued for its recyclability and eco-friendly properties. It has a melting point of 160 °C, significantly higher than XLPE (cross-linked polyethylene), a common cable insulation material with a melting point of 110 °C. This elevated thermal threshold allows PP-based insulation to potentially enhance cable transmission capacity [4]. However, thermoplastic materials are inherently rigid, posing challenges during cable transport, laying, and installation. To mitigate this, additives have been used to improve their flexibility [7,8]. Thus, optimizing and evaluating their mechanical properties is essential for effective cable insulation use.

Table 1. Comparison of XLPE and PP Materials.

Category	XLPE (Cross Linked Polyethylene)	PP (Polypropylene)
Material Type	Thermoset (cross-linked structure)	Thermoplastic (non-cross-linked structure)
Thermal Properties	Continuous operating temperature 90 °C Melting point 110 °C	Continuous operating temperature 110 °C Melting point 160 °C
Electrical Properties	Excellent performance with low dielectric loss	Excellent performance with low moisture absorption
Mechanical Properties	Excellent flexibility and durability	Inherently hard and rigid (flexibility can be improved with additives)
Recyclability	Difficult to recycle	Recyclable and environmentally friendly
Application	Used in various insulation application such as power cables	Suitable for high temperature cables, as well as advanced application

compares key properties of XLPE and PP. While PP shows advantages such as better recyclability, thermal stability, and lower space charge accumulation, its lower mechanical flexibility necessitates improvement. Accordingly, this study focuses on assessing the mechanical characteristics of thermoplastic insulation.

2.2. Aging Index and Aging Condition Index

Deriving an ACI through the application of an aging coefficient is essential, as an accurate evaluation of aging allows for predicting the remaining lifetime of cables, optimizing maintenance schedules, and reducing operational costs. This metric enables an objective assessment of the insulation’s condition, and the resulting aging index serves as a foundational tool for maintenance strategies.

To calculate the lifetime of a cable, as illustrated in Figure 1, the aging coefficient must first be determined in order to establish the aging model. Based on this model, the Aging Condition Index (ACI) and the remaining lifetime can then be derived.

• Aging coefficient: A numerical parameter that quantifies the rate of insulation property aging under specific conditions, such as temperature and time.
• Aging condition index: A normalized index ranging from 0 to 1 that represents the current degree of insulation aging relative to its initial condition.

2.3. Necessity of Aging Condition Index and Limitations of Existing Studies

Previous studies have primarily focused on conventional insulation materials such as XLPE, while research on the derivation of the ACI for thermoplastic insulation materials in MVDC (medium voltage direct current) applications remains insufficient. In particular, there is a lack of research on calculating the aging coefficient related to the mechanical property enhancement of thermoplastic insulation materials, highlighting the need for further investigation in this area. A systematic study on the derivation of AI (aging index) and HI (health index) for thermoplastic insulation-based MVDC power cables has yet to be conducted.

Notably, research addressing the aging coefficient to account for the mechanical vulnerabilities of these materials is nearly absent. The absence of such studies indicates that a quantitative evaluation based on the aging coefficient has not been fully established, which poses challenges in developing accurate diagnostic and predictive models necessary for long-term reliability and the efficient asset management of power cables.

3. Experiment

3.1. Test Specimens

In this study, experiments were conducted on power cables with thermoplastic insulation. Figure 2 illustrates a thermoplastic insulated cable designed for DC 35 kV applications. The cable consists of an aluminum conductor with a cross-sectional area of 95 mm² and PP insulation with a thickness of 6.75 mm. Additionally, the thicknesses of the inner and outer semiconductive layers are 0.75 mm and 1.01 mm, respectively. The detailed specifications of the thermoplastic insulated cable are presented in

Table 2. Details of thermoplastic insulated cables.

Classification	Size	Note
Conductor	Diameter: 11.35 mm	Aluminum
Inner-semi conductive	Thickness: 0.75 mm
Insulation	Thickness: 6.75 mm	Thermoplastic
Outer-semi conductive	Thickness: 1.01 mm

.

To evaluate the mechanical properties of the thermally aged cable insulation, thin sheet-shaped test specimens were prepared. The specimens were obtained by removing the conductor from the test cable and peeling off the insulation using a precision cutting machine in Figure 3. Figure 5 illustrates the test specimens prepared for the mechanical property evaluation.

• Test cable: Thermoplastic insulated power cable in Figure 2.
• Test specimen: Sheet specimen created by peeling from the aged cable in Figure 3.
• Dumbbell-shaped specimen: Measuring tensile strength and elongation in Figure 5.

3.2. Thermal Aging Test

For the thermal aging test of cable insulation, the outer jacket, neutral wires, and swellable tape were removed from the test cable, after which thermal aging was conducted using an oven [12,13]. The thermal aging test was performed under the conditions outlined in

Table 3. Test conditions for thermal aging.

Aging Condition	Detailed	Note
Time	Max 5000 h	Interval of 1000 h
Temperature	90 °C, 110 °C, 130 °C	Interval of 20 °C (IEC 60216)

, and the aging process is depicted in Figure 4. Initially, the test specimen was white, but it turned brown after the aging process. After 5000 h of aging at 130 °C, the specimen became rigid and brittle, and it was no longer possible to process it into a thin sheet form.

3.3. Mechanical Test After Thermal Aging Test

The tensile strength and elongation of the test specimens were measured according to the IEC 60811-501 standard [14], with the measurement conditions summarized in

Table 4. Measurement conditions for mechanical test.

Measurement Condition	Detailed	Note
Temperature	25 °C	IEC 60811-501
Humidity	Below 50%
Number of samples	For each condition, 4–10 EA
Separation rate	25 mm/min
Sample size	Dumb-bell shape 75 mm × 12.5 mm × 4 mm

. A minimum of four test specimens were used, and the tensile force was increased at a rate of 25 mm/min until the specimen fractured. The maximum tensile force and the elongation (gauge length increase) at fracture were recorded [15,16]. For each aging condition, a minimum of 4 to 10 specimens were tested. In particular, for samples aged beyond 4000 h, at least 4 specimens were used due to material brittleness and handling limitations. The measurement devices used were DAEHA’s QC-548M1F-M and QC-551 models. Figure 5 shows the dumbbell-shaped test specimen used for tensile strength and elongation measurements, and illustrates the tensile strength and elongation measurement process.

3.4. Application of Aging Model

3.4.1. Basic Model

The general exponential decay aging model for materials over time is given by Equation (1). In this equation, P(t) represents the material performance at time t, P₀ denotes the initial performance at t = 0, α is the aging coefficient, and t corresponds to the elapsed time or operating duration. The exponential function has been applied as an aging model [17].

$$P\left(t\right)=P_0·{e\mathrm{x}\mathrm{p}}^{-\alpha t}$$

(1)

3.4.2. Extended Model

The parameter of a general exponential aging model is typically derived from time-dependent insulation property data. In this study, a composite exponential aging model incorporating two parameters, temperature and time, was developed. The corresponding base model is represented by Equation (2).

$$P\left(T, t\right)=-A·{e\mathrm{x}\mathrm{p}}^{\left({\displaystyle \frac{T}{\mathrm{B}}}+{\displaystyle \frac{t}{\mathrm{C}}}\right)}+\left(T{P}_0\right)$$

(2)

In this study, P(T,t) represents the tensile strength and elongation at a given aging time t and temperature T. The parameter A denotes the maximum reduction in tensile strength and elongation, while T is the aging test temperature. The terms 1/B and 1/C correspond to the aging coefficients related to temperature and time, respectively. t indicates the aging duration, and TP₀ represents the initial tensile strength and elongation values

4. Result Experiment

4.1. Tensile Strength and Elongation of Aged Test Samples

Table 5. Tensile strength of test samples as a function of aging conditions.

Tensile Strength (Mpa)
Aging Time (Hour)	Aging Temperature (°C)
	25	90	110	130
0	21.4	-	-	--
1000		20.4	19.7	19
2000	-	20.9	18.3	18.9
3000	-	19.9	18.4	18.2
4000	-	11.7	10.8	10.0
5000	-	10.5	10.3	-

and

Table 6. Elongation of test samples as a function of aging conditions.

Elongation (%)
Aging Time (Hour)	Aging Temperature (°C)
	25	90	110	130
0	1075	-	-	-
1000		1012	960	895
2000	-	1078	950	995
3000	-	957	871	991
4000	-	420	287	153
5000	-	260	226	-

present the variations in tensile strength and elongation of the test samples under different aging conditions. Before aging, the mechanical properties measured at room temperature (25 °C) were 21.4 MPa for tensile strength and 1075% for elongation. After 4000 h of thermal aging at 90 °C, 110 °C, and 130 °C, both tensile strength and elongation were observed to decrease by more than 40% compared to the initial values. When the aging duration reached 5000 h, the tensile strength decreased by over 50%, and the elongation dropped by more than 75%, indicating a significant degradation of mechanical properties with prolonged thermal exposure.

To quantitatively evaluate the effects of aging temperature and time on mechanical properties, curve fitting was performed using the measured tensile strength and elongation data. The results are shown in Figure 6a,b, where both the experimental data and the fitted curves are displayed. The black, green, and red data points represent samples aged at 90 °C, 110 °C, and 130 °C, respectively. Notably, the degradation in both tensile strength and elongation at 130 °C followed an exponential decay pattern with respect to aging time, which was more pronounced compared to the samples aged at 90 °C and 110 °C.

4.2. Extended Aging Model and Aging Coefficient

A three-dimensional (3D) aging index model was developed to predict tensile strength and elongation as functions of aging conditions (temperature and time). Figure 7a,b illustrates this model, where the X-axis represents aging time, the Y-axis indicates aging temperature, and the Z-axis corresponds to tensile strength and elongation, respectively. The blue spheres represent the measured mechanical properties of the aged specimens, while the yellow diamonds indicate the surface fitting results derived from the experimental data. Under all aging conditions, both tensile strength and elongation exhibited exponential decreases with increasing aging time and temperature. This trend was quantified through the aging models presented in Equations (3) and (4), which were developed based on the exponential functional form described in Equation (2). The corresponding model parameters are summarized in

Table 7. Detailed parameters of the extended aging model and aging coefficients.

Classification	Aging Model: P(T,t) = −A × exp(T/B) × exp(t/C) + TP0				Note
	Maximum Reduction	Aging Coefficient		Initial Values	R2
	A	1/B (Temp)	1/C (Time)	TP0
Tensile strength	0.46	0.011831519	0.000391489	21.4	0.845
Elongation	12.43	0.013933398	0.000521521	1010.18	0.834

. The goodness-of-fit for the 3D degradation models was evaluated using the coefficient of determination (R²), yielding values of 0.845 for tensile strength and 0.834 for elongation, indicating relatively high predictive accuracy.

A sensitivity analysis of the aging parameters revealed that, for tensile strength, the aging coefficient for temperature was 0.01 and for time was 0.0003, suggesting that temperature had a more significant effect on degradation than time. A similar trend was observed for elongation, with an aging coefficient of 0.01 for temperature and 0.005 for time.

$$z_{Tensile strength}(T, t)=-0.46{exp}^{\left({\displaystyle \frac{T_{temp}}{84.52}}+{\displaystyle \frac{t_{time}}{2554.35}}\right)}+21.4$$

(3)

$$z_{Elongation}(T, t)=-12.43{exp}^{\left({\displaystyle \frac{T_{temp}}{71.77}}+{\displaystyle \frac{t_{time}}{1917.47}}\right)}+1010.18$$

(4)

4.3. Definition of Aging Condition Index (ACI)

To evaluate the aging condition and estimate the life of a PP insulated cable subjected to mechanical aging, aging indices were developed. Equation (5) represents the index based on tensile strength, while Equation (6) pertains to elongation at break. The aging index is expressed as a normalized value between 0 and 1, where 1 indicates an undegraded, pristine condition, and 0 represents a fully aged state. The critical threshold values of 12.5 MPa for tensile strength and 350% for elongation were selected based on the minimum mechanical property requirements specified in relevant standards for cable-grade insulation materials. The threshold values for tensile strength (12.5 MPa) and elongation at break (350%) were determined based on the Korean industrial standard SPS-C-KWS-501-7524:2022 [18], established by the Korea Electric Wire Industry Cooperative. When the measured property falls below these thresholds, the material is considered mechanically failed, and the degradation index is accordingly set to 0.

$${ACI }_{Tensile strength}\left(T, t\right)=\left\{\begin{array}{c}{\displaystyle \frac{z \left(T,t\right)-Z_{Minmum}}{Z_0-Z_{Minmum}}}={\displaystyle \frac{z \left(T,t\right)-12.5}{20.94-12.5}} if z\left(T,t\right)>12.5 \\ 0 if z\left(T, t\right)\le 12.5 \end{array}\right.$$

(5)

where z(T,t) denotes the tensile strength (in MPa) as a function of temperature and time. The z₀ (initial tensile strength) is 20.94 MPa, and the failure threshold is defined as z_minimum (12.5 MPa), which corresponds to the minimum mechanical requirement for the material to be qualified for cable insulation. When the tensile strength falls below this value, the material is regarded as not meeting the minimum specification criteria, and the aging index is accordingly set to zero.

$${ACI }_{Elongation}\left(T, t\right)=\left\{\begin{array}{c}{\displaystyle \frac{z \left(T,t\right)-Z_{Minmum}}{Z_0-Z_{Minmum}}}={\displaystyle \frac{z \left(T,t\right)-350}{997.75-350}} if z\left(T,t\right)>350 \\ 0 if z\left(T, t\right)\le 350 \end{array}\right.$$

(6)

In this case, z(T,t) denotes the elongation at break (in %) over time and temperature. The initial elongation is assumed to be 997.75% as z₀, and the requirement of the criterion is set to 350% as z_minmum, which is the minimum acceptable value for maintaining mechanical integrity. The index reflects the loss of flexibility and ductility of the insulation material during aging.

4.4. Case Study: Estimation of Remaining Lifetime Using ACI

The ACI is a key metric for quantitatively assessing the aging state of cable insulation and estimating the remaining lifetime under specific operating conditions. In this study, ACI is calculated based on aging models for tensile strength and elongation of thermoplastic cable insulation materials, with the goal of predicting the future service life.

Using Equations (3) and (4), the aging behavior of tensile strength and elongation was modeled as functions of temperature and aging time. Based on these results, Equations (5) and (6) define the ACI formulations, which were then applied to predict the progressive mechanical deterioration of the insulation. The following section presents a step-by-step case study illustrating this approach.

4.4.1. Step 1: Characterization of a Cable with Unknown Operating History

• A cable specimen “A” with unknown thermal and aging history is assumed to exhibit a measured tensile strength of 18 MPa.

4.4.2. Step 2: Calculation of ACI for Cable “A”

• The tensile strength-based ACI is defined by Equation (5). This value indicates the current aging level of the insulation in terms of tensile strength performance. Assuming the measured tensile strength of cable “A” is z = 18.0 MPa, the ACI can be calculated as:

$${ACI }_{Tensile strength}\left(T, t\right)={\displaystyle \frac{18.0-12.5}{20.94-12.5}}={\displaystyle \frac{5.5}{8.44}}\approx 0.652$$

(7)

4.4.3. Step 3: Estimation of Remaining Lifetime Until a Target ACI Level

• To estimate the remaining lifetime of the cable “A” specified operating conditions, the time required for the ACI to decrease from its current value to a predefined threshold is calculated.
• Cable “A”, which currently exhibits a tensile strength of 18 MPa, corresponds to an ACI of 0.652, as calculated using Equation (7). Assuming that the cable will be operated under a constant temperature of 30 °C, the remaining lifetime t until the ACI decreases to 0.5 can be estimated. Using Equations (8) and (9), the tensile strength corresponding to an ACI of 0.5 is calculated to be z = 16.72 MPa.

  $$z={ACI }_{Tensile strength}·\left(z_0-z_{Minmum}\right)+z_{Minmum}$$

  (8)

  $$16.72 \mathrm{M}\mathrm{p}\mathrm{a}=0.5·8.44+12.5$$

  (9)
• Using Equation (3), the time required for cable “A” with an initial ACI of 0.652 to reach an ACI of 0.5 under an operating temperature of 30 °C can be calculated using Equation (10).

$$16.72=-0.46{exp}^{\left({\displaystyle \frac{30}{84.52}}+{\displaystyle \frac{t_{time}}{2554.35}}\right)}+21.4, t_{time}\approx 5020 \mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s})$$

(10)

The proposed aging index model provides a quantitative approach for assessing the aging state of cables as a function of operating temperature and time. By applying this model, it is possible not only to evaluate the current condition of the insulation based on mechanical properties but also to predict the remaining lifetime until a predefined ACI threshold is reached. This approach offers a valuable tool for condition-based maintenance and lifecycle management of power cables.

5. Discussion

This study proposed an ACI model capable of quantitatively evaluating the aging condition of thermoplastic insulation based on mechanical properties and estimating the remaining lifetime under specific operating conditions. An exponential aging model was derived from tensile strength and elongation data obtained through accelerated thermal aging at various temperatures. The resulting model demonstrated high goodness-of-fit, with coefficients of determination (R²) of 0.845 for tensile strength and 0.834 for elongation.

Analysis of the aging coefficients revealed that the temperature coefficient (0.01) for tensile strength was significantly higher than the time coefficient (0.0003), indicating that temperature has a much stronger influence on degradation than time. This suggests that temperature control is a critical factor in maintaining the long-term reliability of insulated cables during operation.

The proposed ACI framework not only enables a quantitative assessment of the current aging state of thermoplastic insulation but also facilitates accurate lifetime prediction until a predefined ACI threshold (e.g., ACI = 0.5) is reached. A key contribution of this study lies in its ability to evaluate the aging condition and remaining life of cable insulation even in the absence of a detailed operational history. This feature significantly enhances the practical applicability of the model, supporting the implementation of condition-based maintenance strategies. The originality of the work is further demonstrated by the introduction of a mechanistic aging modeling approach that links accelerated aging data with real-time reliability assessment, providing a novel pathway for insulation health diagnostics and lifecycle asset management in power cable systems.

However, the current model considers only mechanical aging indicators, excluding electrical factors such as partial discharge, space charge, and dielectric loss. In future work, various electrical diagnostic techniques, including partial discharge, space charge, dielectric loss, and conduction characteristics, will be quantitatively evaluated under combined thermal and electrical aging conditions. Each diagnostic parameter will be normalized and indexed to reflect its degradation behavior, and appropriate weighting factors will be assigned based on its correlation with insulation breakdown strength. Furthermore, the selection of the ACI threshold was based on engineering judgment; future studies should incorporate failure history data to establish more objective, reliability-based thresholds. Future work should focus on integrating electrical aging diagnostics with mechanical models to establish a comprehensive health index framework. Additionally, validation of the model’s effectiveness through long-term field data will be essential for practical deployment.

6. Conclusions

This study was initiated to address one of the primary limitations of polypropylene, its inherent mechanical rigidity, which restricts its practical use as a cable insulation material despite its thermal and environmental advantages. By focusing on mechanical aging characteristics, this research sought to quantitatively capture the performance degradation of thermoplastic insulation over time and temperature. To this end, a three-dimensional exponential aging model was established using tensile strength and elongation data under various thermal aging conditions. From this model, an ACI was defined to assess the current degradation level of the insulation and estimate its remaining lifetime under specific operating conditions. Key findings of this research include:

■

Thermoplastic insulation exhibited an exponential decline in mechanical properties with increasing aging time and temperature.

■

The developed degradation models achieved high accuracy, with coefficients of determination R² exceeding 0.83, validating their reliability.

■

The proposed ACI quantitatively represents insulation aging on a 0–1 scale relative to the initial condition, enabling both real-time diagnostic evaluation and future lifetime prediction based on a defined threshold.

These results not only provide a robust methodology for evaluating the mechanical reliability of PP-based insulation but also lay the groundwork for condition-based maintenance and lifecycle asset management in power cable systems. Ultimately, this research offers practical insights into overcoming PP’s mechanical limitations and supports the advancement of more sustainable and high-performance insulation solutions in modern power grids.