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Thermal aging management of underground power cables in electricity distribution networks: a FEM-based Arrhenius analysis of the hot spot effect

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Abstract

The effects of solar irradiation, wind and moisture on the thermal aging of underground power cables in electricity distribution networks cannot be included in the traditional Arrhenius model by means of any temperature rise or any derating factor. Such effects can be taken into account only if the Arrhenius model is coupled with a finite element method (FEM)-based steady-state thermal model and the Miner’s cumulative damage law. Accordingly, this study aims to analyze the effect of an actual hot spot on the thermal lifespan of a 110 kV underground cable line using a FEM-based Arrhenius model and considering solar irradiation, wind velocity, and soil moisture content. The 110 kV underground line consists of cables with cross-linked polyethylene (XLPE) insulation. The considered parameters are logically changed within the frames of the most unfavorable summer conditions and the most common winter conditions. The FEM-based Arrhenius model used was developed for the purpose of thermal aging management of power cables by Klimenta JLj, Panić MV, Stojanović MS et al. in early 2022. The existing calculated and experimental data on XLPE insulation are used for the purposes of verification and validation of the model, respectively. Finally, the hot spot effect is quantified and analyzed for all the considered parameters.

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Abbreviations

FEM:

Finite element method

HDPE:

High-density polyethylene

IEC:

International Electrotechnical Commission

IEC TR:

International Electrotechnical Commission Technical Report

NA2XS(FL)2Y:

Single-core power cable, N–standardized/norm type, A–aluminum conductor, 2X–cross-linked polyethylene insulation, S–copper screen, FL–longitudinally and crosswise water-tight, and 2Y–polyethylene outer sheath

NAEKEBA:

Three-core power cable, N–standardized/norm type, A–aluminum conductor, EK–metal sheath of lead with corrosion protection on each sheath, E–thermoplastic sheath and inner protective covering, lapped bedding with additional layer of plastic tape, B–armor of steel tape, and A–outer protection of fibrous material (jute) in compound

NPP:

Nuclear power plant

XLPE:

Cross-linked polyethylene

A F,p,i :

Fraction of Ltot consumed during the ith interval

A max,p :

Maximum possible fraction of Ltot, %

A tot, h :

Total thermal lifespan consumption, h

A tot,p :

Fraction of Ltot consumed during top, %

E a :

Activation energy, eV

h c :

Heat transfer coefficient due to free or wind-induced convection, W/(m2·K)

I :

Cable ampacity, load current or overload current, A

I cp :

Cable ampacity, A

i :

Designation for the ith interval

K :

Number of intervals tD,i in top

K B :

Boltzmann constant, eV/K

k :

Thermal conductivity, W/(m·K)

k ns :

Thermal conductivity of the native soil, W/(m·K)

L tot :

Total thermal lifespan, h

L tot,e :

Expected total service lifespan, years

M c :

Moisture content in the native soil, %

\( \vec{n} \) :

Normal vector of the boundary

Q S , s :

Solar irradiance, W/m2

Q v :

Volume power of heat sources, W/m3

q 0 :

Specified heat flux or heat flux from the exterior of the heating-pipe duct, W/m2

R a :

Thermal aging rate, %/h

R a, i :

Thermal aging rate taking place during the ith interval, %/h

R ac :

Effective a.c. resistance, Ω/m

\(S_{{\text{c}}}^{\prime }\) :

Geometric cross section area of one conductor, m2

T :

Nodal or surface unknown temperature, K, or service temperature, K or °C

T a :

Temperature of the air contacting the ground surface, °C

T cp :

Continuously permissible temperature of cables, °C

T hp :

Temperature of the exterior of the heating-pipe duct, °C

T ns :

Temperature of reference soil, °C

T R :

Reference or accelerated test temperature, K or °C

T summer :

Summer service temperature, °C

T threshold :

Threshold temperature, °C

T winter :

Winter service temperature, °C

T winter1 :

Winter service temperature for the case where there are the same moisture contents in the native soil outside and in the hot spot area, °C

T winter2 :

Winter service temperature for the case where there are zero or different moisture contents in the native soil outside and in the hot spot area, °C

t :

Service lifespan, h

t D, i :

Duration of the ith interval, h

t op :

Specific operating period, h

t R :

Reference lifespan, h

v a :

Wind velocity, m/s

x, y :

Cartesian spatial coordinates, m

α :

Solar absorptivity

ε :

Thermal emissivity

σ SB :

Stefan–Boltzmann constant, W/(m2·K4)

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Acknowledgements

This paper was based on research conducted within the Program No. NIO 200155 funded by the Ministry of Education, Science, and Technological Development of the Republic of Serbia.

Author information

Authors and Affiliations

  1. Faculty of Electronic Engineering, University of Niš, Niš, Serbia

    Miodrag Stojanović & Dragan Tasić

  2. ProElectric SD, Kraljevo, Serbia

    Jelena Klimenta

  3. Technical Faculty in Bor, University of Belgrade, Bor, Serbia

    Marija Panić

  4. Faculty of Technical Sciences, University of Priština in Kosovska Mitrovica, Kosovska Mitrovica, Serbia

    Dardan Klimenta, Miloš Milovanović & Bojan Perović

Authors
  1. Miodrag Stojanović
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  2. Jelena Klimenta
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  3. Marija Panić
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  4. Dardan Klimenta
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  5. Dragan Tasić
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  6. Miloš Milovanović
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  7. Bojan Perović
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Contributions

M.S.: Conceptualization, Investigation, and Writing - Original draft preparation; J.K.: Conceptualization, Formal analysis, and Writing - Review & Editing. M.P.: Formal analysis, Supervision, Validation, and Writing - Review & Editing. D.K. and D.T.: Investigation, Formal analysis, Data curation, Supervision, Validation, and Administration and funding acquisition; M.M. and B.P.: Visualization, Formal analysis, and Writing - Review & Editing. All authors reviewed the manuscript.

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Correspondence to Dardan Klimenta.

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Stojanović, M., Klimenta, J., Panić, M. et al. Thermal aging management of underground power cables in electricity distribution networks: a FEM-based Arrhenius analysis of the hot spot effect. Electr Eng 105, 647–662 (2023). https://doi.org/10.1007/s00202-022-01689-z

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