Numerical Analysis of Conditions for Partial Discharge Inception in Spherical Gaseous Voids in XLPE Insulation of AC Cables at Rated Voltage and During AC, VLF and DAC Tests
Abstract
:1. Introduction
- Submarine power transmission and distribution, including long-distance interconnection and reliable transfer of electrical power from offshore wind farms to onshore substations;
- Transmission of high power to city centers;
- Reliable power supply in areas where overhead lines are permanently or periodically exposed to high environmental stresses;
- Distribution of electricity in urban areas, etc.
- During cable manufacturing technological processes;
- During their storage phase;
- During transport and logistic operations accompanying it;
- During technological operations related to cable laying (installation);
- During the operation of the cable, in rated conditions and at stresses exceeding them (e.g., during overheating or transient overvoltages).
2. Testing Voltages Used for PD Simulation in the AC Cable Model
- AC 50 Hz;
- VLF 0.1 Hz True-sine;
- VLF 0.1 Hz CR (Cosine-Rectangular);
- DAC 50 Hz.
Test | AC 50 Hz | VLF 0.1 Hz True-Sine | VLF 0.1 Hz CR | DAC 50 Hz | |
---|---|---|---|---|---|
Voltage waveform | |||||
Pre-stress voltage | Voltage | 1.7 U0 | 1.7 U0 | 1.7 U0 | 1.7 U0 |
Time | 30/5 min | 30/5 min | 30/5 min | 50/10 excitations | |
PDEV LL test | Voltage | 1.5 U0 | 1.5 U0 | 1.5 U0 | 1.5 U0 |
Time | 1 min | 2 min | 2 min | 10 excitations |
3. Description of the Single-Core AC Cable Model
4. Description and Discussion of Numerical Modeling Results
4.1. Simulation Results for Cable at Rated AC Voltage
4.2. Simulation Results for AC Cable Under Test Voltage Conditions
4.3. Influence of Cable Core Temperature on PD Inception in AC Cable Insulation
4.4. Influence of Test Voltage Magnitude and Waveform on PD Inception in AC Cable Insulation
5. Conclusions
- The location of the gaseous void in the XLPE insulation of a single-core AC power cable is the main factor determining the value of the E field in the void. This results directly from the radial distribution of the E field in the cable insulation.
- For a loaded cable, the increased core temperature and the resulting temperature field in the cable insulation have a complex effect on the conditions of PD inception in gaseous voids. This influence is partly direct, by increasing the Einc value (resulting from Paschen’s law), and partly indirect, by decreasing the XLPE permittivity, modifying the E field distribution in the AC cable insulation and the field enhancement factor (FEF) value for each gaseous void.
- The waveforms, frequencies and magnitudes of AC, VLF, and DAC voltages, used during withstand voltage tests of AC cable insulation, have a significant influence on the PD inception conditions and statistical parameters of PD pulse sets collected in PRPD patterns.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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No. | Cable Layer | r (mm) |
---|---|---|
1 | Core conductor | 11.9 |
2 | Semicon layer (xmin) | 13.2 |
3 | Insulation (xmax) | 30.7 |
4 | Semicon layer | 31.9 |
5 | Water barrier layer | 36.9 |
6 | Aluminum sheath | 38.9 |
7 | Outer sheath | 42.9 |
No. | Cable Layer | k (W·m−1·K−1) | Cp (J·kg−1·K−1) | ρ (kg·m−3) |
---|---|---|---|---|
1 | Core conductor | 401 | 385 | 8950 |
2 | Semicon layer | 0.23 | 2050 | 1100 |
3 | Insulation (XLPE) | 0.32 | 2250 | 920 |
4 | Semicon layer | 0.23 | 2050 | 1100 |
5 | Water barrier layer | 0.19 | 1900 | 530 |
6 | Aluminum sheath | 238 | 900 | 2700 |
7 | Outer sheath | 0.30 | 2350 | 950 |
Parameter | Value | Unit |
---|---|---|
Cable rated voltage | 110 | kV |
Conductor cross-section | 400 | mm2 |
Conductivity of XLPE | 5.4 × 10−16 | S·m−1 |
Conductivity of air in void | 10−16 | S·m−1 |
Conductivity of air in void during PD | 10−3 | S·m−1 |
Dielectric constant of gas in void | 1.0 | - |
Dielectric constant of XLPE at 10 °C | 2.35 | - |
Dielectric constant of XLPE at 90 °C | 2.10 | - |
Cable core temperature | 10–90 | °C |
External (ground) temperature | 10 | °C |
First void diameter | 0.5 | mm |
First void r position | 14.2 | mm |
Second void diameter | 0.5 | mm |
Second void r position | 29.7 | mm |
Cable Core Temperature | Temperature | Relative Permittivity | Electric Field | ||||||
---|---|---|---|---|---|---|---|---|---|
Txmin (°C) | Txmax (°C) | ΔT (°C) | εxmin (S/m) | εxmax (S/m) | kε (-) | Exmin (kV/mm) | Exmax (kV/mm) | ΔE (kV/mm) | |
10 °C | 10.0 | 10.0 | 0.0 | 2.35 | 2.35 | 1.00 | 8.06 | 3.47 | 4.59 |
30 °C | 28.9 | 22.7 | 6.2 | 2.29 | 2.31 | 0.99 | 8.09 | 3.46 | 4.63 |
50 °C | 47.9 | 35.3 | 12.6 | 2.23 | 2.27 | 0.98 | 8.13 | 3.44 | 4.69 |
70 °C | 66.8 | 48.0 | 18.8 | 2.17 | 2.23 | 0.97 | 8.17 | 3.43 | 4.74 |
90 °C | 85.7 | 60.6 | 25.1 | 2.11 | 2.19 | 0.96 | 8.21 | 3.41 | 4.80 |
Cable Core Temperature | Electric Field | |||||
---|---|---|---|---|---|---|
1st Void | 2nd Void | |||||
Evoid (kV/mm) | Ecable (kV/mm) | FEF (-) | Evoid (kV/mm) | Ecable (kV/mm) | FEF (-) | |
10 °C | 10.45 | 7.49 | 1.40 | 4.99 | 3.58 | 1.39 |
30 °C | 10.41 | 7.52 | 1.38 | 4.94 | 3.57 | 1.38 |
50 °C | 10.37 | 7.55 | 1.37 | 4.90 | 3.55 | 1.38 |
70 °C | 10.32 | 7.58 | 1.36 | 4.85 | 3.54 | 1.37 |
90 °C | 10.28 | 7.61 | 1.35 | 4.80 | 3.52 | 1.36 |
Test | Parameter | 50 Hz AC | VLF 0.1 Hz True-Sine | VLF 0.1 Hz CR | DAC 50 Hz | ||||
---|---|---|---|---|---|---|---|---|---|
1st Void | 2nd Void | 1st Void | 2nd Void | 1st Void | 2nd Void | 1st Void | 2nd Void | ||
Pre-stress voltage | N | 117,149 | 54,931 | 232 | 108 | 237 | 114 | 187 | 68 |
N/half-period | 3.905 | 1.831 | 3.867 | 1.800 | 3.950 | 1.900 | - | - | |
Qavg, C | 3.22 × 10−11 | 2.72 × 10−11 | 3.23 × 10−11 | 2.71 × 10−11 | 3.15 × 10−11 | 2.79 × 10−11 | 2.85 × 10−11 | 2.58 × 10−11 | |
Qmax, C | 1.23 × 10−10 | 6.80 × 10−11 | 8.07 × 10−11 | 3.99 × 10−11 | 6.56 × 10−11 | 4.48 × 10−11 | 5.25 × 10−11 | 3.83 × 10−11 | |
Qtotal, C | 3.77 × 10−6 | 1.49 × 10−6 | 7.50 × 10−9 | 2.93 × 10−9 | 7.47 × 10−9 | 3.18 × 10−9 | 5.33 × 10−9 | 1.76 × 10−9 | |
PDEV LL test | N | 20,950 | 9028 | 86 | 38 | 81 | 39 | 164 | 36 |
N/half-period | 3.492 | 1.505 | 3.583 | 1.583 | 3.375 | 1.625 | - | - | |
Qavg, C | 3.11 × 10−11 | 2.66 × 10−11 | 3.11 × 10−11 | 2.62 × 10−11 | 3.08 × 10−11 | 2.68 × 10−11 | 2.75 × 10−11 | 2.50 × 10−11 | |
Qmax, C | 1.04 × 10−10 | 5.77 × 10−11 | 7.66 × 10−11 | 3.59 × 10−11 | 6.11 × 10−11 | 3.83 × 10−11 | 5.56 × 10−11 | 3.03 × 10−11 | |
Qtotal, C | 6.52 × 10−7 | 2.41 × 10−7 | 2.68 × 10−9 | 9.97 × 10−10 | 2.49 × 10−9 | 1.05 × 10−9 | 4.51 × 10−9 | 9.00 × 10−10 |
Test | 1st Void | 2nd Void |
---|---|---|
Pre-stress voltage 50 Hz AC 1.7 U0—300 s | ||
Pre-stress voltage VLF 0.1 Hz Sine 1.7 U0—300 s | ||
Pre-stress voltage VLF 0.1 Hz CR 1.7 U0—300 s | ||
Pre-stress voltage DAC 50 Hz 1.7 U0—10 excitations |
Test | 1st Void | 2nd Void |
---|---|---|
PDEV LL test 50 Hz AC 1.5 U0—60 s | ||
PDEV LL test VLF 0.1 Hz Sine 1.5 U0—120 s | ||
PDEV LL test VLF 0.1 Hz CR 1.5 U0—120 s | ||
PDEV LL test DAC 50 Hz 1.5 U0—10 excitations |
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Mikrut, P.; Zydroń, P. Numerical Analysis of Conditions for Partial Discharge Inception in Spherical Gaseous Voids in XLPE Insulation of AC Cables at Rated Voltage and During AC, VLF and DAC Tests. Energies 2025, 18, 2949. https://doi.org/10.3390/en18112949
Mikrut P, Zydroń P. Numerical Analysis of Conditions for Partial Discharge Inception in Spherical Gaseous Voids in XLPE Insulation of AC Cables at Rated Voltage and During AC, VLF and DAC Tests. Energies. 2025; 18(11):2949. https://doi.org/10.3390/en18112949
Chicago/Turabian StyleMikrut, Paweł, and Paweł Zydroń. 2025. "Numerical Analysis of Conditions for Partial Discharge Inception in Spherical Gaseous Voids in XLPE Insulation of AC Cables at Rated Voltage and During AC, VLF and DAC Tests" Energies 18, no. 11: 2949. https://doi.org/10.3390/en18112949
APA StyleMikrut, P., & Zydroń, P. (2025). Numerical Analysis of Conditions for Partial Discharge Inception in Spherical Gaseous Voids in XLPE Insulation of AC Cables at Rated Voltage and During AC, VLF and DAC Tests. Energies, 18(11), 2949. https://doi.org/10.3390/en18112949