Analysis of Propagation Delay for Multi-Terminal High Voltage Direct Current Networks Interconnecting the Large-Scale Off-Shore Renewable Energy
Abstract
:1. Introduction
2. Reflection Coefficient
3. System Modeling
3.1. Cable Model
3.2. Converter and Network Model
4. Methodology
5. Proposed Model
6. Results and Evaluation
6.1. Propagation Time Delay Testing for Cable
6.2. Different Cases for Propagation Time Delay
6.3. Terminal Voltage and Fault Current Dependence
6.4. Validation of Propagation Delay with Real-Time Digital Simulator (RTDS)
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Symbol | Parameter |
Dirac pulse | |
Rc | Concentrated cable resistance, in Ω |
u(t) | Step function |
C | DC capacitance, in μF |
Z | Surge impedence, in Ω |
R | Resistance per unit length |
L | Inductance per unit length |
G | Conductance per unit length |
Y | Admittance, in ℧ |
K(s) | Propagation constant |
Amplitude of the Forward Traveling Waves | |
Amplitude of the Backward Traveling Waves | |
K | Skin effect |
Z0(s) | Characteristic impedance, in Ω |
c | Propagation speed km/ms |
Rf | Fault resistance, in Ω |
Tp | Time for propagation, in seconds |
R0 | Impedance of cable, in Ω |
V0 | Initial voltage step |
erfc | Complementary error function |
N | Reflection index of the optical fiber |
Tf | Time of fault, in seconds |
T1–4 | Time delay for Terminals 1–4, in seconds |
VSC1–4 | Voltage-source converter voltage 1–4, in kV |
If1–4 | Fault current in Terminals 1–4, in kA |
TVSC1–4 (CALC) | Calculated time delay for Terminals 1–4, in seconds |
TVSC1–4 (MEAS) | Measured time delay for Terminals 1–4, in seconds |
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Layer | Material | Outer Radius (mm) | Resistivity (mΩ) | Relative Permittivity | Relative Permeability |
---|---|---|---|---|---|
Core | Copper | 40.0 | 1 | 1 | |
Insulation 1 | XLPE | 59.5 | - | 2.3 | 1 |
Sheath | Lead | 64.0 | 1 | 1 | |
Insulation 2 | XLPE | 67.5 | - | 2.3 | 1 |
Armor | Steel | 78.3 | 1 | 400 | |
Insulation 3 | PP | 83.5 | - | 2.1 | 1 |
Parameters | Values |
---|---|
Rated converter power | 1000 MW |
Alternating current (AC) voltage (P–P, RMS) | 500 kV |
Direct current voltage | ±300 kV |
Reactance to resistance ratio of AC network | 10 |
Transformer leakage reactance | 0.1 p.u. |
Total resistance of converter diodes | 0.005 p.u. |
Converter phase reactor | 0.05 p.u. |
Fault Type | Fault Location | Distance (km) | Propagation Delay (ms) |
---|---|---|---|
F2 | F-T1 | 0 | 0 |
F-T2 | 400 | 2 | |
F-T3 | 500 | 2.5 | |
F-T4 | 900 | 4.5 | |
F3 | F-T1 | 400 | 2 |
F-T2 | 0 | 0 | |
F-T3 | 100 | 0.5 | |
F-T4 | 500 | 2.5 | |
F4 | F-T1 | 500 | 2.5 |
F-T2 | 100 | 0.5 | |
F-T3 | 0 | 0 | |
F-T4 | 400 | 2 | |
F5 | F-T1 | 900 | 4.5 |
F-T2 | 500 | 2.5 | |
F-T3 | 400 | 2 | |
F-T4 | 0 | 0 |
Fault Name | Tvsc1 (CALC) | Tvsc1 (MEAS) | Tvsc2 (CALC) | Tvsc2 (MEAS) | Tvsc3 (CALC) | Tvsc3 (MEAS) | Tvsc4 (CALC) | Tvsc4 (MEAS) |
---|---|---|---|---|---|---|---|---|
A | 1.00000 | 1.000000 | 1.00300 | 1.003001 | 1.00300 | 1.003001 | 1.0060 | 1.006012 |
B | 1.00075 | 1.000754 | 1.00225 | 1.002248 | 1.00375 | 1.003748 | 1.00525 | 1.005261 |
C | 1.00150 | 1.001496 | 1.00150 | 1.001503 | 1.00450 | 1.004500 | 1.00450 | 1.004495 |
D | 1.00450 | 1.004504 | 1.00150 | 1.001497 | 1.00150 | 1.001501 | 1.00450 | 1.005453 |
E | 1.00600 | 1.006007 | 1.00300 | 1.003000 | 1.00300 | 1.003007 | 1.00000 | 1.000000 |
F | 1.00375 | 1.003745 | 1.00525 | 1.005298 | 1.00075 | 1.000749 | 1.00225 | 1.002248 |
G | 1.00300 | 1.003002 | 1.00600 | 1.006003 | 1.00000 | 1.00000 | 1.00600 | 1.006012 |
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Nadeem, M.H.; Zheng, X.; Tai, N.; Gul, M.; Tahir, S. Analysis of Propagation Delay for Multi-Terminal High Voltage Direct Current Networks Interconnecting the Large-Scale Off-Shore Renewable Energy. Energies 2018, 11, 2115. https://doi.org/10.3390/en11082115
Nadeem MH, Zheng X, Tai N, Gul M, Tahir S. Analysis of Propagation Delay for Multi-Terminal High Voltage Direct Current Networks Interconnecting the Large-Scale Off-Shore Renewable Energy. Energies. 2018; 11(8):2115. https://doi.org/10.3390/en11082115
Chicago/Turabian StyleNadeem, Muhammad Haroon, Xiaodong Zheng, Nengling Tai, Mehr Gul, and Sohaib Tahir. 2018. "Analysis of Propagation Delay for Multi-Terminal High Voltage Direct Current Networks Interconnecting the Large-Scale Off-Shore Renewable Energy" Energies 11, no. 8: 2115. https://doi.org/10.3390/en11082115