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High Frequency Modeling of LV Underground Power Cable Systems: Case studies on cable connections
Student : N.Song (0809313)
Content
IntroductionSignal transmission in LV cables
Case 1: Interconnection • 1. Simulation OIP cable• 2. Interconnection network Case 2: Simulated partial discharges at substation• 1. Interconnection • 2. Branching• 3. Parallel cables connected at the substation
Conclusions
EES PAGE 201-05-2023
Introduction
EES PAGE 301-05-2023
TransformerSubstation Low-voltage
Cable
Low voltage grid
Content
IntroductionSignal transmission in LV cables
Case 1: Interconnection • 1. Simulation OIP cable• 2. Interconnection network Case 2: Simulated partial discharge at substation• 1. Interconnection • 2. Branching• 3. Parallel cables connect at the substation
Conclusion
EES PAGE 401-05-2023
Case studies on cable connections
• Case 1To analyze the effects
when different types of 4-conductor cables are used in interconnection.
EES PAGE 501-05-2023
Oil-impregnated-paper(OIP) insulated cable
PVC cable
Case 1: Simulation OIP cable
EES PAGE 601-05-2023
Cross-section of the cable used in software
• Cable Under Test (CUT)Lead
Oil-impregnated-paper(OIP)
Copper
Case 1: Simulation OIP cable
• Telegrapher’s equations
/ name of department PAGE 701-05-2023
R: Resistance L: InductanceG: Conductance C: Capacitance
Case 1: Simulation OIP cable
• Modal voltages and currents
is the propagation coefficients for each mode.
EES PAGE 801-05-2023
Case 1: Simulation OIP cable
EES PAGE 901-05-2023
• Four modes of voltage
𝑽𝒎 ,𝟏=𝟏𝟒 (𝑽𝟏+𝑽 𝟐+𝑽𝟑+𝑽 𝟒)
𝑽𝒎 ,𝟐𝒂=𝟏𝟐 (𝑽 𝟏−𝑽 𝟑)
𝑽𝒎 ,𝟐𝒃=𝟏𝟐 (𝑽 𝟐−𝑽𝟒)
𝑽𝒎 ,𝟑=𝟏𝟒 (𝑽𝟏−𝑽 𝟐+𝑽 𝟑−𝑽 𝟒)
mode 1
--- positive--- negative
mode 2a mode 2b
mode 3
Case 1: Simulation OIP cable
EES PAGE 1001-05-2023
• Characteristic impedance matrix
• Modal characteristic impedance matrix for the CUT
Case 1: Simulation OIP cable
/ EESPAGE 1101-05-2023
Simulated modal characteristic impedance (top: magnitude, bottom: phase)
mode 1
mode 2
mode 3
Mode 1: Mode 2:
Mode 3:
Case 1: Simulation OIP cable
EES PAGE 1201-05-2023
• Propagation coefficients
is the attenuation coefficient for mode x is the phase velocity for mode x
Case 1: Interconnection network
• Schematic of simulated interconnection network
EES PAGE 1301-05-2023
𝑰𝒄𝒂𝒃𝒍𝒆𝒕𝒆𝒓𝒎𝒊𝒏𝒂𝒕𝒊𝒐𝒏 / 𝒊𝒏𝒕𝒆𝒓𝒄𝒐𝒏𝒏𝒆𝒄𝒕𝒊𝒐𝒏
EES
Case 1: Interconnection network
• Relation between the beginning and end of a cable
PAGE 1401-05-2023
EES
Case 1: Interconnection network
• Network equations
indicates the network on the opposite side of the respective cable section.
PAGE 1501-05-2023
Case 1: Interconnection network
• Constraint condition at the interconnection
EES PAGE 1601-05-2023
=0=0=0=0
=0=0=0=0
=0=0=0=0
=0=0=0=0
𝑌 𝑖1′ 𝑌 𝑗
2
𝑍 𝑗2𝑍 𝑖
1′
Case 1: Interconnection network
• Constraint condition at the termination
EESPAGE 1701-05-2023
111 1
111 1
𝑌 𝑖1 𝑍 𝑖
1
Case 1: Interconnection network
• Admittance matrix
EES PAGE 1801-05-2023
Case 1: Interconnection network
EES PAGE 1901-05-2023
Reflection
𝒓 :+¿
𝒓 :−
70 m 10 m 70 m
Case 1: Interconnection network
EES PAGE 2001-05-2023
𝒓 :+¿
𝒓 :−
70 m 70 m10 m
Case 1: Interconnection network
EES PAGE 2101-05-2023
The length change from 1 m~10 m
Content
IntroductionSignal transmission in LV cables
Case 1: Interconnection • 1. Simulation OIP cable• 2. Interconnection network Case 2: Simulated partial discharge at substation• 1. Interconnection • 2. Branching• 3. Parallel cables connect at the substation
Conclusion
EES PAGE 2201-05-2023
Case studies on cable connections
PAGE 2301-05-2023
• Case 2To analyze the effects of the discharges which will
be observed in the substation for different network models of the cable.
Case 2: Interconnection network
PAGE 2401-05-2023
A resistance of 5.1 mΩ and reactance of 56 µH in series per phase.
EES
Transformer substation
Current source at 130 m
Case 2: Branching
PAGE 2501-05-2023EES
A 10 kVA household branch is jointed at 50 meters of the main cable
Transformer substation
Current source at 130 m
Case 2: Simulated PD
• The current at the substation is calculated by the admittance of the cable and voltage:
is the voltage at the substation, is the voltage at the node where the cable to the substation is connected.
PAGE 2601-05-2023EES
Case 2: Simulated PD (Result)
PAGE 2701-05-2023
Cur
rent
(mA
)
Without PVC cable
Interconnection
Branching
Time (ms)
Case 2: Simulated PD
PAGE 2801-05-2023
Without PVC cable
Interconnection
Reflection
Branching
OIP OIP OIP
OIP PVC OIP
Case 2: Parallel cables at the substation
EES PAGE 2901-05-2023
Case 2: Parallel cables at the substation
PAGE 3001-05-2023
The simplified model of the substation which is connected with five cables at the bus-bar.
The impedance of the parallel cables is equal to the characteristic impedance of the cable divided by 4.
EES
Case 2: Simulated PD (Result)
PAGE 3101-05-2023
Cur
rent
(mA
)
Without PVC cable
Interconnection
Branching
Time (ms)
Case 2: Simulated PD (Result)
EES PAGE 3201-05-2023
Comparison of different network models, the parallel cables are either included or not included
Conclusions
The effect is not significant, since the PVC section makes up only for a short length in the complete connection.
The branching point is effected the PDs.More parallel cables will be effected the PDs. In the future?
PAGE 3301-05-2023EES
Thank you for your listening !
EES PAGE 3401-05-2023
