![Case 1: Interconnection network
• Constraint condition at the interconnection
EES PAGE 1526-2-2016
[𝑉 𝑖
1
]′1 − [𝑉 𝑗
2
]1=0
[𝑉 𝑖
1
]′2 − [𝑉 𝑗
2
]2=0
[𝑉 𝑖
1
]′3 − [𝑉 𝑗
2
]3=0
[𝑉 𝑖
1
]′4 − [𝑉 𝑗
2
]4=0
[𝑉 𝑗
2
]′1 − [𝑉 𝑘
3
]1=0
[𝑉 𝑗
2
]′2 − [𝑉 𝑘
3
]2=0
[𝑉 𝑗
2
]′3 − [𝑉 𝑘
3
]3=0
[𝑉 𝑗
2
]′4 − [𝑉 𝑘
3
]4=0
[𝐼 𝑖
1
]′1 + [𝐼 𝑗
2
]1=0
[𝐼 𝑖
1
]′2 + [𝐼 𝑗
2
]2=0
[𝐼 𝑖
1
]′3 + [𝐼 𝑗
2
]3=0
[𝐼 𝑖
1
]′4 + [𝐼 𝑗
2
]4=0
[𝐼 𝑗
2
]′1 + [𝐼 𝑘
3
]1=0
[𝐼 𝑗
2
]′2 + [𝐼 𝑘
3
]2=0
[𝐼 𝑗
2
]′3 + [𝐼 𝑘
3
]3=0
[𝐼 𝑗
2
]′4 + [𝐼 𝑘
3
]4=0
𝒀 𝒄
𝒏
𝑽 𝒄
𝒏
+ 𝒁 𝒄
𝒏
𝑰 𝒄
𝒏
= 𝑷 𝒏
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
∗ 𝑉𝑖
1′
+
−1 0 0 0
0 −1 0 0
0 0 −1 0
0 0 0 −1
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
∗ 𝑉𝑗
2
+
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
∗ 𝐼𝑖
1′
+
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
∗ 𝐼𝑗
2
=
0
0
0
0
0
0
0
0
𝑌𝑖
1′
𝑌 𝑗
2
𝑍 𝑗
2
𝑍 𝑖
1′](https://image.slidesharecdn.com/58045472-5085-4a42-ac54-8ff68fe04d9d-160226215309/85/High-frequency-modeling-16-320.jpg)
![Case 1: Interconnection network
• Constraint condition at the termination
EES
PAGE 1626-2-2016
1∗ [𝑉 𝑖
1
]1 = 𝑉𝑠 𝑡 − 50 ∗ [𝐼 𝑖
1
]1
1∗ [𝑉 𝑖
1
]2 = −50 ∗ [𝐼 𝑖
1
]2
1∗ [𝑉 𝑖
1
]3 = −50 ∗ [𝐼 𝑖
1
]3
1∗ [𝑉 𝑖
1
]4 = −50 ∗ [𝐼 𝑖
1
]4
1∗ [𝑉 𝑘
4
]1 = −50 ∗ [𝐼 𝑘
4
]1
1∗ [𝑉 𝑘
4
]2 = −50 ∗ [𝐼 𝑘
4
]2
1∗ [𝑉 𝑘
4
]3 = −50 ∗ [𝐼 𝑘
4
]3
1∗ [𝑉 𝑘
4
]4 = −50 ∗ [𝐼 𝑘
4
]4
𝒀 𝒄
𝒏
𝑽 𝒄
𝒏
+ 𝒁 𝒄
𝒏
𝑰 𝒄
𝒏
= 𝑷 𝒏
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
∗ 𝑉 𝑖
1
+
50 0 0 0
0 50 0 0
0 0 50 0
0 0 0 50
∗ 𝐼 𝑖
1
=
𝑉𝑠(𝑡)
0
0
0
𝑌𝑖
1
𝑍𝑖
1](https://image.slidesharecdn.com/58045472-5085-4a42-ac54-8ff68fe04d9d-160226215309/85/High-frequency-modeling-17-320.jpg)
High frequency modeling
- 1. High Frequency Modeling of LV Underground Power Cable Systems: Case studies on cable connections Student : N.Song (0809313)
- 2. Content Introduction Signal 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 126-2-2016
- 4. Content Introduction Signal 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 326-2-2016
- 5. Case studies on cable connections • Case 1 To analyze the effects when different types of 4-conductor cables are used in interconnection. EES PAGE 426-2-2016 Oil-impregnated-paper(OIP) insulated cable PVC cable
- 6. Case 1: Simulation OIP cable EES PAGE 526-2-2016 Cross-section of the cable used in software • Cable Under Test (CUT) Lead Oil-impregnated-paper(OIP) Copper
- 7. Case 1: Simulation OIP cable • Telegrapher’s equations 𝑑 𝑑𝑧 𝑉 𝑧 = −𝐙 𝐼 𝑧 𝒁 = 𝑹 + 𝑗ω𝑳 𝑑 𝑑𝑧 𝐼 𝑧 = −𝒀𝑉 𝑧 𝒀 = 𝑮 + 𝑗ω𝑪 / name of department PAGE 626-2-2016 R: Resistance L: Inductance G: Conductance C: Capacitance
- 8. Case 1: Simulation OIP cable • Modal voltages and currents 𝑉 𝑧 = 𝑻 𝑽 𝑉𝑚(𝑧) 𝐼 𝑧 = 𝑻 𝑰 𝐼 𝑚(𝑧) 𝑑2 𝑑𝑧2 𝑉𝑚 𝑧 = 𝑻 𝑽 −𝟏 𝒁𝒀𝑻 𝑽 𝑉𝑚 𝑧 = 𝜸 𝟐 𝑉𝑚 𝑧 𝑑2 𝑑𝑧2 𝐼 𝑚 𝑧 = 𝑻 𝑰 −𝟏 𝒀𝒁𝑻 𝑰 𝐼 𝑚 𝑧 = 𝜸 𝟐 𝐼 𝑚 𝑧 𝜸 is the propagation coefficients for each mode. EES PAGE 726-2-2016
- 9. Case 1: Simulation OIP cable EES PAGE 826-2-2016 • Four modes of voltage 𝑽 𝒎,𝟏 = 𝟏 𝟒 (𝑽 𝟏 + 𝑽 𝟐 + 𝑽 𝟑 + 𝑽 𝟒) 𝑽 𝒎,𝟐𝒂 = 𝟏 𝟐 (𝑽 𝟏 − 𝑽 𝟑 ) 𝑽 𝒎,𝟐𝒃 = 𝟏 𝟐 ( 𝑽 𝟐 −𝑽 𝟒) 𝑽 𝒎,𝟑 = 𝟏 𝟒 (𝑽 𝟏 − 𝑽 𝟐 + 𝑽 𝟑 − 𝑽 𝟒) mode 1 --- positive --- negative mode 2a mode 2b mode 3
- 10. Case 1: Simulation OIP cable EES PAGE 926-2-2016 • Characteristic impedance matrix 𝒁 𝒄 = 𝒀−𝟏 𝑻 𝑰γ𝑻 𝑰 −𝟏 • Modal characteristic impedance matrix for the CUT 𝒁 𝒄,𝒎 = 𝑻 𝑽 −𝟏 𝒁 𝒄 𝑻 𝑰
- 11. Case 1: Simulation OIP cable / EES PAGE 1026-2-2016 Simulated modal characteristic impedance (top: magnitude, bottom: phase) mode 1 mode 2 mode 3 Mode 1: 𝑽 𝒎,𝟏 = 𝟏 𝟒 (𝑽 𝟏 + 𝑽 𝟐 + 𝑽 𝟑 + 𝑽 𝟒) Mode 2: 𝑽 𝒎,𝟐𝒂 = 𝟏 𝟐 (𝑽 𝟏 − 𝑽 𝟑 ) 𝑽 𝒎,𝟐𝒃 = 𝟏 𝟐 ( 𝑽 𝟐 −𝑽 𝟒) Mode 3: 𝑽 𝒎,𝟑 = 𝟏 𝟒 (𝑽 𝟏 − 𝑽 𝟐 + 𝑽 𝟑 − 𝑽 𝟒)
- 12. Case 1: Simulation OIP cable EES PAGE 1126-2-2016 • Propagation coefficients γ 𝒙 = α 𝒙 + 𝒋β 𝒙 𝒗 𝒑,𝒙 = β 𝒙 ω α 𝒙 is the attenuation coefficient for mode x 𝒗 𝒑,𝒙 is the phase velocity for mode x
- 13. Case 1: Interconnection network • Schematic of simulated interconnection network EES PAGE 1226-2-2016 𝑽 𝒄𝒂𝒃𝒍𝒆 𝒕𝒆𝒓𝒎𝒊𝒏𝒂𝒕𝒊𝒐𝒏/𝒊𝒏𝒕𝒆𝒓𝒄𝒐𝒏𝒏𝒆𝒄𝒕𝒊𝒐𝒏 𝑰 𝒄𝒂𝒃𝒍𝒆 𝒕𝒆𝒓𝒎𝒊𝒏𝒂𝒕𝒊𝒐𝒏/𝒊𝒏𝒕𝒆𝒓𝒄𝒐𝒏𝒏𝒆𝒄𝒕𝒊𝒐𝒏
- 14. Case 1: Interconnection network • Relation between the beginning and end of a cable 𝑰(𝟎) − 𝑰(𝒍) = 𝒀 𝑺 𝒀 𝑴 𝒀 𝑴 𝒀 𝑺 𝑽(𝟎) 𝑽(𝒍) EES PAGE 1326-2-2016
- 15. Case 1: Interconnection network • Network equations ∑ 𝒄=𝒊−𝒌|𝒄𝒐𝒏𝒏𝒆𝒄𝒕𝒆𝒅 𝒀 𝒄 𝒏 𝑽 𝒄 𝒏 + 𝒁 𝒄 𝒏 𝑰 𝒄 𝒏 = 𝑷 𝒏 ∊ 𝒏𝒆𝒕𝒘𝒐𝒓𝒌 ∑ 𝒄=𝒊−𝒌|𝒄𝒐𝒏𝒏𝒆𝒄𝒕𝒆𝒅 𝒀 𝑺𝒄 𝑽 𝒄 𝒏 + 𝒀 𝑴𝒄 𝑽 𝒄 𝒏 ′ = 𝑰 𝒄 𝒏 ∑ 𝒄=𝒊−𝒌|𝒄𝒐𝒏𝒏𝒆𝒄𝒕𝒆𝒅 𝒀 𝒄 𝒏 + 𝒁 𝒄 𝒏 𝒀 𝑺𝒄 𝑽 𝒄 𝒏 + 𝒁 𝒄 𝒏 𝒀 𝑴𝒄 𝑽 𝒄 𝒏 ′ = 𝑷 𝒏 𝑽 𝒄 𝒏′ indicates the network on the opposite side of the respective cable section. EES PAGE 1426-2-2016
- 16. Case 1: Interconnection network • Constraint condition at the interconnection EES PAGE 1526-2-2016 [𝑉 𝑖 1 ]′1 − [𝑉 𝑗 2 ]1=0 [𝑉 𝑖 1 ]′2 − [𝑉 𝑗 2 ]2=0 [𝑉 𝑖 1 ]′3 − [𝑉 𝑗 2 ]3=0 [𝑉 𝑖 1 ]′4 − [𝑉 𝑗 2 ]4=0 [𝑉 𝑗 2 ]′1 − [𝑉 𝑘 3 ]1=0 [𝑉 𝑗 2 ]′2 − [𝑉 𝑘 3 ]2=0 [𝑉 𝑗 2 ]′3 − [𝑉 𝑘 3 ]3=0 [𝑉 𝑗 2 ]′4 − [𝑉 𝑘 3 ]4=0 [𝐼 𝑖 1 ]′1 + [𝐼 𝑗 2 ]1=0 [𝐼 𝑖 1 ]′2 + [𝐼 𝑗 2 ]2=0 [𝐼 𝑖 1 ]′3 + [𝐼 𝑗 2 ]3=0 [𝐼 𝑖 1 ]′4 + [𝐼 𝑗 2 ]4=0 [𝐼 𝑗 2 ]′1 + [𝐼 𝑘 3 ]1=0 [𝐼 𝑗 2 ]′2 + [𝐼 𝑘 3 ]2=0 [𝐼 𝑗 2 ]′3 + [𝐼 𝑘 3 ]3=0 [𝐼 𝑗 2 ]′4 + [𝐼 𝑘 3 ]4=0 𝒀 𝒄 𝒏 𝑽 𝒄 𝒏 + 𝒁 𝒄 𝒏 𝑰 𝒄 𝒏 = 𝑷 𝒏 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ∗ 𝑉𝑖 1′ + −1 0 0 0 0 −1 0 0 0 0 −1 0 0 0 0 −1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ∗ 𝑉𝑗 2 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ∗ 𝐼𝑖 1′ + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ∗ 𝐼𝑗 2 = 0 0 0 0 0 0 0 0 𝑌𝑖 1′ 𝑌 𝑗 2 𝑍 𝑗 2 𝑍 𝑖 1′
- 17. Case 1: Interconnection network • Constraint condition at the termination EES PAGE 1626-2-2016 1∗ [𝑉 𝑖 1 ]1 = 𝑉𝑠 𝑡 − 50 ∗ [𝐼 𝑖 1 ]1 1∗ [𝑉 𝑖 1 ]2 = −50 ∗ [𝐼 𝑖 1 ]2 1∗ [𝑉 𝑖 1 ]3 = −50 ∗ [𝐼 𝑖 1 ]3 1∗ [𝑉 𝑖 1 ]4 = −50 ∗ [𝐼 𝑖 1 ]4 1∗ [𝑉 𝑘 4 ]1 = −50 ∗ [𝐼 𝑘 4 ]1 1∗ [𝑉 𝑘 4 ]2 = −50 ∗ [𝐼 𝑘 4 ]2 1∗ [𝑉 𝑘 4 ]3 = −50 ∗ [𝐼 𝑘 4 ]3 1∗ [𝑉 𝑘 4 ]4 = −50 ∗ [𝐼 𝑘 4 ]4 𝒀 𝒄 𝒏 𝑽 𝒄 𝒏 + 𝒁 𝒄 𝒏 𝑰 𝒄 𝒏 = 𝑷 𝒏 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ∗ 𝑉 𝑖 1 + 50 0 0 0 0 50 0 0 0 0 50 0 0 0 0 50 ∗ 𝐼 𝑖 1 = 𝑉𝑠(𝑡) 0 0 0 𝑌𝑖 1 𝑍𝑖 1
- 18. Case 1: Interconnection network • Admittance matrix 𝒀 𝑺𝒄 𝑽 𝒄 𝒏 + 𝒀 𝑴𝒄 𝑽 𝒄 𝒏 ′ = 𝑰 𝒄 𝒏 𝒀 𝒄 𝒏 + 𝒁 𝒄 𝒏 𝒀 𝑺𝒄 𝑽 𝒄 𝒏 + 𝒁 𝒄 𝒏 𝒀 𝑴𝒄 𝑽 𝒄 𝒏 ′ = 𝑷 𝒏 EES PAGE 1726-2-2016
- 19. Case 1: Interconnection network EES PAGE 1826-2-2016 Reflection ∶ 𝒓 = 𝒁 𝒍−𝒁 𝟎 𝒁 𝒍+𝒁 𝟎 𝒖 𝒓𝒆𝒇𝒍𝒆𝒄𝒕𝒆𝒅 = 𝒓 ∗ 𝑼 𝒖 𝒕𝒓𝒂𝒏𝒔𝒎𝒊𝒕𝒕𝒆𝒅 = 𝟏 + 𝒓 ∗ 𝑼 𝑼 = 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒊𝒏𝒄𝒐𝒎𝒊𝒏𝒈 𝒘𝒂𝒗𝒆 𝒓 ∶ + 𝒓 ∶ − 70 m 10 m 70 m
- 20. Case 1: Interconnection network EES PAGE 1926-2-2016 𝒓 ∶ + 𝒓 ∶ − 70 m 70 m10 m
- 21. Case 1: Interconnection network EES PAGE 2026-2-2016 The length change from 1 m~10 m
- 22. Content Introduction Signal 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 2126-2-2016
- 23. Case studies on cable connections PAGE 2226-2-2016 • Case 2 To analyze the effects of the discharges which will be observed in the substation for different network models of the cable.
- 24. Case 2: Interconnection network PAGE 2326-2-2016 A resistance of 5.1 mΩ and reactance of 56 µH in series per phase. EES Transformer substation Current source at 130 m
- 25. Case 2: Branching PAGE 2426-2-2016EES A 10 kVA household branch is jointed at 50 meters of the main cable Transformer substation Current source at 130 m
- 26. Case 2: Simulated PD • The current at the substation is calculated by the admittance of the cable and voltage: 𝑰 𝒔𝒖𝒃 = 𝒀 𝑺 𝑽 𝒔𝒖𝒃 + 𝒀 𝑴 𝑽 𝒄𝒂𝒃𝒍𝒆_𝒆𝒏𝒅 𝑽 𝒔𝒖𝒃 is the voltage at the substation, 𝑽 𝒄𝒂𝒃𝒍𝒆_𝒆𝒏𝒅 is the voltage at the node where the cable to the substation is connected. PAGE 2526-2-2016EES
- 27. Case 2: Simulated PD (Result) PAGE 2626-2-2016 Current(mA) Without PVC cable Interconnection Branching Time (ms)
- 28. Case 2: Simulated PD PAGE 2726-2-2016 Without PVC cable Interconnection Reflection ∶ 𝒓 = 𝒁 𝒍−𝒁 𝟎 𝒁 𝒍+𝒁 𝟎 𝒊 𝒓𝒆𝒇𝒍𝒆𝒄𝒕𝒆𝒅 = −𝒓 ∗ 𝑰 𝒊 𝒕𝒓𝒂𝒏𝒔𝒎𝒊𝒕𝒕𝒆𝒅 = 𝟏 − 𝒓 ∗ 𝑰 𝑰 = 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒊𝒏𝒄𝒐𝒎𝒊𝒏𝒈 𝒘𝒂𝒗𝒆 Branching OIP OIP OIP OIP PVC OIP
- 29. Case 2: Parallel cables at the substation EES PAGE 2826-2-2016
- 30. Case 2: Parallel cables at the substation PAGE 2926-2-2016 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
- 31. Case 2: Simulated PD (Result) PAGE 3026-2-2016 Current(mA) Without PVC cable Interconnection Branching Time (ms)
- 32. Case 2: Simulated PD (Result) EES PAGE 3126-2-2016 Comparison of different network models, the parallel cables are either included or not included
- 33. 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 3226-2-2016EES
- 34. Thank you for your listening ! EES PAGE 3326-2-2016
Editor's Notes
- #2: Good morning, Thank you for coming my final presetion, my graduated project is serval case studies on low voltage cable connections.
- #3: I’m going to start with a introduction part. Then second part is a detailed explanation focus on the two case studies. Finally the conclusions will be given.
- #4: Let’s beginning from introduction. This picture is a simplified low voltage grid. The electrical(扣) power will be delivered from medium voltage system. then through the transformer substation become the low voltage electrical power and distribute（特） power to homes and businesses. Compared with the medium and high voltage systems, low voltage system is regarded as the most reliable electric power distribution system. because the few customers are connected to a feed（扁嘴：飞的） cable, so the impact（因怕） of cable failure in the low voltage system on the power grid operator is lower. That’s why the research and attention（饿ten神） on the condition monitoring （重音在前）of the low voltage cable are so limited. but, as the working life of the cable is extending（以可四ten订）, it was found that the number of failures in low voltage cable is increasing slowly but steadily（四带的李).Therefore, it is necessary to study an effective way of condition monitoring of low voltage cables.
- #5: In order to monitor the cable system, the first thing is need to analyze the transmission characteristics of the cable.
- #6: In the Netherlands, OIP cable has been used in the low voltage power system for many years. When a cable failure, the new cable need to replace the fault section. however, due to environmental and health with manufacturing issues, OIP cable is not produced any more. PVC is used for insulation in new cables, and is used to replace OIP cable when faults happen. But the two cables present different cable characteristics due to different applied materials. Therefore, when these two cables are connected, the new transmission line characteristics need to be known. The PVC cable already was modeled in previous research. the model of OIP insulated cables is simulated in this project.
- #7: The cable under test consists of four copper conductors, a lead（里的） earth screen and OIP insulation. For high-frequency signals the cable can be considered as a 4-fold rotation symmetric（涩买track） transmission line with earth screen. The number definition（带for 内神） for the four currents and voltages are shown in figure.
- #8: The model(麻都) is base on mulit-conductor transmission line theory. The theory gives the differential equations of the voltage and current which are related with impedance and admittance. impedance and admittance are four-by-four matrice(美垂死) of per-unit length parameters of resistance, inductance, conductance and capacitance. These per-unit parameters are measured in electromagnetic field simulation software. voltage and current are four dimensional（带门神no） vectors（外） at position z along the length of the cable.
- #9: In order to find out the voltage and current at any point along the Z-axis. The relation between the actual and modal（某都）voltages and currents need to be understood. The objective is to decouple these second-order equations by finding a appropriate Tv and Ti. Tv and Ti need to diagonalize（带艾格no来自） the product by ZY. This part will be equal to the supare of the gamma, so gamma is a diagonal matrix.
- #10: According to Tv and Ti, the voltage can be divided four mode. because of the symmetry(塞米吹) of the cable, the second and third mode have equal properties. Therefore, in the following analysis will focuses on three different modes, show with 1,2 and 3. Red
- #11: the characteristic impedance matrix is related with per-unit-length parameters, transformation matrix and gamma. And also can use the transformation matrice to get the modal charactersitc impednace matrix.
- #12: Here is the simulated modal characteristic impedance for the three modes. Compare with PVC previous reach, the impedance of OIP is lower than PVC cable.
- #13: As the frequency increase, the propagation velocities increase become a steady value at high frequency. They are similar for all propagation modes, since homogenous (厚某真你啊四) insulation material is assumed. The attenuation coefficient is realted to losses in the dielectrics（带） and losses in conductor and earth screen. These losses also increase with higher frequency.
- #14: the transmission line characteristic for OIP and PVC cable are known. the interconnection network can be simulated in matlab. The network model include two OIP cables and one PVC cable. This model consists of four network. At the termination connect with 50 Ohm impedances.
- #15: the relation between the beginning and end of cable for currents and voltages are given also from multi-conductor transmission line theory. Ys is the self admittance and Ym is the mutual(谬 戳) admittance of the cable.
- #16: And current can be presented by voltage and self and mutul(谬 戳) admittance. And a source vector P can be defined for all sources at the network. The final equation can be presented the relation for each cable section at each network.
- #17: each network equations need to satisfied with the kirchhoff’s(可吃hoff) voltage and current law. The constraint（肯四坠t） conditions set 1 for column（call） of Y means that V has a corresponding（course 帮顶） voltage fore each cable line. Set 1 for a column of Z means that I has a corresponding current and a corresponding voltage for each cable line. They are added together should be equal the source vector.
- #18: At the tremination network, all cables are terminated in 50ohm impedances , so 50 is placed into Z, meanwhile, set Vs(t) into P as the corresponding equation.
- #19: Total The admittance matrix related with voltage and source vector
- #20: The input voltage source is a Gaussian(高神) signal with a pulse width（po四 胃子（咬舌））of 30 nanosecond（纳no）in time domain. In the simulation, the voltage measured with a the phase-to-phase and phase-to-ground. Because the results have same properties, so take the phase-to-phase result as an example. In order to compare the PVC section effect of the voltage signal, the OIP cable without PVC cable section also be simulated. The solid(骚里的) lines is with PVC section. Dashed(带是t) line is without PVC section.
- #21: The solid(骚里的) lines is with PVC section. Dashed(带是t) line is without PVC section.
- #22: because the PVC section will increase loss and damping, the output voltage decrease slightly with the length of the PVC section is increasing. And observe the reflected signal, a larger part is reflected back with decreasing the length of last OIP section and transmitted remainder(瑞闷der) is less（来s）.
- #23: Condition monitoring(重音在前) actually is to monitor the signal transient（穿znt）. In these systems, certain discharges may happen at damage points. These discharges induce fast current transients. Such signals can be measured at substation. in case 2, mainly simulated the effects of the discharges which will be observed in the substation for different network models.
- #24: This partial discharge signal is extracted from previous experiments for an artificially（儿提飞show里） damaged PVC cable. this fault will induced partial discharge. In this simulation is cut off a part of the signal inject into the different network model.
- #25: a power transformer replaces the voltage source, the total length of the cable still 150 meters. First OIP cable is 70 meters. PVC cable section is 10 meters and last OIP cable section is 70 meters. Inserting(因色儿厅) a fault signal as a current source at a distance of 130 meters. the other side is terminated with 10 kilo-ohm resistance as an open circuit state. The current signal source is in parallel with a an infinite impedance.
- #26: An other model is an OIP cable with a household branch(不软吃). The OIP cable with 150 meters and with 10 meters branch cable length. The household branch is jointed at 50 meters of the main cable.
- #27: The current at the substation is calculated by previous equation.
- #28: In order to compare the PVC section effect of the voltage signal, the OIP cable without PVC cable section also be simulated. The current shape of OIP cable without PVC cable and interconnection cable are similar. But the model of the OIP cable with a household branch(不软吃), the signal loss at the substation is largest and can be seen as distortion(第四到神).
- #29: Can be analyzed three model separately. Due to the reflection equation, in the model without PVC cable. the current signal will be reflected between the substation and the end of the cable. at the model of interconnection, the reflected signal also will be produced at the joint cable. at the branching（不软） model, the substation and the branch section can be seen as parallel circuits. The signal will go into two cables separately. Therefore, the different reflection and transmission coefficient will affect the signal. The superposition is produced by the injected current and reflected current at the branching point. A large attenuation and distortion（第四到神） of the signal will happen.
- #30: In a practical（铺ruai提扣） situation, many cables are in parallel to transport electricity from substation. therefore, the impact of the parallel cables on the substation is also simulated.
- #31: This is a simplified model of the substation which is connected with five cables at the bus-bar. The one at the bottom is the configurations are connected with different network model. In this simulation, the parallel cables are regards as the impedance. so the impedance of the substation will be changed.
- #32: From the results can be seen that parallel cables have strong impact on the current signal at the substation.
- #33: The rms value is taken to compare. In real low voltage transformer substation, more than five cables can be connected to one bus-bar. And many branches will be connected to the cable in an actual low voltage grid. The signal will be flowed to these cables and produced reflated and transmitted signals. Therefore, it would make it more attenuation and distortion（第四到神） of the signal .
- #34: The PVC cable will effect the signal transmission in interconnection network because more losses and damping will happen in PVC cable. However, the effect is not significant(say个你飞肯t), since the PVC section makes up only for a short length in the complete connection. In the future, the branch connect with interconnect network. The PD signal become short circuit, what signal can be observed at the substation. 10 kilo-power household. If connected a factory or more branches connect with one main cable. how the signal changes.