Modeling of Overhead Power Lines for Broadband PLC Applications.

Size: px

Start display at page:

Download "Modeling of Overhead Power Lines for Broadband PLC Applications."

Curtis Alexander
5 years ago
Views:

1 Modeling of Overhead Power Lines for Broadband PLC Applications. T. A. Papadopoulos, G. K. Papagiannis, D. P. Labridis Power Systems Laboratory Dept. of Electrical & Computer Engineering Aristotle University of Thessaloniki PLC Workshop 08 Thessaloniki 2-3 October

2 Outline Introduction. Problem formulation. Proposed model. Numerical results. Wave propagation characteristics. Signal profiles. Conclusions. 2

3 Introduction (1) Channel Modeling: Models using the black box idea. In stochastic and statistical models. Models based on the Traveling wave approach. Detailed knowledge of the per unit length (pul) parameters of the line. Limited to simple arrangements. 3

4 Introduction (2) Scope of the contribution: Propose a channel model suitable for multiconductor power lines and Broadband PLC. Investigate the propagation characteristics of overhead MV Multiconductor Power Transmission Lines. Special emphasis is given on the influence of earth. 4

5 Equivalent circuit of one conductor Z w Z pg Z g Z e Y pg Y g Y pg pul impedances: Z = Z + Z + Z w pg g pul admittances: ( ) 1 Y j P P = ω pg + g Skin effect. Influence of perfectly conducting earth. Influence of imperfect earth (earth correction terms). The equivalent circuit of the one conductor is extended to multiconductor systems including the mutual parameters between the conductors. 5

6 Mutual earth impedance: λ( hi+ hj) jωμ0 e Z g = cos( y ) ij ijλ d π 0 μ 0 a0+ a1 μ1 Generalized formulation λ i h 1 y h 2 j Mutual earth potential coefficient: μ ( hi hj) 1 P g = ij πε μ γ μ y d 1 λ + α0 α1 e + μ 0 cos ( ) 2 ijλ λ α0+ α1 α 2 0+ α1 μ1 γ0 μ0 Air μ 0, ε 0 Earth σ 1, μ 1, ε 1 Self parameters: y ij outer radius of conductor, h j h i a k = λ + k + γ k ( j ) γ = jωμ σ + ωε k k k EM properties of media: Semi infinite integrals: Proper integration technique. 6

7 Approximations of the generalized formulation Carson Disregarding earth permittivity (displacement currents). Disregarding admittance earth correction terms. Sunde Disregarding admittance earth correction terms. D Amore & Sarto. Taking into account all parameters of earth. Numerically evaluate the integrals with logarithmic approximations. 7

8 Calculation of propagation characteristics and signal profiles (1) Calculation of earth correction terms for self and mutual impedances and admittances. N N full matrices of the pul parameters. Due to the mutual parameters, the propagation characteristics cannot be defined. 8

9 Calculation of propagation characteristics and signal profiles (2) Modal transformation: N equivalent decoupled circuits which correspond to N modes of propagation. Calculation of the propagation characteristics of each mode. Calculation of voltages and currents for each mode equivalent circuit. Inverse transformation from modal to phase quantities. 9

10 Transmission line configuration Transmission line. 3phase 20 kv ACSR phase conductors Earth cases. ρ 1 : 100 Ω m to 1000 Ω m. ε r1 : 5 to15 α b c

11 Propagation characteristics of modes Attenuation constants for ρ 1 =100 Ω m, ε r1 = E E-03 ground mode aerial #1 mode aerial #2 mode neper/m 1.50E E E E+00 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 frequency (Hz) 11

12 Propagation characteristics of the ground mode Attenuation constant for ρ 1 =100 Ω m, ε r1 =10. 8.E-03 6.E-03 proposed sunde carson neper/m 4.E-03 2.E-03 0.E+00 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 frequency (Hz) 12

13 Propagation characteristics of the ground mode Attenuation constant for ρ 1 =1000 Ω m, ε r1 = E E E-02 proposed sunde carson neper/m 1.2E E E E+00 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 frequency (Hz) 13

14 Propagation characteristics of the ground mode Attenuation constant for ε r1 =10, variable earth resistivity. 3.0E E-03 ρ=100 Ωm ρ=500 Ωm ρ=1000 Ωm neper/m 2.0E E E E E+00 1.E+05 1.E+06 1.E+07 1.E+08 frequency (Hz) 14

15 Propagation characteristics of the ground mode Attenuation constant for ρ=1000, variable earth permittivity 3.0E E E-03 εr1=5 εr1=10 εr1=15 neper/m 1.5E E E E+00 1.E+05 1.E+06 1.E+07 1.E+08 frequency (Hz) 15

16 Signal: Simulation procedure Sinusoidal signal, 1 V (rms), 1 30 MHz. Wire to Ground signal injection. Line length: 1 km Earth parameters: ρ 1 =1000 Ωm, ε r1 = 10 Transfer function: V Hf ( ) = V rms out in out 16

17 Injected signal transfer function at phase α Proposed Sunde H(f) (rms) E E E E E E E+07 frequency (Hz) 17

18 Crosstalk transfer function at phase b H(f) (rms) Proposed Sunde 1.0E E E E E E E+07 frequency (Hz) 18

19 Crosstalk transfer function at phase c 1.4 H(f) (rms) Proposed Sunde 1.0E E E E E E E+07 frequency (Hz) 19

20 Conclusions A generalized formulation for the calculation of overhead transmission line propagation characteristics in high frequencies is presented. Special emphasis is given to the influence of the earth EM properties. The admittance earth correction term is very important in the HF region and must not be omitted. Wire to Ground Coupling: The injected signal as well as the crosstalk are strongly affected by the earth parameters. 20

21 Thank you very much for your attention! This work was performed within the framework of the project PENED 2003, funded by the European Union-European Social Fund, and from the GSRT of the Hellenic Ministry of Development. 21

On the Influence of Earth Conduction Effects on the Propagation Characteristics of Aerial and Buried Conductors

On the Influence of Earth Conduction Effects on the Propagation Characteristics of Aerial and Buried Conductors T. A. Papadopoulos, A. I. Chrysochos, G. K. Papagiannis Abstract-- In this paper, the propagation