LineCableLab

Toolbox in MATLAB for modelling of overhead and underground transmission lines (per-unit-length parameters, propagation characteristics, frequency scan, transient simulations).

Highlight of the main features

• LineCableLab is distributed with a GUI designed to aid data entry. You can save your projects in MAT-files and recover them for later use.
• Several impedance and admittance formulas, frequency-dependent soil models and modal decomposition techniques are available.
• It is possible to work with overhead, underground and mixed overhead-underground conductor arrangements, using analytical formulations or finite element method (requires external solver).
• It is possible to include your own computation methods, via scripting or MAT-files, or to import models from EMTP® LineCable_Data (CYZ files). These pul parameters can be refactored into new line models via advanced modal decomposition and vector fitting techniques.
• Parameters are computed for any number of phases with any number of conductors per phase, with or without Kron elimination.
• You can export the computed data as a XML file compatible with ATPDraw 7.5 (ZY matrices), ATP-ULM 3.2 (De Conti et al.) fitULM.dat file, also available in ATPDraw 7.5, or to a EMTP-compliant MAT-file to be used with the LineCable_Data routine available in the EMTP® software.
• You can save the line cross-section directly to ATPDraw as a Cable Constants object (XML file).
• Time-domain transient simulations using the Laplace transform, with several energization sources available.

Basic instructions

The use of the toolbox is quite self-explanatory. Launch the file linecablelab.mlapp from MATLAB workspace and input the necessary information. You can save your design by clicking 'Save input session' or recover an existing design by clicking 'Load input session'.

You will be prompted to specify a JobID and this is mandatory. The JobID is a text string which will be used to identify all the output files and folders. When you are satisfied with the data entry, hit the button 'Start'. This will create a subfolder named JobID inside the working directory. Inside this folder you will find two files: LineData_fun.m and RunJob_JobID.m. Call the run job script and that's it. Note that the GUI does not actually perform any calculations, it is only a wrapper to the main function call.

The columns under the header 'Line cross-section & conductor data' are described as follows:

| Order | Label | Description | | --- | --- | --- | | 1 column | PhaseNum | number of phase (set to 0 for Kron reduction, map to the same phase for bundled conductors). | | 2 column | Horiz | y position of each conductor in meters. | | 3 column | Vert | z position of each conductor in meters. Use negative values for underground conductors. | | 4 column | IntRadius | internal radius of each conductor in meters. | | 5 column | ExtRadius | external radius of each conductor in meters. | | 6 column | CondResist | resistivity of the conductor in ohms-meter. | | 7 column | CondPerm | relative permeability of the conductor in pu. | | 8 column | InsulRadius | external radius of insulation in meters. Set to nan if bare conductor. | | 9 column | InsulPerm | relative permeability of insulation in pu. Set to nan if bare conductor. | | 10 column | InsulPermit | relative permittivity of insulation in pu. Set to nan if bare conductor. |

Loading custom parameters from MAT-files

To load pul parameters from your own MAT-file, store the workspace variables as Z (NxNxNs array), Y (NxNxNs array) and f (1xNs vector), where N is the number of phases and Ns is the number of frequency samples. An optional extra variable is possible, namely label (char), which is the string used to identify the data in the rendered plots. If none is supplied, legend entries in the plots will read as 'Imported from MAT-file'.

Running an external process to compute pul parameters

In order to enable a user-defined computation process, check the corresponding box in the '⚗️ Experiments' tab and specify a MATLAB script file. This script must return Z and Y as NxNxNs arrays, where N is the number of phases and Ns is the number of frequency samples. For a seamless integration, these outcomes should be appended to the allZ_pul and allY_pul variables. A sample snippet is provided below:

```matlab % Sample script: myCustomZY.m % This file should be specified in the 'Experiments' tab.

%% This is where the fun begins for k=1:freqsiz % variable freqsiz is already defined in the execution context myCustomZ(:,:,k) = ... % do your magic here, note that the frequency is the third dimension myCustomY(:,:,k) = ... end

% Note: function findElementByField() is supplied with the toolbox. o=findElementByField(allZpul, 'VarName', 'myCustomZ'); % find myCustomZ in the allZpul struct allZpul(o).VarName='myCustomZ'; allZpul(o).Label='My custom Z formula'; allZ_pul(o).Values=myCustomZ;

o=findElementByField(allYpul, 'VarName', 'myCustomY'); % find myCustomY in the allYpul struct allYpul(o).VarName='myCustomY'; allYpul(o).Label='My custom Y formula'; allY_pul(o).Values=myCustomY; ```

To recover these results as defaults for subsequent calculations (e.g. propagation characteristics, fitting of line models etc.), modify the corresponding lines accordingly in the main run job script:

matlab % Modal decomposition Z=selectZ('myCustomZ'); Y=selectY('myCustomY');

Loading the fitULM data file into ATPDraw 7.5

To load ULM models generated via the toolbox into ATPDraw 7.5, click 'Lines/Cables' ➜ 'Read PCH file...' and choose your RunJob_fitULM.dat file. ATPDraw will complain with a message 'Unknown punch file format!' and ask if a ULM file is to be assumed. Hit 'Yes' and you are set.

Acknowledgements

LineCableLab has been actively maintained and improved by Theofilos Papadopoulos, Andreas Chrysochos and Amauri Martins-Britto. The authors acknowledge and wish to thank for the efforts of all external contributors. Due to the dynamic and open nature of this project, it became unmanageable to keep an exhaustive list, so we decided to let GitHub handle it via issues reports, pull requests and/or commit history. You all are real badasses!

Important information

LineCableLab uses external tools that must be downloaded from the corresponding sources and placed in the appropriate directories, listed below:

• vfit3 - Fast Relaxed Vector Fitting, developed by Gustavsen et al. Available: https://www.sintef.no/globalassets/project/vectfit/vfit3.zip. Unzip the file into the folder line_export_funs/vfit3. The vector fitting toolbox is used to create the ULM and JMarti line models from the modal parameters, if requested by the user.
• Eigenshuffle - Consistently sorted eigenvalue and eigenvector sequences, developed by John D'Errico. Available: https://www.mathworks.com/matlabcentral/fileexchange/22885-eigenshuffle. Unzip the file into the folder mode_decomp_funs. The Eigenshuffle code is used as an additional method to perform the modal decomposition avoiding switchovers in the frequency-domain.
• Bodefit - Bode process program, developed by E. S. Bañuelos-Cabral et al. Available: https://www.intechopen.com/chapters/57667. Deploy the file Bode_process.m to the folder JMartiModelFun/functions. In case the VF does not converge to a stable solution (real poles only) for JMarti, the Bodefit is used as alternative, at the cost of accuracy.
• Carson's integral - Closed-form solution proposed by T. P. Theodoulidis. Available: https://www.mathworks.com/matlabcentral/fileexchange/50134-carson-s-integral. The files are packaged in the toolbox and no further action is required.
• FEMM - Finite Element Method Magnetics, developed by David Meeker. Available: https://www.femm.info/wiki/HomePage. For finite element computations. Install the program normally and specify the path to the mfiles folder under the '⚗️ Experiments' tab.

These codes are properties of the respective authors, with all due credits given. Observe any restrictions and licensing/usage requirements in the corresponding websites.

On the computational methods implemented in LineCableLab

The toolbox incorporates several impedance and admittance formulas, under different assumptions to represent the imperfect earth in the line models. For a comprehensive analysis, please refer to the following scientific publications:

• Transient Electromagnetic Interference between Overhead and Underground Conductors
• Closed-form expressions for the analysis of wave propagation in overhead distribution lines
• A generalized model for the calculation of the impedances and admittances of overhead power lines above stratified earth

Restrictions of use

We appreciate the interest in our work and we invite the interested users to use our codes as necessary, as long as they are not embedded in any commercial software, which is strictly prohibited. However, if you use LineCableLab as a part of scientific research, we kindly ask you to refer to one of our published papers:

• A. G. Martins-Britto, T. A. Papadopoulos and A. I. Chrysochos, "Transient Electromagnetic Interference between Overhead and Underground Conductors," in IEEE Transactions on Electromagnetic Compatibility, Mar. 2024, doi: 10.1109/TEMC.2024.3376971.

• T. A. Papadopoulos, Z. G. Datsios, A. I. Chrysochos, A. G. Martins-Britto, G. K. Papagiannis, "Transient induced voltages on aboveground pipelines parallel to overhead transmission lines," in Electric Power Systems Research, 109631, ISSN 0378-7796, Jun 2023, doi: 10.1016/j.epsr.2023.109631.

• T. A. Papadopoulos, A. I. Chrysochos, C. K. Traianos, and G. Papagiannis, “Closed-Form Expressions for the Analysis of Wave Propagation in Overhead Distribution Lines,” in Energies, vol. 13, no. 17, p. 4519, Sep. 2020, doi: 10.3390/en13174519.

• A. I. Chrysochos, T. A. Papadopoulos and G. K. Papagiannis, "Robust Calculation of Frequency-Dependent Transmission-Line Transformation Matrices Using the Levenberg–Marquardt Method," in IEEE Transactions on Power Delivery, vol. 29, no. 4, pp. 1621-1629, Aug. 2014, doi: 10.1109/TPWRD.2013.2284504.

• A. G. Martins-Britto, T. A. Papadopoulos, Z. G. Datsios, A. I. Chrysochos and G. K. Papagiannis, "Influence of Lossy Ground on High-Frequency Induced Voltages on Aboveground Pipelines by Nearby Overhead Transmission Lines," in IEEE Transactions on Electromagnetic Compatibility, vol. 64, no. 6, pp. 2273-2282, Dec. 2022, doi: 10.1109/TEMC.2022.3201874.