LineCableModels.jl

LineCableModels.jl is a Julia package for computing the series impedances and shunt admittances per unit length of arbitrary arrangements of underground and overhead power cables, with uncertainty propagation. A computation is defined by a problem, which describes the cables, the earth, the operating temperature and the frequencies of interest, and by a formulation, which selects the formulas for each physical contribution. The computation is carried out either by the coaxial analytical backend of the package or by the finite-element backend of the Gmsh extension.

Main features

• High-fidelity cable modeling: Detailed representation of solid and stranded conductors, with round wires or rectangular strands laid on helices, semicon screens, insulation layers, sheaths, beddings, armors of round wires, jackets and fillers. Any number of cables can be placed in the same cross-section to form a cable system.
• Equivalent tubular representation: Each terminal of a cable is represented by an equivalent tubular conductor that preserves the DC resistance and the geometric mean radius of its regions, including the overlength of the round wires and rectangular strands laid on helices. The relative permeability of the insulation layers is corrected to account for the solenoid effect introduced by the helical path of the current in stranded conductors.
• Internal impedances and admittances: Internal impedances of multilayered coaxial cables based on the surface impedances of Schelkunoff and on the general formulation of Ametani, with conductor resistivities corrected to the operating temperature.
• Earth-return impedances and admittances: Earth-return impedances and potential coefficients of underground, overhead and mixed systems in homogeneous earth, computed by a unified formulation with a prescribed longitudinal wavenumber.
• Phase-domain matrices: Series impedance and shunt admittance matrices of polyphase systems with any number of conductors per phase, with bundling of bonded conductors, Kron elimination of grounded conductors and ideal transposition.
• Finite element modeling: Computation of the same problems on a mesh of the actual cross-section of the cables, by means of Gmsh and GetDP.
• Uncertainty quantification: Linear propagation of the uncertainties of materials, dimensions, positions, earth properties and temperature to the line parameters, by means of the Measurements.jl package.

Installation

Add the registered package to the Julia environment:

pkg> add LineCableModels

Then, in your Julia code, import the package:

using LineCableModels

The extensions are loaded together with their packages, namely using Measurements for the propagation of uncertainties and using Gmsh for the finite-element backend. The finite-element backend uses the GetDP executable found on PATH when it is suitable, and otherwise downloads GetDP 3.5.0 at its first use.

Example

The following example computes the line parameters of two insulated copper wires, buried at 1 m depth with a horizontal spacing of 1 m, in a homogeneous earth of 100 Ω·m:

using LineCableModels

copper = Material(:conductor, 1.7241e-8, 1, 1, 20, 0.00393)
polyethylene = Material(:insulator, 1.0e14, 2.3)
wire = @cable "insulated_wire" begin
    @terminal :core begin
        core(copper; r = 4.0e-3) # [m]
    end
    insulation(polyethylene; t = 1.0e-3) # [m]
end
system = build(CableSystem, [wire, wire], [Placement(0.0, -1.0), Placement(1.0, -1.0)];
    connections = [(core = 1,), (core = 2,)], id = "two_wires", line_length = 1000.0)
problem = LineParametersProblem(system, homogeneous(rho = 100.0);
    frequencies = [50.0, 1e3, 1e6]) # [Hz]
result = compute(problem, CoaxialFormulation())
result.Z[:, :, 1] # [Ω/m] at 50 Hz
result.terminals

Finite element solver

After using Gmsh, the same problem is computed with Gmsh and GetDP by compute(problem, FEM()). The finite-element guide describes the options of the backend, its run directory and its accuracy on the reference systems.

Uncertainty quantification

After using Measurements, any input of the problem can be given as an uncertain value, such as Circle(4.0e-3 ± 1.0e-5), and the resulting Z and Y have uncertain real and imaginary parts. The uncertainty guide describes the propagation and the tests that verify it.

Documentation

See the full documentation for detailed usage instructions, technical background and examples.

Contributing

Contributions are welcome. CONTRIBUTING.md gives the principles, the checks and the form of a pull request, and the developer section of the documentation describes the architecture, the rules and the conventions.

License

The source code is provided under the BSD 3-Clause License.

Acknowledgements

This work is supported by the Etch Competence Hub of EnergyVille, financed by the Flemish Government. The primary developer is Amauri Martins (@amaurigmartins).