380 kV cables in flat formation

This example demonstrates how to model a three-phase underground system composed of 380 kV single-core cables without armor. Each cable consists of a stranded copper core, inner and outer semicon screens, XLPE insulation, a water-blocking layer, a lead sheath, an inner polyethylene layer and an outer jacket. The cables are buried at 1 m depth in a flat formation, with a horizontal spacing of 1 m, in a homogeneous earth of 1000 Ω·m.

This example covers:

1. Representing a compacted stranded core with rectangular strands.
2. Examining the equivalent tubular conductor of the stranded core and the solenoid correction of the insulation permeability.
3. Computing the line parameters of the six conductors of the system.
4. Eliminating the sheaths of a system with sheaths grounded at both ends.
5. Applying the ideal transposition to the phase conductors.

Load the package:

using LineCableModels

Materials

The semicon screens are defined as materials of the :semicon class, with resistivities of 1000 Ω·m and 500 Ω·m for the inner and outer screens, respectively, and a relative permittivity of 1000. The XLPE and the outer jacket include the relative permeability given by the cable data.

Conductor, semicon and insulation materials:

core_metal = Material(:conductor, 2.3853e-8, 1.0, 1.01663, 20.0, 0.00393) # [Ω·m]
semicon_inner = Material(:semicon, 1_000.0, 1_000.0) # [Ω·m]
semicon_outer = Material(:semicon, 500.0, 1_000.0) # [Ω·m]
xlpe = Material(:insulator, 1.0e14, 2.77781, 1.59891) # [Ω·m]
lead = Material(:conductor, 2.14e-7, 1.0, 0.999983, 20.0, 0.004) # [Ω·m], [°C], [1/°C]
pe = Material(:insulator, 1.97e14, 2.51862) # [Ω·m]
pp = Material(:insulator, 1.0e15, 2.8, 1.1263) # [Ω·m]

Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)

Stranded core with rectangular strands

The core consists of 127 copper wires with a diameter of 3.66 mm, arranged as a central wire and six layers of 6, 12, 18, 24, 30 and 36 wires, all with a lay ratio of 15. In the actual cable, the wires are compacted to fill a circle with the total area of the 127 wires. This compacted core is represented with rectangular strands: layer k occupies a ring between two radii, and each of its 6k rectangular strands has the area of one wire. The CircularPattern bends each rectangle into an annular sector of the same area, so that the central wire and the sectors tile the full cross-section of the conductor.

Strand radius, strand area and outer radius of each layer:

strand_radius = 3.66e-3 / 2 # strand_diameter / 2 [m]
strand_area = π * strand_radius^2 # [m²]
rings = [strand_radius * sqrt(1 + 3k * (k + 1)) for k in 0:6] # [m]

7-element Vector{Float64}:
 0.00183
 0.0048417248992482015
 0.007976785066679433
 0.011131455430445742
 0.014292756906909176
 0.017457087385930103
 0.020623052635339898

Layers of rectangular strands, laid on helices around the central wire:

courses = [Lay(Helix(LayRatio(15.0)), # core_lay_ratio
               Repeat(CircularPattern(6k; r = Offset(0)),
                   Region(Symbol(:core_strands_, k),
                       Rectangle(strand_area / (rings[k + 1] - rings[k]),
                           rings[k + 1] - rings[k]),
                       core_metal)))
           for k in 1:6]
rings[end] # [m]

0.020623052635339898

Cable design

The central wire is declared with the core builder, followed by the strand layers in the same @terminal block. The screen builder declares the semicon screens and the water-blocking layer, the sheath builder declares the lead sheath, and the jacket builder declares the inner polyethylene and the outer jacket.

Build the cable design and inspect its outer radius:

design = @cable "cable_380kv_no_armour" begin
    @terminal :core begin
        core(core_metal; r = strand_radius, tag = :core_center)
        courses...
    end
    screen(semicon_inner; t = 2.0e-3, tag = :core_semicon_inner) # inner_semicon_thickness [m]
    insulation(xlpe; t = 20.0e-3, tag = :core_insulation) # insulation_thickness [m]
    screen(semicon_outer; t = 1.5e-3, tag = :core_semicon_outer) # outer_semicon_thickness [m]
    screen(semicon_outer; t = 0.3e-3, tag = :core_water_blocking) # water_blocking_thickness [m]
    @terminal :sheath begin
        sheath(lead; t = 3.3e-3, tag = :sheath_lead) # lead_sheath_thickness [m]
    end
    jacket(pe; t = 3.0e-3, tag = :sheath_inner_pe) # inner_pe_thickness [m]
    jacket(pp; t = 10.0e-3, tag = :sheath_outer_jacket) # jacket_thickness [m]
end
r_ex(design.outer) # [m]

0.060723052635339905

Lay parameters of the core

Each strand layer corresponds to one row in the table of lays of the design, containing the lay radius of the rectangular strands, the pitch of the helix and the overlength, defined as the length of a strand per unit length of cable. For a constant lay ratio, the overlength is the same for all layers.

Lay radius, pitch and overlength of each layer:

[(radius = row.radii[1], pitch = row.pitches[1], overlength = row.overlengths[1])
 for row in design.lays] # [m], [m], [dimensionless]

6-element Vector{@NamedTuple{radius::Float64, pitch::Float64, overlength::Float64}}:
 (radius = 0.003401891739858035, pitch = 0.10205675219574105, overlength = 1.0216970727418604)
 (radius = 0.006462628574642966, pitch = 0.19387885723928897, overlength = 1.0216970727418604)
 (radius = 0.009592051447683344, pitch = 0.2877615434305003, overlength = 1.0216970727418604)
 (radius = 0.012741161082823877, pitch = 0.3822348324847163, overlength = 1.0216970727418604)
 (radius = 0.015898389240805576, pitch = 0.47695167722416726, overlength = 1.0216970727418604)
 (radius = 0.019059726628392993, pitch = 0.5717917988517898, overlength = 1.0216970727418604)

Equivalent coaxial representation

The function LineCableModels.flatten reduces each terminal to one equivalent tubular conductor. The central wire and the six layers conduct in parallel. The central wire is straight, whereas the strands of each layer are longer than the cable by their overlength, which increases their resistance per unit length of cable. The equivalent tube of the core then has a resistivity higher than that of copper, and its relative permeability reproduces the geometric mean radius of the central wire and the rectangular strands.

Equivalent conductors, with radii in m and resistivity in Ω·m:

blueprint = LineCableModels.flatten(design)
[(terminal = conductor.terminal, r_in = conductor.r_in, r_ex = conductor.r_ex,
     rho = conductor.material.rho, mu_r = conductor.material.mu_r)
 for conductor in blueprint.conductors] # [m], [m], [Ω·m], [dimensionless]

2-element Vector{@NamedTuple{terminal::Int64, r_in::Float64, r_ex::Float64, rho::Float64, mu_r::Float64}}:
 (terminal = 1, r_in = 0.0, r_ex = 0.020623052635339898, rho = 2.4366377448836256e-8, mu_r = 1.0015676954020325)
 (terminal = 2, r_in = 0.0444230526353399, r_ex = 0.0477230526353399, rho = 2.1400000000000004e-7, mu_r = 0.9999830000000054)

Ratio of the core equivalent resistivity to the copper resistivity:

blueprint.conductors[1].material.rho / core_metal.rho

1.0215225526699474

The dielectric layers between the core and the sheath form the insulation interval of the core. The semicon screens are included in this interval as dielectrics with a relative permittivity of 1000. Due to this high permittivity, their contribution to the potential coefficient of the interval is small compared to that of the XLPE.

Dielectric layers of the core and sheath intervals:

[(conductor = layer.conductor, r_in = layer.r_in, r_ex = layer.r_ex,
     eps_r = layer.material.eps_r, mu_r = layer.material.mu_r)
 for layer in blueprint.dielectrics] # [m], [m], [dimensionless], [dimensionless]

6-element Vector{@NamedTuple{conductor::Int64, r_in::Float64, r_ex::Float64, eps_r::Float64, mu_r::Float64}}:
 (conductor = 1, r_in = 0.020623052635339898, r_ex = 0.022623052635339896, eps_r = 1000.0, mu_r = 1.0)
 (conductor = 1, r_in = 0.022623052635339896, r_ex = 0.0426230526353399, eps_r = 2.77781, mu_r = 1.59891)
 (conductor = 1, r_in = 0.0426230526353399, r_ex = 0.0441230526353399, eps_r = 1000.0, mu_r = 1.0)
 (conductor = 1, r_in = 0.0441230526353399, r_ex = 0.0444230526353399, eps_r = 1000.0, mu_r = 1.0)
 (conductor = 2, r_in = 0.0477230526353399, r_ex = 0.0507230526353399, eps_r = 2.51862, mu_r = 1.0)
 (conductor = 2, r_in = 0.0507230526353399, r_ex = 0.060723052635339905, eps_r = 2.8, mu_r = 1.1263)

The current in a stranded core follows the helices of its rectangular strands and also circulates around the cable axis, like the current in a solenoid. This effect introduces additional magnetic energy in the insulation interval. The relative permeability of each interval, mu_r_ins, combines this solenoid correction with the mean permeability of the layers. Since the sheath has no lay, the value of its interval is the mean permeability of its layers.

Relative permeability of the core and sheath intervals:

blueprint.mu_r_ins

2-element Vector{Float64}:
 2.004487977855449
 1.094337715595818

Three-phase system in flat formation

The cables are placed at x = −1, 0, 1 m. Each terminal is assigned its own conductor index, with core and sheath of cable i connected to conductors 2i − 1 and 2i, respectively.

Homogeneous earth model and frequency range:

earth = homogeneous(rho = 1_000.0, eps_r = 10.0) # [Ω·m]
frequencies = 10.0 .^ range(-1, 7; length = 101) # [Hz]

101-element Vector{Float64}:
 0.1
 0.12022644346174127
 0.14454397707459277
 0.17378008287493754
 0.20892961308540392
 0.251188643150958
 0.3019951720402016
 0.36307805477010135
 0.436515832240166
 0.5248074602497725
 ⋮
 2.2908676527677746e6
 2.754228703338169e6
 3.3113112148259077e6
 3.9810717055349695e6
 4.786300923226381e6
 5.754399373371567e6
 6.918309709189363e6
 8.317637711026709e6
 1.0e7

Cable positions and cable system for a line 20 km long:

placements = [Placement(x, -1.0) for x in (-1.0, 0.0, 1.0)] # [m]
system = build(CableSystem, fill(design, 3), placements;
    connections = [(core = 2i - 1, sheath = 2i) for i in 1:3],
    id = "cable_380kv_no_armour_ac_flat", line_length = 20_000.0) # [m]

CableSystem{Float64, Vector{CableDesign{Float64, Stack{Vector{AbstractCablePart}}, Vector{LineCableModels.DataModel.PlacedRegion}, Circle{Float64}}}, Vector{LineCableModels.DataModel.PlacedRegion}}("cable_380kv_no_armour_ac_flat", 20000.0, CableDesign{Float64, Stack{Vector{AbstractCablePart}}, Vector{LineCableModels.DataModel.PlacedRegion}, Circle{Float64}}[CableDesign{Float64, Stack{Vector{AbstractCablePart}}, Vector{LineCableModels.DataModel.PlacedRegion}, Circle{Float64}}("cable_380kv_no_armour", Stack{Vector{AbstractCablePart}}(AbstractCablePart[Terminal{Stack{Vector{AbstractCablePart}}}(:core, Stack{Vector{AbstractCablePart}}(AbstractCablePart[Region{Circle{Float64}, Material{Float64, :conductor}}(:core_center, Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(6, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(12, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(18, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_3, Rectangle{Float64}(0.0033350171093775244, 0.003154670363766309, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(24, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_4, Rectangle{Float64}(0.003328021612597551, 0.0031613014764634347, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(30, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_5, Rectangle{Float64}(0.003324835919433458, 0.003164330479020927, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(36, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0))))])), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_inner, Offset{Float64}(0.002), Material{Float64, :semicon}(1000.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :insulator}}(:core_insulation, Offset{Float64}(0.02), Material{Float64, :insulator}(1.0e14, 2.77781, 1.59891, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_outer, Offset{Float64}(0.0015), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_water_blocking, Offset{Float64}(0.0003), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Terminal{Stack{Vector{AbstractCablePart}}}(:sheath, Stack{Vector{AbstractCablePart}}(AbstractCablePart[Region{Offset{Float64}, Material{Float64, :conductor}}(:sheath_lead, Offset{Float64}(0.0033), Material{Float64, :conductor}(2.14e-7, 1.0, 0.999983, 20.0, 0.004, 0.0, 90.0, 0.0, 0.0))])), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_inner_pe, Offset{Float64}(0.003), Material{Float64, :insulator}(1.97e14, 2.51862, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_outer_jacket, Offset{Float64}(0.01), Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0))]), LineCableModels.DataModel.PlacedRegion[LineCableModels.DataModel.PlacedRegion{Region{Circle{Float64}, Material{Float64, :conductor}}, Circle{Float64}}(Region{Circle{Float64}, Material{Float64, :conductor}}(:core_center, Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 1.0471975511965976))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 2.0943951023931953))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 3.141592653589793))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 4.1887902047863905))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, 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Material{Float64, :semicon}}(:core_semicon_outer, Offset{Float64}(0.0015), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_water_blocking, Offset{Float64}(0.0003), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Terminal{Stack{Vector{AbstractCablePart}}}(:sheath, Stack{Vector{AbstractCablePart}}(AbstractCablePart[Region{Offset{Float64}, Material{Float64, :conductor}}(:sheath_lead, Offset{Float64}(0.0033), Material{Float64, :conductor}(2.14e-7, 1.0, 0.999983, 20.0, 0.004, 0.0, 90.0, 0.0, 0.0))])), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_inner_pe, Offset{Float64}(0.003), Material{Float64, :insulator}(1.97e14, 2.51862, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_outer_jacket, Offset{Float64}(0.01), Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0))]), 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LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 1.0471975511965976))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), 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0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 4.1887902047863905))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 5.235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, 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Placement{Float64}(0.0, 0.0, 3.141592653589793), Placement{Float64}(0.0, 0.0, 4.1887902047863905), Placement{Float64}(0.0, 0.0, 5.235987755982988)], copies = [2:2, 3:3, 4:4, 5:5, 6:6, 7:7]), (placements = [Placement{Float64}(0.0, 0.0, 0.0), Placement{Float64}(0.0, 0.0, 0.5235987755982988), Placement{Float64}(0.0, 0.0, 1.0471975511965976), Placement{Float64}(0.0, 0.0, 1.5707963267948966), Placement{Float64}(0.0, 0.0, 2.0943951023931953), Placement{Float64}(0.0, 0.0, 2.617993877991494), Placement{Float64}(0.0, 0.0, 3.141592653589793), Placement{Float64}(0.0, 0.0, 3.665191429188092), Placement{Float64}(0.0, 0.0, 4.1887902047863905), Placement{Float64}(0.0, 0.0, 4.71238898038469), Placement{Float64}(0.0, 0.0, 5.235987755982988), Placement{Float64}(0.0, 0.0, 5.759586531581287)], copies = [8:8, 9:9, 10:10, 11:11, 12:12, 13:13, 14:14, 15:15, 16:16, 17:17, 18:18, 19:19]), (placements = [Placement{Float64}(0.0, 0.0, 0.0), Placement{Float64}(0.0, 0.0, 0.3490658503988659), Placement{Float64}(0.0, 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20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(-1.0, -1.0, 0.5235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(-1.0, -1.0, 1.0471975511965976)))  …  LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(1.0, -1.0, 5.759586531581287))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(1.0, -1.0, 5.93411945678072))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(1.0, -1.0, 6.1086523819801535))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_inner, Offset{Float64}(0.002), Material{Float64, :semicon}(1000.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.020623052635339898, 0.022623052635339896, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:core_insulation, Offset{Float64}(0.02), Material{Float64, :insulator}(1.0e14, 2.77781, 1.59891, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.022623052635339896, 0.0426230526353399, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_outer, Offset{Float64}(0.0015), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0426230526353399, 0.0441230526353399, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_water_blocking, Offset{Float64}(0.0003), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0441230526353399, 0.0444230526353399, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :conductor}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :conductor}}(:sheath_lead, Offset{Float64}(0.0033), Material{Float64, :conductor}(2.14e-7, 1.0, 0.999983, 20.0, 0.004, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0444230526353399, 0.0477230526353399, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_inner_pe, Offset{Float64}(0.003), Material{Float64, :insulator}(1.97e14, 2.51862, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0477230526353399, 0.0507230526353399, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_outer_jacket, Offset{Float64}(0.01), Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0507230526353399, 0.060723052635339905, Placement{Float64}(1.0, -1.0, 0.0)))], [(cable = 1, terminal = 1, connection = 1, regions = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  118, 119, 120, 121, 122, 123, 124, 125, 126, 127]), (cable = 1, terminal = 2, connection = 2, regions = [132]), (cable = 2, terminal = 1, connection = 3, regions = [135, 136, 137, 138, 139, 140, 141, 142, 143, 144  …  252, 253, 254, 255, 256, 257, 258, 259, 260, 261]), (cable = 2, terminal = 2, connection = 4, regions = [266]), (cable = 3, terminal = 1, connection = 5, regions = [269, 270, 271, 272, 273, 274, 275, 276, 277, 278  …  386, 387, 388, 389, 390, 391, 392, 393, 394, 395]), (cable = 3, terminal = 2, connection = 6, regions = [400])])

Line parameters problem at 70 °C:

problem = LineParametersProblem(system, earth; temperature = 70.0, frequencies) # [°C]

LineParametersProblem{Float64, CableSystem{Float64, Vector{CableDesign{Float64, Stack{Vector{AbstractCablePart}}, Vector{LineCableModels.DataModel.PlacedRegion}, Circle{Float64}}}, Vector{LineCableModels.DataModel.PlacedRegion}}, EarthModel{Float64, 2}}(CableSystem{Float64, Vector{CableDesign{Float64, Stack{Vector{AbstractCablePart}}, Vector{LineCableModels.DataModel.PlacedRegion}, Circle{Float64}}}, Vector{LineCableModels.DataModel.PlacedRegion}}("cable_380kv_no_armour_ac_flat", 20000.0, CableDesign{Float64, Stack{Vector{AbstractCablePart}}, Vector{LineCableModels.DataModel.PlacedRegion}, Circle{Float64}}[CableDesign{Float64, Stack{Vector{AbstractCablePart}}, Vector{LineCableModels.DataModel.PlacedRegion}, Circle{Float64}}("cable_380kv_no_armour", Stack{Vector{AbstractCablePart}}(AbstractCablePart[Terminal{Stack{Vector{AbstractCablePart}}}(:core, Stack{Vector{AbstractCablePart}}(AbstractCablePart[Region{Circle{Float64}, Material{Float64, :conductor}}(:core_center, Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(6, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(12, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(18, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_3, Rectangle{Float64}(0.0033350171093775244, 0.003154670363766309, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(24, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_4, Rectangle{Float64}(0.003328021612597551, 0.0031613014764634347, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(30, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_5, Rectangle{Float64}(0.003324835919433458, 0.003164330479020927, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(36, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0))))])), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_inner, Offset{Float64}(0.002), Material{Float64, :semicon}(1000.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :insulator}}(:core_insulation, Offset{Float64}(0.02), Material{Float64, :insulator}(1.0e14, 2.77781, 1.59891, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_outer, Offset{Float64}(0.0015), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_water_blocking, Offset{Float64}(0.0003), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Terminal{Stack{Vector{AbstractCablePart}}}(:sheath, Stack{Vector{AbstractCablePart}}(AbstractCablePart[Region{Offset{Float64}, Material{Float64, :conductor}}(:sheath_lead, Offset{Float64}(0.0033), Material{Float64, :conductor}(2.14e-7, 1.0, 0.999983, 20.0, 0.004, 0.0, 90.0, 0.0, 0.0))])), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_inner_pe, Offset{Float64}(0.003), Material{Float64, :insulator}(1.97e14, 2.51862, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_outer_jacket, Offset{Float64}(0.01), Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0))]), LineCableModels.DataModel.PlacedRegion[LineCableModels.DataModel.PlacedRegion{Region{Circle{Float64}, Material{Float64, :conductor}}, Circle{Float64}}(Region{Circle{Float64}, Material{Float64, :conductor}}(:core_center, Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 1.0471975511965976))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 2.0943951023931953))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 3.141592653589793))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 4.1887902047863905))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 5.235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 0.5235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 1.0471975511965976)))  …  LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(0.0, 0.0, 5.759586531581287))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(0.0, 0.0, 5.93411945678072))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, 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0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 4.1887902047863905))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 5.235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 0.5235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 1.0471975511965976)))  …  LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 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:insulator}}(:core_insulation, Offset{Float64}(0.02), Material{Float64, :insulator}(1.0e14, 2.77781, 1.59891, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_outer, Offset{Float64}(0.0015), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_water_blocking, Offset{Float64}(0.0003), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Terminal{Stack{Vector{AbstractCablePart}}}(:sheath, Stack{Vector{AbstractCablePart}}(AbstractCablePart[Region{Offset{Float64}, Material{Float64, :conductor}}(:sheath_lead, Offset{Float64}(0.0033), Material{Float64, :conductor}(2.14e-7, 1.0, 0.999983, 20.0, 0.004, 0.0, 90.0, 0.0, 0.0))])), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_inner_pe, Offset{Float64}(0.003), Material{Float64, :insulator}(1.97e14, 2.51862, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_outer_jacket, Offset{Float64}(0.01), Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0))]), LineCableModels.DataModel.PlacedRegion[LineCableModels.DataModel.PlacedRegion{Region{Circle{Float64}, Material{Float64, :conductor}}, Circle{Float64}}(Region{Circle{Float64}, Material{Float64, :conductor}}(:core_center, Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 1.0471975511965976))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 2.0943951023931953))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 3.141592653589793))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 4.1887902047863905))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 5.235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 0.5235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 1.0471975511965976)))  …  LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(0.0, 0.0, 5.759586531581287))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(0.0, 0.0, 5.93411945678072))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(0.0, 0.0, 6.1086523819801535))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_inner, Offset{Float64}(0.002), Material{Float64, :semicon}(1000.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.020623052635339898, 0.022623052635339896, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:core_insulation, Offset{Float64}(0.02), Material{Float64, :insulator}(1.0e14, 2.77781, 1.59891, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.022623052635339896, 0.0426230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_outer, Offset{Float64}(0.0015), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0426230526353399, 0.0441230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_water_blocking, Offset{Float64}(0.0003), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0441230526353399, 0.0444230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :conductor}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :conductor}}(:sheath_lead, Offset{Float64}(0.0033), Material{Float64, :conductor}(2.14e-7, 1.0, 0.999983, 20.0, 0.004, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0444230526353399, 0.0477230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_inner_pe, Offset{Float64}(0.003), Material{Float64, :insulator}(1.97e14, 2.51862, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0477230526353399, 0.0507230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_outer_jacket, Offset{Float64}(0.01), Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0507230526353399, 0.060723052635339905, Placement{Float64}(0.0, 0.0, 0.0)))], Circle{Float64}(0.060723052635339905, Placement{Float64}(0.0, 0.0, 0.0)), [(name = :core, scope = @NamedTuple{repeat::Int64, copy::Int64}[], regions = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  118, 119, 120, 121, 122, 123, 124, 125, 126, 127]), (name = :sheath, scope = @NamedTuple{repeat::Int64, copy::Int64}[], regions = [132])], @NamedTuple{at::Placement{Float64}, regions::Vector{Int64}, members::Vector{Int64}}[(at = Placement{Float64}(0.0, 0.0, 0.0), regions = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  125, 126, 127, 128, 129, 130, 131, 132, 133, 134], members = [])], @NamedTuple{placements::Vector{Placement{Float64}}, copies::Vector{UnitRange{Int64}}}[(placements = [Placement{Float64}(0.0, 0.0, 0.0), Placement{Float64}(0.0, 0.0, 1.0471975511965976), Placement{Float64}(0.0, 0.0, 2.0943951023931953), Placement{Float64}(0.0, 0.0, 3.141592653589793), Placement{Float64}(0.0, 0.0, 4.1887902047863905), Placement{Float64}(0.0, 0.0, 5.235987755982988)], copies = [2:2, 3:3, 4:4, 5:5, 6:6, 7:7]), (placements = [Placement{Float64}(0.0, 0.0, 0.0), Placement{Float64}(0.0, 0.0, 0.5235987755982988), Placement{Float64}(0.0, 0.0, 1.0471975511965976), Placement{Float64}(0.0, 0.0, 1.5707963267948966), Placement{Float64}(0.0, 0.0, 2.0943951023931953), Placement{Float64}(0.0, 0.0, 2.617993877991494), Placement{Float64}(0.0, 0.0, 3.141592653589793), Placement{Float64}(0.0, 0.0, 3.665191429188092), Placement{Float64}(0.0, 0.0, 4.1887902047863905), Placement{Float64}(0.0, 0.0, 4.71238898038469), Placement{Float64}(0.0, 0.0, 5.235987755982988), Placement{Float64}(0.0, 0.0, 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:insulator}}(:sheath_inner_pe, Offset{Float64}(0.003), Material{Float64, :insulator}(1.97e14, 2.51862, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0477230526353399, 0.0507230526353399, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_outer_jacket, Offset{Float64}(0.01), Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0507230526353399, 0.060723052635339905, Placement{Float64}(1.0, -1.0, 0.0)))], [(cable = 1, terminal = 1, connection = 1, regions = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  118, 119, 120, 121, 122, 123, 124, 125, 126, 127]), (cable = 1, terminal = 2, connection = 2, regions = [132]), (cable = 2, terminal = 1, connection = 3, regions = [135, 136, 137, 138, 139, 140, 141, 142, 143, 144  …  252, 253, 254, 255, 256, 257, 258, 259, 260, 261]), (cable = 2, terminal = 2, connection = 4, regions = [266]), (cable = 3, terminal = 1, connection = 5, regions = [269, 270, 271, 272, 273, 274, 275, 276, 277, 278  …  386, 387, 388, 389, 390, 391, 392, 393, 394, 395]), (cable = 3, terminal = 2, connection = 6, regions = [400])]), EarthModel{Float64, 2}((EarthLayer{Float64}(Inf, 1.0, 1.0, Inf), EarthLayer{Float64}(1000.0, 10.0, 1.0, Inf))), 70.0, [0.1, 0.12022644346174127, 0.14454397707459277, 0.17378008287493754, 0.20892961308540392, 0.251188643150958, 0.3019951720402016, 0.36307805477010135, 0.436515832240166, 0.5248074602497725  …  1.9054607179632483e6, 2.2908676527677746e6, 2.754228703338169e6, 3.3113112148259077e6, 3.9810717055349695e6, 4.786300923226381e6, 5.754399373371567e6, 6.918309709189363e6, 8.317637711026709e6, 1.0e7])

Line parameters at power frequency

The bundle and Kron reductions are enabled by default. Since no two terminals share an index and no terminal has the index zero, the result retains the six conductors of the system. The matrices at the frequency closest to 50 Hz are presented below, with Z in Ω/km and Y in µS/km, rounded.

Compute the line parameters and inspect the row labels:

result = compute(problem, CoaxialFormulation())
result.terminals

6-element Vector{String}:
 "cable:1:core"
 "cable:1:sheath"
 "cable:2:core"
 "cable:2:sheath"
 "cable:3:core"
 "cable:3:sheath"

Frequency closest to 50 Hz:

k = argmin(abs.(result.frequencies .- 50.0))
result.frequencies[k] # [Hz]

52.48074602497726

Series resistance matrix:

round.(real(result.Z[:, :, k]) .* 1e3; digits = 4) # [Ω/km]

6×6 Matrix{Float64}:
 0.0773  0.0518  0.0518  0.0518  0.0518  0.0518
 0.0518  0.3207  0.0518  0.0518  0.0518  0.0518
 0.0518  0.0518  0.0773  0.0518  0.0518  0.0518
 0.0518  0.0518  0.0518  0.3207  0.0518  0.0518
 0.0518  0.0518  0.0518  0.0518  0.0773  0.0518
 0.0518  0.0518  0.0518  0.0518  0.0518  0.3207

Series reactance matrix:

round.(imag(result.Z[:, :, k]) .* 1e3; digits = 4) # [Ω/km]

6×6 Matrix{Float64}:
 0.8487  0.7296  0.5252  0.5252  0.4795  0.4795
 0.7296  0.7288  0.5252  0.5252  0.4795  0.4795
 0.5252  0.5252  0.8487  0.7296  0.5252  0.5252
 0.5252  0.5252  0.7296  0.7288  0.5252  0.5252
 0.4795  0.4795  0.5252  0.5252  0.8487  0.7296
 0.4795  0.4795  0.5252  0.5252  0.7296  0.7288

Shunt conductance matrix:

round.(real(result.Y[:, :, k]) .* 1e9; digits = 4) # [µS/km]

6×6 Matrix{Float64}:
  0.0  -0.0      0.0   0.0      0.0  -0.0
 -0.0   0.1165   0.0   0.0966  -0.0   0.0903
  0.0   0.0      0.0  -0.0     -0.0   0.0
  0.0   0.0966  -0.0   0.1165   0.0   0.0966
  0.0  -0.0     -0.0  -0.0      0.0  -0.0
  0.0   0.0903   0.0   0.0966  -0.0   0.1165

Shunt susceptance matrix:

round.(imag(result.Y[:, :, k]) .* 1e9; digits = 1) # [µS/km]

6×6 Matrix{Float64}:
  80.4  -80.4    0.0   -0.0   -0.0   -0.0
 -80.4  287.7    0.0   -0.0    0.0   -0.0
  -0.0   -0.0   80.4  -80.4   -0.0   -0.0
  -0.0   -0.0  -80.4  287.7    0.0   -0.0
   0.0    0.0   -0.0    0.0   80.4  -80.4
  -0.0   -0.0    0.0   -0.0  -80.4  287.7

Sheaths grounded at both ends

Sheaths grounded at both ends of the line are represented by setting their voltage to zero. This condition is declared with the index 0, and the Kron reduction eliminates the sheaths from the matrices. The resulting system retains the three cores, with the effect of the sheath currents included in the reduced matrices.

Cable system with grounded sheaths:

grounded = build(CableSystem, fill(design, 3), placements;
    connections = [(core = i, sheath = 0) for i in 1:3],
    id = "cable_380kv_grounded_sheaths", line_length = 20_000.0) # [m]
grounded_problem = LineParametersProblem(grounded, earth; temperature = 70.0, frequencies)

LineParametersProblem{Float64, CableSystem{Float64, Vector{CableDesign{Float64, Stack{Vector{AbstractCablePart}}, Vector{LineCableModels.DataModel.PlacedRegion}, Circle{Float64}}}, Vector{LineCableModels.DataModel.PlacedRegion}}, EarthModel{Float64, 2}}(CableSystem{Float64, Vector{CableDesign{Float64, Stack{Vector{AbstractCablePart}}, Vector{LineCableModels.DataModel.PlacedRegion}, Circle{Float64}}}, Vector{LineCableModels.DataModel.PlacedRegion}}("cable_380kv_grounded_sheaths", 20000.0, CableDesign{Float64, Stack{Vector{AbstractCablePart}}, Vector{LineCableModels.DataModel.PlacedRegion}, Circle{Float64}}[CableDesign{Float64, Stack{Vector{AbstractCablePart}}, Vector{LineCableModels.DataModel.PlacedRegion}, Circle{Float64}}("cable_380kv_no_armour", Stack{Vector{AbstractCablePart}}(AbstractCablePart[Terminal{Stack{Vector{AbstractCablePart}}}(:core, Stack{Vector{AbstractCablePart}}(AbstractCablePart[Region{Circle{Float64}, Material{Float64, :conductor}}(:core_center, Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(6, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(12, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(18, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_3, Rectangle{Float64}(0.0033350171093775244, 0.003154670363766309, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(24, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_4, Rectangle{Float64}(0.003328021612597551, 0.0031613014764634347, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(30, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_5, Rectangle{Float64}(0.003324835919433458, 0.003164330479020927, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(36, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0))))])), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_inner, Offset{Float64}(0.002), Material{Float64, :semicon}(1000.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :insulator}}(:core_insulation, Offset{Float64}(0.02), Material{Float64, :insulator}(1.0e14, 2.77781, 1.59891, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_outer, Offset{Float64}(0.0015), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_water_blocking, Offset{Float64}(0.0003), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Terminal{Stack{Vector{AbstractCablePart}}}(:sheath, Stack{Vector{AbstractCablePart}}(AbstractCablePart[Region{Offset{Float64}, Material{Float64, :conductor}}(:sheath_lead, Offset{Float64}(0.0033), Material{Float64, :conductor}(2.14e-7, 1.0, 0.999983, 20.0, 0.004, 0.0, 90.0, 0.0, 0.0))])), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_inner_pe, Offset{Float64}(0.003), Material{Float64, :insulator}(1.97e14, 2.51862, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_outer_jacket, Offset{Float64}(0.01), Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0))]), LineCableModels.DataModel.PlacedRegion[LineCableModels.DataModel.PlacedRegion{Region{Circle{Float64}, Material{Float64, :conductor}}, Circle{Float64}}(Region{Circle{Float64}, Material{Float64, :conductor}}(:core_center, Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 1.0471975511965976))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 2.0943951023931953))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 3.141592653589793))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 4.1887902047863905))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 5.235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 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Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(18, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_3, Rectangle{Float64}(0.0033350171093775244, 0.003154670363766309, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(24, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_4, 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0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 4.1887902047863905))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 5.235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 0.5235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 1.0471975511965976)))  …  LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 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Material{Float64, :insulator}(1.0e14, 2.77781, 1.59891, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.022623052635339896, 0.0426230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_outer, Offset{Float64}(0.0015), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0426230526353399, 0.0441230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_water_blocking, Offset{Float64}(0.0003), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0441230526353399, 0.0444230526353399, Placement{Float64}(0.0, 0.0, 0.0))), 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:conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)))), Lay{Helix{LayRatio{Float64}, Float64}, Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}}(Helix{LayRatio{Float64}, Float64}(LayRatio{Float64}(15.0), 1, 0.0), Repeat{CircularPattern{Float64, Offset{Float64}}, Region{Rectangle{Float64}, Material{Float64, :conductor}}}(CircularPattern{Float64, Offset{Float64}}(36, Offset{Float64}(0.0), 0.0, 6.283185307179586, 0.0), Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0))))])), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_inner, Offset{Float64}(0.002), Material{Float64, :semicon}(1000.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :insulator}}(:core_insulation, Offset{Float64}(0.02), Material{Float64, :insulator}(1.0e14, 2.77781, 1.59891, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_outer, Offset{Float64}(0.0015), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :semicon}}(:core_water_blocking, Offset{Float64}(0.0003), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Terminal{Stack{Vector{AbstractCablePart}}}(:sheath, Stack{Vector{AbstractCablePart}}(AbstractCablePart[Region{Offset{Float64}, Material{Float64, :conductor}}(:sheath_lead, Offset{Float64}(0.0033), Material{Float64, :conductor}(2.14e-7, 1.0, 0.999983, 20.0, 0.004, 0.0, 90.0, 0.0, 0.0))])), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_inner_pe, Offset{Float64}(0.003), Material{Float64, :insulator}(1.97e14, 2.51862, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_outer_jacket, Offset{Float64}(0.01), Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0))]), LineCableModels.DataModel.PlacedRegion[LineCableModels.DataModel.PlacedRegion{Region{Circle{Float64}, Material{Float64, :conductor}}, Circle{Float64}}(Region{Circle{Float64}, Material{Float64, :conductor}}(:core_center, Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), Circle{Float64}(0.00183, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 1.0471975511965976))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 2.0943951023931953))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 3.141592653589793))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 4.1887902047863905))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_1, Rectangle{Float64}(0.003493306988375041, 0.0030117248992482014, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.00183, 0.0048417248992482015, 1.0471975511965974, Placement{Float64}(0.0, 0.0, 5.235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 0.5235987755982988))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_2, Rectangle{Float64}(0.0033558780615771506, 0.0031350601674312315, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.004841724899248202, 0.007976785066679433, 0.523598775598299, Placement{Float64}(0.0, 0.0, 1.0471975511965976)))  …  LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(0.0, 0.0, 5.759586531581287))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(0.0, 0.0, 5.93411945678072))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(0.0, 0.0, 6.1086523819801535))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_inner, Offset{Float64}(0.002), Material{Float64, :semicon}(1000.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.020623052635339898, 0.022623052635339896, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:core_insulation, Offset{Float64}(0.02), Material{Float64, :insulator}(1.0e14, 2.77781, 1.59891, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.022623052635339896, 0.0426230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_outer, Offset{Float64}(0.0015), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0426230526353399, 0.0441230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_water_blocking, Offset{Float64}(0.0003), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0441230526353399, 0.0444230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :conductor}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :conductor}}(:sheath_lead, Offset{Float64}(0.0033), Material{Float64, :conductor}(2.14e-7, 1.0, 0.999983, 20.0, 0.004, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0444230526353399, 0.0477230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_inner_pe, Offset{Float64}(0.003), Material{Float64, :insulator}(1.97e14, 2.51862, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0477230526353399, 0.0507230526353399, Placement{Float64}(0.0, 0.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_outer_jacket, Offset{Float64}(0.01), Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0507230526353399, 0.060723052635339905, Placement{Float64}(0.0, 0.0, 0.0)))], Circle{Float64}(0.060723052635339905, Placement{Float64}(0.0, 0.0, 0.0)), [(name = :core, scope = @NamedTuple{repeat::Int64, copy::Int64}[], regions = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  118, 119, 120, 121, 122, 123, 124, 125, 126, 127]), (name = :sheath, scope = @NamedTuple{repeat::Int64, copy::Int64}[], regions = [132])], @NamedTuple{at::Placement{Float64}, regions::Vector{Int64}, members::Vector{Int64}}[(at = Placement{Float64}(0.0, 0.0, 0.0), regions = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  125, 126, 127, 128, 129, 130, 131, 132, 133, 134], members = [])], @NamedTuple{placements::Vector{Placement{Float64}}, copies::Vector{UnitRange{Int64}}}[(placements = [Placement{Float64}(0.0, 0.0, 0.0), Placement{Float64}(0.0, 0.0, 1.0471975511965976), Placement{Float64}(0.0, 0.0, 2.0943951023931953), Placement{Float64}(0.0, 0.0, 3.141592653589793), Placement{Float64}(0.0, 0.0, 4.1887902047863905), Placement{Float64}(0.0, 0.0, 5.235987755982988)], copies = [2:2, 3:3, 4:4, 5:5, 6:6, 7:7]), (placements = [Placement{Float64}(0.0, 0.0, 0.0), Placement{Float64}(0.0, 0.0, 0.5235987755982988), Placement{Float64}(0.0, 0.0, 1.0471975511965976), Placement{Float64}(0.0, 0.0, 1.5707963267948966), Placement{Float64}(0.0, 0.0, 2.0943951023931953), Placement{Float64}(0.0, 0.0, 2.617993877991494), Placement{Float64}(0.0, 0.0, 3.141592653589793), Placement{Float64}(0.0, 0.0, 3.665191429188092), Placement{Float64}(0.0, 0.0, 4.1887902047863905), Placement{Float64}(0.0, 0.0, 4.71238898038469), Placement{Float64}(0.0, 0.0, 5.235987755982988), Placement{Float64}(0.0, 0.0, 5.759586531581287)], copies = [8:8, 9:9, 10:10, 11:11, 12:12, 13:13, 14:14, 15:15, 16:16, 17:17, 18:18, 19:19]), (placements = [Placement{Float64}(0.0, 0.0, 0.0), Placement{Float64}(0.0, 0.0, 0.3490658503988659), Placement{Float64}(0.0, 0.0, 0.6981317007977318), Placement{Float64}(0.0, 0.0, 1.0471975511965976), Placement{Float64}(0.0, 0.0, 1.3962634015954636), Placement{Float64}(0.0, 0.0, 1.7453292519943295), Placement{Float64}(0.0, 0.0, 2.0943951023931953), Placement{Float64}(0.0, 0.0, 2.443460952792061), Placement{Float64}(0.0, 0.0, 2.792526803190927), Placement{Float64}(0.0, 0.0, 3.141592653589793), Placement{Float64}(0.0, 0.0, 3.490658503988659), Placement{Float64}(0.0, 0.0, 3.839724354387525), Placement{Float64}(0.0, 0.0, 4.1887902047863905), Placement{Float64}(0.0, 0.0, 4.537856055185257), Placement{Float64}(0.0, 0.0, 4.886921905584122), Placement{Float64}(0.0, 0.0, 5.235987755982989), Placement{Float64}(0.0, 0.0, 5.585053606381854), Placement{Float64}(0.0, 0.0, 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0.523598775598299, Placement{Float64}(-1.0, -1.0, 1.0471975511965976)))  …  LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(1.0, -1.0, 5.759586531581287))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(1.0, -1.0, 5.93411945678072))), LineCableModels.DataModel.PlacedRegion{Region{Rectangle{Float64}, Material{Float64, :conductor}}, LineCableModels.DataModel.AnnularSector{Float64}}(Region{Rectangle{Float64}, Material{Float64, :conductor}}(:core_strands_6, Rectangle{Float64}(0.0033231191149581257, 0.0031659652494097947, Placement{Float64}(0.0, 0.0, 0.0)), Material{Float64, :conductor}(2.3853e-8, 1.0, 1.01663, 20.0, 0.00393, 0.0, 90.0, 0.0, 0.0)), LineCableModels.DataModel.AnnularSector{Float64}(0.017457087385930103, 0.020623052635339898, 0.17453292519943295, Placement{Float64}(1.0, -1.0, 6.1086523819801535))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_inner, Offset{Float64}(0.002), Material{Float64, :semicon}(1000.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.020623052635339898, 0.022623052635339896, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:core_insulation, Offset{Float64}(0.02), Material{Float64, :insulator}(1.0e14, 2.77781, 1.59891, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.022623052635339896, 0.0426230526353399, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_semicon_outer, Offset{Float64}(0.0015), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0426230526353399, 0.0441230526353399, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :semicon}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :semicon}}(:core_water_blocking, Offset{Float64}(0.0003), Material{Float64, :semicon}(500.0, 1000.0, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0441230526353399, 0.0444230526353399, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :conductor}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :conductor}}(:sheath_lead, Offset{Float64}(0.0033), Material{Float64, :conductor}(2.14e-7, 1.0, 0.999983, 20.0, 0.004, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0444230526353399, 0.0477230526353399, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_inner_pe, Offset{Float64}(0.003), Material{Float64, :insulator}(1.97e14, 2.51862, 1.0, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0477230526353399, 0.0507230526353399, Placement{Float64}(1.0, -1.0, 0.0))), LineCableModels.DataModel.PlacedRegion{Region{Offset{Float64}, Material{Float64, :insulator}}, Annulus{Float64}}(Region{Offset{Float64}, Material{Float64, :insulator}}(:sheath_outer_jacket, Offset{Float64}(0.01), Material{Float64, :insulator}(1.0e15, 2.8, 1.1263, 20.0, 0.0, 0.0, 90.0, 0.0, 0.0)), Annulus{Float64}(0.0507230526353399, 0.060723052635339905, Placement{Float64}(1.0, -1.0, 0.0)))], [(cable = 1, terminal = 1, connection = 1, regions = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  118, 119, 120, 121, 122, 123, 124, 125, 126, 127]), (cable = 1, terminal = 2, connection = 0, regions = [132]), (cable = 2, terminal = 1, connection = 2, regions = [135, 136, 137, 138, 139, 140, 141, 142, 143, 144  …  252, 253, 254, 255, 256, 257, 258, 259, 260, 261]), (cable = 2, terminal = 2, connection = 0, regions = [266]), (cable = 3, terminal = 1, connection = 3, regions = [269, 270, 271, 272, 273, 274, 275, 276, 277, 278  …  386, 387, 388, 389, 390, 391, 392, 393, 394, 395]), (cable = 3, terminal = 2, connection = 0, regions = [400])]), EarthModel{Float64, 2}((EarthLayer{Float64}(Inf, 1.0, 1.0, Inf), EarthLayer{Float64}(1000.0, 10.0, 1.0, Inf))), 70.0, [0.1, 0.12022644346174127, 0.14454397707459277, 0.17378008287493754, 0.20892961308540392, 0.251188643150958, 0.3019951720402016, 0.36307805477010135, 0.436515832240166, 0.5248074602497725  …  1.9054607179632483e6, 2.2908676527677746e6, 2.754228703338169e6, 3.3113112148259077e6, 3.9810717055349695e6, 4.786300923226381e6, 5.754399373371567e6, 6.918309709189363e6, 8.317637711026709e6, 1.0e7])

Compute the line parameters and inspect the row labels:

grounded_result = compute(grounded_problem, CoaxialFormulation())
grounded_result.terminals

3-element Vector{String}:
 "cable:1:core"
 "cable:2:core"
 "cable:3:core"

Series impedance of the three cores:

grounded_result.Z[:, :, k] # [Ω/m]

3×3 Matrix{ComplexF64}:
 0.000188224+0.000220371im  …   3.76581e-5-3.27319e-5im
  5.73724e-5-2.96363e-5im       5.73724e-5-2.96363e-5im
  3.76581e-5-3.27319e-5im      0.000188224+0.000220371im

Ideal transposition

Since the central cable of a flat formation occupies a position different from the outer cables, the matrices are not symmetric under a cyclic permutation of the phases. A transposed line permutes the positions of the phases along its length. The option transposition = true replaces each matrix by the mean over the cyclic permutations of its rows and columns, so that the entries of each cyclic diagonal become equal.

Compute the transposed line parameters:

transposed = compute(grounded_problem, CoaxialFormulation(transposition = true))
transposed.Z[:, :, k] # [Ω/m]

3×3 Matrix{ComplexF64}:
 0.000183385+0.000218651im  …    5.0801e-5-3.06682e-5im
   5.0801e-5-3.06682e-5im        5.0801e-5-3.06682e-5im
   5.0801e-5-3.06682e-5im      0.000183385+0.000218651im

Size of the impedance array and number of frequencies:

size(result.Z), length(result.frequencies)

((6, 6, 101), 101)

Conclusion

This example has demonstrated how to:

1. Represent a compacted stranded core with rectangular strands bent into annular sectors.
2. Examine the lay parameters, the equivalent resistivity and the solenoid correction of the stranded core.
3. Compute the line parameters of a three-phase system in flat formation.
4. Eliminate grounded sheaths with the Kron reduction.
5. Apply the ideal transposition to the reduced matrices.