Dielectrics

The dielectric layers between a conductor and the next conductor outward form its interval. The magnetic field in the interval adds a series term to the loop impedance of the conductor [2], with the relative permeability mu_r_ins of the interval. For a stranded conductor, that permeability includes the solenoid factor of the helical current of its wires, as Cable data model describes.

Each layer also has an admittivity $\kappa$, which the shunt formula reads to build the potential coefficients inside the cable by the series chain of the layers, which the matrix formulation page gives. An insulator takes the law of insulation_admittance and a semicon the law of semicon_admittance, by the class of its material. The one law of this release, :lossless, leaves out conduction and polarization loss in both.

Insulation impedance

LineCableModels.Engine.InsulationImpedance — Module

LineCableModels.Engine.InsulationImpedance

Compute the magnetic series-impedance term across an annular dielectric.

Formulas

Formula{:ametani1980}

Magnetic term of the series impedance across an annular dielectric layer, from the field between its radii [2, 7]:

\[z = \frac{s \mu_0 \mu_r}{2 \pi} \ln \frac{r_\mathrm{ex}}{r_\mathrm{in}},\]

where $s$ is the complex frequency [1/s], $r_\mathrm{in}$ and $r_\mathrm{ex}$ are the inner and outer radii of the layer [m], and $\mu_r$ is its relative permeability [dimensionless]. The constant $\mu_0$ is vacuum_permeability. The term is zero when $r_\mathrm{in}$ is zero or equals $r_\mathrm{ex}$.

LineCableModels.Engine.InsulationImpedance.FORMULAS — Constant

Identifiers of the insulation-impedance formulas.

LineCableModels.Engine.InsulationImpedance.Formula — Type

struct Formula{ID, O<:LineCableModels.Commons.FormulationOptions} <: LineCableModels.Engine.AbstractInsulationImpedance

Represent a magnetic series-impedance formula for an annular dielectric. Its options form a record of type FormulationOptions{Formula{ID}}, with ID the formula identifier.

options::LineCableModels.Commons.FormulationOptions: Options of the formula.

LineCableModels.Engine.InsulationImpedance.Formula — Method

Formula(
    ::Val{ID};
    kw...
) -> LineCableModels.Engine.InsulationImpedance.Formula

Build the formula named by ID with its declared defaults and supplied options.

Arguments

Val{ID}: formula identifier from FORMULAS.

Keywords

kw...: options declared by defaults for Formula{ID}.

Returns

A Formula with a typed option record.

Errors

Throws ArgumentError for an unknown identifier or option.

LineCableModels.Engine.impedance — Method

impedance(
    _::LineCableModels.Engine.InsulationImpedance.Formula{:ametani1980},
    r_in::Real,
    r_ex::Real,
    mu_r::Real,
    s::Complex{T<:Real}
) -> Any

Return the magnetic term of the series impedance across an annular dielectric layer by the formula Formula{:ametani1980}, whose equation is in the section "Formulas" of InsulationImpedance.

Arguments

Formula{:ametani1980}: magnetic annular-dielectric formula.
r_in: inner radius [m].
r_ex: outer radius, in [m].
mu_r: relative permeability [dimensionless].
s: complex frequency, j 2π f, in [1/s].

Returns

Impedance [Ω/m].

Insulation admittance

LineCableModels.Engine.InsulationAdmittance — Module

LineCableModels.Engine.InsulationAdmittance

Compute the admittivity of insulator layers.

Formulas

Formula{:lossless}

Admittivity of a dielectric without conduction or polarization loss, the frequency-domain constitutive relation of its displacement current:

\[\kappa = \mathrm{j} 2 \pi f \varepsilon_0 \varepsilon_r,\]

where $f$ is the frequency [Hz], $\kappa$ is the admittivity [S/m] and $\varepsilon_r$ is the relative permittivity eps_r of the material [dimensionless]. The constant $\varepsilon_0$ is vacuum_permittivity.

LineCableModels.Engine.InsulationAdmittance.FORMULAS — Constant

Identifiers of the insulation-admittance formulas.

LineCableModels.Engine.InsulationAdmittance.Formula — Type

struct Formula{ID, O<:LineCableModels.Commons.FormulationOptions} <: LineCableModels.Engine.AbstractInsulationAdmittance

Represent an admittivity law for an insulator layer. Its options form a record of type FormulationOptions{Formula{ID}}, with ID the formula identifier.

options::LineCableModels.Commons.FormulationOptions: Options of the formula.

LineCableModels.Engine.InsulationAdmittance.Formula — Method

Formula(
    ::Val{ID};
    kw...
) -> LineCableModels.Engine.InsulationAdmittance.Formula

Build the formula named by ID with its declared defaults and supplied options.

Arguments

Val{ID}: formula identifier from FORMULAS.

Keywords

kw...: options declared by defaults for Formula{ID}.

Returns

A Formula with a typed option record.

Errors

Throws ArgumentError for an unknown identifier or option.

LineCableModels.Engine.admittivity — Method

admittivity(
    _::LineCableModels.Engine.InsulationAdmittance.Formula{:lossless},
    material::Material{T<:Real},
    f::Real
) -> Any

Return the admittivity of an insulator layer of material at the frequency f, by the formula Formula{:lossless}, whose equation is in the section "Formulas" of InsulationAdmittance.

Arguments

Formula{:lossless}: dielectric law without conduction or polarization loss.
material: material of the layer.
f: frequency [Hz].

Returns

Admittivity [S/m].

Semicon admittance

LineCableModels.Engine.SemiconAdmittance — Module

LineCableModels.Engine.SemiconAdmittance

Compute the admittivity of semicon layers.

Formulas

Formula{:lossless}

Admittivity of a dielectric without conduction or polarization loss, the frequency-domain constitutive relation of its displacement current:

\[\kappa = \mathrm{j} 2 \pi f \varepsilon_0 \varepsilon_r,\]

where $f$ is the frequency [Hz], $\kappa$ is the admittivity [S/m] and $\varepsilon_r$ is the relative permittivity eps_r of the material [dimensionless]. The constant $\varepsilon_0$ is vacuum_permittivity.

LineCableModels.Engine.SemiconAdmittance.FORMULAS — Constant

Identifiers of the semicon-admittance formulas.

LineCableModels.Engine.SemiconAdmittance.Formula — Type

struct Formula{ID, O<:LineCableModels.Commons.FormulationOptions} <: LineCableModels.Engine.AbstractSemiconAdmittance

Represent an admittivity law for a semicon layer. Its options form a record of type FormulationOptions{Formula{ID}}, with ID the formula identifier.

options::LineCableModels.Commons.FormulationOptions: Options of the formula.

LineCableModels.Engine.SemiconAdmittance.Formula — Method

Formula(
    ::Val{ID};
    kw...
) -> LineCableModels.Engine.SemiconAdmittance.Formula

Build the formula named by ID with its declared defaults and supplied options.

Arguments

Val{ID}: formula identifier from FORMULAS.

Keywords

kw...: options declared by defaults for Formula{ID}.

Returns

A Formula with a typed option record.

Errors

Throws ArgumentError for an unknown identifier or option.

LineCableModels.Engine.admittivity — Method

admittivity(
    _::LineCableModels.Engine.SemiconAdmittance.Formula{:lossless},
    material::Material{T<:Real},
    f::Real
) -> Any

Return the admittivity of a semicon layer of material at the frequency f, by the formula Formula{:lossless}, whose equation is in the section "Formulas" of SemiconAdmittance.

Arguments

Formula{:lossless}: dielectric law without conduction or polarization loss.
material: material of the layer.
f: frequency [Hz].

Returns

Admittivity [S/m].

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