SaturatingInductor Icon

`SaturatingInductor`

Inductor model exhibiting magnetic saturation.

Represents an inductor where the inductance value decreases as the current increases, simulating the effect of magnetic core saturation. The model defines the inductance L_actual as a function of current i, transitioning from L_zero (inductance at zero current) to L_inf (inductance at large currents). The relationship between magnetic flux (\psi), current (i), and voltage (v) is governed by:

\[L_{actual} = L_{inf} + (L_{zero} - L_{inf}) \frac{atan(i/I_{par})}{i/I_{par}}\]

\[\psi = L_{inf}i + (L_{zero} - L_{inf})I_{par}atan(i/I_{par})\]

\[v = \frac{d\psi}{dt}\]

where I_par is a characteristic current derived from nominal values:

\[I_{par} = \frac{I_{nominal}}{tan(\frac{L_{nominal} - L_{inf}}{L_{zero} - L_{inf}})}\]

OnePort

Usage

SaturatingInductor(I_nominal=1, L_nominal=1, L_zero=2*L_nominal, L_inf=L_nominal/2, I_par=I_nominal/tan((L_nominal-L_inf)/(L_zero-L_inf)))

Parameters:

Name	Description	Units	Default value
`I_nominal`	Nominal operating current for defining saturation characteristics.	A	1
`L_nominal`	Inductance value at the nominal current I_nominal.	H	1
`L_zero`	Inductance value at or near zero current (maximum inductance).	H	2 * L_nominal
`L_inf`	Inductance value at large currents (fully saturated inductance, minimum inductance).	H	L_nominal / 2

Connectors

p - This connector represents an electrical pin with voltage and current as the potential and flow variables, respectively. (Pin)
n - This connector represents an electrical pin with voltage and current as the potential and flow variables, respectively. (Pin)

Variables

Name	Description	Units
`v`	Voltage across the component (between pin p and pin n).	V
`i`	Current flowing through the component (from pin p to pin n).	A
`L_actual`	The actual current-dependent inductance of the component (psi/i).	H
`psi`	The magnetic flux linking the inductor windings.	Wb

Behavior

\[ \begin{align} v\left( t \right) &= \mathtt{p.v}\left( t \right) - \mathtt{n.v}\left( t \right) \\ i\left( t \right) &= \mathtt{p.i}\left( t \right) \\ \mathtt{n.i}\left( t \right) + \mathtt{p.i}\left( t \right) &= 0 \\ \mathtt{L\_actual}\left( t \right) &= \mathtt{L\_inf} + \frac{\mathtt{I\_par} \left( - \mathtt{L\_inf} + \mathtt{L\_zero} \right) \arctan\left( \frac{i\left( t \right)}{\mathtt{I\_par}} \right)}{i\left( t \right)} \\ \mathtt{psi}\left( t \right) &= \mathtt{L\_inf} i\left( t \right) + \mathtt{I\_par} \left( - \mathtt{L\_inf} + \mathtt{L\_zero} \right) \arctan\left( \frac{i\left( t \right)}{\mathtt{I\_par}} \right) \\ v\left( t \right) &= \frac{\mathrm{d} \mathtt{psi}\left( t \right)}{\mathrm{d}t} \end{align} \]

Source

# Inductor model exhibiting magnetic saturation.
#
# Represents an inductor where the inductance value decreases as the current increases,
# simulating the effect of magnetic core saturation. The model defines the inductance
# `L_actual` as a function of current `i`, transitioning from `L_zero` (inductance at
# zero current) to `L_inf` (inductance at large currents). The relationship between
# magnetic flux (`\psi`), current (`i`), and voltage (`v`) is governed by:
# ```math
# L_{actual} = L_{inf} + (L_{zero} - L_{inf}) \frac{atan(i/I_{par})}{i/I_{par}}
# ```
# ```math
# \psi = L_{inf}i + (L_{zero} - L_{inf})I_{par}atan(i/I_{par})
# ```
# ```math
# v = \frac{d\psi}{dt}
# ```
# where `I_par` is a characteristic current derived from nominal values:
# ```math
# I_{par} = \frac{I_{nominal}}{tan(\frac{L_{nominal} - L_{inf}}{L_{zero} - L_{inf}})}
# ```
component SaturatingInductor
  extends OnePort
  # Nominal operating current for defining saturation characteristics.
  parameter I_nominal::Current = 1
  # Inductance value at the nominal current I_nominal.
  parameter L_nominal::Inductance = 1
  # Inductance value at or near zero current (maximum inductance).
  parameter L_zero::Inductance = 2*L_nominal
  # Inductance value at large currents (fully saturated inductance, minimum inductance).
  parameter L_inf::Inductance = L_nominal/2
  # The actual current-dependent inductance of the component (psi/i).
  variable L_actual::Inductance
  # The magnetic flux linking the inductor windings.
  variable psi::MagneticFlux
  # Characteristic current parameter used in the saturation function, derived from other inductance and current parameters.
  final parameter I_par::Current = I_nominal/tan((L_nominal-L_inf)/(L_zero-L_inf))
relations
  # assert L_zero > L_nominal "L_zero $(L_zero) should be greater than L_nominal $(L_nominal)"
  # assert L_inf < L_nominal "Linf $(Linf) should be less than L_nominal $(L_nominal)"
  L_actual = L_inf+(L_zero-L_inf)*atan(i/I_par)/(i/I_par)
  psi = L_inf*i+(L_zero-L_inf)*I_par*atan(i/I_par)
  v = der(psi)
end

Flattened Source

# Inductor model exhibiting magnetic saturation.
#
# Represents an inductor where the inductance value decreases as the current increases,
# simulating the effect of magnetic core saturation. The model defines the inductance
# `L_actual` as a function of current `i`, transitioning from `L_zero` (inductance at
# zero current) to `L_inf` (inductance at large currents). The relationship between
# magnetic flux (`\psi`), current (`i`), and voltage (`v`) is governed by:
# ```math
# L_{actual} = L_{inf} + (L_{zero} - L_{inf}) \frac{atan(i/I_{par})}{i/I_{par}}
# ```
# ```math
# \psi = L_{inf}i + (L_{zero} - L_{inf})I_{par}atan(i/I_{par})
# ```
# ```math
# v = \frac{d\psi}{dt}
# ```
# where `I_par` is a characteristic current derived from nominal values:
# ```math
# I_{par} = \frac{I_{nominal}}{tan(\frac{L_{nominal} - L_{inf}}{L_{zero} - L_{inf}})}
# ```
component SaturatingInductor
  # Positive electrical pin.
  p = Pin() [{
    "Dyad": {
      "placement": {"icon": {"iconName": "pos", "x1": -50, "y1": 450, "x2": 50, "y2": 550}}
    }
  }]
  # Negative electrical pin.
  n = Pin() [{
    "Dyad": {
      "placement": {"icon": {"iconName": "neg", "x1": 950, "y1": 450, "x2": 1050, "y2": 550}}
    }
  }]
  # Voltage across the component (between pin p and pin n).
  variable v::Voltage
  # Current flowing through the component (from pin p to pin n).
  variable i::Current
  # Nominal operating current for defining saturation characteristics.
  parameter I_nominal::Current = 1
  # Inductance value at the nominal current I_nominal.
  parameter L_nominal::Inductance = 1
  # Inductance value at or near zero current (maximum inductance).
  parameter L_zero::Inductance = 2*L_nominal
  # Inductance value at large currents (fully saturated inductance, minimum inductance).
  parameter L_inf::Inductance = L_nominal/2
  # The actual current-dependent inductance of the component (psi/i).
  variable L_actual::Inductance
  # The magnetic flux linking the inductor windings.
  variable psi::MagneticFlux
  # Characteristic current parameter used in the saturation function, derived from other inductance and current parameters.
  final parameter I_par::Current = I_nominal/tan((L_nominal-L_inf)/(L_zero-L_inf))
relations
  v = p.v-n.v
  i = p.i
  p.i+n.i = 0
  # assert L_zero > L_nominal "L_zero $(L_zero) should be greater than L_nominal $(L_nominal)"
  # assert L_inf < L_nominal "Linf $(Linf) should be less than L_nominal $(L_nominal)"
  L_actual = L_inf+(L_zero-L_inf)*atan(i/I_par)/(i/I_par)
  psi = L_inf*i+(L_zero-L_inf)*I_par*atan(i/I_par)
  v = der(psi)
metadata {}
end

Test Cases

No test cases defined.

Examples
Experiments
Analyses
Tests
- SaturatingInductorTest