LIBRARY

Analog.Basic.MTransformer

Generic transformer with N mutually coupled inductors.

Each inductor has a positive pin p[j] and negative pin n[j]. The voltage across each inductor depends on the rate of change of current in ALL inductors, coupled through the symmetric inductance matrix Lm:

$$v=Lm\cdot \frac{di}{dt}$$

The user supplies the upper-triangular entries of Lm as a flat vector L in row-major order:

L = [L_{11}, L_{12}, \ldots, L_{1N}, L_{22}, L_{23}, \ldots, L_{2N}, \ldots, L_{NN}]

with length N_L = N*(N+1)/2. The model constructs the full symmetric matrix internally via ElectricalComponents.build_inductance_matrix, guaranteeing Lm[j,k] = Lm[k,j].

For example, with N = 3 and L = [1, 0.1, 0.2, 2, 0.3, 3]:

$$Lm=\left[\begin{array}{ccc}1& 0.1& 0.2\\ 0.1& 2& 0.3\\ 0.2& 0.3& 3\end{array}\right]$$

Corresponds to Modelica.Electrical.Analog.Basic.M_Transformer.

Usage

ElectricalComponents.Analog.Basic.MTransformer(L=[1.0, 0.1, 0.2, 2.0, 0.3, 3.0], Lm=ElectricalComponents.build_inductance_matrix(L, N))

Parameters:

Name	Description	Units	Default value
N	Number of coupled inductors	–	3
N_L	Length of the inductance vector L, computed as N*(N+1)/2	–	div(N * (N + 1), 2)
L	Inductances and coupling inductances (upper-triangular, row-major)	–	[1, 0.1, 0.2, 2, 0.3, 3]

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 each inductor	V
i	Current through each inductor	A

Behavior

using ElectricalComponents #hide
using ModelingToolkit #hide
@variables L #hide
@named sys = ElectricalComponents.Analog.Basic.MTransformer(L=L) #hide
full_equations(sys) #hide

<< @example-block not executed in draft mode >>

Source

"""
Generic transformer with N mutually coupled inductors.

Each inductor has a positive pin `p[j]` and negative pin `n[j]`. The voltage
across each inductor depends on the rate of change of current in ALL inductors,
coupled through the symmetric inductance matrix `Lm`:

math v = Lm \cdot \frac{di}

The user supplies the upper-triangular entries of `Lm` as a flat vector `L`
in row-major order:

L = [L_{11}, L_{12}, \ldots, L_{1N}, L_{22}, L_{23}, \ldots, L_{2N}, \ldots, L_{NN}]

with length `N_L = N*(N+1)/2`. The model constructs the full symmetric matrix
internally via `ElectricalComponents.build_inductance_matrix`, guaranteeing
`Lm[j,k] = Lm[k,j]`.

For example, with `N = 3` and `L = [1, 0.1, 0.2, 2, 0.3, 3]`:

math Lm = \begin{bmatrix} 1 & 0.1 & 0.2 \ 0.1 & 2 & 0.3 \ 0.2 & 0.3 & 3 \end

Corresponds to `Modelica.Electrical.Analog.Basic.M_Transformer`.
"""
component MTransformer
  "Positive pins of each inductor"
  p = [Pin() for i in 1:N] {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -40, "y1": 450, "x2": 60, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Negative pins of each inductor"
  n = [Pin() for i in 1:N] {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 960, "y1": 450, "x2": 1060, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Number of coupled inductors"
  structural parameter N::Integer = 3
  "Length of the inductance vector L, computed as N*(N+1)/2"
  final structural parameter N_L::Integer = div(N * (N + 1), 2)
  "Inductances and coupling inductances (upper-triangular, row-major)"
  parameter L::Real[N_L] = [1.0, 0.1, 0.2, 2.0, 0.3, 3.0]
  "Complete symmetric inductance matrix, computed from L"
  final parameter Lm::Real[N, N] = ElectricalComponents.build_inductance_matrix(L, N)
  "Voltage across each inductor"
  variable v::Voltage[N]
  "Current through each inductor"
  variable i::Current[N]
relations
  # Port equations: voltage, current, and KCL for each inductor
  for j in 1:N
    v[j] = p[j].v - n[j].v
    0 = p[j].i + n[j].i
    i[j] = p[j].i
  end
  # Initial conditions on full array (avoid per-element AtomicArrayDict issue)
  initial i = zeros(N)
  # Inductance matrix equation
  v = Lm * der(i)
metadata {
  "Dyad": {
    "labels": [{"label": "$(instance)", "x": 500, "y": 100, "rot": 0}],
    "icons": {"default": "dyad://ElectricalComponents/MTransformer.svg"}
  }
}
end

Flattened Source

"""
Generic transformer with N mutually coupled inductors.

Each inductor has a positive pin `p[j]` and negative pin `n[j]`. The voltage
across each inductor depends on the rate of change of current in ALL inductors,
coupled through the symmetric inductance matrix `Lm`:

math v = Lm \cdot \frac{di}

The user supplies the upper-triangular entries of `Lm` as a flat vector `L`
in row-major order:

L = [L_{11}, L_{12}, \ldots, L_{1N}, L_{22}, L_{23}, \ldots, L_{2N}, \ldots, L_{NN}]

with length `N_L = N*(N+1)/2`. The model constructs the full symmetric matrix
internally via `ElectricalComponents.build_inductance_matrix`, guaranteeing
`Lm[j,k] = Lm[k,j]`.

For example, with `N = 3` and `L = [1, 0.1, 0.2, 2, 0.3, 3]`:

math Lm = \begin{bmatrix} 1 & 0.1 & 0.2 \ 0.1 & 2 & 0.3 \ 0.2 & 0.3 & 3 \end

Corresponds to `Modelica.Electrical.Analog.Basic.M_Transformer`.
"""
component MTransformer
  "Positive pins of each inductor"
  p = [Pin() for i in 1:N] {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -40, "y1": 450, "x2": 60, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Negative pins of each inductor"
  n = [Pin() for i in 1:N] {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 960, "y1": 450, "x2": 1060, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Number of coupled inductors"
  structural parameter N::Integer = 3
  "Length of the inductance vector L, computed as N*(N+1)/2"
  final structural parameter N_L::Integer = div(N * (N + 1), 2)
  "Inductances and coupling inductances (upper-triangular, row-major)"
  parameter L::Real[N_L] = [1.0, 0.1, 0.2, 2.0, 0.3, 3.0]
  "Complete symmetric inductance matrix, computed from L"
  final parameter Lm::Real[N, N] = ElectricalComponents.build_inductance_matrix(L, N)
  "Voltage across each inductor"
  variable v::Voltage[N]
  "Current through each inductor"
  variable i::Current[N]
relations
  # Port equations: voltage, current, and KCL for each inductor
  for j in 1:N
    v[j] = p[j].v - n[j].v
    0 = p[j].i + n[j].i
    i[j] = p[j].i
  end
  # Initial conditions on full array (avoid per-element AtomicArrayDict issue)
  initial i = zeros(N)
  # Inductance matrix equation
  v = Lm * der(i)
metadata {
  "Dyad": {
    "labels": [{"label": "$(instance)", "x": 500, "y": 100, "rot": 0}],
    "icons": {"default": "dyad://ElectricalComponents/MTransformer.svg"}
  }
}
end

Test Cases

No test cases defined.

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