# Mutual Inductance

Implement inductances with mutual coupling

## Library

Fundamental Blocks/Elements

## Description

The Mutual Inductance block can be used to model two- or three-windings inductances with equal mutual coupling, or to model a generalized multi-windings mutual inductance with balanced or unbalanced mutual coupling.

If you choose to model two- or three-windings inductances with equal mutual coupling, you specify the self-resistance and inductance of each winding plus the mutual resistance and inductance. The electrical model for this block in this case is given below:

If you choose to model a general mutual inductance, you need to specify the number of self windings (not just limited to 2 or 3 windings) plus the Resistance and Inductance matrices that define the mutual coupling relationship between the windings (balanced or not).

## Dialog Box and Parameters

### Two or three windings inductances with equal mutual coupling:

Type of mutual inductance

Set to Two or Three windings with equal mutual terms to implement a three-phase mutual inductance with equal mutual coupling between the windings

Winding 1 self impedance

The self-resistance and inductance for winding 1, in ohms (Ω) and henries (H).

Winding 2 self impedance

The self-resistance and inductance for winding 2, in ohms (Ω) and henries (H).

Three windings Mutual Inductance

If selected, implements three coupled windings; otherwise, it implements two coupled windings.

Winding 3 self impedance

The Winding 3 self impedance parameter is not available if the Three windings Mutual Inductance parameter is not selected. The self-resistance and inductance in ohms (Ω) and henries (H) for winding 3.

Mutual impedance

The mutual resistance and inductance between windings, in ohms (Ω) and henries (H). The mutual resistance and inductance corresponds to the magnetizing resistance and inductance on the standard transformer circuit diagram. If the mutual resistance and reactance are set to ```[0 0]```, the block implements three separate inductances with no mutual coupling.

### Generalized mutual inductance:

Type of mutual inductance

Set to Generalized mutual inductance to implement a multi windings mutual inductance with mutual coupling defined by an inductance and a resistance matrix.

Number of windings

The number of self inductances.

Inductance matrix L

The inductance matrix, in Henrys, that define the mutual coupling relationship between the self windings. It must be a N-by-N symmetrical matrix.

Resistance matrix R

The resistance matrix, in ohms, that define the mutual coupling relationship between the self windings. It must be a N-by-N symmetrical matrix.

Measurements

Select `Winding voltages` to measure the voltage across the winding terminals.

Select `Winding currents` to measure the current flowing through the windings.

Select `Winding voltages and currents` to measure the winding voltages and currents.

Place a Multimeter block in your model to display the selected measurements during the simulation.

In the Available Measurements list box of the Multimeter block, the measurements are identified by a label followed by the block name.

Measurement

Label

Winding voltages

`Uw1:, Uw2:, Uw3:`

Winding currents

`Iw1:, Iw2:, Iw3:`

## Limitations

If you choose to model two or three windings inductances with equal mutual coupling , the following restrictions apply:

R1, R2, ..., RNRm
L1, L2, ..., LNLm.

Negative values are allowed for the self- and mutual inductances as long as the self-inductances are different from the mutual inductance.

Windings can be left floating (not connected by an impedance to the rest of the circuit). However an internal resistor between the floating winding and the main circuit is automatically added. This internal connection does not affect voltage and current measurements.

## Example

The `power_mutual``power_mutual` example uses three coupled windings to inject a third harmonic voltage into a circuit fed at 60 Hz.

Simulation produces the following load voltage waveform: