Implement inductances with mutual coupling
Simscape / Electrical / Specialized Power Systems / Passives
The Mutual Inductance block can be used to model two or threewindings inductances with equal mutual coupling, or to model a generalized multiwindings mutual inductance with balanced or unbalanced mutual coupling.
If you choose to model two or threewindings inductances with equal mutual coupling, you specify the selfresistance 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, specify the number of selfwindings (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).
The resistance and inductance matrices are defined as
$$R=\left[\begin{array}{cc}R1& Rm\\ Rm& R2\end{array}\right]$$
and
$$L=\left[\begin{array}{cc}L1& Lm\\ Lm& L2\end{array}\right],$$
where:
R is the resistance.
R1 is the selfresistance of resistor R1.
R2 is the selfresistance of resistor R2.
Rm is the mutual resistance, such that $$Rm<R1$$ and $$Rm<R2$$.
L is the inductance.
L1 is the selfinductance of inductor L1.
L2 is the selfinductance of inductor L2.
Lm is the mutual inductance, such that $$Lm\le \sqrt{L1\cdot L2}$$
Select Two or Three windings with equal mutual terms
to
implement a threephase mutual inductance with equal mutual coupling between the windings.
This is the default.
The selfresistance and inductance for winding 1, in ohms (Ω) and henries (H). Default
is [1.1 1.1e03]
.
The selfresistance and inductance for winding 2, in ohms (Ω) and henries (H). Default
is [ 1.1 1.1e03]
.
If selected, implements three coupled windings; otherwise, it implements two coupled windings. Default is cleared.
The Winding 3 self
impedance parameter is not available if the Three windings Mutual
Inductance parameter is not selected. The selfresistance and inductance in ohms
(Ω) and henries (H) for winding 3. Default is [ 1.1 1.1e03]
.
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. Default is [1.0 1.0e03]
.
The mutual inductance can be expressed as a relationship between two self inductances as
L_{m} = k*sqrt(L_{1}*L_{2}),
where k is the coupling coefficient (−1 ≤ k ≤ 1).
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.
Default is None
.
Place a Multimeter block in your model to display the selected measurements during the simulation.
Select Generalized mutual inductance
to implement a multi
windings mutual inductance with mutual coupling defined by an inductance and a resistance
matrix.
The number of self inductances. Default is 3
.
The inductance matrix, in Henrys, that define the mutual coupling relationship between
the self windings. It must be a NbyN symmetrical matrix. Default is [1.0 0.9 0.9
; 0.9 1.0 0.9; 0.9 0.9 1.0 ] * 1e3
.
The resistance matrix, in ohms, that define the mutual coupling relationship between
the self windings. It must be a NbyN symmetrical matrix. Default is [1.0 0.9 0.9
; 0.9 1.0 0.9; 0.9 0.9 1.0 ]
.
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.
Default is None
.
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 

Winding currents 

If you choose to model two or three windings inductances with equal mutual coupling, the following restrictions apply:
R_{1}, R_{2}, ..., R_{N} ≠ R_{m}L_{1}, L_{2}, ..., L_{N}≠ L_{m}.
Negative values are allowed for the self and mutual inductances as long as the selfinductances 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.
The power_mutual
example
uses three coupled windings to inject a third harmonic voltage into a circuit fed at 60
Hz.