Three-Winding Mutual Inductor

Three coupled inductors

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• Simscape / Electrical / Passive / Transformers

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Description

The Three-Winding Mutual Inductor block represents a set of three coupled inductors or windings. The voltage across the three windings is

$$\begin{array}{l}{V}_1=L_1\frac{d{I}_1}{dt}+M_{12}\frac{d{I}_2}{dt}+M_{13}\frac{d{I}_3}{dt}\\ V_2=M_{12}\frac{d{I}_1}{dt}+L_2\frac{d{I}_2}{dt}+M_{23}\frac{d{I}_3}{dt}\\ V_3=M_{13}\frac{d{I}_1}{dt}+M_{23}\frac{d{I}_2}{dt}+L_3\frac{d{I}_3}{dt}\end{array}$$

where:

• V_i is voltage across the ith winding.

• I_i is current through the ith winding.

• L_i is self inductance of the ith winding.

• M_ij is mutual inductance of the ith and jth windings, $$M_{ij}=K_{ij}\sqrt{L_i{L}_j}$$.

In the preceding equations, currents are positive when flowing into the positive node of their respective inductor terminals.

When you run a simulation that includes this block, the software checks the specified parameter values to ensure that the resulting device is passive. If it is not, the software issues an error.

Ports

Conserving

1+ — First inductor positive voltage

electrical

Electrical conserving port associated with the positive voltage of the first mutual inductor.

1- — First inductor negative voltage

electrical

Electrical conserving port associated with the negative voltage of the first mutual inductor.

2+ — Second inductor positive voltage

electrical

Electrical conserving port associated with the positive voltage of the second mutual inductor.

2- — Second inductor negative voltage

electrical

Electrical conserving port associated with the negative voltage of the second mutual inductor.

3+ — Third inductor positive voltage

electrical

Electrical conserving port associated with the positive voltage of the third mutual inductor.

3- — Third inductor negative voltage

electrical

Electrical conserving port associated with the negative voltage of the third mutual inductor.

Parameters

Inductance L1 — First winding self inductance

0.001 H (default)

Self inductance of the first winding.

Inductance L2 — Second winding self inductance

0.001 H (default)

Self inductance of the second winding.

Inductance L3 — Third winding self inductance

0.001 H (default)

Self inductance of the third winding.

Coefficient of coupling, K12 — Coefficient of coupling between the first and second windings

0.9 (default)

Coefficient that defines the mutual inductance between the first and second windings. The absolute value must be between 0 and 1, exclusive.

Coefficient of coupling, K13 — Coefficient of coupling between the first and third windings

0.9 (default)

Coefficient that defines the mutual inductance between the first and third windings. The absolute value must be between 0 and 1, exclusive.

Coefficient of coupling, K23 — Coefficient of coupling between the second and third windings

0.9 (default)

Coefficient that defines the mutual inductance between the second and third windings. The absolute value must be between 0 and 1, exclusive.

Specify initial condition? — Initial condition option

No (default) | Yes

Select one of the following options for specifying an initial condition:

• No — Do not specify an initial condition for the model. This is the default option.

• Yes — Specify the initial inductor currents.

Initial current port 1, IC1 — First winding initial current

0 A (default)

The current flowing through the first winding at the start of the simulation.

Dependencies

This parameter is visible only when you select Yes for the Specify initial condition parameter.

Initial current port 2, IC2 — Second winding initial current

0 A (default)

The current flowing through the second winding at the start of the simulation.

Dependencies

This parameter is visible only when you select Yes for the Specify initial condition parameter.

Initial current port 3, IC3 — Third winding initial current

0 A (default)

The current flowing through the third winding at the start of the simulation.

Dependencies

This parameter is visible only when you select Yes for the Specify initial condition parameter.

Model Examples

DC-DC LLC Converter

A DC-DC LLC power converter with frequency control. A simple integral control is implemented in Simulink® in the Controller block, and is designed to achieve a nominal output voltage defined by the variable Vout_nominal. The Output scope shows the frequency control signal, the output voltage, and the reference value for the output voltage. During startup, the reference value is ramped up to its desired setpoint. The design of the LLC powertrain is computed automatically using the first harmonic approximation.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.