Mutual Inductor

Mutual inductor in electrical systems

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Libraries:
Simscape / Foundation Library / Electrical / Electrical Elements

Description

The Mutual Inductor block models a mutual inductor, described with the following equations:

$$V1=L1\frac{dI1}{dt}+M\frac{dI2}{dt}$$

$$V2=L2\frac{dI2}{dt}+M\frac{dI1}{dt}$$

$$M=k\sqrt{L1·L2}$$

where:

• V1 is the voltage across the primary winding.

• V2 is the voltage across the secondary winding.

• I1 is the current flowing into the + terminal of the primary winding.

• I2 is the current flowing out of the + terminal of the secondary winding.

• L1, L2 are the winding self-inductances.

• M is the mutual inductance.

• k is the coefficient of coupling, 0 < k < 1.

• t is time.

The two electrical networks connected to the primary and secondary windings must each have their own Electrical Reference block.

Use this block to represent an AC transformer. If inductance and mutual inductance terms are not important in a model, or are unknown, you can use the Ideal Transformer block instead.

Simscape™ and Simscape Electrical™ libraries include several blocks than can model the same type of transformer device. However, these blocks make different modeling assumptions. To choose the right block for your application, you must understand how these assumptions impact the block behavior as a function of frequency. For more information, see Choose Blocks to Model Transformers (Simscape Electrical).

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Examples

A Comparison of the Mutual Inductor and Ideal Transformer Library Blocks

The differences in behavior between the Mutual Inductor and Ideal Transformer blocks in the Simscape™ Foundation Library. These two blocks both represent the same system of electromagnetically-coupled windings but make different simplifying assumptions. It is important to understand the assumptions and how they impact model fidelity as a function of frequency. With this, you can make an informed decision about which block to use in a model of your circuit.

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Ports

Conserving

1+ — Primary winding positive terminal

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Electrical conserving port associated with the positive terminal of the primary winding.

1- — Primary winding negative terminal

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Electrical conserving port associated with the negative terminal of the primary winding.

2+ — Secondary winding positive terminal

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Electrical conserving port associated with the positive terminal of the secondary winding.

2- — Secondary winding negative terminal

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Electrical conserving port associated with the negative terminal of the secondary winding.

Parameters

Inductance L1 — Self-inductance of primary winding

10 H (default) | positive scalar

Self-inductance of the primary winding.

Inductance L2 — Self-inductance of secondary winding

0.1 H (default) | positive scalar

Self-inductance of the secondary winding.

Perfect coupling – no leakage — Use ideal mutual inductor

Off (default) | On

If you select this checkbox, the block sets the coefficient of coupling to 1 and the leakage reluctances to 0. In this case, the block represents the ideal mutual inductor with no leakages and no fast pole, while also retaining the correct low-frequency behavior, blocking DC.

Coefficient of coupling — Coefficient of coupling for mutual inductance

0.9 (default) | scalar in the range (0,1)

Coefficient of coupling, which defines the mutual inductance. The parameter value should be greater than zero and less than 1. Avoid setting this parameter to values close to 1 (such as 0.9999) because that can introduce fast simulation dynamics.

Dependencies

To enable this parameter, clear the Perfect coupling – no leakage check box.

Extended Capabilities

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

Version History

Introduced in R2007a