Winding

Electromagnetic converter with ohmic and magnetic flux losses

Library:
Simscape / Electrical / Passive

Description

The Winding block represents an electromagnetic converter with winding resistance and leakage reluctance. You can use this block as a base component for building custom transformers. For an ideal electromagnetic converter, see the Electromagnetic Converter.

When you apply a positive current across the electrical ports of the block, a positive magnetomotive force (MMF) is induced across the magnetic terminals.

$F = N i$

Where:

ℱ is the MMF across the magnetic terminals of the block
N is the number of winding turns
i is the current through the winding

When you apply a positive time-varying flux across the magnetic terminals of the block, a negative voltage is induced across the electrical terminals of the block.

$v = - N \frac{d ϕ}{d t} + \frac{N^{2}}{R_{l}} \frac{d i}{d t} + R_{w} i$

Where:

φ is the flux through the magnetic terminals of the block
i is the current through the electrical terminals of the block
ℛ_l is the leakage reluctance
R_w is the winding resistance
ℱ is the magnetomotive force across the magnetic terminals of the block
v is the voltage drop across the electrical terminals of the block

This figure shows the equivalent circuit for the block.

In the diagram, φ_mp corresponds to the main-path flux, or the flux through the main winding. You can set the initial condition for this flux in the block's Variables tab.

Ports

Conserving

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`+` — Positive terminal
electrical

Electrical conserving port associated with the positive terminal of the block.

`-` — Negative terminal
electrical

Electrical conserving port associated with the negative terminal of the block.

`N` — North terminal
magnetic

Magnetic conserving port associated with the north terminal of the block.

`S` — South terminal
magnetic

Magnetic conserving port associated with the south terminal of the block.

Parameters

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`Number of winding turns` — Winding turn count
`10` (default) | positive number

Number of wire turns on the transformer winding.

`Winding resistance` — Series resistance
`1e-3` `Ohm` (default) | positive number

Power loss in the winding.

`Leakage reluctance` — Parallel reluctance
`1e5` `1/H` (default) | positive number

Magnetic flux loss in the winding.

Model Examples

Three-Phase Custom Zigzag Transformer

Two different ways to create a custom transformer component. The first uses built-in library blocks to lay out the magnetic circuit as a masked Simulink® subsystem. The second builds a custom Simscape™ component using the Simscape language.

Push-Pull Buck Converter in Continuous Conduction Mode

Control the output voltage of a push-pull buck converter. The current flowing through the inductor is never zero, therefore the DC-DC converter operates in Continuous Conduction Mode (CCM). To convert and maintain the nominal output voltage, the PI Controller subsystem uses a simple integral control. During startup, the reference voltage is ramped up to the desired output voltage.

Push-Pull Buck Converter in Discontinuous Conduction Mode

Control the output voltage of a push-pull buck converter. The current flowing through the inductor reaches zero during the switch off cycle of the MOSFETs and therefore the DC-DC converter operates in Discontinuous Conduction Mode (DCM). This mode of conduction is mostly used for low-power applications. To convert and maintain the input DC voltage as a nominal output voltage, the PI Controller subsystem uses a simple integral control. During startup, the reference voltage is ramped up to the desired output voltage.

Documentation

Winding

Description