# Winding

Electromagnetic converter with ohmic and magnetic flux losses

Libraries:
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.

$\mathcal{F}=Ni$

Where:

• 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.

$v=-N\frac{d\varphi }{dt}+\frac{{N}^{2}}{{\mathcal{R}}_{l}}\frac{di}{dt}+{R}_{w}i$

Where:

• φ is the flux through the magnetic terminals of the block

• i is the current through the electrical terminals of the block

• l is the leakage reluctance

• Rw is the winding resistance

• 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, φmp corresponds to the main-path flux and φ to the total flux. You can set the initial condition for the total flux in the block's Variables tab.

### Faults

Instantaneous changes in the winding parameters are unphysical. Therefore, when the Winding block enters the faulted state, short-circuit and open-circuit voltages transition to their faulted values over a period of time based on this formula:

CurrentValue = FaultedValue – (FaultedValueUnfaultedValue) · sech(∆t / τ)

where:

• ∆t is time since the onset of the fault condition.

• τ is user-defined time constant associated with the fault transition.

For short-circuit faults, the conductance of the short-circuit path also changes according to the sech(∆t / τ) function from a small value (representing an open-circuit path) to a large value.

The block can trigger the start of fault transition:

• At a specific time.

• After voltage exceeds the maximum permissible value a certain number of times.

• When current exceeds the maximum permissible value for longer than a specific time interval.

If you want to trigger a fault at a specific time, set the Fault trigger parameter to Temporal. If you want to determine whether a system fails and, if so, when it fails, set the Fault Trigger parameter to Behavioral.

If you select the behavioral trigger, the component fails as soon as one of the trigger conditions is true.

You can also choose whether to issue an assertion when a fault occurs, by using the Reporting when a fault occurs parameter. The assertion can take the form of a warning or an error. By default, the block does not issue an assertion.

Faultable windings often require that you use the fixed-step local solver, especially if your model transitions to a faulted state that includes short circuits. For more information, see Making Optimal Solver Choices for Physical Simulation.

### 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 System Scaling by Nominal Values.

## Ports

### Conserving

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

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

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

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

## Parameters

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### Main

Number of wire turns on the transformer winding.

Power loss in the winding.

Magnetic flux loss in the winding. If you do not want to model the leakage internally to the Winding block, set this parameter to inf.

Parallel leakage path, Simulation of some circuits may require the presence of a small parallel conductance.

### Thermal Port

Whether to model the thermal port of the winding. The thermal port reports the winding resistance losses.

The temperature for which the winding parameters are quoted.

#### Dependencies

To enable this parameter, set Thermal port to Model.

Coefficient α in the equation relating resistance to temperature, as described in Thermal Model for Actuator Blocks. The default value is for copper.

#### Dependencies

To enable this parameter, set Thermal port to Model.

The thermal mass value for the winding. The thermal mass is the energy required to raise the temperature by one degree.

#### Dependencies

To enable this parameter, set Thermal port to Model.

### Faults

Whether to enable faults modeling. The associated parameters in the Faults section become visible to let you select the reporting method and specify the trigger mechanism (temporal or behavioral). You can enable these trigger mechanisms separately or use them together.

Faults are enabled by segmenting the faulted winding into two coupled subinductors, connected in a series. The inductance is proportional to the square of the number of turns in the respective segment, and the series resistance of each subinductor is proportional to the number of turns in each segment. The parallel conductance spans both segments.

This parameter indicates the percentage of turns that are assigned to the subinductor that is in contact with the port of the faulted winding. The remaining turns are assigned to the other subinductor. The default value is 50, which means that the overall inductance of the faulted winding is divided into two equal, coupled subinductors.

#### Dependencies

To enable this parameter, set Enable faults to On.

Choose whether to issue an assertion when a fault occurs:

• None — The block does not issue an assertion.

• Warn — The block issues a warning.

• Error — Simulation stops with an error.

#### Dependencies

To enable this parameter, set Enable faults to On.

Select whether the fault results in one of the subinductor segments being short-circuited:

• No — The fault does not produce a short circuit.

• To negative terminal — The fault short-circuits the subinductor that is in contact with the port of the block.

• To positive terminal — The fault short-circuits the subinductor that is in contact with the + port of the block.

#### Dependencies

To enable this parameter, set Enable faults to On.

Select whether to apply an open-circuit fault between the two subinductor segments. Even with an open-circuit fault, the characteristics of the subinductors are still related because they are magnetically coupled even in the faulted state.

#### Dependencies

To enable this parameter, set Enable faults to On.

Select whether, in case of fault, there is a path for current to flow towards the ground node:

• No — The fault does not result in a connection to ground.

• Negative terminal side of fault node — The side that is in contact with the port of the block is connected to ground.

• Positive terminal side of fault node — The side that is in contact with the + port of the block is connected to ground.

If the Open-circuit at fault node parameter is set to Yes, you must specify which side (negative or positive) is connected to ground. If there is no open circuit, the two options behave similarly. Physically, this corresponds to a breakdown in the insulation between the windings and the grounded core or chassis.

#### Dependencies

To enable this parameter, set Enable faults to On.

Conductance of the current path to ground. For example, if the path to ground is through the core material, then specify a small conductance value depending on the core material being used. For highly conductive core material or for chassis-shorts, specify a higher conductance value.

#### Dependencies

To enable this parameter, set Ground fault to Negative terminal side of fault node or Positive terminal side of fault node.

Time constant associated with the transition to the faulted state, as described in Faults.

#### Dependencies

To enable this parameter, set Enable faults to On.

Since R2023a

Set this parameter to Temporal to enable time-based fault triggering.

Set this parameter to Behavioral to enable behavioral fault triggering.

#### Dependencies

To enable this parameter, set Enable faults to On.

Simulation time at which the block enters the faulted state.

#### Dependencies

To enable this parameter, set Fault trigger to Temporal.

Voltage threshold to a fault transition. If the voltage value exceeds this threshold a certain number of times, specified by the Number of events to fail when exceeding voltage parameter value, then the block enters the fault state.

#### Dependencies

To enable this parameter, set Fault trigger to Behavioral.

Number of voltage overshoots that the inductor can withstand before the fault transition begins. This block does not check the time spent in the overvoltage condition, only the number of transitions.

#### Dependencies

To enable this parameter, set Fault trigger to Behavioral.

Current threshold to a fault transition. If the current exceeds this value for longer than the Time to fail when exceeding current parameter value, then the block enters the faulted state.

#### Dependencies

To enable this parameter, set Fault trigger to Behavioral.

Maximum length of time that the current can exceed the maximum permissible value without triggering the fault.

#### Dependencies

To enable this parameter, set Fault trigger to Behavioral.

## Version History

Introduced in R2018a

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