# Inductor

Inductor including optional tolerance, operational limits and fault behavior

Libraries:
Simscape / Electrical / Passive

## Description

The Inductor block lets you model linear inductors, including the following effects:

You can turn these modeling options on and off independently of each other. When all the additional options are turned off, the component behavior is identical to the Simscape™ Foundation library Inductor block.

In its simplest form, the Inductor block models a linear inductor, described with the following equation:

`$V=L\frac{dI}{dt}$`

where:

• V is voltage.

• L is inductance.

• I is current.

• t is time.

To model a nonlinear inductor, use the Nonlinear Inductor block.

### Tolerances

You can apply tolerances to the nominal value you provide for the Inductance parameter. Datasheets typically provide a tolerance percentage for a given inductor type. The table shows how the block applies tolerances and calculates inductance based on the selected Tolerance application option.

OptionInductance Value

`None — use nominal value`

L

`Random tolerance`

Uniform distribution: L · (1 – tol + 2· tol· `rand`)

Gaussian distribution: L · (1 + tol · `randn` / nSigma)

`Apply maximum tolerance value`

L · (1 + tol )

`Apply minimum tolerance value`

L · (1 – tol )

In the table,

• L is the Inductance parameter value, nominal inductance.

• tol is fractional tolerance, Inductance tolerance (%) /100.

• nSigma is the value you provide for the Number of standard deviations for quoted tolerance parameter.

• `rand` and `randn` are standard MATLAB® functions for generating uniform and normal distribution random numbers.

Note

If you choose the `Random tolerance` option and you are in "Fast Restart" mode, the random tolerance value is updated on every simulation if at least one between the fractional tolerance, tol, or the Number of standard deviations for quoted tolerance, nSigma, is set to Run-time and is defined with a variable (even if you do not modify that variable).

### Operating Limits

Inductors are typically rated with a particular saturation current, and possibly with a maximum allowable power dissipation. You can specify operating limits in terms of these values, to generate warnings or errors if the inductor is driven outside its specification.

When an operating limit is exceeded, the block can either generate a warning or stop the simulation with an error. For more information, see the Operating Limits parameters section.

### Faults

To model a fault in the Inductor block, in the Faults section, click the Add fault hyperlink in the parameter that corresponds to the specific fault that you want to model. When the Create Fault window opens, you use it to specify the fault properties. For more information about fault modeling, see Fault Behavior Modeling and Fault Triggering.

Instantaneous changes in inductor parameters are unphysical. Therefore, when the Inductor 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` – (`FaultedValue``UnfaultedValue`) · `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 the voltage exceeds the maximum permissible value a certain number of times.

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

If you want to trigger a fault at a specific time, in the Fault Inspector window, set Trigger type to `Timed`. If you want to determine whether a system fails and, if so, when it fails, in the Fault Inspector window, set Trigger type to `Behavioral`.

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

Faultable inductors 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 before 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.

Use nominal values 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 these sources is the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

The Inductor current variable lets you specify a high-priority target for the initial inductor current at the start of simulation.

## Ports

### Conserving

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Electrical conserving port associated with the inductor positive terminal.

Electrical conserving port associated with the inductor negative terminal.

## Parameters

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### Main

Nominal inductance value. Inductance value must be greater than zero.

Inductor tolerance as defined on the manufacturer datasheet.

Select how to apply tolerance during simulation:

• `None — use nominal value` — The block does not apply tolerance, it uses the nominal inductance value.

• `Random tolerance` — The block applies random offset to the inductance value, within the tolerance value limit. You can choose Uniform or Gaussian distribution for calculating the random number by using the Tolerance distribution parameter.

• `Apply maximum tolerance value` — The inductance is increased by the specified tolerance percent value.

• `Apply minimum tolerance value` — The inductance is decreased by the specified tolerance percent value.

Select the distribution type for random tolerance:

• `Uniform` — Uniform distribution

• `Gaussian` — Gaussian distribution

#### Dependencies

Enabled when the Tolerance application parameter is set to `Random tolerance`.

Number of standard deviations for calculating the Gaussian random number.

#### Dependencies

Enabled when the Tolerance distribution parameter is set to `Gaussian`.

Equivalent series resistance (ESR) of the inductor, as sometimes specified on manufacturer datasheets. The default value is consistent with the Simscape Foundation library Inductor block. If you model faults, specify a positive value for this parameter.

Parallel leakage path associated with the inductor. Simulation of some circuits may require the presence of a small parallel conductance. You can also use this parameter to model the inductor core losses.

### Operating Limits

Select `Yes` to enable reporting when the operational limits are exceeded. The associated parameters in the Operating Limits section become visible to let you select the reporting method and specify the operating limits in terms of power and current.

Select what happens when an operating limit is exceeded:

• `Warn` — The block issues a warning.

• `Error` — Simulation stops with an error.

#### Dependencies

To enable this parameter, set Enable operating limits to `Yes`.

Inductor saturation current, as defined in the manufacturer datasheets. If the current exceeds this value, the core material enters saturation.

#### Dependencies

To enable this parameter, set Enable operating limits to `Yes`.

Maximum instantaneous power dissipation in the resistance and conductance elements associated with the inductor.

#### Dependencies

To enable this parameter, set Enable operating limits to `Yes`.

### Faults

Option to model a fault in the Inductor block.

In practice, faults are enabled by segmenting the inductor 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 block. The remaining turns are assigned to the other subinductor. The default value is `50`, which means that the overall inductance is divided into two equal, coupled subinductors.

#### Dependencies

To enable this parameter, add a fault to the Inductor block by clicking the Add fault hyperlink in the Inductor fault parameter.

After you create the fault, you can change the properties in the Fault Inspector window. When you open a block that has a fault, the Open Fault Inspector hyperlink appears instead of the Add fault hyperlink. For an example that shows how to include faults, see Analyze a DC Armature Winding Fault.

Faulted value for the mutual coupling between the two subinductors. The differential equations governing such a construction break down in the limit of perfect coupling, so the coupling should be less than unity. A value of `0` corresponds to no coupling at all between the subinductors. Physically, this corresponds to a fault that affects the flux within the inductor core. This could be a crack in the core material, or windings coming away from the core.

The default value of this parameter is also the internal value the block uses when computing a faultable inductor in the unfaulted state. For an unfaultable inductor, there is only a single equation being solved, and this corresponds to the ideal case of perfect mutual coupling.

#### Dependencies

To enable this parameter, add a fault to the Inductor block by clicking the Add fault hyperlink in the Inductor fault parameter.

After you create the fault, you can change the properties in the Fault Inspector window. When you open a block that has a fault, the Open Fault Inspector hyperlink appears instead of the Add fault hyperlink. For an example that shows how to include faults, see Analyze a DC Armature Winding Fault.

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, add a fault to the Inductor block by clicking the Add fault hyperlink in the Inductor fault parameter.

After you create the fault, you can change the properties in the Fault Inspector window. When you open a block that has a fault, the Open Fault Inspector hyperlink appears instead of the Add fault hyperlink. For an example that shows how to include faults, see Analyze a DC Armature Winding Fault.

Select whether to apply an open-circuit fault between the two subinductor segments. Even with an open-circuit fault, the characteristics of the subinductors may still be related, depending on the value of the Faulted coupling factor parameter:

• If the coupling factor is not zero, the subinductors are galvanically isolated from each other, but they are still magnetically coupled. Physically, this corresponds to a break in the winding.

• With zero coupling factor, the subinductors are galvanically and magnetically isolated.

#### Dependencies

To enable this parameter, add a fault to the Inductor block by clicking the Add fault hyperlink in the Inductor fault parameter.

After you create the fault, you can change the properties in the Fault Inspector window. When you open a block that has a fault, the Open Fault Inspector hyperlink appears instead of the Add fault hyperlink. For an example that shows how to include faults, see Analyze a DC Armature Winding Fault.

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 need to 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, add a fault to the Inductor block by clicking the Add fault hyperlink in the Inductor fault parameter.

After you create the fault, you can change the properties in the Fault Inspector window. When you open a block that has a fault, the Open Fault Inspector hyperlink appears instead of the Add fault hyperlink. For an example that shows how to include faults, see Analyze a DC Armature Winding Fault.

If there is a ground fault, this parameter represents the 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, add a fault to the Inductor block by clicking the Add fault hyperlink in the Inductor fault parameter and set Ground fault to `Negative terminal side of fault node` or `Positive terminal side of fault node`..

After you create the fault, you can change the properties in the Fault Inspector window. When you open a block that has a fault, the Open Fault Inspector hyperlink appears instead of the Add fault hyperlink. For an example that shows how to include faults, see Analyze a DC Armature Winding Fault.

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

#### Dependencies

To enable this parameter, add a fault to the Inductor block by clicking the Add fault hyperlink in the Inductor fault parameter.

After you create the fault, you can change the properties in the Fault Inspector window. When you open a block that has a fault, the Open Fault Inspector hyperlink appears instead of the Add fault hyperlink. For an example that shows how to include faults, see Analyze a DC Armature Winding Fault.

Simulation time at which the block enters the faulted state.

#### Dependencies

To enable this parameter, in the Fault Inspector window, set Trigger Type to `Timed`.

This parameter appears in the Trigger section of the Fault Inspector window. For more information, see Set Fault Triggers.

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, in the Fault Inspector window, set Trigger Type to `Behavioral`.

This parameter appears in the Trigger section of the Fault Inspector window. For more information, see Set Fault Triggers.

Since the physical mechanism underlying voltage-based failures depends on one or more partial discharge events occurring, this parameter allows you to set the number of voltage overshoots that the inductor can withstand before the fault transition begins. Note that the block does not check the time spent in the overvoltage condition, only the number of transitions.

#### Dependencies

To enable this parameter, in the Fault Inspector window, set Trigger Type to `Behavioral`.

This parameter appears in the Trigger section of the Fault Inspector window. For more information, see Set Fault Triggers.

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, in the Fault Inspector window, set Trigger Type to `Behavioral`.

This parameter appears in the Trigger section of the Fault Inspector window. For more information, see Set Fault Triggers.

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

#### Dependencies

To enable this parameter, in the Fault Inspector window, set Trigger Type to `Behavioral`.

This parameter appears in the Trigger section of the Fault Inspector window. For more information, see Set Fault Triggers.

## Version History

Introduced in R2016a

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