Inductor including optional tolerance, operational limits and fault behavior
Simscape / Electrical / Passive
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.
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.
Option | Inductance Value |
---|---|
| L |
| Uniform distribution: L · (1
– tol + 2· tol· Gaussian
distribution: L · (1 + tol · |
| L · (1 + tol ) |
| 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).
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.
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 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
You can enable or disable these trigger mechanisms separately, or use them together if more than one trigger mechanism is required in a simulation. When more than one mechanism is enabled, the first mechanism to trigger the fault transition takes precedence. In other words, a component fails no more than once per simulation.
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 inductors often require that you use the fixed-step local solver rather than the variable-step solver. In particular, if you model transitions to a faulted state that include short circuits, MathWorks recommends that you use the fixed-step local solver. For more information, see Making Optimal Solver Choices for Physical Simulation.
Use the Variables section of the block interface to set the priority and initial target values for the block variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables.
The Inductor current variable lets you specify a high-priority target for the initial inductor current at the start of simulation.
Capacitor | Fault | Mutual Inductor | Nonlinear Inductor | Resistor