Mutual Inductor
Mutual inductor model with nominal inductance optional tolerances for each
winding, operating limits and faults
Description
The Mutual Inductor block lets you model a mutual
inductor (two-winding transformer) with nominal inductance tolerances for each winding.
The model includes the following effects:
You can turn these modeling options on and off independently of each other.
In the unfaulted state, the following equations describe the Mutual
Inductor block behavior:
where:
v1 and
v2 are voltages across the
primary and secondary winding, respectively.
L1 and
L2 are inductances of the
primary and secondary winding.
R1 and
R2 are series resistances of
the primary and secondary winding.
M is mutual inductance.
k is coefficient of coupling. To reverse one of the winding
directions, use a negative value.
t is time.
A parallel conductance is placed across the + and – terminals of the primary and
secondary windings, so that iL1 =
i1 –
G1v1, where G1 is the parallel
conductance of the primary winding, and i1 is
the terminal current into the primary. Similar definitions and equation apply to
iL2.
Tolerances
You can apply tolerances separately for each winding. Datasheets typically provide
a tolerance percentage for a given inductor type. Therefore, this value is the same
for both windings. The table shows how the block applies tolerances to the nominal
inductance value and calculates inductance based on the selected tolerance
application option for the winding, L1 tolerance application or
L2 tolerance application.
| Option | Inductance 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 nominal inductance for the primary or secondary
winding, Inductance L1 or Inductance
L2 parameter value.
tol is fractional tolerance, 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
Instantaneous changes in inductor parameters are unphysical. Therefore, when the
Mutual 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:
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 Mutual Inductor block lets you select whether
the faults occur in the primary or secondary winding. The block models the faulted
winding as a faulted inductor. The unfaulted winding is coupled to the faulted
winding. As a result, the actual equations involve a total of three coupled
windings: two for the faulted winding and one for the unfaulted winding. The
coupling between the primary and secondary windings is defined by the
Coefficient of coupling parameter.
The block can trigger the start of fault transition:
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.
Variables
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 Primary current and Secondary
current variables let you specify a high-priority target for the
initial inductor current in the respective winding at the start of simulation.
Ports
Conserving
expand all
1+ — Positive terminal of the primary winding
electrical
Electrical conserving port associated with the primary winding
positive terminal.
1- — Negative terminal of the primary winding
electrical
Electrical conserving port associated with the primary winding
negative terminal.
2+ — Positive terminal of the secondary winding
electrical
Electrical conserving port associated with the secondary winding
positive terminal.
2- — Negative terminal of the secondary winding
electrical
Electrical conserving port associated with the secondary winding
negative terminal.
Parameters
expand all
Main
Inductance L1 — Nominal inductance value in the primary winding
10
H (default)
The nominal inductance value in the primary winding. Inductance value
must be greater than zero.
Inductance L2 — Nominal inductance value in the secondary winding
0.1
H (default)
The nominal inductance value in the secondary winding. Inductance
value must be greater than zero.
Coefficient of coupling — Mutual inductance coupling between windings
0.9 (default)
The coupling between the primary and secondary windings. This
coefficient defines the mutual inductance. To reverse one of the winding
directions, use a negative value.
Tolerance (%) — Inductor tolerance, in percent
20 (default)
The inductor tolerance as defined on the manufacturer datasheet.
Datasheets typically provide a tolerance percentage for a given inductor
type. Therefore, this value is the same for both windings.
L1 tolerance application — Select how to apply tolerance to primary winding
None — use nominal
value (default) | Random tolerance | Apply maximum tolerance value | Apply minimum tolerance value
Select how to apply tolerance during simulation to the primary
winding:
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.
L1 tolerance distribution — Select the distribution type for primary winding
Uniform (default) | Gaussian
Select the distribution type for random tolerance:
Dependencies
Enabled when the L1 tolerance application
parameter is set to Random
tolerance.
L1 number of standard deviations for quoted tolerance — Used for calculating the Gaussian random number for primary winding
4 (default)
Number of standard deviations for calculating the Gaussian random
number.
Dependencies
Enabled when the L1 tolerance distribution
parameter is set to Gaussian.
L2 tolerance application — Select how to apply tolerance to secondary winding
None — use nominal
value (default) | Random tolerance | Apply maximum tolerance value | Apply minimum tolerance value
Select how to apply tolerance during simulation to the secondary
winding:
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.
L2 tolerance distribution — Select the distribution type for secondary winding
Uniform (default) | Gaussian
Select the distribution type for random tolerance:
Dependencies
Enabled when the L2 tolerance application
parameter is set to Random
tolerance.
L2 number of standard deviations for quoted tolerance — Used for calculating the Gaussian random number for secondary winding
4 (default)
Number of standard deviations for calculating the Gaussian random
number.
Dependencies
Enabled when the L2 tolerance distribution
parameter is set to Gaussian.
Resistance
Series resistance, [R_primary R_secondary] — Equivalent series resistance of the primary and secondary
winding
[0.001, 0.001]
Ohm (default)
Equivalent series resistance of the primary and secondary winding,
specified as a two-element vector. The first number corresponds to the
primary winding, the second number to the secondary winding. For a
faulted winding, the block allocates the resistance to each segment in
proportion to the number of turns in that segment.
Parallel conductance, [G_primary G_secondary] — Parallel leakage path associated with the primary and secondary winding
[1e-9,1e-9]
1/Ohm (default)
Parallel leakage path associated with the primary and secondary
winding, specified as a two-element vector. The first number corresponds
to the primary winding, the second number to the secondary winding. The
parallel conductances are placed directly across the + and – terminals
of the primary and secondary winding, respectively.
Operating Limits
Enable operating limits — Select Yes to enable reporting when the operational
limits are exceeded
No (default) | Yes
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.
Reporting when operating limits exceeded — Select the reporting method
Warn (default) | Error
Select what happens when an operating limit is exceeded:
Dependencies
Enabled when the Enable operating limits
parameter is set to Yes.
Saturation current — Inductor saturation current
1
A (default)
Inductor saturation current, as defined in the manufacturer
datasheets. If the net current into the primary and secondary windings
exceeds this value, the core material enters saturation, and the block
reports an operating limits violation. That is, the block compares the
limit against |i1 +
i2|, where currents are defined as being positive when
they are into the + nodes.
Dependencies
Enabled when the Enable operating limits
parameter is set to Yes.
Power rating — Maximum power dissipation in the inductor
1
A (default)
Maximum instantaneous (total) power dissipation in the resistance and
conductance elements associated with the mutual inductor. If the total
power (including both primary and secondary winding) exceeds this
number, the block reports an operating limits violation.
Dependencies
Enabled when the Enable operating limits
parameter is set to Yes.
Faults
Enable faults — Select Yes to enable faults modeling
No (default) | Yes
Select Yes 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.
Reporting when a fault occurs — Choose whether to issue an assertion when a fault occurs
None (default) | Warn | Error
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
Enabled when the Enable faults parameter is
set to Yes.
Faulted winding — Select winding to use for fault modeling
Primary (default) | Secondary
Select whether the faults occur in the primary or secondary
winding.
Dependencies
Enabled when the Enable faults parameter is
set to Yes.
Location of fault node (% of total turns from - terminal) — Percentage of turns in the subinductor that is in contact with the – port of the faulted winding
50 (default)
In practice, 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
Enabled when the Enable faults parameter is
set to Yes.
Short-circuit turns — Select whether fault results in one of the segments being short-circuited
No (default) | To negative terminal | To positive terminal
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
Enabled when the Enable faults parameter is
set to Yes.
Open-circuit at fault node — Select whether to apply an open-circuit fault between the segments
No (default) | Yes
Select whether to apply an open-circuit fault between the two
subinductor segments. The default is No. 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
Enabled when the Enable faults parameter is
set to Yes.
Ground fault — Select whether fault results in one of the segments being short-circuited
No (default) | Negative terminal side of fault
node | Positive terminal side of fault
node
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
Enabled when the Enable faults parameter is
set to Yes.
Conductance of faulted ground path — Mutual coupling between the two subinductors
0
1/Ohm (default)
If there is a ground fault, this parameter represents 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
Enabled when the Ground fault parameter is
set to Negative terminal side of fault
node or Positive terminal side of
fault node.
Fault transition time constant — Time constant for the transition to faulted state
1e-3
s (default)
Time constant associated with the transition to the faulted state, as
described in Faults.
Dependencies
Enabled when the Enable faults parameter is
set to Yes.
Enable temporal fault trigger — Select Yes to enable time-based fault triggering
No (default) | Yes
Select Yes to enable time-based fault triggering.
You can enable the temporal and behavioral trigger mechanisms separately
or use them together.
Dependencies
Enabled when the Enable faults parameter is
set to Yes.
Simulation time for fault event — Time before entering faulted state
1
s (default)
Set the simulation time at which you want the block to start entering
the fault state.
Dependencies
Enabled when the Enable temporal fault
trigger parameter is set to
Yes.
Enable behavioral fault trigger — Select Yes to enable behavioral fault triggering
No (default) | Yes
Select Yes to enable behavioral fault triggering.
You can enable the temporal and behavioral trigger mechanisms separately
or use them together.
Dependencies
Enabled when the Enable faults parameter is
set to Yes.
Maximum permissible voltage — Voltage threshold to fault transition
100
V (default)
Define the 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 starts entering the fault state.
Dependencies
Enabled when the Enable behavioral fault
trigger parameter is set to
Yes.
Number of events to fail when exceeding voltage — Maximum number of times the voltage exceeds the threshold
1 (default)
Because 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
Enabled when the Enable behavioral fault
trigger parameter is set to
Yes.
Maximum permissible current — Current threshold to fault transition
1
A (default)
Define the current threshold to a fault transition. If the current
value exceeds this threshold for longer than the Time to fail
when exceeding current parameter value, then the block
starts entering the fault state.
Dependencies
Enabled when the Enable behavioral fault
trigger parameter is set to
Yes.
Time to fail when exceeding current — Maximum length of time the current exceeds the threshold
1
s (default)
Set the maximum length of time that the current can exceed the maximum
permissible value without triggering the fault.
Dependencies
Enabled when the Enable behavioral fault
trigger parameter is set to
Yes.
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