Capacitor (Advanced)

A linear or non-linear capacitor that takes into account the capacitance error.

blockType: AcausalElectricPowerSystems.Passive.Capacitor

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/Physical Modeling/Electrical/Passive/Capacitor (Advanced)

Description

Block Capacitor (Advanced) It allows you to model linear, nonlinear (specified by tabular characteristics) and frequency-dependent capacitors that take into account the error.

When a linear capacitor is modeled and the capacitance error is not taken into account, the behavior of the component is identical to the block Capacitor.

In its simplest form, the block Capacitor (Advanced) simulates a linear capacitor described by the following equation:

where

— current;
— capacity;
— tension;
— the time.

To simulate a nonlinear or polar capacitor, set the parameter Capacitance model meaning Lookup table and fill in the table of voltage-capacity values:

For polar capacitors, this reference table is asymmetric with respect to the applied terminal voltage, uncheck the option Symmetric C-V table.

For other types of nonlinear capacitors, the symmetry of the capacitance table relative to the applied voltage at the terminals is ensured by setting a flag for the parameter Symmetric C-V table.

To simulate a frequency-dependent capacitor with ohmic and dielectric losses, set the parameter Capacitance model meaning Dielectric relaxation (Debye). The Debye relaxation model considers a set of non-interacting dipoles in the frequency domain. The result is expressed in the complex dielectric constant. Valid ( ) and imaginary ( ) the parts of the complex dielectric constant are given by the equations:

where

— radial frequency;
— real permeability at very high frequency;
— real permeability at low frequency;
— constant relaxation time.

In the time domain, the characteristic equation for a capacitor in the Debye model has the form

where

— low frequency capacity;
;
— charge;
— current;
— voltage across the capacitor.

Most specifications do not specify explicit values of the complex permeability and relaxation time, however, the tangent of the dielectric loss angle at two frequencies is often given. Parameters and can be derived from these values as described in the equations:

where

and — two different frequencies;
and — dissipation coefficients calculated at the specified frequencies, respectively.

For the Debye model to be adjusted correctly, the square root argument must be positive.

Errors

You can add the error to the nominal value set for the parameter. Capacitance. Such an error is usually indicated in the technical descriptions. The table shows how the unit applies the error and calculates the capacity depending on the selected parameter value. Tolerance application.

Parameter value Tolerance application The value of the inductance

Parameter value Tolerance application	The value of the inductance
`None - use nominal value`
`Random tolerance`	Uniform distribution: Normal distribution:
`Apply maximum tolerance value`
`Apply minimum tolerance value`

None - use nominal value

Random tolerance

Uniform distribution:

Normal distribution:

Apply maximum tolerance value

Apply minimum tolerance value

In the table:

— nominal capacity, parameter value Capacitance;
— error, parameter value Tolerance (%)/100;
— parameter value Number of standard deviations for quoted tolerance;
and — standard functions for generating random numbers with uniform and normal distribution.

Variables

Use the parameter group Initial Targets to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

Ports

Conserving

# + — positive
electricity

Details

The electrical port is a positive terminal.

Program usage name

p

# – — negative
electricity

Details

The electrical port represents the negative terminal.

Program usage name

n

Parameters

Main

# Capacitance model — type of capacitor
Constant | Lookup table | Dielectric relaxation (Debye)

Details

Select the type of capacitor:

Constant — a linear capacitor with a nominal capacity set by the parameter value Capacitance.
Lookup table — a nonlinear capacitor, where the nominal value of the capacitance varies depending on the value of the applied voltage at the terminals.
Dielectric relaxation (Debye) — frequency-dependent capacitor with ohmic and dielectric losses.

Values	`Constant` \| `Lookup table` \| `Dielectric relaxation (Debye)`
Default value	`Constant`
Program usage name	`capacitance_model_type`
Evaluatable	No

# Capacitance — nominal capacity value
F | pF | nF | uF | mF

Details

The nominal value of the capacitance for a linear capacitor or the low-frequency capacitance in the Debye parameterization.

Dependencies

To use this parameter, set for the parameter Capacitance model meaning Constant or Dielectric relaxation (Debye).

Units	`F` \| `pF` \| `nF` \| `uF` \| `mF`
Default value	`1e-6 F`
Program usage name	`C_nominal`
Evaluatable	Yes

# Capacitance values — vector of capacity values
F | pF | nF | uF | mF

Details

A vector of capacitance values to search in the table by the corresponding voltage value. The length of the vector must be the same as the length of the vector of voltage values.

Dependencies

To use this parameter, set for the parameter Capacitance model meaning Lookup table.

Units	`F` \| `pF` \| `nF` \| `uF` \| `mF`
Default value	`[1e-5, 1e-6] F`
Program usage name	`C_vector`
Evaluatable	Yes

# Corresponding voltage values — input vector of voltage values
V | uV | mV | kV | MV

Details

The input vector of voltage values for calculating the capacitance based on the table. The length of the vector must be greater than or equal to 2, and the values must be strictly monotonic, either increasing or decreasing.

Dependencies

To use this parameter, set for the parameter Capacitance model meaning Lookup table.

Units	`V` \| `uV` \| `mV` \| `kV` \| `MV`
Default value	`[0.0, 10.0] V`
Program usage name	`V_vector`
Evaluatable	Yes

# Symmetric C-V table — table data

Details

Specify how to use the table data.:

If this option is selected, the symmetry of the capacitance relative to the applied voltage at the terminals is ensured.
If this option is not selected, the value for modeling polar capacitors is used. For example, with the default parameter values for the tabular capacitance, the applied voltage is −10 B will give the nominal capacity 1e−6 F. However, if you remove the flag Symmetric C-V table, the resulting capacity value will be 1e−5 F, because the block uses the nearest input value for extrapolation.

Dependencies

To use this parameter, set for the parameter Capacitance model meaning Lookup table.

Default value	`true (switched on)`
Program usage name	`is_CV_table_symmetric`
Evaluatable	No

# Frequencies for specifying dissipation factors [f1, f2] — frequencies for calculating the tangent of the dielectric loss angle
Hz | kHz | MHz | GHz

Details

The frequencies at which the tangents of the dielectric loss angle [DF1 DF2] are calculated, in kHz.

Dependencies

To use this parameter, set for the parameter Capacitance model meaning Dielectric relaxation (Debye).

Units	`Hz` \| `kHz` \| `MHz` \| `GHz`
Default value	`[1.0, 10.0] kHz`
Program usage name	`frequencies_vector`
Evaluatable	Yes

# Dissipation factors (%) at f1 and f2 [DF1, DF2] — dielectric loss coefficients

Details

The ratio between the equivalent series resistance and the capacitive reactance, or the tangent of the loss angle. Dielectric loss coefficients are a common metric for capacitors.

Dependencies

To use this parameter, set for the parameter Capacitance model meaning Dielectric relaxation (Debye).

Default value	`[0.8, 1.2]`
Program usage name	`dissipation_factors_vector`
Evaluatable	Yes

# Tolerance application — applying the margin of error
None - use nominal value | Random tolerance | Apply maximum tolerance value | Apply minimum tolerance value

Details

Choose how to apply the error during the simulation:

None - use nominal value — the unit does not apply an error, uses the nominal capacity value.
Random tolerance — The unit applies a random offset to the capacity value within the margin of error. You can choose a uniform or normal distribution for calculating a random number using the parameter Tolerance distribution.
Apply maximum tolerance value — The capacity is increased by the specified error value.
Apply minimum tolerance value — The capacity is reduced by the specified error value.

Values	`None - use nominal value` \| `Random tolerance` \| `Apply maximum tolerance value` \| `Apply minimum tolerance value`
Default value	`None - use nominal value`
Program usage name	`tolerance_application_type`
Evaluatable	No

# Averaging period for power logging — the averaging period for recording power
s | ns | us | ms | min | hr | d

Details

The averaging period for recording power, in seconds.

If this parameter is set to 0, then the output will be instantaneous power.

Dependencies

To use this parameter, set for the parameter Capacitance model meaning Dielectric relaxation (Debye).

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`0.0 s`
Program usage name	`averaging_period`
Evaluatable	Yes

# Tolerance (%) — capacity error

Details

The capacity error specified in the technical data sheet. For capacitors whose characteristics are specified in the table, this error is applied immediately to the entire table.

Default value	`5`
Program usage name	`tolerance`
Evaluatable	Yes

# Tolerance distribution — type of error distribution
Uniform | Gaussian

Details

Select the type of distribution:

Uniform — uniform distribution.
Gaussian — normal distribution.

Dependencies

To use this parameter, set for the parameter Tolerance application meaning Random tolerance.

Values	`Uniform` \| `Gaussian`
Default value	`Uniform`
Program usage name	`tolerance_distribution_type`
Evaluatable	No

# Number of standard deviations for quoted tolerance — It is used to calculate normally distributed random numbers.

Details

The number of standard deviations for calculating normally distributed random numbers .

Dependencies

To use this parameter, set for the parameter Tolerance distribution meaning Gaussian.

Default value	`4.0`
Program usage name	`number_of_standard_deviations`
Evaluatable	Yes

# Series resistance — consistent resistance
Ohm | mOhm | kOhm | MOhm | GOhm

Details

Modeling some circuits may require a small series resistance. The equivalent series resistance (ESR) is sometimes specified in manufacturers' technical data sheets. If there is none, you can determine this resistance for a linear capacitor through the tangent of the dielectric loss angle (DF), which is also specified in many specifications. This ratio looks like this: , where — the frequency of the signal. For the Debye capacitor, the value of the parameter Dissipation factors (%) at f1 and f2 [DF1 DF2] is adjusted for this additional series resistance before calculating 𝛼 and 𝜏.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`1e-6 Ohm`
Program usage name	`r`
Evaluatable	Yes

# Parallel conductance — parallel conduction
S | nS | uS | mS | 1/Ohm

Details

Parallel conductivity of the capacitor. For capacitors connected in series, having a small parallel conduction can help in convergence.

Units	`S` \| `nS` \| `uS` \| `mS` \| `1/Ohm`
Default value	`0.0 1/Ohm`
Program usage name	`g`
Evaluatable	Yes