Capacitor (Advanced)
A linear or non-linear capacitor that takes into account the capacitance error.
blockType: AcausalElectricPowerSystems.Passive.Capacitor
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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
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— current;
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— capacity;
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— tension;
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— the time.
To simulate a nonlinear or polar capacitor, set the Capacity model parameter to Lookup table and fill in the table of voltage-capacity values:
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For polar capacitors, this reference table is asymmetric with respect to the applied terminal voltage, uncheck the Symmetrical C-V table option.
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For other types of nonlinear capacitors, the symmetry of the capacitance table relative to the applied terminal voltage is ensured by checking the box for the parameter Symmetrical C-V table.
To simulate a frequency-dependent capacitor with ohmic and dielectric losses, set the Capacity model parameter to 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:
,
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where
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— radial frequency;
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— real permeability at very high frequency;
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— real low frequency permeability;
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— constant relaxation time.
In the time domain, the characteristic equation for a capacitor in the Debye model has the form
,
where
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— low frequency capacity;
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;
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— charge;
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— current;
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— 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
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and — two different frequencies;
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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 Capacity parameter. Such an error is usually indicated in the technical descriptions. The table shows how the block applies the error and calculates the capacity depending on the selected value of the Tolerance application parameter.
| The value of the Tolerance application parameter | The value of the inductance |
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Uniform distribution: Normal distribution: |
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In the table:
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Parameters
Main
Capacity model — capacitor type
Constant (by default) | Lookup table | Dielectric relaxation (Debye)
Select the type of capacitor:
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Constant— a linear capacitor with a nominal capacity set by the value of the Capacity parameter. -
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.
Capacity — nominal value of pass capacity:q[<br>] 1e−6F (default) | positive | scalar
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 the Capacity model parameter to Constant or Dielectric relaxation (Debye).
Capacity values — vector of pass capacity values:q[<br>] [1e−05, 1e−06] F (default) | positive vector
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 the Capacity model parameter to Lookup table.
Corresponding voltage values — input vector of voltage values
[0, 10] In (default)
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 the Capacity model parameter to Lookup table.
Symmetrical C-V table — data of the pass table:q[<br>] enabled (by default) | turned off
Specify how to use the table data.:
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enabled— ensuring the symmetry of the capacitance relative to the applied voltage at the terminals. -
turned off— value for modeling polar capacitors. For example, with the default parameter values for the tabular capacitance, the applied voltage is-10B will give the nominal capacity1e−6F. However, if you uncheck the Symmetrical C-V table flag, the resulting capacity value will be1e−5F, because the block uses the nearest input value for extrapolation.
Dependencies
To use this parameter, set the Capacity model parameter to Lookup table.
Frequencies for specifying dissipation factors [f1 f2] — frequencies for calculating the tangent of the dielectric loss angle
[1, 10] kHz (default)
The frequencies at which the tangents of the dielectric loss angle [DF1 DF2] are calculated, in kHz.
Dependencies
To use this parameter, set the Capacity model parameter to Dielectric relaxation (Debye).
Dissipation factors (%) at f1 and f2 [DF1 DF2] — dielectric loss coefficients
[0.8, 1.2] (default)
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 the Capacity model parameter to Dielectric relaxation (Debye).
Tolerance (%) — pass capacity error:q[<br>] 5 (default)
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.
Tolerance application — application of the pass error:q[<br>] None — use nominal value (by default) | Random tolerance | Apply maximum tolerance value | Apply minimum tolerance value
Choose how to apply the error during the simulation:
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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 to calculate a random number using the Tolerance distribution parameter. -
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.
Tolerance distribution — type of error distribution
Uniform (by default) | Gaussian
Select the type of distribution:
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Uniform— uniform distribution. -
Gaussian— normal distribution.
Dependencies
To use this parameter, set the Tolerance application parameter to Random tolerance.
Number of standard deviations for quoted tolerance — used to calculate normally distributed random numbers
4 (default)
The number of standard deviations for calculating normally distributed random numbers .
Dependencies
To use this parameter, set the Tolerance distribution parameter to Gaussian.
Series resistance — sequential resistance
1e−6 ohms (default)
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.
Parallel conduction — parallel conduction
0 (default)
Parallel conductivity of the capacitor. For capacitors connected in series, having a small parallel conduction can help in convergence.
Averaging period for power logging — the averaging period for recording power
0 s (default)
The averaging period for recording power, in seconds.
If this parameter is set to 0, then the output will be instantaneous power.
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Dependencies
To use this parameter, set the Capacity model parameter to Dielectric relaxation (Debye).