Capacitor (Advanced)
Linear or non-linear capacitor, accounting for capacitance error.
blockType: AcausalElectricPowerSystems.Passive.Capacitor
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Description
The Capacitor block allows modelling of linear, non-linear (specified by tabular characteristics) and frequency-dependent capacitors, accounting for error.
When a linear capacitor is simulated and no capacitance error is considered, the behaviour of the component is identical to block Capacitor.
In its simplest form, the Capacitor block models a linear capacitor described by the following equation:
Where:
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- current.
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- capacitance.
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- voltage.
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- time.
To model a non-linear or polar capacitor, set the Capacitance model parameters to Lookup table and fill in the voltage-capacitance table:
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For polar capacitors, this reference table is asymmetric with respect to the applied terminal voltage, uncheck the parameter Symmetric C-V table.
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For other types of nonlinear capacitors, the symmetry of the capacitance table with respect to the applied terminal voltage is ensured by checking the Symmetric C-V table parameters.
To model a frequency-dependent capacitor with ohmic and dielectric losses, set the Capacitance model parameters to Dielectric relaxation (Debye). The Debye relaxation model considers a set of non-interacting dipoles in the frequency domain. The result is expressed in terms of complex dielectric constant. The real ( ) and imaginary ( ) parts of the complex permittivity are given by Eqs:
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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 permeability at low frequency.
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- relaxation time constant.
In the time domain, the characteristic equation for the capacitor in the Debye model is as follows
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where
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- is the low-frequency capacitance.
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.
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- charge.
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- current.
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- capacitor voltage.
Most specifications do not explicitly state the complex permittivity and relaxation time values, but the dissipation angle tangent of the dielectric loss at two frequencies is often given. The parameters and can be derived from these values as described in Eqs:
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Where:
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and are two different frequencies.
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and are dissipation coefficients calculated at the indicated frequencies, respectively.
For correct tuning in the Debye model, the square root argument must be positive.
Errors
You can add an error to the nominal value specified for the Capacitance parameters. Technical descriptions usually specify such an error. The table shows how the block applies the error and calculates the capacitance depending on the selected value of the Tolerance application parameters.
| Parameters Tolerance application value | Inductance value |
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Uniform distribution: Normal distribution: |
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In the table:
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Parameters
Main
Capacitance model - capacitor type
Constant (By default) | Lookup table | Dielectric relaxation (Debye)
Select the type of capacitor:
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Constantis a linear capacitor with nominal capacitance given by the Capacitance parameters. -
Lookup table- non-linear capacitor, where the nominal capacitance value varies depending on the value of the applied voltage at the terminals. -
Dielectric relaxation (Debye)- frequency dependent capacitor with ohmic and dielectric losses.
Capacitance - rated capacitance value
1e-6 F (by default) | positive | scalar
Nominal capacitance value for a linear capacitor or low-frequency capacitance in Debye parameterization.
Dependencies
To use this parameter, set the Capacitance model parameters to Constant or Dielectric relaxation (Debye).
Capacitance values is a vector of capacitance values
[1e-05, 1e-06] F (by default) | `positive vector'.
Vector of capacitance values to search 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 Capacitance model parameters to Lookup table.
Corresponding voltage values - input vector of voltage values
[0, 10] V (by default).
Input vector of voltage values for table-based capacitance calculation. The vector length 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 Capacitance model parameter to Lookup table.
Symmetric C-V table - table data
On (By default) | Off
Specify how to use the table data:
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On- to ensure symmetry of the capacitance with respect to the applied terminal voltage. -
off- value for modelling polar capacitors. For example, with the By default parameters for table capacitance, an applied voltage of-10V will give a nominal capacitance of1e-6F. However, if the Symmetric C-V table flag is cleared, the resulting capacitance value will be1e-5F, as the block uses the nearest input value for extrapolation.
Dependencies
To use this parameter, set the Capacitance model parameter to `Lookup table'.
Frequencies for specifying dissipation factors [f1 f2] - frequencies for calculating the dissipation angle tangent.
[1, 10] kHz (by default)
Frequencies at which dissipation factor tangents [DF1 DF2] are calculated, in kHz.
Dependencies
To use this parameter, set the Capacitance model parameters to Dielectric relaxation (Debye).
Dissipation factors (%) at f1 and f2 [DF1 DF2] - dielectric loss factors
[0.8, 1.2] (By default)
The ratio between the equivalent series resistance and the capacitive reactance, or loss angle tangent. Dielectric loss coefficients are a common metric for capacitors.
Dependencies
To use this parameter, set the Capacitance model parameters to Dielectric relaxation (Debye).
Tolerance (%) is the capacitance error
5 (By default).
Capacitance error specified in the data sheet. For capacitors whose characteristics are specified in a table, this error is applied to the whole table at once.
Tolerance application - error application
None - use nominal value (by default) | Random tolerance | Apply maximum tolerance value | Apply minimum tolerance value.
Select how the error is applied during modelling:
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None - use nominal value- the block does not apply tolerance, it uses the nominal value of the capacitance. -
Random tolerance- the block applies a random offset to the capacitance value within the error. You can select uniform or normal distribution to calculate the random number using the *Tolerance distribution` parameters. -
Apply maximum tolerance value- the capacitance is increased by the specified tolerance value. -
Apply minimum tolerance value- the capacity is decreased by the specified tolerance value.
Tolerance distribution - type of error distribution
Uniform (by default) | Gaussian.
Select the distribution type:
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Uniform- uniform distribution. -
Gaussian- normal distribution.
Dependencies
To use this parameter, set the Tolerance application parameters to Random tolerance.
Number of standard deviations for quoted tolerance - used to calculate normally distributed random numbers
4 (By default).
Number of standard deviations for calculating normally distributed random numbers .
Dependencies
To use this parameter, set the Tolerance distribution parameters to Gaussian.
Series resistance - series resistance
1e-6 ohms (by default).
Modelling some circuits may require a small series resistance. The equivalent series resistance (ESR) is sometimes listed on manufacturers' datasheets. If it is not available, you can determine this resistance for a linear capacitor through the dissipation factor (DF) tangent of the dielectric loss angle, which is also listed in many specifications. This ratio looks like this: , where is the signal frequency. For a Debye capacitor, the parameters Dissipation factors (%) at f1 and f2 [DF1 DF2] are corrected for this additional series resistance before calculating 𝛼 and 𝜏.
Parallel conductance is the parallel conductance
0 (By default)
Parallel conductance of the capacitor. For capacitors connected in series, having a small parallel conductance can help with convergence.
Averaging period for power logging - averaging period for power logging
`0 s (By default).
Averaging period for power logging, in sec.
If this parameter is set to 0, the output will be instantaneous power.
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Dependencies
To use this parameter, set the Capacitance model parameters to Dielectric relaxation (Debye).