SCL2C
Voltage regulator
SCL2C
generic
Opensource
CIM model
RMS
phasor
MRL4
Single phase
IEEE
dynawo
#236
IEEE SCL2C model
Context
This stator current limiter model first appeared in the IEEE Std 421.5-2016 [1].
Model use, assumptions, validity domain and limitations
This model is associated to one of the voltage regulators (types AC, DC, ST) defined by the IEEE Std 421.5-2016 [1].
The model provides two stator current limiter signals (one for overexcitation, the other for under excitation) for the purposes of :
- takeover : the stator current limiter signals act as upper and lower limits (respectively) on the voltage regulator main signal which then becomes the excitation voltage ;
- summation : the stator current limiter signals are added to the stator voltage deviation from the reference, thus being taken into account in the calculation of the excitation voltage.
Model inputs and outputs
The input signals are :
| Variable | Description | Unit |
|---|---|---|
| \(itPu\) | Complex stator current | \(pu\) (base \(SnRef\), \(UNom\)) |
| \(PGenPu\) | Active power generated by the synchronous machine | \(pu\) (base \(SnRef\)) |
| \(QGenPu\) | Reactive power generated by the synchronous machine | \(pu\) (base \(SnRef\)) |
| \(utPu\) | Complex stator voltage | \(pu\) (base \(UNom\)) |
Both \(PGenPu\) and \(QGenPu\) follow the generator convention.
The output signals are :
| Variable | Description | Unit |
|---|---|---|
| \(USclOelPu\) | Stator current overexcitation limitation output voltage | \(pu\) (base \(UNom\)) |
| \(USclUelPu\) | Stator current underexcitation limitation output voltage | \(pu\) (base \(UNom\)) |
Model parameters
| Parameter | Description | Unit | Value (set 1) | Value (set 2) | Value (set 3) |
|---|---|---|---|---|---|
| \(C1\) | SCL exponent for calculation of first error | \(-\) | \(0\) | \(0\) | \(0\) |
| \(C2\) | SCL exponent for calculation of second error | \(-\) | \(2\) | \(2\) | \(2\) |
| \(FixedRd\) | SCL fixed cooling-down time output | \(pu\) | \(-0.001\) | \(-0.001\) | \(-0.001\) |
| \(FixedRu\) | SCL fixed delay time output | \(pu\) | \(0\) | \(0\) | \(0\) |
| \(IInstPu\) | SCL instantaneous stator current limit | \(pu\) (base \(SnRef\), \(UNom\)) | \(5\) | \(5\) | \(5\) |
| \(IInstUelPu\) | Underexcited region instantaneous stator current limit | \(pu\) (base \(SnRef\), \(UNom\)) | \(1.1\) | \(1.1\) | \(1.1\) |
| \(ILimPu\) | SCL thermal stator current limit | \(pu\) (base \(SnRef\), \(UNom\)) | \(1.1\) | \(1.1\) | \(1.1\) |
| \(IqOelMinPu\) | SCL OEL minimum reactive current reference value | \(pu\) (base \(SnRef\), \(UNom\)) | \(0.02\) | \(0.02\) | \(0.02\) |
| \(IqUelMaxPu\) | SCL UEL maximum reactive current reference value | \(pu\) (base \(SnRef\), \(UNom\)) | \(-0.02\) | \(-0.02\) | \(-0.02\) |
| \(IResetPu\) | SCL reset-reference, if inactive | \(pu\) (base \(SnRef\), \(UNom\)) | \(100\) | \(100\) | \(100\) |
| \(ITfPu\) | SCL thermal reference for inverse time calculations | \(pu\) (base \(SnRef\), \(UNom\)) | \(1.1\) | \(1.1\) | \(1.1\) |
| \(IThOffPu\) | SCL reset threshold value | \(pu\) (base \(SnRef\), \(UNom\)) | \(0.05\) | \(0.05\) | \(0.05\) |
| \(K1\) | SCL gain for calculation of first error | \(pu\) | \(0\) | \(0\) | \(0\) |
| \(K2\) | SCL gain for calculation of second error | \(pu\) | \(0.0333\) | \(0.0333\) | \(0.0333\) |
| \(KdOel\) | Overexcited PID regulator differential gain | \(pu\) | \(0\) | \(0\) | \(0\) |
| \(KdUel\) | Underexcited PID regulator differential gain | \(pu\) | \(0\) | \(0\) | \(0\) |
| \(KFb\) | SCL timer feedback gain | \(pu\) | \(0\) | \(0\) | \(0\) |
| \(KiOel\) | Overexcited PID regulator integral gain | \(pu\) | \(0\) | \(0\) | \(1\) |
| \(KiUel\) | Underexcited PID regulator integral gain | \(pu\) | \(0\) | \(0\) | \(1\) |
| \(KpOel\) | Overexcited PID regulator proportional gain | \(pu\) | \(0.5\) | \(250\) | \(0.3\) |
| \(KPRef\) | SCL reference scaling factor based on active current | \(pu\) | \(0\) | \(0\) | \(0\) |
| \(KpUel\) | Underexcited PID regulator proportional gain | \(pu\) | \(0.5\) | \(250\) | \(0.3\) |
| \(KIpOel\) | Overexcited active current scaling factor | \(pu\) | \(1\) | \(1\) | \(1\) |
| \(KIpUel\) | Underexcited active current scaling factor | \(pu\) | \(1\) | \(1\) | \(1\) |
| \(KIqOel\) | Overexcited reactive current scaling factor | \(pu\) | \(1\) | \(1\) | \(1\) |
| \(KIqUel\) | Underexcited reactive current scaling factor | \(pu\) | \(1\) | \(1\) | \(1\) |
| \(Krd\) | SCL reference ramp-down rate | \(pu/s\) (base \(SnRef\), \(UNom\)) | \(-1000\) | \(-1000\) | \(-1000\) |
| \(Kru\) | SCL reference ramp-up rate | \(pu/s\) (base \(SnRef\), \(UNom\)) | \(1000\) | \(1000\) | \(1000\) |
| \(Kzru\) | SCL thermal reference release threshold | \(pu\) | \(0.99\) | \(0.99\) | \(0.99\) |
| \(Sw1\) | OEL reference ramp logic selection | \(-\) | \(false\) | \(false\) | \(false\) |
| \(tAScl\) | SCL reference filter time constant | \(s\) | \(0.04\) | \(0.04\) | \(0.04\) |
| \(tB1Oel\) | Overexcited regulator lag time constant 1 | \(s\) | \(0.1\) | \(12.5\) | \(0.1\) |
| \(tB1Uel\) | Underexcited regulator lag time constant 1 | \(s\) | \(0.1\) | \(12.5\) | \(0.1\) |
| \(tB2Oel\) | Overexcited regulator lag time constant 2 | \(s\) | \(0.1\) | \(0.1\) | \(0.1\) |
| \(tB2Uel\) | Underexcited regulator lag time constant 2 | \(s\) | \(0.1\) | \(0.1\) | \(0.1\) |
| \(tC1Oel\) | Overexcited regulator lead time constant 1 | \(s\) | \(0.1\) | \(1.5\) | \(0.1\) |
| \(tC1Uel\) | Underexcited regulator lead time constant 1 | \(s\) | \(0.1\) | \(1.5\) | \(0.1\) |
| \(tC2Oel\) | Overexcited regulator lead time constant 2 | \(s\) | \(0.1\) | \(0.1\) | \(0.1\) |
| \(tC2Uel\) | Underexcited regulator lead time constant 2 | \(s\) | \(0.1\) | \(0.1\) | \(0.1\) |
| \(tDOel\) | Overexcited PID regulator differential time constant | \(s\) | \(0.1\) | \(0.1\) | \(0.1\) |
| \(tDUel\) | Underexcited PID regulator differential time constant | \(s\) | \(0.1\) | \(0.1\) | \(0.1\) |
| \(tEnOel\) | Overexcited activation delay time | \(s\) | \(0.01\) | \(0.01\) | \(0.01\) |
| \(tEnUel\) | Underexcited activation delay time | \(s\) | \(0\) | \(0\) | \(0\) |
| \(tIpOel\) | Overexcited active current time constant | \(s\) | \(0.01\) | \(0.01\) | \(0.01\) |
| \(tIpUel\) | Underexcited active current time constant | \(s\) | \(0.01\) | \(0.01\) | \(0.01\) |
| \(tIqOel\) | Overexcited reactive current time constant | \(s\) | \(0.01\) | \(0.01\) | \(0.01\) |
| \(tIqUel\) | Underexcited reactive current time constant | \(s\) | \(0.01\) | \(0.01\) | \(0.01\) |
| \(tItScl\) | Stator current transducer time constant | \(s\) | \(0.01\) | \(0.01\) | \(0.01\) |
| \(tMax\) | SCL timer maximum level | \(s\) | \(1\) | \(1\) | \(1\) |
| \(tMin\) | SCL timer minimum level | \(s\) | \(0\) | \(0\) | \(0\) |
| \(tOff\) | SCL reset delay time | \(s\) | \(5\) | \(5\) | \(5\) |
| \(tScl\) | SCL timer reference | \(s\) | \(1\) | \(1\) | \(1\) |
| \(tVtScl\) | Terminal voltage transducer time constant | \(s\) | \(0.01\) | \(0.01\) | \(0.01\) |
| \(VInvMaxPu\) | SCL maximum inverse time output | \(pu\) | \(100\) | \(100\) | \(100\) |
| \(VInvMinPu\) | SCL minimum inverse time output | \(pu\) | \(0\) | \(0\) | \(0\) |
| \(VOel1MaxPu\) | Maximum OEL output limit | \(pu\) (base \(UNom\)) | \(10\) | \(10\) | \(0\) |
| \(VOel1MinPu\) | Minimum OEL output limit | \(pu\) (base \(UNom\)) | \(-10\) | \(-8.7\) | \(-0.1\) |
| \(VOel2MaxPu\) | Maximum OEL lead-lag 1 output limit | \(pu\) (base \(UNom\)) | \(100\) | \(20\) | \(0\) |
| \(VOel2MinPu\) | Minimum OEL lead-lag 1 output limit | \(pu\) (base \(UNom\)) | \(-100\) | \(-20\) | \(-0.1\) |
| \(VOel3MaxPu\) | Maximum OEL PID output limit | \(pu\) (base \(UNom\)) | \(100\) | \(100\) | \(0\) |
| \(VOel3MinPu\) | Minimum OEL PID output limit | \(pu\) (base \(UNom\)) | \(-100\) | \(-100\) | \(-0.1\) |
| \(VtMinPu\) | SCL OEL minimum voltage reference value | \(pu\) (base \(UNom\)) | \(0.9\) | \(0.9\) | \(0.9\) |
| \(VtResetPu\) | SCL OEL voltage reset value | \(pu\) (base \(UNom\)) | \(0.8\) | \(0.8\) | \(0.8\) |
| \(VUel1MaxPu\) | Maximum UEL output limit | \(pu\) (base \(UNom\)) | \(10\) | \(10\) | \(0.1\) |
| \(VUel1MinPu\) | Minimum UEL output limit | \(pu\) (base \(UNom\)) | \(-10\) | \(-8.7\) | \(0\) |
| \(VUel2MaxPu\) | Maximum UEL lead-lag 1 output limit | \(pu\) (base \(UNom\)) | \(100\) | \(100\) | \(0.1\) |
| \(VUel2MinPu\) | Minimum UEL lead-lag 1 output limit | \(pu\) (base \(UNom\)) | \(-100\) | \(-100\) | \(0\) |
| \(VUel3MaxPu\) | Maximum UEL PID output limit | \(pu\) (base \(UNom\)) | \(100\) | \(100\) | \(0.1\) |
| \(VUel3MinPu\) | Minimum UEL PID output limit | \(pu\) (base \(UNom\)) | \(-100\) | \(-100\) | \(0\) |
The parameter sets correspond to a stator current limitation output : - 1 : with a takeover action at the AVR input; - 2 : with a takeover action at the AVR output; - 3 : added to the summation point in the AVR.
Model diagram
The SCL reference current is calculated with the following model :
The SCL OEL activation logic has four inputs (on the left, from top to bottom, \(IOelActPu\), \(tErr\), \(IRefPu\), at the top right corner, \(VtFiltPu\)) and one output (\(IOelBiasPu\)) calculated as follows :
if ($VtFiltPu > VtMinPu$ and ($tErr <= 0$ or ($IOelActPu > IOelRefPu$ for a duration $>= tEnOel$))) or $tEnOel == 0$
$IOelBiasPu = 0$
elseif ($IOelRefPu == IInstPu$ and ($IOelRefPu > IOelActPu + IThOffPu$ for a duration $> tOff$)) or $VtFiltPu < VtResetPu$
$IOelBiasPu = IResetPu$
else
$IOelBiasPu = 0$The SCL UEL activation logic has three inputs (from top to bottom, \(IUelActPu\), \(tErr\), \(IUelRefPu\)) and one output (\(IUelBiasPu\)) calculated as follows :
if $tErr <= 0$ or ($IUelActPu > IUelRefPu$ for a duration $>= tEnUel$) or $tEnUel == 0$
$IUelBiasPu = 0$
elseif $IRefPu == IInstUelPu$ and ($IUelRefPu > IUelActPu + IThOffPu$ for a duration $> tOff$)
$IUelBiasPu = IResetPu$
else
$IUelBiasPu = 0$The SCL reference logic has two inputs (from top to bottom, \(IPRefPu\), \(I'RefPu\)) and one output (\(IRefPu\)) calculated as follows :
if $KPRef > 0$ and $abs(I'RefPu) > abs(IPRefPu)$
$IRefPu = sqrt(I'RefPu ^ 2 - IPRefPu ^ 2)$
else
$IRefPu = I'RefPu$Open source implementations
This model has been successfully implemented in :
| Software | URL | Language | Open-Source License | Last consulted date | Comments |
|---|---|---|---|---|---|
| Dynawo | Link | Modelica | MPL v2.0 | 09/10/2024 |
References
1.
Electrical TI of, Engineers E (2016) IEEE recommended practice for excitation system models for power system stability studies. IEEE Std 4215-2016