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Constant Param, 6-ph with Fault

Owned by Sylvain Ménard
Last updated: Jul 05, 2023 by Victoria Bruny
7 min read

Description

The constant parameter (CP) line model assumes that the line parameters R , L and C are are independent of the frequency effects caused by the skin effect on phase conductors and on the ground. The model considers L and C to be distributed (ideal line) and R to be lumped at three places (R/4 on both ends and R/2 in the middle). The shunt conductance G is taken as zero. The frequency dependence of the line parameters (represented in the FD model) is an important factor for the accurate simulation of waveform and peak values. However, the CP model is very robust, simple and fast. It also provides a good alternative for a first approximation analysis.

A transposed or untransposed CP line is represented by a) its sequences, or b) by its propagation modes and the transformation matrix (Ti) between mode currents and phase currents. Implementation details can be found in [1]

The 6-phase CP model is used to simulate a double-circuit line or two lines with the same right of way. The parameters for 6-phase lines are the same as for 3-phase lines. The only difference is that the modal transformation matrix of double transmission lines is a 6x6 matrix because each bundle of conductors is considered as a separate phase.

This model can be used to simulate an internal fault. However, the number of operations allowed in this model is four (4) per fault element, instead of ten (10) in normal cases.

Table of Contents

Mask and Parameters

General Parameters

NameDescriptionUnitVariable = {Possible Values}
DescriptionUse this field to add information about the component
Description = {'string'}
EMTP (.pun) file for line parameters calculation

The location (path) of the EMTP file (pun file) containing the line parameters


File = {' path.name '}
L-C units in EMTP (.pun) fileThe units from the pun file can be selected from the two options:
L-C units = { 0, 1}
mH/km, uF/km {0}Inductance (L), capacitance (C) 
Ohm/km, uS/km {1}Inductive reactance (Xl) and capacitive susceptance (1/Xc) 
Line LengthThe length of the linekm

length = {0, 1e64}

Distance of fault from (+) sideDistance of fault from (+) side kmfault_loc = {0, 1e64}
Base power (perPhase)Base value for PU conversionMVA per phase

pBase = { [1, 1e64] }

Base voltage (rmsLN)Base value for PU conversionkV rms LN

vBase = { [1, 1e64] }

Base frequencyBase value for PU conversionHz

fBase = { [1, 1e64] }

Line 1Fault resistanceFault resistance value per phaseΩRDef1 = {0, 1e64}
RopenOpen resistance value per phaseΩROpen1 = {0, 1e64}
RcloseClosed resistance value per phaseΩRClose1 = {0, 1e64}
Chopping currentCurrent threshold for the opening permission operationAImargin1 = {0, 1e64}
Line 2Fault resistanceFault resistance value per phaseΩRDef2 = {0, 1e64}
RopenOpen resistance value per phaseΩROpen2 = {0, 1e64}
RcloseClosed resistance value per phaseΩRClose2 = {0, 1e64}
Chopping currentCurrent threshold for the opening permission operationAImargin2 = {0, 1e64}

Line Data Parameters

NameDescriptionUnitVariable = {Possible Values}
Continuously transposed lineTransposition (Untransposed/Transposed)
transp = { 0, 1}
No {0} Untransposed line
Yes {1}Transposed line
RPer unit length resistance for each phase (mode)Ω/kmR = {'-1e64, 1e64'}
LPer unit length inductance for each phase (mode)H/kmL = {'-1e64, 1e64'}
CPer unit length capacitance for each phase (mode)F/kmC = {'-1e64, 1e64'}
Transformation matrixTransformation matrix between mode current and phase current ([Iphase] = [Ti] x [Imode]); not used in the case of transposed line.
Ti = { [-1e64, 1e64] }

Timing Parameters

NameDescriptionUnitVariable = {Possible Values}
Time unitsUnits applied to the programmed state transition operations





Ut = {s, ms, c}


Second {s}All operations Tn are in seconds

Millisecond {ms}All operations Tn are in milliseconds

Cycle {c}All operations Tn are in electrical cycles (setting the frequency is mandatory)
Time programming

Master switch that determines whether the programmed operations will occur upon triggering an acquisition





EnaGen = {0, 1}


Disable {0}
Programmed operations are disabled

Enable {1}
Programmed operations are enabled
Steady-state condition

Line 1State of phase breakers for Line 1 in steady-state; “colored” if the breaker is open and “grey” if the breaker is closed

iniStateA = {0, 1}

iniStateB = {0, 1}

iniStateC = {0, 1}

iniStateN1 = {0, 1}


Line 2State of phase breakers for Line 2 in steady-state; “colored” if the breaker is open and “grey” if the breaker is closed

iniStateD = {0, 1}

iniStateE = {0, 1}

iniStateF = {0, 1}

iniStateN2 = {0, 1}

Frequency
Should be set using the parameter "Base frequency".HzFreq = { [45, 70] }

Switching times

Line 1Enable/disable the state transition operation on Line 1.


EnaT1 = {0, 1}

EnaT2 = {0, 1}

...

Disable {0}
Disable the state transition operation on the same line
Enable {1}
Enable the state transition operation on the same line. If the line is enabled but no information is filled, the state transition operation is ignored.
Line 2Enable/disable the state transition operation on Line 1.

EnaT1_2 = {0, 1}

EnaT2_2 = {0, 1}

...

Disable {0}Disable the state transition operation on the same line
Enable {1}Enable the state transition operation on the same line. If the line is enabled but no information is filled, the state transition operation is ignored.

Type(f,i,u,ug)




Relative time (with respect to POW synchronization) when the command is sent to the breaker (or switch) to change state. There are four ways to input this time.

Important notes:

  • For changes of state to occur, programmed operation times must always respect Tn>Tn-1.
  • If a parameter field is blank or contains “-”, no switching will occur for this line.
  • There is no alias for the type of timing in the API. The timing type and values are entered as a single string.
  • If using referenced operations, the calculated time is applied after it received the command from the other component. See the Referenced Operations section for more information.







Refer to "Time units" parameter






T1 = {'string'}

T2 = {'string'}

...


T1_2 = {'string'}

T2_2 = {'string'}

...


Fixed

{f: fixed time}

At each acquisition, Tn command is sent at the same time for all phases selected in "Phase operated".


Incremental

{i: initial time/final time/time increment}

For the first acquisition, Tn command is sent at the set initial time for all phases selected in "Phase operated". Then at each acquisition, Tn command is sent a time increment later than the previous acquisition. Once the final time is reached, the next acquisition will be done using the initial time again.


Uniform

{u: minimal time/maximal time}

At each acquisition, Tn command is sent at a random time. The probability is uniform over the specified range. All phases selected in "Phase operated" DO NOT receive the command at the same time, it is also random.


Uniform gaussian

{ug: minimal time/maximal time/ dispersion}

At each acquisition, Tn command is sent at a random time. The probability follows a gaussian distribution over the specified range. All phases selected in "Phase operated" DO NOT receive the command at the same time, it is also random.

Referenced operations

Use to refer the triggering of Tn to another breaker programmed state transition. See the Referenced Operations section for more information.

NB: all columns must be filled for the referenced operation to work.





Line 1		Ref operationName (or path) of the breaker to which the timing is referenced

Eref1 = {'path.name'}

Eref2 = {'path.name'}

...

Ref timeTime Tn ID of the referenced breaker's step to which the timing is referenced

Tref1 = {Tn}

Tref2 = {Tn}

...

Phase/CommandActivate (Phase {1}) or deactivate (Command {0}) the reference dependency

T1RPh = {0, 1}

T2RPh = {0, 1}

...

Line 2Ref operationName (or path) of the breaker to which the timing is referenced

Eref1_2 = {'path.name'}

Eref2_2 = {'path.name'}

...

Ref timeTime Tn ID of the referenced breaker's step to which the timing is referenced

Tref1_2 = {Tn}

Tref2_2 = {Tn}

...

Phase/CommandActivate (Phase {1}) or deactivate (Command {0}) the reference dependency

T1_2RPh = {0, 1}

T2_2RPh = {0, 1}

...

Phase operated


The list of all phases that will change state when the timing condition is reached. So if after Tn-1 the A and C phases are OFF and Tn triggers B and C, after Tn phases A and B will be OFF, and C will be ON




Line 1ON {1}"Colored" when a state transition shall occur (Line 2)

T1Pa, T1Pb, T1Pc = {0, 1}

T2Pa, T2,Pb, T2Pc = {0, 1}

...

OFF {0}"Grayed out" when no state transition shall occur (Line 2)
Line 2ON {1}"Colored" when a state transition shall occur (Line 2)

T1_2Pa, T1_2Pb, T1_2Pc = {0, 1}

T2_2Pa, T2_2,Pb, T2_2Pc = {0, 1}

...

OFF {0}"Grayed out" when no state transition shall occur (Line 2)

Line Generator

For more information see Line Generator 

Ports, Inputs, Outputs and Signals Available for Monitoring

Ports

This component supports a 6-phase transmission line 

Name

Description

net_1_1(a,b,c)Network connection of phases (a,b,c) of the left (+) side of line 1
net_1_2(a,b,c)Network connection of phases (a,b,c) of the right side of line 1
net_2_1(a,b,c)Network connection of phases (a,b,c) of the left (+) side of line 2
net_2_2(a,b,c)Network connection of phases (a,b,c) of the right side of line 2

Inputs

None

Outputs

None

Sensors

At acquisition, the signals available by the sensors are:

Name

Description

Unit

V(a,b,c)1_Node1_(1,2)Bus voltage for each phase (a,b,c) of line 1V
V(a,b,c)2_Node2_(1,2)Bus voltage for each phase (a,b,c) of line 2V
I(a,b,c)1_Node1_(1,2)Current for each phase (a,b,c) of line 1A
I(a,b,c)2_Node2_(1,2)Current for each phase (a,b,c) of line 2A
V(a,b,c)_FLT1Voltage on fault bus of line 1 phases (a,b,c)V
V(a,b,c)_FLT2Voltage on fault bus of line 2 phases (a,b,c)V
I(a,b,c,n)_FLT1Fault current of line 1 (a,b,c,n)A
I(a,b,c,n)_FLT2Fault current of line 2 (a,b,c,n)A
CMD(a,b,c,n)_FLT1Command for states of phase and ground breakers of line 1
CMD(a,b,c,n)_FLT2Command for states of phase and ground breakers of line 2

Note that the Fault bus referred in the previous table is the point of fault on the line indicated in the form of the model (distance of fault from (+) side).

Electrical Parameters

Calculation of electrical parameters

The Electrical parameters of CP lines can be calculated by using the Line Generator.

Propagation Delay

The propagation delay is calculated as follows: 

Where i is for each of the phases, L and C stands for the inductance and capacitance of the line per unit length.



When the propagation delay is smaller than the time step, the Constant Param block is automatically replaced by an equivalent PI Line.



If the 'Transposed' parameter is set to 'yes', the following warning is printed in the console:

WARNING in line: <Name of Block>: The propagation delay ( X ) is less than the sample time ( Y ). A PI line is automatically used.

If the 'Transposed' parameter is set to 'no', an error message with similar text appears.

Types of fault

The fault breakers are shown in the following figure. The types of faults according to the state of the breakers are listed in the table.



Note: For a phase to ground fault, we strongly recommend using the ground in steady state instead of programming a time of operation in transient state.



Types of fault according to state of breakers

State of BreakerA BCGround
No fault0000
Fault between phase C and Ground0011
Fault between phase B and Ground0101
Fault between phases B and C0110
Fault between phases B, C and Ground0111
Fault between phases A and Ground1001
Fault between phases A and C1010
Fault between phases A, C and Ground1011
Fault between phases A and B1100
Fault between phases A, B and Ground1101
Fault between phases A, B and C1110
Fault between phases A, B, C and Ground1111

References

  1. H. W. Dommel, "Digital computer solution of electromagnetic transients in single and multiphase networks," IEEE Trans. Power App. Syst., vol. pas-88, pp. 388-99, 04/ 1969.

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