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

Name	Description			Unit	Variable = {Possible Values}
Description	Use 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) file	The 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 Length	The length of the line			km	length = {0, 1e64}
Distance of fault from (+) side	Distance of fault from (+) side			km	fault_loc = {0, 1e64}
Base power (perPhase)	Base value for PU conversion			MVA per phase	pBase = { [1, 1e64] }
Base voltage (rmsLN)	Base value for PU conversion			kV rms LN	vBase = { [1, 1e64] }
Base frequency	Base value for PU conversion			Hz	fBase = { [1, 1e64] }
Line 1	Fault resistance	Fault resistance value per phase		Ω	RDef1 = {0, 1e64}
	Ropen	Open resistance value per phase		Ω	ROpen1 = {0, 1e64}
	Rclose	Closed resistance value per phase		Ω	RClose1 = {0, 1e64}
	Chopping current	Current threshold for the opening permission operation		A	Imargin1 = {0, 1e64}
Line 2	Fault resistance	Fault resistance value per phase		Ω	RDef2 = {0, 1e64}
	Ropen	Open resistance value per phase		Ω	ROpen2 = {0, 1e64}
	Rclose	Closed resistance value per phase		Ω	RClose2 = {0, 1e64}
	Chopping current	Current threshold for the opening permission operation		A	Imargin2 = {0, 1e64}

Line Data Parameters

Name	Description		Unit	Variable = {Possible Values}
Continuously transposed line	Transposition (Untransposed/Transposed)			transp = { 0, 1}
	No {0}	Untransposed line
	Yes {1}	Transposed line
R	Per unit length resistance for each phase (mode)		Ω/km	R = {'-1e64, 1e64'}
L	Per unit length inductance for each phase (mode)		H/km	L = {'-1e64, 1e64'}
C	Per unit length capacitance for each phase (mode)		F/km	C = {'-1e64, 1e64'}
Transformation matrix	Transformation matrix between mode current and phase current ([Iphase] = [Ti] x [Imode]); not used in the case of transposed line.			Ti = { [-1e64, 1e64] }

Timing Parameters

Name	Description			Unit	Variable = {Possible Values}
Time units	Units applied to the programmed state transition operations				Ut = {s, ms, c}
		Second {s}	All operations T_n are in seconds
		Millisecond {ms}	All operations T_n are in milliseconds
		Cycle {c}	All operations T_n 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 1	State 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}
Steady-state condition		Line 2	State 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".			Hz	Freq = { [45, 70] }
Switching times	Line 1	Enable/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 2	Enable/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 T_n>T_n-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, T_n 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, T_n command is sent at the set initial time for all phases selected in "Phase operated". Then at each acquisition, T_n 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, T_n 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, T_n 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 T_n 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 operation	Name (or path) of the breaker to which the timing is referenced		Eref1 = {'path.name'} Eref2 = {'path.name'} ...
		Ref time	Time T_n ID of the referenced breaker's step to which the timing is referenced		Tref1 = {T_n} Tref2 = {T_n} ...
		Phase/Command	Activate (Phase {1}) or deactivate (Command {0}) the reference dependency		T1RPh = {0, 1} T2RPh = {0, 1} ...
	Line 2	Ref operation	Name (or path) of the breaker to which the timing is referenced		Eref1_2 = {'path.name'} Eref2_2 = {'path.name'} ...
		Ref time	Time T_n ID of the referenced breaker's step to which the timing is referenced		Tref1_2 = {T_n} Tref2_2 = {T_n} ...
		Phase/Command	Activate (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 T_n-1 the A and C phases are OFF and T_n triggers B and C, after T_n phases A and B will be OFF, and C will be ON
	Line 1	ON {1}	"Colored" when a state transition shall occur (Line 2)		T1Pa, T1Pb, T1Pc = {0, 1} T2Pa, T2,Pb, T2Pc = {0, 1} ...
	Line 1	OFF {0}	"Grayed out" when no state transition shall occur (Line 2)		T1Pa, T1Pb, T1Pc = {0, 1} T2Pa, T2,Pb, T2Pc = {0, 1} ...
	Line 2	ON {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} ...
	Line 2	OFF {0}	"Grayed out" when no state transition shall occur (Line 2)

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 1	V
*V(a,b,c)2_Node2_(1,2)*	Bus voltage for each phase (a,b,c) of line 2	V
*I(a,b,c)1_Node1_(1,2)*	Current for each phase (a,b,c) of line 1	A
*I(a,b,c)2_Node2_(1,2)*	Current for each phase (a,b,c) of line 2	A
V(a,b,c)_FLT1	Voltage on fault bus of line 1 phases (a,b,c)	V
V(a,b,c)_FLT2	Voltage on fault bus of line 2 phases (a,b,c)	V
I(a,b,c,n)_FLT1	Fault current of line 1 (a,b,c,n)	A
I(a,b,c,n)_FLT2	Fault current of line 2 (a,b,c,n)	A
CMD(a,b,c,n)_FLT1	Command for states of phase and ground breakers of line 1
CMD(a,b,c,n)_FLT2	Command 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 calculation of the electrical parameters for a CP line can be done with the Line Data auxiliary module. The pun file generated with this module must be loaded in the form.

Alternatively, the electrical parameters of CP lines can be calculated by using the HyperView Line Tab module in HyperView.

Steps are as follows:

Load a file into the Line Data GUI or enter the geometrical line parameters; details are found in Line Geometry
Select the transpositions options
Run the program
The electrical parameters are displayed in the Line Data Report

To transfer the electrical parameters to the CP model, follow these steps:

Go to the Line Data GUI
All the names of the lines in your network appear at the bottom of the page
To transfer electrical parameters, choose the name of the line and click Apply
See the parameters in the forms of the line

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 Breaker	A	B	C	Ground
No fault	0	0	0	0
Fault between phase C and Ground	0	0	1	1
Fault between phase B and Ground	0	1	0	1
Fault between phases B and C	0	1	1	0
Fault between phases B, C and Ground	0	1	1	1
Fault between phases A and Ground	1	0	0	1
Fault between phases A and C	1	0	1	0
Fault between phases A, C and Ground	1	0	1	1
Fault between phases A and B	1	1	0	0
Fault between phases A, B and Ground	1	1	0	1
Fault between phases A, B and C	1	1	1	0
Fault between phases A, B, C and Ground	1	1	1	1

References

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.

Constant Param, 6-ph with Fault