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.
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Mask and Parameters
General Parameters
| Name | Description | Unit | Variable = {Possible Values} | |||
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| 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 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 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} | ||
| 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:
| 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 operation | Name (or path) of the breaker to which the timing is referenced | Eref1 = {'path.name'} Eref2 = {'path.name'} ... | ||
| Ref time | Time Tn ID of the referenced breaker's step to which the timing is referenced | Tref1 = {Tn} Tref2 = {Tn} ... | |||
| 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 Tn ID of the referenced breaker's step to which the timing is referenced | Tref1_2 = {Tn} Tref2_2 = {Tn} ... | |||
| 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 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 1 | ON {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 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} ... | ||
| OFF {0} | "Grayed out" when no state transition shall occur (Line 2) | ||||
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 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 Dataauxiliary module. The pun file generated with this module must be loaded in the form. Alternatively, the electrical 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 Generator | Line Geometry
- Select the transpositions options
- Run the program
- The electrical parameters are displayed in the Line Line Generator | Line Data Log
To transfer the electrical parameters to the CP model, follow these steps:
Propagation Delay
The propagation delay is calculated as follows:
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Propagation\_delay = length\_of\_line * \sqrt {L[i] * C[i] } |
Where i is for each of the phases, L and C stands for the inductance and capacitance of the line per unit length.
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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.
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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.