Alternative Transients Program - Comparison oftransmission line models

Orlando P. Hevia Gorostiaga 1483Argentina 3000 Santa Fe

Argentinaemail: heviaop@ssdfe.com.ar

1. Introduction.

The ATP allows to model transmission lines on different ways. The limitations of a simplemodel may produce useless simulations. Although a complex model may produce a bettermodel representation, the accuracy of the result will depend on the event that it is wanted tosimulate. In the following section a description of the available models is given, after thatseveral simulation examples are presented to compare the models. These examples are: 1)Open-ended line connection 2) Three phase short circuit 3) Single phase to ground shortcircuit 4) Open-ended line disconnection.

Comparison of the steady state solution, aerial and ground mode values, and the response ofcircuits with trapped charges will be given.

2. Available models.

The available models in the ATP are:1) PI circuit2) Constant distributed parameter model (or K. C. Lee model)3) Frequency dependent models based on the modal decomposition a)SEMLYEN SETUP b)JMARTI SETUP4) TAKU NODA SETUP model.

2.1 PI Circuits

The PI circuit is a discrete approximation to the constant distributed parameter model. Linemodels based on PI circuits were used as a first solution for transient studies either using theATP program or Transient Network Analyzers.

The PI circuit is not generally the best model for transient studies. The solution of thesimulations using the distributed parameter model is faster and commonly gives moreaccurate results.The cascade connection of PI circuits can be useful for untransposed lines since it is notnecessary to consider approximations of the phase to mode transformation matrix.

By default, lines with frequency dependent parameter elements can not be represented by PIcircuits. Moreover, spurious oscillations generated by lumped parameter elements must beaccepted. However, resistances connected in parallel with the R-L branches can compensatethe spurious oscillations. The correct number of PI circuits depends on each particular systemto be simulated.

The main advantages of the PI circuit are:a) The model does not condition the calculation time step.b) The steady state solution is exact.

2.2 Constant distributed parameter models

The constant distributed parameter model calculates the different time propagation of thedecoupled mode components. In each extreme of the line, the values are converted frommode domain to phase domain using a transformation matrix. For transposed lines, thismatrix is constant, however, for untransposed lines, the transformation matrix varies with thefrequency. The variation with the frequency is more significant for cables than for lines. Thismakes necessary to take cautions upon adopting the frequency value where the parameterswill be calculated.

In addition, if the time step is not a sub-multiple of the line propagation time, the results ofthe simulation will be incorrect. Moreover, since the values are calculated by linearinterpolation, the results may differ for different time step calculation if the signal containshigh peak values.

The main limitation of the constant distributed parameter models is the assumption ofconsidering the parameters constant with respect to the frequency variation. Larger error isproduced for the ground mode, i.e. for those transient signals in which the zero sequencecomponent of voltage and current are present.

For short lines or cables, the constant distributed parameter model requires that the time stepmust be less than the propagation time. Therefore, it requires greater calculation time.

Despite its limitations, this model improves substantially the results with respect to themodels based on PI circuits.

2.3 Semlyen's model

This model (SEMLYEN SETUP) approximates the characteristic admittance and thepropagation constant of each mode through two exponential. Even though it was not the firstmodel that takes into account the variation of the parameters with the frequency, it is theoldest model that is available in the ATP.The simplicity of the equations causes that the approximation becomes insufficient even forline parameters without discontinuities. Therefore, the use of this model is becoming rare andits availability in ATP may be discontinued, as it happened with the WEIGHTING andHAUER SETUP.

2.4 José Martí's model

This model (JMARTI SETUP) approximates the characteristic admittance and thepropagation constant by rational functions.

Even though it has limitations, among all the variable parameter models it is the mostfrequently used. One of the limitations is that it uses a constant transformation matrix toconvert from mode domain to phase domain. For overhead lines this is not as important as itis for cables.

The model presents an unstable behavior for very low frequencies; for example casesincluding trapped charge. Furthermore, in some cases, the voltage can be increased withoutlimits.

One of the parameters required by this model is the mode conductance. The model issensitive respect to this parameter for trapped charge studies. Even though it is possible toobtain accurate results, it requires data manipulation. For example, the fitting must start froma very low frequency value to adjust the model (i.e. 0.0001 Hz).

The J. Martí's model employed in the program developed by the University of BritishColumbia (UBC) has been modified to eliminate some of the above limitations, however itrequires several tests before obtaining an adequate model.

2.5 Taku Noda's Model.

The TAKU NODA SETUP model differs from the previous models because the calculation ismade directly in phase domain. Therefore, eliminates the approximation errors produced bythe use of the transformation matrix.

The characteristic admittance and the deformation coefficients are fitted through rationalfunctions.

For a given line, to obtain an adequate model using Taku Noda's model is generally moredifficult, however it has the advantage that allows to define a time step independent of thepropagation time, but this demands to employ this time step for the simulation. If anothertime step is necessary for the simulations, the model must be recalculated.

The creation of a model requires two steps; first from the line data an auxiliary file is createdusing ATP (allowed by all ATP versions), second this file is converted to the final file thatwill model the line in the simulation. An adjustment program called ARMAFIT that adjuststhe values using rational functions is used to generate the final file. The users group of Japanis who supplies this program.

This file is included in the program through the adequate instructions. Up to date, Salfordversion does not include this model. Therefore another version called gnu djgpp was used.

3. Simulation results

To compare the performance of each one of the above line models, a 132 kV, 100 kmtransmission line was tested. This type of line is typically used by the utilities in the state ofSanta Fe, Argentina.

For the PI circuit model case, 100 PI circuits in cascade represent the line. Where eachelement represents 1 km of the line. For the trapped charge calculation the conductance toground was modeled by resistances to ground at the sending end of each PI circuit. TheCASCADE LINE option was employed for this model. Resistances to attenuate the spuriousoscillations were not added.

The same horizontal and vertical axes were used to plot all the simulation results in order tocompare the models easily.

3.1. Three phase connection of an open-ended line

The simulation of an open-ended line is useful to compare the voltage and current reflectionat the receiving end of the line. Furthermore, the attenuation of the high frequencycomponents and trend toward the steady state solution can be compared.

3.2 Single phase connection of an open-ended line

In this case, the coupling between the connected phase with the disconnected phases and theground mode attenuation can be compared.

For the case where the line is modeled using the constant distributed parameter model, it canbe observed that the phase voltages are in phase opposition. This effect is due to fact that theline parameters were calculated at a particular frequency value. The selection of a smallerfrequency value will produce smaller de-phase, however at lower frequencies the attenuationof the oscillations is reduced substantially producing invalidating the results. This limitationof the constant distributed parameter model produced the development of the frequencydependent line models.

3.3 Three phase short circuit

The simulation of a three phase short circuit permits to compare the steady state value of thepositive sequence component using different models.

From the simulation results can be conclude that the Semlyen's model produces an incorrectrepresentation of the steady state solution, leading to different values respect to the resultsproduced using the other models.

3.4 Single phase to ground short circuit

The simulation of a single phase to ground short circuit permits to compare the steady statevalue of the zero sequence components using different models. In this case, the resultsproduced by the Semlyen's model differ considerably respect to the results produced by theother models. In addition, Martí's model and Noda's model generate an attenuated directcurrent component during a single-phase short circuit simulation.

3.5 Disconnection of an open-ended line

The disconnection of an open-ended line permits to compare the voltage variation when theline has a trapped charge using different line models.

Resistances to ground were added in the line modeled using PI circuits to simulate the sameconductance. Semlyen's model has no conductance to ground therefore the voltages remainconstant. Martí's model and Noda's model produce incorrect results where data manipulationmay be required to improve the behavior of these models. The voltage attenuation producedusing the constant distributed parameter model and Noda's model is inherent to the model andcan not be control by the user.

References

[1] A. Semlyen and A. Dabuleanu, "Fast and accurate switching transientcalculations on transmission lines with ground return using recursiveconvolutions", IEEE Transactions on Power Apparatus and Systems, Vol. PAS-94(2), p. 561-571, 1975.

[2] J. R. Martí, "Accurate modelling of frequency-dependent transmission linesin electromagnetic transients simulations", IEEE Transactions on PowerApparatus and Systems, Vol. PAS 101(1), p. 147-155, 1982.

[3] T. Noda, N. Nagaoka and A. Ametani, "Phase Domain modelling ofFrequency-Dependent Transmission Lines by Means of an ARMA Model",IEEE Transactions on Power Delivery, Vol. 11, No.1, January 1996, p 401 -411, 1996.

[4] Hermann W. Dommel, "EMTP THEORY BOOK", Microtran Power SystemAnalysis Corporation, Vancouver, British Columbia, Canada, May 1992.

[5] Canadian/American EMTP User Group, "Alternative Transients ProgramRule Book", 1987-1995.

[6] Taku Noda, "Development of a transmission-line model considering theskin and corona effects for power system transient analysis", Doctoral Thesis,1996.

[7] Taku Noda, "User Instructions of Noda Setup in ATP", march 28, 1997

Appendix:

The data files are provided for each study case in order to facilitate the reader further researchon the comparison of the different line models available in ATP.

File name description

The last two letters of the file name indicate the model as follow:

pi : PI circuit modeldi : constant distributed parameter modelsm : Semlyen's modeljm : J. Martí's modelns : Noda's model

The first letters indicate the following:

par : parameter calculationsim : three phase connection of an open-ended linesim0 : single phase connection of an open-ended linecc3 : three phase short circuitcc1 : single phase to ground short circuittrap : disconnection of an open-ended line

Example:

The file simns.dat corresponds to the three phase connection of an open-ended line using theNoda's model (NODA SETUP).