One of the main difficulties when dealing with transient simulation studies in a digital simulator program is the correct representation of transmission lines.
Lumped and Distributed Transmission Line Model:
If travelling time of signals in transmission line is small than time step than we can model transmission line in to lumped parameter model. If travelling time is much larger than time than we have to make a distributed parameter model. We cannot take line parameter as lumped parameter.
Lumped Parameter Model:
PI Model:
The nominal PI model are often used for the short transmission line about 15 km, as the travel time of this model is less than time-step, but this model is not appropriate for the long transmission line. All parameters in this model are used in the lumped form. This model is useful for the steady-state analysis, as for single frequency.
Distributed Parameter Model (Travelling Wave Model):
Three types of model based on distributed parameter model.
1. Bergeron model
2. Frequency-Dependent Phase Model
3. Frequency-Dependent Mode Model
· Transmission line models which take into account the frequency dependence of the line parameters have become very important tools in the modern analysis of transient phenomena.
· This model have advantages over constant frequency model. Constant-Frequency models are very easy to use and require relatively little input information.
· On the other hand, frequency-dependent models require detailed knowledge of the tower configuration and conductor characteristics in order to evaluate the variation of R and L over the frequency range of interest to power transient simulations (i.e. dc to 1 MHz).
· In the simulation of large power systems, the relative complexity in the manipulation of input data for frequency-dependent models makes their use impractical for all except the most important lines.
· It is true that constant-parameters models are computationally faster and easier to use, it should be realized that their poor accuracy could adversely affect the outcome of the overall simulation.
· A compromise between simplicity and accuracy in the modelling of transmission lines is therefore desirable.
Bergeron Model:
· Bergeron Model is a constant frequency model. In this model, line parameters are taken as a constant frequency. Therefore this model is not accurate for transient analysis of transmission line.
· Bergeron Model is very easy to implement compared to frequency dependent model. So if a system is very large then it is not possible to implement frequency dependent model in that condition Bergeron model is used. The accuracy of this model is low compared to frequency dependent model.
· It requires R, L, C and G parameters for each propagation mode (+Ve seq. and zero seq.).
Frequency-Dependent Phase Model:
· Frequency-dependent phase model is a very accurate model for transient analysis of transmission line.
· Transmission line parameters are calculated from tower configuration. So, input for this model is tower configuration and conductors’ specification.
· It is difficult to implement this model if a system is very large. So this model is not applied to secondary transmission line it is useful to model primary transmission for transient analysis.
Frequency-Dependent Mode Model:
· This model approximates the phase to mode transformation as a constant. It is useful for studies wherever the transient and harmonic behavior of the transmission line is important.
· It works very well for single conductor lines, 2 horizontal conductors, or for ideally transposed line geometry. It should not be used for untransposed or when multiple towers are modeled on the same right of way.
· Modal transformation matrix is used to convert phase-domain (ABC) voltage and current to mode domain voltage and current (αβο).
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