Line Modeling

7/27/2019 Line Modeling

1/4

Advanced Power System Analysis

Line Modeling

Frequency DependentTransmission Line ModelingUtilizing Transposed Conditions

IEEE 2002

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 17, NO. 3,JULY 2002

Author:

Bjrn Gustavsen, Member, IEEE

SINTEF Energy Research,N-7465

Trondheim,

Norway

A CRITICAL ANALYSIS

Presented By : Nikhil Mundra07/PS/2010

MTech 1st Semester

Power Systems


2/4

Introduction:

This paper utilizes the existing phase-domain line modeling technique, which is

considered to be highly accurate and efficient both for Overhead as well asUnderground lines. It aims to reduce the computation time involved in thetechnique without compromising on the accuracy. This is done by introducing ahybrid line model and considering one or many of the lines to be continuouslytransposed. For this, a constant transformation matrix is utilized, along with aregular phase-domain line model and multiple single line models. The resultsshow an increase in the computation speed, and if the circuits are untransposed,the single line model becomes a full phase model.

Detailed Analysis:

Phase-domain models, though more accurate than the frequency domain ones,are extremely slow in their progress. In case of EMTP programs, we haveoptions of assigning lines as continuously transposed. This helps in usage of acontinuous transformation matrix, leading to diagonal and fewer off-diagonalelements. Though zero sequence coupling can be employed, it leads tofrequency analysis. Therefore, with a hybrid model, with a small phase block isideal for taking coupling into consideration.

The transmission line equations are:

,

Here Z,Y are square symmetrical matrices. With the principle of continuoustransposition, all conductors within a circuit get the same coupling withconductors outside the circuit. The Z and Y matrices can be viewed as havingindividual 3x3 blocks, and can be further modified by averaging the terms. Thepaper stresses that pure untransposed terms are left unchanged, while thoseterms that are either a combination of transposed and untransposed or are purelytransposed, are averaged. As an example, the paper presents the following:


3/4

The aim is to finally obtain elements only on the diagonal terms, and this is doneusing Clarkes transformation. The modified matrix is given as:

, where T is based on Clarkes matrix, given as:

After applying various guidelines, the paper arrives at the fact that the method isapplicable to any generalized system, such that with m transposed and n

untransposed lines, the number of modes is 2m and size of phase block is m+3n.

Following the above conclusions, it can be seen that a model can be made with aphase block with several modes in parallel, and the interfacing can be done usingT matrix. The phase block is modeled using a frequency dependent phase-domain model, while trapezoidal integration leads to a time-domain conductancematrix in parallel with a current source. This is also done for each of the modes,iterated from 1 to n.

Thus, a line model can be adapted by the main program using the Nortonsequivalent. The current and voltage vectors can be calculated as above, usingthe Clarkes transformation matrix and the value of voltage Vk specified in theproblem.


4/4

The paper then puts this theory to practice, and tests the hybrid model on 3different line models 1 transposed, 2 transposed and 3 transposed circuits. TheZ, Y and H (propagation) matrices are all fitted using a 12 th order approximationvector fitting technique. The efficiency of the hybrid model can be determinedbased on the number of flops (floating point operations) consumed by the

models. The results in the case of a regular phase model and the hybrid modelare tabulated as follows:

Phase model Hybrid model Ratio

1-tranposed 1 0.28 3.57

2-transposed 9.57 1.32 6.95

3-transposed 24.89 2.70 9.21

Thus, we see a marked increase in efficiency in the use of the Hybrid model.

Conclusions:

Though comparisons have been made with a higher degree of fitting thanneeded by the phase-model, it is observed that even with a lower order,the hybrid model is 3-4 times more efficient than its counterpart.

It is assumed that the length of each transposition cycle is extremelysmall, lending it negligible. Here, the reflections occurring in each cycleare unaccounted. Even then, this is not a problem in low-frequency cases.

The method works well with continuous or arbitrary phase-numbering, sothat is not a constraint.

Thus, the hybrid line model uses the computational accuracy of the phase-domain model and adds the efficiency factor to it.

The increase in efficiency may seem small for a single line, but whenapplied to a large system, its effects will be easily appreciated.

Drawbacks:

This model is specifically designed only for the continuous transposed lines, afeature available in programs dealing in power systems.

Documents

Line Modeling