**1. Introduction**

268 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

[3] http://aabi.tripod.com/notes/modeling\_control\_neutralization\_wswater.pdf.

[9] Salehi S., Shahrokhi M. And Nejati M. "Adaptive nonlinear control of pH neutralization process using fuzzy approximators" Control Engineering Practice 17, (2009) 1329-1337 [10] Duan S., Shi P., Feng H., DUan Z. And Mao Z. "An on-line Adaptive Control Based on DO/pH measurements and ANN Pattern Recognition Model For Fed-Batch

[4] https://boc.com.au/boc\_sp/.../BOC\_Carbon\_Dioxide\_for\_Water.pdf.

Cultivation" Biochemical Engineering Journal, 30 (2006) 88-86

[5] Zadeh, L., Fuzzy sets, Information Control 8, 338–353, 1965 [6] http://www.mathworks.com/products/daq/index.html. [7] www.eusflat.org/publications/.../295\_Nortcliffe.pdf. [8] http://discuss.itacumens.com/index.pHp?topic=27299.0

*Chemical Engineering, University of Bahrain, Bahrain* 

[1] faolex.fao.org/docs/pdf/mal13278.pdf. [2] www.skcct.com/EQA%20Summary.htm.

**Author details** 

Mostefa Ghassoul

**5. References** 

The design and operation of power systems, as well as of power apparatuses, each time depends more on accurate simulations of Electromagnetic Transients (EMTs). Essential to this is to count with advanced models for representing power transmission lines and cables. Electromagnetic Transients Program (EMTP), the most used EMT software, offer various line models. Among these, the most important ones are: 1) the Constant Parameters Line model (CP), 2) the Frequency Dependent or J. Marti Line model (FD) and 3) the Universal Line Model (ULM). The CP Line model is the simplest and most efficient one from the computational point of view. Nevertheless, it tends to overestimate the transient phenomena as it considers that line parameters are constant. Thus, it is recommended only for modeling lines on zones distant to an area where a transient event occurs. The FD Line model (Marti, 1982) evaluates multi–conductor line propagation in the modal domain and takes into account effects due to frequency dependence of the line parameters. Nevertheless, as the transformations between the modal and the phase domains are approximated by real and constant matrices, its accuracy is limited to cases of aerial lines which are symmetric or nearly symmetric. The FD model tends to underestimate the transient phenomena. ULM (Morched et al., 1999) takes into account the full-frequency dependence of line parameters. ULM works directly in phase domain, thus avoiding simplifying assumptions regarding modal–to–phase transformations. So far it is the most general model, capable to accurately represent asymmetric aerial lines as well as underground cables.

The development of ULM is fairly recent and these authors consider that it still is a subject for further research and development. The authors believe also that researchers and power system analysts will benefit considerably from the full understanding of the theoretical basis

© 2012 Ramos-Leaños et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Ramos-Leaños et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

of the ULM, as well as from counting with a ULM–type code that is easy to understand and modify. One problem with this is that the theoretical basis of ULM includes various topics and subjects that are scattered through several dozens of highly specialized papers. Another difficulty with this is the high complexity of the code for a ULM–type model. This chapter aims at providing a clear and complete description of the theoretical basis for this model. Although this description is intended for power engineers with an interest in electromagnetic transient phenomena, it can be of interest also to electronic engineers involved in the analysis and design of interconnects. The chapter includes as well the description of Matlab program of a ULM–type model, along with executable code and basic examples.
