\documentclass[11pt,twoside]{article}\makeatletter

\IfFileExists{xcolor.sty}%
  {\RequirePackage{xcolor}}%
  {\RequirePackage{color}}
\usepackage{colortbl}
\usepackage{wrapfig}
\usepackage{ifxetex}
\ifxetex
  \usepackage{fontspec}
  \usepackage{xunicode}
  \catcode`⃥=\active \def⃥{\textbackslash}
  \catcode`❴=\active \def❴{\{}
  \catcode`❵=\active \def❵{\}}
  \def\textJapanese{\fontspec{Noto Sans CJK JP}}
  \def\textChinese{\fontspec{Noto Sans CJK SC}}
  \def\textKorean{\fontspec{Noto Sans CJK KR}}
  \setmonofont{DejaVu Sans Mono}
  
\else
  \IfFileExists{utf8x.def}%
   {\usepackage[utf8x]{inputenc}
      \PrerenderUnicode{–}
    }%
   {\usepackage[utf8]{inputenc}}
  \usepackage[english]{babel}
  \usepackage[T1]{fontenc}
  \usepackage{float}
  \usepackage[]{ucs}
  \uc@dclc{8421}{default}{\textbackslash }
  \uc@dclc{10100}{default}{\{}
  \uc@dclc{10101}{default}{\}}
  \uc@dclc{8491}{default}{\AA{}}
  \uc@dclc{8239}{default}{\,}
  \uc@dclc{20154}{default}{ }
  \uc@dclc{10148}{default}{>}
  \def\textschwa{\rotatebox{-90}{e}}
  \def\textJapanese{}
  \def\textChinese{}
  \IfFileExists{tipa.sty}{\usepackage{tipa}}{}
\fi
\def\exampleFont{\ttfamily\small}
\DeclareTextSymbol{\textpi}{OML}{25}
\usepackage{relsize}
\RequirePackage{array}
\def\@testpach{\@chclass
 \ifnum \@lastchclass=6 \@ne \@chnum \@ne \else
  \ifnum \@lastchclass=7 5 \else
   \ifnum \@lastchclass=8 \tw@ \else
    \ifnum \@lastchclass=9 \thr@@
   \else \z@
   \ifnum \@lastchclass = 10 \else
   \edef\@nextchar{\expandafter\string\@nextchar}%
   \@chnum
   \if \@nextchar c\z@ \else
    \if \@nextchar l\@ne \else
     \if \@nextchar r\tw@ \else
   \z@ \@chclass
   \if\@nextchar |\@ne \else
    \if \@nextchar !6 \else
     \if \@nextchar @7 \else
      \if \@nextchar (8 \else
       \if \@nextchar )9 \else
  10
  \@chnum
  \if \@nextchar m\thr@@\else
   \if \@nextchar p4 \else
    \if \@nextchar b5 \else
   \z@ \@chclass \z@ \@preamerr \z@ \fi \fi \fi \fi
   \fi \fi  \fi  \fi  \fi  \fi  \fi \fi \fi \fi \fi \fi}
\gdef\arraybackslash{\let\\=\@arraycr}
\def\@textsubscript#1{{\m@th\ensuremath{_{\mbox{\fontsize\sf@size\z@#1}}}}}
\def\Panel#1#2#3#4{\multicolumn{#3}{){\columncolor{#2}}#4}{#1}}
\def\abbr{}
\def\corr{}
\def\expan{}
\def\gap{}
\def\orig{}
\def\reg{}
\def\ref{}
\def\sic{}
\def\persName{}\def\name{}
\def\placeName{}
\def\orgName{}
\def\textcal#1{{\fontspec{Lucida Calligraphy}#1}}
\def\textgothic#1{{\fontspec{Lucida Blackletter}#1}}
\def\textlarge#1{{\large #1}}
\def\textoverbar#1{\ensuremath{\overline{#1}}}
\def\textquoted#1{‘#1’}
\def\textsmall#1{{\small #1}}
\def\textsubscript#1{\@textsubscript{\selectfont#1}}
\def\textxi{\ensuremath{\xi}}
\def\titlem{\itshape}
\newenvironment{biblfree}{}{\ifvmode\par\fi }
\newenvironment{bibl}{}{}
\newenvironment{byline}{\vskip6pt\itshape\fontsize{16pt}{18pt}\selectfont}{\par }
\newenvironment{citbibl}{}{\ifvmode\par\fi }
\newenvironment{docAuthor}{\ifvmode\vskip4pt\fontsize{16pt}{18pt}\selectfont\fi\itshape}{\ifvmode\par\fi }
\newenvironment{docDate}{}{\ifvmode\par\fi }
\newenvironment{docImprint}{\vskip 6pt}{\ifvmode\par\fi }
\newenvironment{docTitle}{\vskip6pt\bfseries\fontsize{22pt}{25pt}\selectfont}{\par }
\newenvironment{msHead}{\vskip 6pt}{\par}
\newenvironment{msItem}{\vskip 6pt}{\par}
\newenvironment{rubric}{}{}
\newenvironment{titlePart}{}{\par }

\newcolumntype{L}[1]{){\raggedright\arraybackslash}p{#1}}
\newcolumntype{C}[1]{){\centering\arraybackslash}p{#1}}
\newcolumntype{R}[1]{){\raggedleft\arraybackslash}p{#1}}
\newcolumntype{P}[1]{){\arraybackslash}p{#1}}
\newcolumntype{B}[1]{){\arraybackslash}b{#1}}
\newcolumntype{M}[1]{){\arraybackslash}m{#1}}
\definecolor{label}{gray}{0.75}
\def\unusedattribute#1{\sout{\textcolor{label}{#1}}}
\DeclareRobustCommand*{\xref}{\hyper@normalise\xref@}
\def\xref@#1#2{\hyper@linkurl{#2}{#1}}
\begingroup
\catcode`\_=\active
\gdef_#1{\ensuremath{\sb{\mathrm{#1}}}}
\endgroup
\mathcode`\_=\string"8000
\catcode`\_=12\relax

\usepackage[a4paper,twoside,lmargin=1in,rmargin=1in,tmargin=1in,bmargin=1in,marginparwidth=0.75in]{geometry}
\usepackage{framed}

\definecolor{shadecolor}{gray}{0.95}
\usepackage{longtable}
\usepackage[normalem]{ulem}
\usepackage{fancyvrb}
\usepackage{fancyhdr}
\usepackage{graphicx}
\usepackage{marginnote}

\renewcommand{\@cite}[1]{#1}


\renewcommand*{\marginfont}{\itshape\footnotesize}

\def\Gin@extensions{.pdf,.png,.jpg,.mps,.tif}

  \pagestyle{fancy}

\usepackage[pdftitle={Enhancement of Transient Stability in a Deregulated Power System using Facts Devices},
 pdfauthor={}]{hyperref}
\hyperbaseurl{}

	 \paperwidth210mm
	 \paperheight297mm
              
\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}
\clubpenalty=8000
\emergencystretch 3em
\hbadness=4000
\hyphenpenalty=400
\pretolerance=750
\tolerance=2000
\vbadness=4000
\widowpenalty=10000

\renewcommand\section{\@startsection {section}{1}{\z@}%
     {-1.75ex \@plus -0.5ex \@minus -.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\Large\bfseries}}
\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
     {-1.75ex\@plus -0.5ex \@minus- .2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\Large}}
\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%
     {-1.5ex\@plus -0.35ex \@minus -.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\large}}
\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}%
     {-1ex \@plus-0.35ex \@minus -0.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\normalsize}}
\renewcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}%
     {1.5ex \@plus1ex \@minus .2ex}%
     {-1em}%
     {\reset@font\normalsize\bfseries}}


\def\l@section#1#2{\addpenalty{\@secpenalty} \addvspace{1.0em plus 1pt}
 \@tempdima 1.5em \begingroup
 \parindent \z@ \rightskip \@pnumwidth 
 \parfillskip -\@pnumwidth 
 \bfseries \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}\par
 \endgroup}
\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
\@ifundefined{c@section}{\newcounter{section}}{}
\@ifundefined{c@chapter}{\newcounter{chapter}}{}
\newif\if@mainmatter 
\@mainmattertrue
\def\chaptername{Chapter}
\def\frontmatter{%
  \pagenumbering{roman}
  \def\thechapter{\@roman\c@chapter}
  \def\theHchapter{\roman{chapter}}
  \def\thesection{\@roman\c@section}
  \def\theHsection{\roman{section}}
  \def\@chapapp{}%
}
\def\mainmatter{%
  \cleardoublepage
  \def\thechapter{\@arabic\c@chapter}
  \setcounter{chapter}{0}
  \setcounter{section}{0}
  \pagenumbering{arabic}
  \setcounter{secnumdepth}{6}
  \def\@chapapp{\chaptername}%
  \def\theHchapter{\arabic{chapter}}
  \def\thesection{\@arabic\c@section}
  \def\theHsection{\arabic{section}}
}
\def\backmatter{%
  \cleardoublepage
  \setcounter{chapter}{0}
  \setcounter{section}{0}
  \setcounter{secnumdepth}{2}
  \def\@chapapp{\appendixname}%
  \def\thechapter{\@Alph\c@chapter}
  \def\theHchapter{\Alph{chapter}}
  \appendix
}
\newenvironment{bibitemlist}[1]{%
   \list{\@biblabel{\@arabic\c@enumiv}}%
       {\settowidth\labelwidth{\@biblabel{#1}}%
        \leftmargin\labelwidth
        \advance\leftmargin\labelsep
        \@openbib@code
        \usecounter{enumiv}%
        \let\p@enumiv\@empty
        \renewcommand\theenumiv{\@arabic\c@enumiv}%
	}%
  \sloppy
  \clubpenalty4000
  \@clubpenalty \clubpenalty
  \widowpenalty4000%
  \sfcode`\.\@m}%
  {\def\@noitemerr
    {\@latex@warning{Empty `bibitemlist' environment}}%
    \endlist}

\def\tableofcontents{\section*{\contentsname}\@starttoc{toc}}
\parskip0pt
\parindent1em
\def\Panel#1#2#3#4{\multicolumn{#3}{){\columncolor{#2}}#4}{#1}}
\newenvironment{reflist}{%
  \begin{raggedright}\begin{list}{}
  {%
   \setlength{\topsep}{0pt}%
   \setlength{\rightmargin}{0.25in}%
   \setlength{\itemsep}{0pt}%
   \setlength{\itemindent}{0pt}%
   \setlength{\parskip}{0pt}%
   \setlength{\parsep}{2pt}%
   \def\makelabel##1{\itshape ##1}}%
  }
  {\end{list}\end{raggedright}}
\newenvironment{sansreflist}{%
  \begin{raggedright}\begin{list}{}
  {%
   \setlength{\topsep}{0pt}%
   \setlength{\rightmargin}{0.25in}%
   \setlength{\itemindent}{0pt}%
   \setlength{\parskip}{0pt}%
   \setlength{\itemsep}{0pt}%
   \setlength{\parsep}{2pt}%
   \def\makelabel##1{\upshape ##1}}%
  }
  {\end{list}\end{raggedright}}
\newenvironment{specHead}[2]%
 {\vspace{20pt}\hrule\vspace{10pt}%
  \phantomsection\label{#1}\markright{#2}%

  \pdfbookmark[2]{#2}{#1}%
  \hspace{-0.75in}{\bfseries\fontsize{16pt}{18pt}\selectfont#2}%
  }{}
      \def\TheFullDate{2014-01-15 (revised: 15 January 2014)}
\def\TheID{\makeatother }
\def\TheDate{2014-01-15}
\title{Enhancement of Transient Stability in a Deregulated Power System using Facts Devices}
\author{}\makeatletter 
\makeatletter
\newcommand*{\cleartoleftpage}{%
  \clearpage
    \if@twoside
    \ifodd\c@page
      \hbox{}\newpage
      \if@twocolumn
        \hbox{}\newpage
      \fi
    \fi
  \fi
}
\makeatother
\makeatletter
\thispagestyle{empty}
\markright{\@title}\markboth{\@title}{\@author}
\renewcommand\small{\@setfontsize\small{9pt}{11pt}\abovedisplayskip 8.5\p@ plus3\p@ minus4\p@
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus2\p@
\belowdisplayshortskip 4\p@ plus2\p@ minus2\p@
\def\@listi{\leftmargin\leftmargini
               \topsep 2\p@ plus1\p@ minus1\p@
               \parsep 2\p@ plus\p@ minus\p@
               \itemsep 1pt}
}
\makeatother
\fvset{frame=single,numberblanklines=false,xleftmargin=5mm,xrightmargin=5mm}
\fancyhf{} 
\setlength{\headheight}{14pt}
\fancyhead[LE]{\bfseries\leftmark} 
\fancyhead[RO]{\bfseries\rightmark} 
\fancyfoot[RO]{}
\fancyfoot[CO]{\thepage}
\fancyfoot[LO]{\TheID}
\fancyfoot[LE]{}
\fancyfoot[CE]{\thepage}
\fancyfoot[RE]{\TheID}
\hypersetup{citebordercolor=0.75 0.75 0.75,linkbordercolor=0.75 0.75 0.75,urlbordercolor=0.75 0.75 0.75,bookmarksnumbered=true}
\fancypagestyle{plain}{\fancyhead{}\renewcommand{\headrulewidth}{0pt}}

\date{}
\usepackage{authblk}

\providecommand{\keywords}[1]
{
\footnotesize
  \textbf{\textit{Index terms---}} #1
}

\usepackage{graphicx,xcolor}
\definecolor{GJBlue}{HTML}{273B81}
\definecolor{GJLightBlue}{HTML}{0A9DD9}
\definecolor{GJMediumGrey}{HTML}{6D6E70}
\definecolor{GJLightGrey}{HTML}{929497} 

\renewenvironment{abstract}{%
   \setlength{\parindent}{0pt}\raggedright
   \textcolor{GJMediumGrey}{\rule{\textwidth}{2pt}}
   \vskip16pt
   \textcolor{GJBlue}{\large\bfseries\abstractname\space}
}{%   
   \vskip8pt
   \textcolor{GJMediumGrey}{\rule{\textwidth}{2pt}}
   \vskip16pt
}

\usepackage[absolute,overlay]{textpos}

\makeatother 
      \usepackage{lineno}
      \linenumbers
      
\begin{document}

             \author[1]{J.Srinivasa  Rao}

             \affil[1]{  }

\renewcommand\Authands{ and }

\date{\small \em Received: 12 December 2013 Accepted: 2 January 2014 Published: 15 January 2014}

\maketitle


\begin{abstract}
        


In a deregulated power system, the electric power demand is increasing day to day which may lead to overloads and loss of generation. Transient stability studies place an important role in power systems, which provide information related to the capability of a power system to remain in synchronism during major disturbances resulting from either the loss of generation or transmission facilities, sudden or sustained load changes. The analysis of transient stability is very important to operate the power system more secure and this paper focuses on increasing the transient stability [1] using FACTS devices like TCSC (Thyristor Controlled Series Capacitor), TCPAR (Thyristor Controlled Phase Angle Regulator), SVC (Static Var Compensator). These FACTS devices are optimally placed on transmission system using Sensitivity approach method. The proposed method is to enhance the transient stability on Modified IEEE-14 bus system and IEEE-24 bus system Using Power World Simulator 17 software.

\end{abstract}


\keywords{deregulated power system, ATC, TCSC, TCPAR, SVC.}

\begin{textblock*}{18cm}(1cm,1cm) % {block width} (coords) 
\textcolor{GJBlue}{\LARGE Global Journals \LaTeX\ JournalKaleidoscope\texttrademark}
\end{textblock*}

\begin{textblock*}{18cm}(1.4cm,1.5cm) % {block width} (coords) 
\textcolor{GJBlue}{\footnotesize \\ Artificial Intelligence formulated this projection for compatibility purposes from the original article published at Global Journals. However, this technology is currently in beta. \emph{Therefore, kindly ignore odd layouts, missed formulae, text, tables, or figures.}}
\end{textblock*}


\let\tabcellsep& 	 	 		 \par
Introduction n a deregulated power system structure, customers share a common transmission network for wheeling power from the point of generation to the point of consumption. All parties in this open access environment may try to produce the energy from the cheaper source for greater profit margin. It may lead to overload of the power system. This may result in violation of stability limits and thereby undermine the system security. Transient stability of a system refers to the stability when subjected to large disturbances such as faults and switching of lines. The resulting system response involves large excursions of generator rotor angles and is influenced by the nonlinear power angle relationship.\par
Transient stability \hyperref[b1]{[2]} studies place an important role in power systems, which provide information related to the capability of a power system to remain in synchronism during major disturbances resulting from either the loss of generation or transmission facilities, sudden or sustained load changes, in the voltages, currents, powers, speeds and torques of the machines of the power systems as explained.\par
FACTS devices are capable of controlling the network condition in a very fast manner and this unique feature of FACTS devices can be exploited to enlarge the decelerating area and hence improving the first swing stability limit of a system. Due to FACTS device placement in the main power transfer path of the critical machine, the output power of the machine and hence its first swing stability limit can be increased by operating the FACTS device at its full capacitive rating. Control strategy was proposed based upon local input signals can be used for series and shunt compensator devices to damp power swings. Using the proposed control strategies [8], the series and shunt connected compensators can be located in several locations.\par
Flexible AC Transmission Systems (FACTS), provide proven technical solutions to address these new operating challenges being presented today. Thyristor Controlled Series Capacitor (TCSC), Thyristor Controlled Phase Angle Regulator (TCPAR) and Static VAR Compensator (SVC) are used for enhancement of Transient Stability using Sensitivity based methods. 
\section[{II.}]{II.} 
\section[{Structure of Regulated And Deregulated Systems}]{Structure of Regulated And Deregulated Systems}\par
The former vertically integrated utility, which perform all the functions involved in power,( i.e., generation, transmission, distribution and retail sales) known as regulated system, is dis-aggregated in to separate companies devoted to their functions called as Deregulated system.\par
The main aim of restructuring \hyperref[b5]{[6]} the power market is as follows: ? To secure that all reasonable demands for the electricity are met. ? Promote competition in the generation and supply of electricity. ? Protect the interests of electricity customers in respect to prices charged, continuity of supply and the quality of services provided. ? Promote efficiency and economy on the part of licensees in supplying and transmitting electricity.\par
The following figure-1 shows the typical structure of regulated power system which is simply vertically integrated where the cash flow is unidirectional from consumers to electric utility.  
\section[{System}]{System}\par
For developing countries, the main issues have been a high demand growth coupled with inefficient system management and irrational tariff policies. This has affected the availability of financial resources to support investments in improving generation and transmission capacities.\par
The goal of changing the way of operation, i.e., re-regulation or de-regulation, as we say, is to enhance competition and bring consumers new choices and economic benefits. In a deregulated system a system operator is appointed for the whole system and it is entrusted with the responsibility of keeping the system in balance, i.e. to ensure that the production and imports continuously match consumption and exports. Different power sellers will deliver their product to the customers (via retailers), over a common set of T and D wires, operated by the independent system operator (ISO). The generators, T and D utility and retailers communicate with the ISO.    
\section[{III.}]{III.} 
\section[{Facts Controllers}]{Facts Controllers}?? ???? = ??? ?? 2 ??? ???? + ?? ??? ? ? ?? ?? ?? ?? [?? ???? sin??? ???? ? ? ?? ???? cos??? ???? ?] (3.2)\par
Where ?ij = ?i-?j, similarly the real and reactive power flow from bus-j to bus-i is;?? ???? = ?? 1 2 ?? ???? ? ?? ?? ?? ?? [?? ???? cos??? ???? ? + ?? ???? sin??? ???? ?] (3.3) ???? ???? = ??? ?? 2 ??? ???? + ?? ??? ? ? ?? ?? ?? ?? ??? ???? sin??? ???? ? ? ?? ???? cos??? ???? ?? (3.4)\par
Figure  {\ref 5} : Model of Transmission line\par
The model of transmission line with a TCSC connected between bus-i and bus-j is shown in Fig.  {\ref During} the steady state the TCSC can be considered as a static reactance -jXc. The real and reactive power flow from bus-i to bus-j, and from bus-j to bus-i of a line having series impedance and a series reactance are, The change in the line flow due to series capacitance can be represented as a line without series capacitance with power injected at the receiving and sending ends of the line as shown in Figure  {\ref .} The real and reactive power injections at bus-i and bus-j can be expressed as, ?? ???? ?? =?? ?? 2 ?? ???? ? ? ?? ?? ?? ?? (?? ???? ? ???????? ???? + ?? ???? ? ???????? ???? ) (3.?? ???? = ?? ?? 2 ??? ???? ???? ???? 2 + ?? ???? 2 ?(?? ???? 2 + ??? ???? ? ?? ?? ?2)\par
This Model of TCSC is used to properly modify the parameters of transmission line with TCSC for optimal location.\par
ii. Thyristor Controlled Phase Angle Regulator (Tcpar) Thyristor Controlled Phase Angle Regulator 'TCPAR' for power flow studies and the role of that modeling in the study of Flexible Alternating Current Transmission Systems 'FACTS' for power flow control are discussed. In order to investigate the impact of TCPAR on power systems effectively, it is essential to formulate a correct and appropriate model for it. The TCPAR, thus, makes it possible to increase or decrease the power forwarded in the line where it is inserted in a considerable way, which makes of it an ideal tool for this kind of use. Knowing that the TCPAR does not inject any active power, it offers a good solution with a less consumption. 
\section[{a. Static Modelling of Tcpar}]{a. Static Modelling of Tcpar}\par
It is modeled by a voltage source, which represents the branch series, and of a power source representing the branch shunt. In computing the power flow, these devices are modeled using an ideal transformer with complex transformation ratio ?. In the case of the TCPAR \hyperref[b4]{[5]}, the transformation ratio is expressed as:?? = ?? ???? (3.13)\par
Thus, it only affects the voltage angle while its magnitude remains constant. Considering above equations, the new expressions of the currents become:???? = ?? ???? ?? * ???? + ?? ???? ?? * ?? ???? + ?? ???? ?? * ?? ?? ?? ?? = ?? ???? ?? * ?? ?? + ?? ???? ?? ??\par
The admittance matrix of the new line has the form:? ???? ?? ?? ?=[??] ? ???? ?? ???? ?? ?? ? b) Static Var Compensators (Svc)\par
A common practice of system voltage adjustment is shunt reactive power compensation. The synchronous condenser was historically an important tool of shunt reactive power compensation. Since it is a rotating machine, its operation and maintenance are quite complicated. New synchronous condensers are now seldom installed. The static shunt reactive power compensation, as opposed to the rotating synchronous condenser, has wide industrial application due to its low cost and simple operation and maintenance.\par
Conventional static shunt reactive power compensation is to install capacitors, reactors, or their combination, at the compensated buses to inject or extract reactive power from the system. Mechanical switches are used to put the shunt capacitor/reactors into or out of operation. Where L is the inductance of the reactor, Vm is the magnitude of the system voltage. 
\section[{Its general solution is}]{Its general solution is}?? ?? = ?? ? ?? ?? ???? ?????????? (3.24)\par
Where K is the integral constant. Since the inductor current is zero at firing, the above equation yields?? ?? = ?? ? ?? ?? ?? ?? cos(?? + ????) =0 (3.25)\par
Substituting the solution of K in to equation 3.25 gives rise to the inductor current.?? ?? = ?? ?? ???? [??????(?? + ????) ? ??????????] ?? = 0,1,2, ? ?. 
\section[{Global Journal of Researches in Engineering ( )}]{Global Journal of Researches in Engineering ( )}\par
Based on the above equation, inductor current returns to zero at ???? = (?? + 2)?? ? ?? Thus the valve conducting period is???? ?? [???? + ??, (?? + 2)?? ? ??] ?? = 1,2,3, ?.\par
The adjustment of firing angles changes the current peak values and conducting periods. Applying Fourier analysis to the current yields the magnitude of the fundamental frequency Component.?? ??1 = 2 ?? ? ?? ?? ???? (???????? ? ????????) cos ?? ???? = ?? ?? ?????? 2????? ?? [2(?? ? ??) ? ??????2??] (3.26)\par
And the instantaneous value of fundamental frequency component is?? ??1 = ?? ??1 ?????????? = ?? ?? ?????? (2?? ? ??????2??)?????? ????? ? ?? 2 ? (3.27)\par
The equivalent fundamental frequency reactance of the TCR branch is?? ?? (??) = ?????? 2?? ??????? 2?? ?? ? [0, ?? 2 ]\par
Thus the TCR equivalent reactance of fundamental frequency components is the function of conducting angle ? or the firing angle ?. The control of firing angle ? can smoothly adjust the equivalent shunt reactance. The reactive power consumed by TCR is?? ?? = ?? ?????1 * = ?? 2 ?? ?? (?? ) = 2?? ??????? 2?? ?????? ?? 2 (3.28)\par
The TSC branch consists of a capacitor connected in series with two thyristors connected in parallel and in opposite directions. The TSC source voltage is the same as TCR. Its waveforms are in Figure  {\ref .} The TSC creates two operating states for the capacitors through valve control: shunt capacitors in service or out of service. Stopping the firing can simply put the capacitor out of service. Note that the natural switch-off from conduction happens when the capacitor current is zero and its voltage at the peak of source voltage. Neglecting the capacitor leakage current, capacitor voltage maintains the peak value if firing stops after the Natural switch-off. We need to pay attention to the timing of putting the capacitor into service. The reactive power injection of the capacitors is?? ?? = ?????? 2 (3.29)\par
Where C is the capacitance of the capacitor. From above two equations [3.28] \& [3.29] we have the reactive power injection from the SVC is 2  (3.30)?? ?????? = ?? ?? ? ?? ?? = (???? ? 2?? ??????? 2?? ?????? )??\par
The SVC reactive power injection can be smoothly adjusted when ?? [0,??/2]. To expand the regulation ranges of SVC, we can have many TSC branches in one SVC, based on the compensation requirements. Figure shows an SVC with three TSCs. When all three TSCs are in service, the C in above equation is C1+C2+C3. To guarantee a continuous adjustment, the TCR capacity should be slightly larger than a group of TSCs, that is, ??C1 < 1/??L. 
\section[{Based on above equation the equivalent reactance of SVC is}]{Based on above equation the equivalent reactance of SVC is}?? ?????? = ? ????? ? 2?? ? ??????2?? ?1 ?????? ? = ?????? 2?? ? ??????2?? ? ???? 2 ????\par
In Figure  {\ref ,} shown below there is a straight line going through the original corresponding to every ?. The slope of the straight line is XSVC. Suppose that the system voltage characteristic is V1. The control scheme is to make the TCR conducting angle ?1= ??/2, corresponding to maximum equivalent inductive reactance. The SVC operating point is the crossover point A between system voltage characteristic V1 and the straight line ?1. With system voltage characteristic V2 and TCR conduction angle ?2 < ?1, XSVC decreases and the SVC operating point shifts accordingly. Until system voltage characteristic is V6 and conduction angle ?6= 0, SVC equivalent reactance is maximum capacitive with operating point B. Where Xe is the slope of the straight line AB in Voltage Characteristics, V and ISVC are the SVC terminal voltage and current. When system voltage is out of the SVC control range, SVC becomes a fixed reactor, XSVCmin or XSVCmax. SVC is considered as a variable shunt reactor in system stability and control analysis. SVC controller determines its admittance. We have introduced SVC basic principles. Special attention needs to be paid in industrial applications of SVC to capacity settings of reactors and capacitors, control strategy, flexibility of adjustments, protection, elimination of harmonics, etc .For example, in practical operation of an SVC, the range of the control angle is slightly less than [??/2, ??] to make sure that valves can be triggered on and turned off securely. 
\section[{IV.}]{IV.}\par
Optimal Location based on Sensitivity Approach for Tcsc, Tcpar and Svc\par
The static devices are considered in order to achieve the following in the power system: 1. Reduction in total system losses 2. Increased transfer capability 3. Reduction in total MVAR losses a) Selection of optimal location of FACTS devices Using loss sensitivity index, the FACTS devices are placed in a suitable location as follows:\par
The Reduction of Total System Reactive Power Losses Method sensitivity factors with respect to the parameters of TCSC , TCPAR and SVC are defined as:\par
? Loss sensitivity with respect to control parameter X ij of TCSC placed between buses i and j,a ij = ?????? ???? ????\par
? Loss sensitivity with respect to control parameter X ij and ?? ij of TCPAR placed at buses i and j b ij= ?????? ???? ????\par
? Loss sensitivity with respect to control parameter Qi of SVC placed at bus i, c i= 
\section[{?????? ???? ??}]{?????? ???? ??}\par
These factors can be computed for a base case power flow solution. Consider a line connected between buses i and j and having a net series impedance of Xij. The loss sensitivities with respect to Xij, ?? ???? and Qi can be computed as:  Where Vi is the voltage at bus i Vj is the voltage at bus j Rij is resistance of line connected between bus i and j Xij is the reactance connected between bus i and j B ij is the susceptance connected between bus i and j ? is the firing angle of SVC ?? ???? is the net phase shift in the line.\par
The FACTS device must be placed on the most sensitive lines. With the sensitive indices computed for each type of FACTS device, TCSC , SVC and TCPAR should be placed in a line (K) having most positive value and absolute value of sensitivity respectively.\par
V. 
\section[{Simulation and Results Discussion}]{Simulation and Results Discussion}\par
The study has been conducted on transient stability of an IEEE 14 BUS system and IEEE 24 BUS system using power world simulator 17.0.\par
For each system the enhancement of Transient stability is determined by placing different FACTS devices like TCSC, TCPAR and SVC in the optimal location using sensitivity approach method. The two systems are modeled internally using power world simulator. The internal models includes generator model, exciter model, stabilizers?e.t.c. The following section contains the detailed results. Table  {\ref 1} : Sensitivity Factors For TCSC, TCPAR In IEEE 14-Bus System For this system, from table-1 the following are considered:\par
? TCSC is placed with a compensation of 40\% in the line 13(12-13) and is operated.\par
? TCPAR is placed with a phase shift of 2 and unity tap ratio. By using sensitivity approach, the sensitivity index at line 13 is more positive than remaining lines hence the compensation is provided at that line. Similarly the sensitivity index at line 3 is the highest absolute value i.e. -0.1565 and -0.0011 for 30\% and 40\% compensation of TCPAR.\par
By placing these devices in a line the transient stability is improved i.e. generator rotor angles, voltages, generator power, accelerated power are improved as shown. 
\section[{i. Rotor angle improvement}]{i. Rotor angle improvement}\par
The following graphs shows the variation of rotor angle with time and it also shows the enhancement Line From Bus To Bus Sensitivity Index TCSC (30\%) (a ij ) This system consists of 14 buses, 17 line sections, 5 generator buses and 8 load buses.          The following table-shows the sensitivity index for IEEE 24-bus system.TCSC (40\%) (a ij ) TCPAR (30\%) (b ij ) TCPAR (40\%) (b ij )\par
From the table below the line 10(6-10) has more positive sensitivity index at 30\% and 40\% compensation of TCSC. Similarly, the line 31(17-22) has high absolute value at 30\% and 40\% compensation.\par
For this system, from table above the following are considered:\par
? TCSC is placed with a compensation of 40\% in the line 10(6-10) and is operated. Table  {\ref 2} :\par
By using sensitivity approach, the sensitivity index at line 10 is more positive than remaining lines hence the compensation is provided at that line. Similarly the sensitivity index at line 31 is the highest absolute value i.e. 0.1326 and 0.1136 for 30\% and 40\% compensation of TCPAR.\par
By placing these devices in a line the transient stability is improved i.e. generator rotor angles, voltages, generator power, accelerated power and MVAR are improved as shown. 
\section[{c) Rotor angle improvement}]{c) Rotor angle improvement}\par
The following graphs shows the variation of rotor angle with time and it also shows the enhancement of rotor angle with and without FACTS device during Transient Stability.      
\section[{Mvar Terminal}]{Mvar Terminal}\par
The following figures show the variation of MVAR with time during Transient stability. The MVAR at the generator terminal decreases by placing the FACTS device as shown.  
\section[{Conclusion}]{Conclusion}\par
In this paper a simple sensitivity method is used for determining optimum location of FACTS devices for improving the transient stability. Based on sensitivity index the device is located. The rotor angle, voltage, speed and MVAR terminal of generator are improved using FACTS devices TCSC, TCPAR, SVC as described in this paper.  \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-6.png}
\caption{\label{fig_4}Figure 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7}\includegraphics[]{image-7.png}
\caption{\label{fig_5}Figure 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{9}\includegraphics[]{image-8.png}
\caption{\label{fig_6}Figure 9 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{11}\includegraphics[]{image-9.png}
\caption{\label{fig_7}Figure 11 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-10.png}
\caption{\label{fig_9}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{13}\includegraphics[]{image-11.png}
\caption{\label{fig_10}Figure 13 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{15}\includegraphics[]{image-12.png}
\caption{\label{fig_11}FigureFigure 15 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-13.png}
\caption{\label{fig_12}Figure}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{19}\includegraphics[]{image-14.png}
\caption{\label{fig_13}Figure 19 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{20}\includegraphics[]{image-15.png}
\caption{\label{fig_14}Figure 20 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{22}\includegraphics[]{image-16.png}
\caption{\label{fig_15}Figure 22 :}\end{figure}
      \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.10365853658536585\textwidth}P{0.7463414634146341\textwidth}}
\tabcellsep (3.12)\\
??? ???? =\tabcellsep ?? ?? ?? ???? (?? ?? ? 2?? ???? ) 2 + ?? ???? ??? ???? 2 ?(?? ???? 2 + ??? ???? ? ?? ?? ?2)\\
??? ???? =\tabcellsep ??? ?? (?? ???? 2 ? ?? ???? 2 + ?? ?? ?? ???? )\end{longtable} \par
 
\caption{\label{tab_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.85\textwidth}}
Year 2014\\
54\\
XIV Issue VI Version I\\
( ) F Volume\\
Global Journal of Researches in Engineering\end{longtable} \par
 
\caption{\label{tab_6}}\end{figure}
 			\footnote{© 2014 Global Journals Inc. (US)} 			\footnote{© 2014 Global Journals Inc. (US) Enhancement of Transient Stability in a Deregulated Power System using Facts Devices} 		 		\backmatter  			 			 			  				\begin{bibitemlist}{1}
\bibitem[Modeling et al.]{b4}\label{b4} 	 		\textit{},  		 			Analysis Modeling 		,  		 			Tcsc Svc 		,  		 			Tcpar In Power Flow 		,  		 			N M G Studies 		,  		 			P Kumar 		,  		 			Venkatesh 		,  		 			. P Dr 		,  		 			Sangamewara Raju 		.  		 	 
\bibitem[Electrical Power Systems: Operation: Trading, And Volatility By Mohammad Shahidehpour, M. Alomoush]{b2}\label{b2} 	 		\textit{Electrical Power Systems: Operation: Trading, And Volatility By Mohammad Shahidehpour, M. Alomoush},  				 	 
\bibitem[A. R. Abhyankar, Prof S. K. Khapardhe (ed.)]{b5}\label{b5} 	 		\textit{Introduction To Deregulation In Power Industry},  		A. R. Abhyankar, Prof S. K. Khapardhe (ed.)  		Mumbai.  		 			Indian Institute Of Technology 		 	 
\bibitem[Module-4 Transmission Congestion Management, Power System Stability Nptel Notes By Ravinder Kumar.Www.Nptel.Ac]{b6}\label{b6} 	 		‘Module-4 Transmission Congestion Management, Power System Stability’.  	 	 		Nptel Notes By Ravinder Kumar.Www.Nptel.Ac  		 	 
\bibitem[Westendorf]{b0}\label{b0} 	 		‘Power System Transient Stability Analysis Of Stiff Systems Using The Multirate Method’.  		 			Alexander M Westendorf 		.  	 	 		\textit{Overbye}  		 		 			Thomas J.University Of Illinois At Urbana-Champaign 		 	 
\bibitem[J. Duncan Glover, Mulukutla Sharma, Thomas Overbye (ed.)]{b1}\label{b1} 	 		\textit{Power Systems Analysis And Design By},  		J. Duncan Glover, Mulukutla Sharma, Thomas Overbye (ed.)  		 	 
\bibitem[Wecc Modeling Workshop (2011)]{b3}\label{b3} 	 		\textit{Wecc Modeling Workshop},  				 (San Francisco)  		July 14, 2011. Jamie Weber.  		 			Power World Transient Stability 		 	 	 (Ph.D) 
\end{bibitemlist}
 			 		 	 
\end{document}
