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\title[]{
Fundamental Investigations on Identifying Generator Model Parameter Values by Utilizing the Synchronization of the Chaotic Behavior
}

\authorlist{%
 \authorentry{KITA Toshihiro}{m}{Kumamoto}
}
\affiliate[Kumamoto]{Kumamoto University, {\tt mail@t-kita.net}}

\newcommand{\wbox}[1]{\psframebox*{#1}}
\newcommand{\graybox}[1]{\psframebox*[fillcolor=gray]{#1}}

\begin{document}
\begin{keyword}
chaos synchronization, parameter value identification, 
chaotic power swing,
single-machine infinite-bus power system, dual-structured system
\end{keyword}
\maketitle\thispagestyle{empty}

Two systems of the same structure and of the same parameter values can
be synchronized by supplying the signal from one to the other 
even when they behave chaotically.
This phenomenon is called synchronization of chaos.
In this paper a method to identify the parameter values of a 
generator model utilizing the chaos synchronization is described.

Combining two single-machine infinite-bus power system models,
dual-structured system as shown in Fig.\ref{si-fig:dualsystem1}
is derived.
In this system, 
if the system1 and system2 are identical and behave chaotically,
chaos synchronization is easily achieved by
adjusting the coupling coefficient $r_a$ and $r_b$ between the systems.
System1 corresponds to a real system, and system2 is 
virtually created by computer simulation.
Checking the synchronization between the two systems and
adjusting the parameter to be estimated, 
parameter value identification is possible because 
chaos synchronization implies that
the parameter values of the two system are identical.

\begin{figure}[p]
\vspace{20zh}
\begin{center}
%\psfrag{ra}[][]{$r_a$}
%\psfrag{1-ra}[][]{1--$r_a$}
%\psfrag{rb}[][]{$r_b$}
%\psfrag{1-rb}[][]{1--$r_b$}
%\psfrag{ef1}[][]{$e_{f1}$}
%\psfrag{Vt1}[][]{$V_{t1}$}
%\psfrag{ef2}[][]{$e_{f2}$}
%\psfrag{Vt2}[][]{$V_{t2}$}
%\includegraphics[width=0.7\columnwidth,clip]{eps-si/dualsystem1.eps}
%%% system1, system2, ef1, ef2, Vt1, Vt2 ���� %%%%%%%%%%%%%%
\ecaption{Dual-structured system}
\label{si-fig:dualsystem1}
\end{center}
\vspace{1zh}
\end{figure}

To let system1 and system2 be chaotic, 
the AVR gain and the AVR time constant of the generator are
intentionally badly tuned, but it is not allowed in realistic 
operation to fluctuate the generator with a large amplitude.
A solution to this problem is adjust the upper bound value of
the AVR limiter.
The chaotic motion utilized in this paper is indicated in Fig.
\ref{si-fig:UlV165ts0}.
This fluctuation is about only $\pm$1.5\% in the voltage
and $\pm$2.5\% in the output power.

Fig.\ref{fig:bifu3D6005-1} shows
correlation between the system1 and system2
for $r_a$ \ and $T_{do2}'$ (a generator time constant of system2)
when $r_b=0.5$.
%
$V_{t2{\rm P}}$ is obtained by
taking the cross section of correlation diagrams of
generator voltage in each system, $V_{t2}$ vs. $V_{t1}$.
It is called cross-sectional correlation diagram in this paper.

If the two systems behave identically, 
the correlation is high and the cross-sectional correlation diagram 
will be small, and will be just a point when they are in 
synchronization.

The closer $T_{do2}'$ becomes to $6.5\ \mbox{s} \ (=T_{do1}')$, 
the higher the correlation between the systems is, and 
the chaos synchronization has been observed.


\begin{figure}[p]
\vspace{20zh}
%\centering
%\epsfile[
%\epsfat(-8mm,18mm){\parbox{2.5em}{\centering $\Vt_1$\\ \pu }}
%\epsfat(45mm,-1mm){time\sec }
%]{file=eps-si/Pm080-TdoD65-Vt-ts0.eps,width=0.6\columnwidth}
%\par
%\epsfile[
%\epsfat(-8mm,18mm){\parbox{2.5em}{\centering $\Pe_1$\\ \pu }}
%\epsfat(45mm,-1mm){time\sec }
%]{file=eps-si/Pm080-TdoD65-Pe-ts0.eps,width=0.6\columnwidth}
\ecaption{Chaotic fluctuation in system1}
\label{si-fig:UlV165ts0}
\vspace{2zh}
\end{figure} 


\begin{figure}[p]
\vspace{20zh}
%\centering
%\epsfile[%
%\epsfat(7mm,58mm){$\Vt_{2{\rm P}}$ \pu}%
%\epsfat(49mm,7mm){$\TdoD_2$\sec}%
%\epsfat(109mm,24mm){\ra}%
%]{file=eps-si/bifu3D6005-1.eps,width=1.0\columnwidth} %hrate=1
\ecaption{Variation of cross-sectional correlation diagrams according to
 $T_{do2}'$ and $r_a$}
\label{fig:bifu3D6005-1}
\end{figure}


\end{document}
