INTRODUCTION
One of the most important problems arising from largescale power systems
is the low frequency oscillation. Excitation control or Automatic Voltage
Regulator (AVR) is well known as an effective means to improve the overall
stability of the power system. Power System Stabilisers (PSS) are introduced
in order to provide additional damping to enhance the stability and the
performance of the electric generating system. The output of the PSS as
supplementary control signal is applied to the machine voltage regulator
terminal.
Conventional PSS have been widely used in power systems. Such PSS ensures
optimal performance only at a nominal operating point and does not guarantee
good performance over an entire range of the system operating conditions.
Several techniques have been proposed for the design of more robust PSS
structures.
To guarantee the desired performance, this paper describes the control
design models of a PSS based on fuzzy logic, which is returned when the
system configuration changes. The control law is presented in both frequency
domain and time domain.
SYSTEM DESCRIPTION
The power system considered in this study is modelled as a synchronous
generator connected to a constant voltage bus through a double transmission
line. In Fig.1 is represented the system structure including
the PSS unit.
A simplified model describing the system dynamics used in this study
is given by the following state space Equations (Anderson and Foud, 1993;
Feliachi et al., 1988).
Where u represents the system input and d is an external disturbance
Where ΔGSC is governor speed changer (produces a change in the mechanical
torque T_{m})
The state variables and the system output are, respectively
The transfer function form of the nominal model is given by

Fig. 1: 
Combined block diagram of linear synchronous machines
and exciter 
Where
Let the generator operating point is defined by
These operating points are associated with a set models (A_{i},
B_{i}, C_{i}, D_{i}, L_{i}). For these
models, uncertainties may be defined and taken into account in the controller
design stage.
PSS DESIGN BASED ON FUZZY STATE FEEDBACK (FSFPSS)
Assuming that a family of linear state space models may be obtained for
different operating points of generator system.
A related global fuzzy model may be formulated by the following rules
(Denia and Attia, 2002; Hassaon et al., 1991; Cao et al.,
1999; Takagi and Sugeno, 1985).
R^{i} rule related to the ith operating point
L number of operating points
F^{i}_{J} are fuzzy sets for the state variables
The nominal model my be described analytically by
With
μ_{i} being the membership factor for the i^{th}
rule based on the Sumprod inference method.
The basic idea is to develop for each rule a state feedback control law
using the classical pole placement topology.
The state feedback is formulated as:
Where K_{i} is the gain vector related to the (A_{i},
B_{i}) state space model.
These local controllers are inferred into one global fuzzy state feedback
controller for the overall operating regimes of the generator system,
Problem formulation: In this study, we present a fuzzy direct
approach of the control multimodels for linear systems at parameter variables,
our method breaks up in fact in two stages: training of the fuzzy local
controllers of type Takagi and Sugeno (1985) around points of operation
which is the power active (Pe = 0.2' 0.4' 0.6' 0.8' 1), Then the synthesis
of a fuzzy switch by serving fuzzy controllers previously determined.
The control applied to proceeds is thus weighting of the controls worked
out by the fuzzy local controllers.
Our objectives are to ensure the stability and the robustness of our
system when it is uncertainty (error of modelling, disturbance influences,
change of point of operating).
To obtain a structure of complete control homogeneous turned towards
the fuzzy formalism, we chose local controllers linear fuzzy rather than
of the local controllers linear traditional.
One defines the functions of membership, these last allowing to convert
into fuzzy values the variables of inputs in their affecting a weight
which one names degree of membership μ Functions of membership of
Pe.

Fig. 2: 
Block diagram of the control device with gain on of
fuzzy state feedback 
Figure 2 presents the block diagram of the system exciter
alternator with PSS has commutation of fuzzy gain. Block PSS comprises
a state feedback or the gain is committed by fuzzy logic. This approach
used exploits the rules of the theory of fuzzy logic, for the assignment
of the gain of the return of state to a zone of point of operation given
ζ.
PERFORMANCE ET EVALUATION
The objective is to order the alternator group having the characteristics
in annex, for variations of the power active of 0.1 pu up to 1 pu activates
been able and thereafter a variation of the reactance of the line of network
x _{e }

Fig. 3a: 
Transient Responses following a 5% 10% change in the
reference at voltage operating condition Pe = 0.9 pu 0.1 pu 

Fig. 3b: 
Transient Responses following a 510% change in the
reference at voltage operating condition Pe = 0.9 pu0.1 pu 

Fig. 3c: 
Transient responses following a 510% change in the
reference at voltage operating condition Pe = 0.9 pu 0.1 pu 

Fig. 3d: 
Transient responses following a 510% change in the
reference at voltage operating condition Pe = 0.9 pu0.1 pu 
The designed PSS must achieve the following requirements:
• 
Ensure sufficient closed loop stability margins to allow
for changes in closed loop transfer such as those which might arise
from unmodeled lowdamped high frequency modes of oscillations. 
• 
Satisfactory performance over a wide range operating conditions. 
The desired poles are:

Fig. 4a: 
Transient responses following a 510% change in the
reference at voltage operating condition Pe = 0.1 pu0.9 pu 

Fig. 4b: 
Transient responses following a 510% change in the
reference at voltage operating condition Pe = 0.1 pu0.9 pu 
The control with placement of pole on of state feedback gives us the
matrix gain K.
Let us introduce the values of point of nominal operation and the change
of the points of operation in a block of fuzification and one adapts the
gain of the return of state.
For an active power fixes of 0.5 been able, the FSFPSS is compared in
simulation with a control optimal with state feedback. The results are
illustrated by the Fig. 3ad which,
respectively represent machine speed of the system, the angle of load
in radian and the terminal voltage.
For a variable power (change of point of operating at the time t = 5
sec dryness the answers temporal are presented in the Fig. 4ad.

Fig. 4c: 
Transient responses following a 510% change in the
reference at voltage operating condition Pe = 0.1 pu0.9 pu 

Fig. 4d: 
Transient responses following a 510% change in the
reference at voltage operating condition Pe = 0.1 pu0.9 pu 
Performance and evaluation: The FSFPSS approach is evaluated in
simulation on different conditions of work
(change of point of working, profile of the line, variation of reference
voltage, as well as the mechanical torque). The results are illustrated
by Fig. 3 and 5 for the operating
points defined by ξ = [ P X_{e}].
Using FSFPSS, it is possible to find a controller that stabilizes the
power systems with the appearance of the system uncertainty and also realize
the robust performance.
One notes an improvement of response time of the loop system closed compared
to optimal controller.
In the final article one goes presented the extension of this method
at the system multimachines illustrated by Fig. 5.

Fig. 5: 
Multimachine system 
CONCLUSIONS
The robustness of the controller has been evaluated with respect to model
uncertainties of the power generator. A comparative study of the proposed
PSS with a conventional optimal controller has been conducted.
The results relating to the system multimachine are the subject of the
final research.