الفهرس 
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Abstract
إStability of electric power systems represents one of the main issues concerning electric utilities. Power system stabilizers are used to damp the low frequency oscillations which is a result of generation and load patterns and different power
system disturbances like torque and mechanical power. Onset of such continuously growing or poorly-damped oscillations usually comes out from generation-load mismatches, set point changes, and faults and may lead to system instability or at
least system separation. Damping out such electromechanical oscillations calls for the necessity of power system stabilizers usage. This Thesis addresses the problem of determining the set of all robust three-parameter power system stabilizers having
the common form of the lead lag compensators (𝑥1 + 𝑥2𝑠)/(1 + 𝑥3𝑠) ,where 𝑥1 and 𝑥2 determine the location of the zero and 𝑥3 is fixed to fix a suitable pole, or
equivalently the form of the PID controllers (𝑘𝑖 + 𝑘𝑝𝑠 + 𝑘𝑑𝑠
2 )/𝑠. Graphical characterization of stabilizing PSSs is carried out using D-decomposition whereas the controller-parameter space is subdivided into root-invariant regions. Rather than
Hurwitz stability, D decomposition can parameterize D-stabilizing PSSs that enforce pole-clustering in a pre-specified region D to ensure better time-domain specifications. The convex region of D-stabilizing PSSs is sketched by mapping the 𝜎 − 𝜁 contours from the 𝑠-plane onto the controller-parameter plane by two parametric functions coming from two unknown controller parameters with the third
parameter kept constant. The frequency range considered for mapping is initially computed to avoid sweeping over unnecessary frequencies. Based on the geometry of the D-stability region, analytical expressions are derived to compute optimal PSSs
with improved damping indices for an arbitrary operating point. Parametric
uncertainties are captured by Kharitonov’s theorem. The reflection of the performance indices improvement on the characteristic polynomial coefficients 5 necessitates the usage of the generalized version of Kharitonov’s theorem. A solution relaxation is given by an image-set polynomial where the region
guarantying robust D-stability of the family is investigated. A computationally effective approach based on stabilizing two vertex plants is concluded from the Dstability region. Extension to multi-machine systems is treated where decentralized
PSSs are synthesized. An iterative algorithm is suggested to modify a set of initial feasible PSSs sequentially while maximizing damping indices. Simulation results confirm the efficacy of the suggested method. Finally, conclusion of the work is
given .