Robustness of Type-l fuzzy logic power system
stabilizers (FLPSSs) often lacks mathematical reasoning where
the performance of such a stabilizer is often reviewed by
transient response of the closed loop system. Necessary and
sufficient conditions that guarantee robust dynamic stability of
an FLPSS are presented. A small-signal model of an FLPSS is
developed to study the dynamic stability of a single-machine
infinite-bus power system. Such a small signal model is proved
to be a conventional proportional-derivative (PD) controller
whose parameters are expressed in terms of normalizing factors
of FLPSS. The parameters of such a PD controller, are tuned to
guarantee robust dynamic stability, thereafter normalizing
factors can be directly computed. Synthesis of a robust PD
controller is based on simultaneous stabilization of a finite
number of extreme characteristic polynomials. Such
polynomials are derived using Kharitonov theorem from an
interval polynomial considered to reflect effect of loading
conditions on characteristic polynomial coefficients. A convex
region in the Kp-Kd parameter plane which guarantees robust
stability is obtained using Routh-Hurwitz array. Such a region
presents the pool for all robust normalizing factors of an
FLPSS. Simulation results are presented to confirm the
effectiveness of the proposed approach.