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Characterization of all robust PD-based PSSs: An interval arithmetic approach

Design of conventional power system stabilizers (PSSs) is load-dependent and thus has to be adjusted at every operating condition. An interval arithmetic (IA) based approach is proposed, to rigorously address load uncertainties associated with the design of PSS. The proposed approach characterizes the set of all robust stabilizing PSSs computed for a single-machine infinite-bus system. A robust PSS can properly function over the full range of operating conditions. An interval plant transfer function is determined over the operating range where upper and lower bounds of the coefficients are precisely computed. Using a proportional-derivative (PD) PSS, an interval characteristic polynomial for the closed loop system is generated. Interval Routh-Hurwitz array is developed to determine the boundaries of robust stability region in Kp-Kd plane via IA computation. Thereafter, the results obtained by interval Routh array are relaxed using degenerate interval array with an image-set polynomial of the plant where the boundaries of the robust stability region is exactly computed. Simulation results confirm the effectiveness of a sample controller, which lies within the solution set, as it is applied to the original nonlinear system model under wide loading conditions.