Design of PSSs for distributed synchronous generators using a system representation based on norm-bounded linear differential inclusions

This paper proposes a systematic method based on linear matrix inequalities for the design of power system stabilizers for synchronous generators connected to distribution grids. The system to be controlled is originally described by a nonlinear dynamical model in state-space form. However, for synthesis purposes we represent it as a norm-bounded linear differential inclusion model. Using an approach based on the mean-value theorem, this linear representation considers the nonlinear terms in the Taylor series expansion of the nonlinear equations as uncertainties in the model. Constraints are included to the control problem formulation in order to guarantee a satisfactory performance of the controlled system. The main objectives, from the application viewpoint, are the enhancement in the damping of electromechanical oscillations, as well as the minimization of the peaks reached by the terminal and field voltages during the transients of interest. The proposed algorithm is a straightforward design procedure and can be easily handled by using LMI solvers. A cogeneration plant of 10 MW added to a distribution network constituted by a feeder and six buses is adopted as test system, and the results show that the two designed objectives are quite satisfactorily achieved.