Decentralized Robust Control of Power Grids Using LPV-Models of DAE-Systems

For large, distributed, and decentrally controlled systems, physical links between subsystems must be considered in designing local controllers to obtain global system stabilization. This manuscript addresses the task of robustly stabilizing systems with nonlinear subsystem dynamics and interconnections given by nonlinear algebraic equations, as motivated by the typical structure of power grids. The proposed approach first transforms the subsystems into a set of LPV-models, and the interconnections are represented by parameter intervals. For each subsystem, a local robustly stabilizing controller is synthesized by solution of a semidefinite program, and the stability of the overall system is implied if interval conditions for the parameters are satisfied. The method is demonstrated for a simple (yet often used) instance of a power grid.