Minimal Input Cardinality Disturbance Decoupling of Coupled Oscillators via Output Feedback with Application to Power Networks

Abstract

In this paper, we identify the smallest set of control input nodes and an associated output feedback law that achieves complete disturbance decoupling for a class of coupled oscillator networks. The focus is specifically on systems linearized around a stable phase-locked synchronized state. The proposed theoretical framework is applied to the linearized swing dynamics of power grids operating near synchronization. In this context, the disturbance decoupling problem corresponds to isolating subsets of nodes from exogenous disturbances by means of batteries that can both add or withdraw active power. Numerical simulations carried out on the IEEE New England 39-bus system show that the proposed methodology not only yields a minimal actuator placement ensuring effective disturbance rejection, but also preserves the internal stability of the closed-loop system.