Design of H∞ Observers for Singular Electromechanical Dynamics in Power Networks using LMIs

In this paper we focus on the design of H
_∞
observers, using linear matrix inequalities (LMIs), to estimate the dynamic state of a power system over a wide-area by using a limited set of sensors. We confine our attention to the electromechanical (or "swing") dynamics of a power system, but our approach can be extended to also monitor the voltage dynamics in the system. A differential algebraic equation (DAE) model is used to describe the swing models that we consider in this paper. At first, we focus on the design of a singular observer using the mixed design approach for a DAE-swing model in a setting where unknown inputs and noisy measurements are present. A design for a 9-bus power system is discussed. Lastly, we investigate the design of singular H
_∞
estimators that are robust to parametric model uncertainties associated with the parameters featured in DAE-swing models (e.g., transmission line impedances, generator inertias, and the damping coefficients of the generator shafts). We illustrate the result of this latter investigation on a 3-bus power system