  We propose a novel decentralized mixed algebraic and dynamic state
observation method for multi-machine power systems with unknown inputs and
equipped with Phasor Measurement Units (PMUs). More specifically, we prove that
for the third-order flux-decay model of a synchronous generator, the local PMU
measurements give enough information to reconstruct algebraically the load
angle and the quadrature-axis internal voltage. Due to the algebraic structure
a high numerical efficiency is achieved, which makes the method applicable to
large scale power systems. Also, we prove that the relative shaft speed can be
globally estimated combining a classical Immersion and Invariance (I&I)
observer with - the recently introduced - dynamic regressor and mixing (DREM)
parameter estimator. This adaptive observer ensures global convergence under
weak excitation assumptions that are verified in applications. The proposed
method does not require the measurement of exogenous inputs signals such as the
field voltage and the mechanical torque nor the knowledge of mechanical
subsystem parameters.
