PMU placement ensuring detectability and impulse observability for DAE-based power network models

Develop a placement methodology for phasor measurement units that guarantees detectability and impulse observability for the linearized differential-algebraic equation model of a multi-machine power network with PMU measurements consisting of bus voltage and line currents, so that the rank conditions for detectability and impulse observability are satisfied.

Background

The authors design observers that require the DAE model to be detectable and impulse observable under a measurement model where PMUs provide bus voltages and line currents. While they assume these conditions hold for their test systems, they note that determining PMU locations to ensure these properties is nontrivial and beyond the scope of this work.

Formulating and solving the PMU placement problem to satisfy detectability (via a PBH-type rank condition) and impulse observability (via an augmented rank condition) would enable principled deployment of PMUs that guarantees observability prerequisites for DAE-based dynamic state estimation.

References

Regardless, the problem of placing PMUs in order to achieve detectability and I-observability is not covered in this work as this problem deserves a standalone dedication and an in-depth analysis which are beyond the scope of this paper and as such, is left for future research.

— Observers for Differential Algebraic Equation Models of Power Networks: Jointly Estimating Dynamic and Algebraic States  (2202.13254 - Nugroho et al., 2022) in Section 3 (Regularity, Index Characterization, and Observability of Power Networks), paragraph after Assumption 3