PMU‐based decentralised mixed algebraic and dynamic state observation in multi‐machine power systems

Abstract

The authors propose a novel decentralised mixed algebraic and dynamic state observation method for multi‐machine power systems with unknown inputs and equipped with phasor measurement units (PMUs). More specifically, they prove that for the third‐order flux‐decay model of a synchronous generator, the local PMU measurements provide enough information to reconstruct algebraically the load angle and 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, they prove that the relative shaft speed can be globally estimated combining a classical immersion and invariance observer with – the recently introduced – dynamic regressor extension and mixing parameter estimator. This adaptive observer ensures global convergence under weak excitation assumptions that are verified in applications. The proposed method neither requires the measurement of exogenous input signals such as the field voltage and the mechanical torque nor the knowledge of mechanical subsystem parameters.

Observers for Differential Algebraic Equation Models of Power Networks: Jointly Estimating Dynamic and Algebraic States

“…Remark 1. Although the satisfaction of LMI (22) ensures the stability of error dynamics (20), the convergence rate to which x(t) approaches x(t) as t → ∞ can be relatively poor. As a potential remedy, one can minimize the maximum eigenvalue of E XE by solving the following convex optimization problem…”

“…Such simplification may not be sufficient to aid frequency regulation in power systems through an output-feedback control framework-for instance, to perform load following control [21]. A new approach to estimate both dynamic and algebraic states of generators in a decentralized framework is recently proposed in [22], where an algebraic observer is developed to estimate the load angle and quadrature-axis internal voltage of each generator. In order to estimate the relative rotor speed, the authors in [22] combine the Immersion and Invariance technique [23] with the Dynamic Regressor and Mixing [24] in their observer design.…”

“…A new approach to estimate both dynamic and algebraic states of generators in a decentralized framework is recently proposed in [22], where an algebraic observer is developed to estimate the load angle and quadrature-axis internal voltage of each generator. In order to estimate the relative rotor speed, the authors in [22] combine the Immersion and Invariance technique [23] with the Dynamic Regressor and Mixing [24] in their observer design. Due to the decentralized fashion however, this DSE approach relies on PMUs placed on generator terminals.…”

“…Unlike other DSE methods, e.g. in [3], [6], [7], [25] and also others that are based on decentralized DSE framework such as [22], this feature allows for flexible PMU placements since every generator terminal may not be equipped with a PMU [14]. In contrast to [18]- [20], our work herein utilizes a DAE representation of power networks with (i) more detailed and comprehensive 4 th -order generator's transient dynamics, stator's algebraic constraints, generator's real and reactive power, and the network's complex power balance equations, and (ii) more realistic and practical PMU-based measurement equations.…”

An Adaptive Observer for Uncertain Linear Time-Varying Systems with Unknown Additive Perturbations

“…This shortcoming was later removed in [19] with the definition of the generalized (G)PEBO, where the properties of the principal matrix solution of an unforced LTV system ẋ(t) = A(t)x(t) are exploited. This novel technique has been successfully applied to reaction systems [20], power systems [14], systems with delayed measurements [2] and distributed state estimation [21]-see also [23] for a related adaptive observer design for a class of nonlinear systems.…”