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

TL;DR

This paper introduces a novel observer-based dynamic state estimation framework for power networks that jointly estimates dynamic and algebraic states using differential-algebraic equations and PMU data, handling noise and sensor failures.

Contribution

It develops the first DSE method based on power network DAEs that simultaneously estimates dynamic and algebraic states with an $$ observer.

Findings

Effective estimation of states in IEEE 9-bus and 39-bus systems.

Robustness to noise, unknown inputs, and sensor failures.

Outperforms existing methods in simulation tests.

Abstract

Phasor measurement units ({PMUs}) have become instrumental in modern power systems for enabling real-time, wide-area monitoring and control. Accordingly, many studies have investigated efficient and robust dynamic state estimation (DSE) methods in order to accurately compute the dynamic states of generation units. Nonetheless, most of them forego the dynamic-algebraic nature of power networks and only consider their nonlinear dynamic representations. Motivated by the lack of DSE methods based on power network's differential-algebraic equations (DAEs), this paper develops a novel observer-based DSE framework in order to perform simultaneous estimation of the dynamic and algebraic states of multi-machine power networks. Specifically, we leverage the DAE dynamics of a power network around an operating point and combine them with a PMU-based measurement model capable of capturing bus voltages and line currents. The proposed $\mathcal{H}_{\infty}$ observer, which only requires detectability and impulse observability conditions which are satisfied for various power networks, is designed to handle various noise, unknown inputs, and input sensor failures. The results obtained from performing extensive numerical simulations on the IEEE $9$-bus and $39$-bus systems showcase the effectiveness of the proposed approach for DSE purposes.