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

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.

• The paper introduces an H-infinity observer for simultaneous estimation of dynamic and algebraic states in DAE-modeled power networks.
• It employs LMIs for robust design to mitigate process noise and sensor failures, validated on IEEE test systems.
• The approach significantly improves state estimation accuracy and computational efficiency in contingency scenarios.

Observers for Differential Algebraic Equation Models of Power Networks

Introduction

The paper "Observers for Differential Algebraic Equation Models of Power Networks: Jointly Estimating Dynamic and Algebraic States" (2202.13254) presents a differential-algebraic equation (DAE)-based framework for dynamic state estimation (DSE) in power networks. The authors focus on leveraging the differential-algebraic nature of power networks by proposing an observer-based method that simultaneously estimates both dynamic and algebraic states using phasor measurement units (PMUs). This approach addresses the limitations of traditional DSE methods that typically overlook algebraic components within power networks.

Methodology

The authors develop a robust $\mathcal{H}_{\infty}$ observer to handle various system uncertainties, including process noise and sensor failures. The development begins with a detailed modeling of power networks using DAEs, capturing the complex interactions between generators, loads, and network elements. These models incorporate generator transient dynamics, stator algebraic constraints, and bus power flow equations, resulting in a model that better reflects the network's actual state.

Key features of the proposed observer include the following:

• Unified DAE Model: The model combines complex generator dynamics and bus-level measurements to better capture the state of power networks.
• $\mathcal{H}_\infty$ Observer Design: The observer is designed using linear matrix inequalities (LMIs), which allows it to be robust against disturbances and uncertainties without relying on noise statistics.
• Simultaneous State Estimation: Both dynamic states (e.g., rotor speeds, voltages) and algebraic states (e.g., bus voltages) are estimated concurrently, using partial-state measurements provided by PMUs.

Numerical Simulations and Results

The paper validates the proposed framework through extensive simulations on IEEE standard test systems, notably the 9-bus and 39-bus systems. The simulations demonstrate the capability of the proposed observers to accurately estimate states under various operating conditions, including contingency scenarios like three-phase faults. Comparative analyses with traditional two-stage methods (e.g., LAV and KF) highlight the proposed method's effectiveness in terms of estimation accuracy and computational efficiency.

Notable results include substantial error reduction in state estimation compared to existing methods, especially under scenarios with noise and unknown inputs. These improvements highlight the robustness of the $\mathcal{H}_{\infty}$ observer in dynamic environments subject to real-world conditions.

Implications and Future Directions

The development of a robust observer for DAE models of power networks has significant implications for real-time power system monitoring and control. By accounting for the network's algebraic constraints, the proposed framework enhances the accuracy and reliability of state estimation, which is crucial for grid stability and fault management.

Potential future research directions include extending the approach to nonlinear DAE models, exploring decentralized estimation strategies, and integrating the framework with advanced control schemes to support autonomous grid operations. Additionally, investigation into the broader applicability of the observer formulation in other domains characterized by DAE dynamics may offer further advancements.

Conclusion

The proposed observer-based DSE framework represents a significant advancement in power system monitoring, particularly by integrating dynamic and algebraic state estimation within a single unified model. The research demonstrates that robust and efficient state estimation can be achieved even in complex and uncertain environments, paving the way for future developments in grid management and control applications.