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Stochastic Hybrid System Modeling and State Estimation of Modern Power Systems under Contingency

Shuo Yuan, Le Yi Wang, George Yin, Masoud H. Nazari

TL;DR

This work develops a stochastic hybrid system (SHS) framework to model modern power systems under sensor, communication, and contingency uncertainties and to design convergent state estimators using limited sensors. By formulating randomly switched linear dynamics (RSLS) and incorporating observation noise through a coordinate observer architecture, the authors establish convergence conditions (e.g., $\gamma<1$) and quantify steady-state estimation variance via Lyapunov analysis. A key contribution is the demonstration of a tradeoff between fast convergence and small steady-state error governed by observer gains and the switching process, plus a design bound on the sampling interval $\tau_{\max}$. Case studies on the IEEE 5-bus and IEEE 33-bus systems illustrate model derivation, observer design, and reliability improvements under random sensor interruptions, underscoring the framework’s practical relevance for resilient monitoring of power grids.

Abstract

This paper introduces a stochastic hybrid system (SHS) framework in state space model to capture sensor, communication, and system contingencies in modern power systems (MPS). Within this new framework, the paper concentrates on the development of state estimation methods and algorithms to provide reliable state estimation under randomly intermittent and noisy sensor data. MPSs employ diversified measurement devices for monitoring system operations that are subject to random measurement errors and rely on communication networks to transmit data whose channels encounter random packet loss and interruptions. The contingency and noise form two distinct and interacting stochastic processes that have a significant impact on state estimation accuracy and reliability. This paper formulates stochastic hybrid system models for MPSs, introduces coordinated observer design algorithms for state estimation, and establishes their convergence and reliability properties. A further study reveals a fundamental design tradeoff between convergence rates and steady-state error variances. Simulation studies on the IEEE 5-bus system and IEEE 33-bus system are used to illustrate the modeling methods, observer design algorithms, convergence properties, performance evaluations, and impact sensor system selections.

Stochastic Hybrid System Modeling and State Estimation of Modern Power Systems under Contingency

TL;DR

This work develops a stochastic hybrid system (SHS) framework to model modern power systems under sensor, communication, and contingency uncertainties and to design convergent state estimators using limited sensors. By formulating randomly switched linear dynamics (RSLS) and incorporating observation noise through a coordinate observer architecture, the authors establish convergence conditions (e.g., ) and quantify steady-state estimation variance via Lyapunov analysis. A key contribution is the demonstration of a tradeoff between fast convergence and small steady-state error governed by observer gains and the switching process, plus a design bound on the sampling interval . Case studies on the IEEE 5-bus and IEEE 33-bus systems illustrate model derivation, observer design, and reliability improvements under random sensor interruptions, underscoring the framework’s practical relevance for resilient monitoring of power grids.

Abstract

This paper introduces a stochastic hybrid system (SHS) framework in state space model to capture sensor, communication, and system contingencies in modern power systems (MPS). Within this new framework, the paper concentrates on the development of state estimation methods and algorithms to provide reliable state estimation under randomly intermittent and noisy sensor data. MPSs employ diversified measurement devices for monitoring system operations that are subject to random measurement errors and rely on communication networks to transmit data whose channels encounter random packet loss and interruptions. The contingency and noise form two distinct and interacting stochastic processes that have a significant impact on state estimation accuracy and reliability. This paper formulates stochastic hybrid system models for MPSs, introduces coordinated observer design algorithms for state estimation, and establishes their convergence and reliability properties. A further study reveals a fundamental design tradeoff between convergence rates and steady-state error variances. Simulation studies on the IEEE 5-bus system and IEEE 33-bus system are used to illustrate the modeling methods, observer design algorithms, convergence properties, performance evaluations, and impact sensor system selections.
Paper Structure (14 sections, 3 theorems, 89 equations, 9 figures, 4 tables)

This paper contains 14 sections, 3 theorems, 89 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Dynamic State Space Models of Microgrids
  4. General Dynamic Modeling Methods
  5. Illustrative Examples of Model Derivations
  6. Contingency and Stochastic Hybrid Systems
  7. Observer Design for State Estimation under Noisy and Randomly Interrupting Sensor Data
  8. Observer Design for Subsystems
  9. Observer Pole Placement Design
  10. Steady-State Estimation Error Variances
  11. Evaluation Case Studies
  12. IEEE 5-Bus System
  13. IEEE 33-Bus System
  14. Conclusions

Key Result

Lemma 1

WY3 Suppose that $e^i(t)$ is a solution of the stochastic differential equation given by dei together with initial data $e^i_k$ and $A^i_c$ is Hurwitz, i.e., all of its eigenvalues are in the open left half plane of the complex plane. Then we have and

Figures (9)

  • Figure 1: Schematics of a link in microgrids.
  • Figure 2: IEEE 5-bus system.
  • Figure 3: State estimation error variance trajectories.
  • Figure 4: State estimation error variance trajectories under a more aggressive observer design.
  • Figure 5: State estimation error variance trajectories under different packet delivery ratios.
  • ...and 4 more figures

Theorems & Definitions (10)

  • Remark 1
  • Example 1
  • Example 2
  • Remark 2
  • Lemma 1
  • Remark 3
  • Theorem 1
  • Theorem 2
  • Example 3
  • Example 4