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Contingency Detection in Modern Power Systems: A Stochastic Hybrid System Method

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

TL;DR

This work introduces a stochastic hybrid system framework for contingency detection in modern power systems by treating contingencies as random mode switches in a virtual dynamic state-space model. It combines dynamic and non-dynamic bus representations, a design-proven probing input, and a two-time-scale estimator to jointly detect contingencies and estimate continuous states using common sensors such as PMUs. Theoretical results establish identifiability (via input design) and exponential convergence of both the discrete mode estimator and continuous-state observer. Case studies on IEEE 5-bus and 33-bus systems demonstrate scalable performance, robustness to measurement noise and packet loss, and the ability to detect line faults and sensor disruptions with limited sensing resources. The approach promises PMU-driven, wide-area contingency detection without relying on expensive local fault measurements.

Abstract

This paper introduces a new stochastic hybrid system (SHS) framework for contingency detection in modern power systems (MPS). The framework uses stochastic hybrid system representations in state space models to expand and facilitate capability of contingency detection. In typical microgrids (MGs), buses may contain various synchronous generators, renewable generators, controllable loads, battery systems, regular loads, etc. For development of SHS models in power systems, this paper introduces the concept of dynamic and non-dynamic buses. By converting a physical power grid into a virtual linearized state space model and representing contingencies as random switching of system structures and parameters, this paper formulates the contingency detection problem as a joint estimation problem of discrete event and continuous states in stochastic hybrid systems. This method offers unique advantages, including using common measurement signals on voltage and current synchrophasors to detect different types and locations of contingencies, avoiding expensive local direct fault measurements and detecting certain contingencies that cannot be directly measured. The method employs a small and suitably-designed probing signal to sustain the ability of persistent contingency detection. Joint estimation algorithms are presented with their proven convergence and reliability properties. Examples that use an IEEE 5-bus system demonstrate the main ideas and derivation steps. Simulation case studies on an IEEE 33-bus system are used for detecting transmission line faults and sensor interruptions.

Contingency Detection in Modern Power Systems: A Stochastic Hybrid System Method

TL;DR

This work introduces a stochastic hybrid system framework for contingency detection in modern power systems by treating contingencies as random mode switches in a virtual dynamic state-space model. It combines dynamic and non-dynamic bus representations, a design-proven probing input, and a two-time-scale estimator to jointly detect contingencies and estimate continuous states using common sensors such as PMUs. Theoretical results establish identifiability (via input design) and exponential convergence of both the discrete mode estimator and continuous-state observer. Case studies on IEEE 5-bus and 33-bus systems demonstrate scalable performance, robustness to measurement noise and packet loss, and the ability to detect line faults and sensor disruptions with limited sensing resources. The approach promises PMU-driven, wide-area contingency detection without relying on expensive local fault measurements.

Abstract

This paper introduces a new stochastic hybrid system (SHS) framework for contingency detection in modern power systems (MPS). The framework uses stochastic hybrid system representations in state space models to expand and facilitate capability of contingency detection. In typical microgrids (MGs), buses may contain various synchronous generators, renewable generators, controllable loads, battery systems, regular loads, etc. For development of SHS models in power systems, this paper introduces the concept of dynamic and non-dynamic buses. By converting a physical power grid into a virtual linearized state space model and representing contingencies as random switching of system structures and parameters, this paper formulates the contingency detection problem as a joint estimation problem of discrete event and continuous states in stochastic hybrid systems. This method offers unique advantages, including using common measurement signals on voltage and current synchrophasors to detect different types and locations of contingencies, avoiding expensive local direct fault measurements and detecting certain contingencies that cannot be directly measured. The method employs a small and suitably-designed probing signal to sustain the ability of persistent contingency detection. Joint estimation algorithms are presented with their proven convergence and reliability properties. Examples that use an IEEE 5-bus system demonstrate the main ideas and derivation steps. Simulation case studies on an IEEE 33-bus system are used for detecting transmission line faults and sensor interruptions.
Paper Structure (28 sections, 3 theorems, 35 equations, 10 figures, 2 tables, 1 algorithm)

This paper contains 28 sections, 3 theorems, 35 equations, 10 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. State Space Models of Microgrids
  4. Dynamic Buses
  5. Non-dynamic Buses
  6. Virtual Dynamic State Space Models
  7. Linearization
  8. Contingencies and Stochastic Hybrid System Models
  9. Sensor Systems and Observability
  10. Contingency Models
  11. Randomly Switched Linear Systems
  12. State Space Decomposition
  13. Contingency Detection
  14. Input Design Principles
  15. Two-Time-Scale Framework and Joint Estimation Algorithms
  16. ...and 13 more sections

Key Result

Theorem 1

WY2 For the set of distinct subsystems $G=\{G_i, i=1,\ldots,m\}$, if the input $u\in {\cal U}$, where ${\cal U}$ is given in Assumption , then for any $\tau>0$, the true subsystem can be uniquely determined from the data set ${\cal D}_\tau=\{y(t)\not\equiv 0, t\in [0,\tau)\}$, regardless of the actual initial state $x(0)$.

Figures (10)

  • Figure 1: A link in microgrids
  • Figure 2: IEEE 5-Bus System
  • Figure 3: The probing input $u(t)$ and the output $y(t)$ in $[0,\tau_0)$.
  • Figure 4: The detection of $\alpha_k$ and the estimation error trajectory.
  • Figure 5: The detection of $\alpha_k$ and the estimation error trajectory.
  • ...and 5 more figures

Theorems & Definitions (7)

  • Remark 1
  • Example 1
  • Remark 2
  • Example 2
  • Theorem 1
  • Lemma 1
  • Theorem 2