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Critical States Identiffcation in Power System via Lattice Partition and Its Application in Reliability Assessment

Han Hu, Wenjie Wan, Feiyu Chen, Xiaoyu Liu, Bo Yu, Kequan Zhao

TL;DR

The paper tackles the challenge of identifying minimal cut sets and quantifying reliability in large-scale power systems. It proposes a lattice-based state space representation and a recursive CSILP algorithm that partitions lattices by 1- and 2-level states, enabling efficient identification of critical states and tight LOLP bounds using $OPF$ calculations. Empirical results on RBTS and RTS79 show CSILP reproduces SE accuracy with orders of magnitude fewer $OPF$ calls and yields tighter LOLP bounds than MCS, demonstrating substantial speedups and reliability insights. This approach supports real-time risk assessment and targeted reliability analysis in complex power grids by exploiting state-space structure and recursive partitioning.

Abstract

With the increasing complexity of power systems,accurately identifying critical states (the states corresponding to minimal cut sets) and assessing system reliability have become crucial tasks. In this paper, a mathematical lattice structure is employed to represent and partition the state space of power system. Based on this structure, a novel recursive method is proposed to efffciently identify critical states by leveraging lattice partitioning and Optimal Power Flow(OPF) calculations. This method not only enables the extension of failure system states,but also calculates the upper and lower bounds of the Loss of Load Probability (LOLP) in a progressively converging manner. Compared to traditional reliability assessment methods such as State Enumeration (SE) and Monte Carlo Simulation (MCS), this approach offers greater accuracy and efffciency. Experiments conducted on the RBTS and RTS79 systems demonstrate that the proposed method accurately identiffes all critical states up to a preset order, which are high-risk states. The contribution of these critical states to LOLP highlights their signiffcance in the system. Moreover, the proposed method achieves the analytical value with signiffcantly fewer OPF calculations in RBTS system, reaching acceptable precision of LOLP up to 100 times faster than SE in both the RBTS and RTS systems.

Critical States Identiffcation in Power System via Lattice Partition and Its Application in Reliability Assessment

TL;DR

The paper tackles the challenge of identifying minimal cut sets and quantifying reliability in large-scale power systems. It proposes a lattice-based state space representation and a recursive CSILP algorithm that partitions lattices by 1- and 2-level states, enabling efficient identification of critical states and tight LOLP bounds using calculations. Empirical results on RBTS and RTS79 show CSILP reproduces SE accuracy with orders of magnitude fewer calls and yields tighter LOLP bounds than MCS, demonstrating substantial speedups and reliability insights. This approach supports real-time risk assessment and targeted reliability analysis in complex power grids by exploiting state-space structure and recursive partitioning.

Abstract

With the increasing complexity of power systems,accurately identifying critical states (the states corresponding to minimal cut sets) and assessing system reliability have become crucial tasks. In this paper, a mathematical lattice structure is employed to represent and partition the state space of power system. Based on this structure, a novel recursive method is proposed to efffciently identify critical states by leveraging lattice partitioning and Optimal Power Flow(OPF) calculations. This method not only enables the extension of failure system states,but also calculates the upper and lower bounds of the Loss of Load Probability (LOLP) in a progressively converging manner. Compared to traditional reliability assessment methods such as State Enumeration (SE) and Monte Carlo Simulation (MCS), this approach offers greater accuracy and efffciency. Experiments conducted on the RBTS and RTS79 systems demonstrate that the proposed method accurately identiffes all critical states up to a preset order, which are high-risk states. The contribution of these critical states to LOLP highlights their signiffcance in the system. Moreover, the proposed method achieves the analytical value with signiffcantly fewer OPF calculations in RBTS system, reaching acceptable precision of LOLP up to 100 times faster than SE in both the RBTS and RTS systems.

Paper Structure

This paper contains 18 sections, 8 theorems, 28 equations, 3 figures, 12 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Structure Analysis of State Space of Power System
  3. Basic Concepts of the Power System States
  4. Critical State
  5. Boolean Lattice Representation of System State Space
  6. Lattice Partition of State Space of Power system
  7. Partition of Lattice by 1-level states
  8. Partition of Lattice by 1-level and 2-level states
  9. Analysis of 1-normal Lattice
  10. Critical States Identification via Lattice Partition
  11. Numerical Experiments
  12. Results on the RBTS system
  13. Results of Critical States
  14. Results of Reliability Assessment
  15. Results on RTS79 system
  16. ...and 3 more sections

Key Result

Proposition 1

$(S, \leq)$ is a partially ordered set, where for any $s \in S$, Here, $\hat{0} = \{\}$ is the minimum element of $S$ and $\hat{1} = \{1, 2, \dots, n\}$ is the maximum element of $S$.

Figures (3)

  • Figure 1: Labeling and examples of partition of a 5-dimension lattice
  • Figure 2: Results of three assessment methods (RBTS)
  • Figure 3: Results of three assessment methods(RTS79)

Theorems & Definitions (23)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Proposition 1
  • Proposition 2
  • Definition 2.6
  • Proposition 3
  • Definition 2.7
  • ...and 13 more