A lattice partition-based approach for critical states identification in a power system

Feiyu Chen; Han Hu; Wenjie Wan; Hongyu Zhang; Xiaoyu Liu; Bo Yu; Kequan Zhao; Feiyu Chen; Han Hu; Wenjie Wan; Hongyu Zhang; Xiaoyu Liu; Bo Yu; Kequan Zhao

doi:10.3934/jimo.2026078

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 4: 2119-2146. doi: 10.3934/jimo.2026078

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Research article

A lattice partition-based approach for critical states identification in a power system

1.
National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing, China
2.
School of Mathematical Sciences, Chongqing Normal University, Chongqing, China

Received: 26 December 2025 Revised: 17 March 2026 Accepted: 24 March 2026 Published: 28 March 2026
90C06, 90C90, 60K05, 06B99

Critical states in power systems, also known as minimum cut sets, are core to quantifying reliability risks as they directly reflect the weakest links causing system failures. Existing methods either fail to comprehensively capture all critical states or suffer from excessive computational complexity, hindering efficient reliability assessment. To address these issues, this paper proposed a lattice partition-based critical states identification (LPCSI) method to identify all critical states up to a preset level and accelerate reliability assessment. First, a mathematical lattice structure was employed to represent and partition the power system state space. Leveraging system coherence, the method directly identifies numerous high-level failure states via lattice partition and simple state comparison, instead of time-consuming optimal power flow(OPF) calculations, enabling efficient critical state identification. Meanwhile, the probability of these high-level failure states is computed using a simple formula based on lattice properties, simplifying reliability index calculation, allowing monotonic convergence to the upper and lower bounds of the loss of load probability (LOLP). Experiments on the Roy Billinton test system (RBTS) and the IEEE reliability test system 1979 (RTS79) demonstrate that the proposed method accurately identifies all preset-order critical states (high-risk states). Compared to traditional methods like state enumeration (SE) and Monte Carlo simulation (MCS), the LPCSI method offers superior accuracy and efficiency in reliability assessment.
- optimization of reliability assessment,
- power system reliability,
- critical states,
- lattice partition,
- state extension
Citation: Feiyu Chen, Han Hu, Wenjie Wan, Hongyu Zhang, Xiaoyu Liu, Bo Yu, Kequan Zhao. A lattice partition-based approach for critical states identification in a power system[J]. Journal of Industrial and Management Optimization, 2026, 22(4): 2119-2146. doi: 10.3934/jimo.2026078

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Abstract

Critical states in power systems, also known as minimum cut sets, are core to quantifying reliability risks as they directly reflect the weakest links causing system failures. Existing methods either fail to comprehensively capture all critical states or suffer from excessive computational complexity, hindering efficient reliability assessment. To address these issues, this paper proposed a lattice partition-based critical states identification (LPCSI) method to identify all critical states up to a preset level and accelerate reliability assessment. First, a mathematical lattice structure was employed to represent and partition the power system state space. Leveraging system coherence, the method directly identifies numerous high-level failure states via lattice partition and simple state comparison, instead of time-consuming optimal power flow(OPF) calculations, enabling efficient critical state identification. Meanwhile, the probability of these high-level failure states is computed using a simple formula based on lattice properties, simplifying reliability index calculation, allowing monotonic convergence to the upper and lower bounds of the loss of load probability (LOLP). Experiments on the Roy Billinton test system (RBTS) and the IEEE reliability test system 1979 (RTS79) demonstrate that the proposed method accurately identifies all preset-order critical states (high-risk states). Compared to traditional methods like state enumeration (SE) and Monte Carlo simulation (MCS), the LPCSI method offers superior accuracy and efficiency in reliability assessment.

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