An approach to characterizing the power system security region by integrating distributionally robust optimization and Transformer-based deep learning

Abstract

Renewable generation and load uncertainty pose significant challenges to power system security, necessitating efficient approaches to characterizing high-dimensional security regions. To overcome the curse of dimensionality, uncertainty neglect, and undue conservatism in existing methods, this paper proposes an approach integrating distributionally robust optimization (DRO) and deep learning for security region characterization. First, to properly account for uncertainty while avoiding excessive conservatism, a DRO-based active search strategy is developed to identify critical boundary points, where diffusion-generated renewable scenarios and load-deviation samples constructed around typical demand profiles are jointly used to build a robust probabilistic ambiguity set. Subsequently, a Transformer-based model learns from these boundary points to reconstruct the full high-dimensional security region. The model’s self-attention mechanism captures the global nonlinear dependencies among dimensions, enabling a precise and efficient boundary fit. Simulations on IEEE test systems confirm that the approach accurately characterizes high-dimensional security regions at a low computational cost, yielding a security region with strong robustness to renewable-load uncertainty. This work offers a new paradigm for security assessment and decision support in power systems under high uncertainty.

1. Introduction

The secure operation of modern power systems is increasingly challenged by the high penetration of variable and uncertain renewable energy sources (Zhang ZY et al., 2023, 2024; Aryani and Song, 2024). Traditional approaches enforce security conditions as constraints to locate a single optimal operating point, providing no global view of the full set of feasible operating points. As a result, operational margins remain opaque and the geometry of the security boundary is not characterized. Moreover, the coupling between individual operating points and the feasible space is not visually intuitive, making it difficult for operators to develop comprehensive strategies.

To address this need, the power system security region (SR) concept was introduced (Wu F and Kumagai, 1982). The SR defines the set of all operating points that satisfy the power flow equations and operational security constraints, offering system operators a global view of operational margins for decision-making (Teng et al., 2024). SRs are commonly classified into steady-state security regions (SSRs) (Wu F and Kumagai, 1982) which capture static characteristics and dynamic security regions (DSRs) (Wu FF et al., 1988) which account for dynamic processes. Recently, the widespread integration of renewables has profoundly altered grid operating characteristics and reshaped steady-state security boundaries (Jin et al., 2023; Lin et al., 2023; Xiao et al., 2024). Under high renewable uncertainty, the dominant operational risks manifest at the power balance and network flow level on minute-to-hour timescales, making the SSR the primary object for scheduling and flexibility assessment. Consequently, accurate characterization of the SSR remains a central challenge and is the focus of this study. In what follows, SR refers to SSR.

Approaches for the characterization of SR are broadly categorized as analytical and numerical (search-and-fit). Analytical methods derive explicit boundary expressions (Dai et al., 2019; Lin et al., 2021; Su et al., 2021; Tinoco et al., 2021), offering high accuracy. Su et al. (2021) proposed a complete characterization for the SR of electricity-gas integrated energy systems. Without any model simplification, the method reveals that the region possesses complex geometric properties. However, despite high accuracy, their mathematical derivation becomes intractable for modern, high-dimensional, and nonlinear power systems. In contrast, numerical approaches first sample discrete points via vertex search (Nguyen et al., 2019; Monteiro et al., 2020; Avila et al., 2021; Li X et al., 2021; Lin et al., 2022) or point-wise simulation (Liu L et al., 2020; Gao et al., 2023) and then employ techniques like hyperplane fitting (Jiang T et al., 2021; Sun and Yu, 2023; Zhang S et al., 2024) or convex hull (Chen et al., 2019) to construct the SR boundary. Sun and Yu (2023) approximated the SR boundary using the hyperplane method, which linearizes the complex boundary into a set of tractable linear inequalities.