Oscillations-Aware Frequency Security Assessment via Efficient Worst-Case Frequency Nadir Computation

TL;DR

This work tackles frequency security in grids with rising low-inertia renewables by moving beyond COI-frequency and introducing an oscillations-aware worst-case frequency nadir computation. Under a proportional-generation-unit assumption, the authors obtain a modal decomposition that decouples dynamics along scaled Laplacian eigenvectors, enabling an efficient worst-case nadir algorithm that reduces the inner optimization to a closed-form dual-norm evaluation. They derive analytical insights for homogeneous networks and demonstrate the method on a 50-bus and a 2000-bus GB network, showing significant computational efficiency and the ability to identify the precise disturbance pattern that yields the severest nadir. The approach provides a practical, scalable tool for frequency security assessment in modern grids, and suggests avenues for extending to intermediate connectivity and heterogeneous parameters.

Abstract

Frequency security assessment following major disturbances has long been one of the central tasks in power system operations. The standard approach is to study the center of inertia frequency, an aggregate signal for an entire system, to avoid analyzing the frequency signal at individual buses. However, as the amount of low-inertia renewable resources in a grid increases, the center of inertia frequency is becoming too coarse to provide reliable frequency security assessment. In this paper, we propose an efficient algorithm to determine the worst-case frequency nadir across all buses for bounded power disturbances, as well as identify the power disturbances leading to that severest scenario. The proposed algorithm allows oscillations-aware frequency security assessment without conducting exhaustive simulations and intractable analysis.

Figures (4)

• Figure 1: Block diagram of power network.
• Figure 2: A $3$-bus example showing that COI frequency is insufficient for frequency security assessment since the oscillations due to weak connectivity can make the transient frequencies on individual buses deviate drastically from the COI frequency.
• Figure 3: Comparison between the worst and a random allocation of power disturbances within a given $2$-norm bound as well as the resultant frequency deviations in a power network with $50$ generation units.
• Figure 4: Comparison between the frequency deviations in the Great Britain network under the worst and a random allocation of power disturbances within a given $2$-norm bound. In this particular example, there are two buses (buses $364$ and $365$) that swing each other in the worst-case.

Theorems & Definitions (13)

• Remark 1: Proportionality extensions
• Lemma 1: Decomposition along scaled Laplacian eigenvectors
• proof
• Definition 1: Dual norm Horn2012MA
• Lemma 2: Solutions to dual norm
• proof
• Theorem 1: Closed-form solution to the inner most problem in \ref{['eq:opt-worst-nadir-decouple-swap']}
• proof
• Lemma 3: Expressions of $h_k(t)$
• proof