Frequency-Aware Sparse Optimization for Diagnosing Grid Instabilities and Collapses

TL;DR

This paper introduces a frequency-aware sparse optimization method to diagnose grid stability issues, identify critical vulnerabilities, and suggest minimal corrective actions to prevent system collapse, validated on large transmission networks.

Contribution

It proposes a novel steady-state, frequency-aware sparse optimization approach for diagnosing and mitigating grid instabilities without transient modeling.

Findings

Successfully localizes vulnerabilities in large systems

Detects minimal corrective actions involving few buses

Operates efficiently on large-scale transmission networks

Abstract

This paper aims to proactively diagnose and manage frequency instability risks from a steady-state perspective, without the need for derivative-dependent transient modeling. Specifically, we jointly address two questions (Q1) Survivability: following a disturbance and the subsequent primary frequency response, can the system settle into a healthy steady state (feasible with an acceptable frequency deviation $\Delta f$)? (Q2) Dominant Vulnerability: if found unstable, what critical vulnerabilities create instability and/or full collapse? To address these questions, we first augment steady-state power flow states to include frequency-dependent governor relationships (i.e., governor power flow). Afterwards, we propose a frequency-aware sparse optimization that finds the minimal set of bus locations with measurable compensations (corrective actions) to enforce power balance and maintain frequency within predefined/acceptable bounds. We evaluate our method on standard transmission systems to empirically validate its ability to localize dominant sources of vulnerabilities. For a 1354-bus large system, our method detects compensations to only four buses under N-1 generation outage (3424.8 MW) while enforcing a maximum allowable steady-state frequency drop of 0.06 Hz (otherwise, frequency drops by nearly 0.08 Hz). We further validate the scalability of our method, requiring less than four minutes to obtain sparse solutions for the 1354-bus system.