Voltage-Regulated Sparse Optimization for Proactive Diagnosis of Voltage Collapses

TL;DR

The paper tackles proactive voltage-collapse diagnosis by formulating a voltage-regulated sparse optimization that enforces AC power balance and per-bus voltage bounds. It builds on circuit-theoretic power-system modeling, introduces a differentiable sparse framework with voltage constraints, and solves it via a circuit-inspired interior-point Newton method in a staged, adaptive-sparsity sequence. Key findings show that large transmission networks can be stabilized by adjusting a small subset of buses (e.g., 20 of 1354) under substantial loading, with average runtimes under $<4$ minutes for 2000+ bus systems, demonstrating strong scalability. The approach supports targeted reactive-power planning and can be extended to include line limits and concrete resources like FACTS devices and storage, enhancing resilience under extreme events.

Abstract

This paper aims to proactively diagnose and manage the voltage collapse risks, i.e., the risk of bus voltages violating the safe operational bounds, which can be caused by extreme events and contingencies. We jointly answer two resilience-related research questions: (Q1) Survivability: Upon having an extreme event/contingency, will the system remain feasible with voltage staying within a (preferred) safe range? (Q2) Dominant Vulnerability: If voltage collapses, what are the dominant sources of system vulnerabilities responsible for the failure? This highlights some key locations worth paying attention to in the planning or decision-making process. To address these questions, we propose a voltage-regulated sparse optimization that finds a minimal set of bus locations along with quantified compensations (corrective actions) that can simultaneously enforce AC network balance and voltage bounds. Results on transmission systems of varying sizes (30-bus to 2383-bus) demonstrate that the proposed method effectively mitigates voltage collapses by compensating at only a few strategically identified nodes, while scaling efficiently to large systems, taking on average less than 4 min for 2000+ bus cases. This work can further serve as a backbone for more comprehensive and actionable decision-making, such as reactive power planning to fix voltage issues.

Figures (5)

• Figure 1: Voltage collapse and restoration. Top Row (baseline simulation): Voltage collapses occur under high demand conditions. Bottom Row (proposed method): The proposed voltage-regulated sparse optimization identifies a few key system vulnerabilities; and compensations at a few identified buses can fix the issue. Red markers denote the magnitude of compensation sources (in per-unit current) needed at a few identified nodes to keep buses voltage within the predefined safe range, localizing and quantifying instability vulnerabilities. In Fig. \ref{['fig: infeasible, sparse graph + VBound']}, we further illustrate how both power imbalance and voltage collapse can be simultaneously fixed.
• Figure 2: Bus voltage magnitudes from the baseline and proposed methods for Case2383wp. The Top plot shows all buses, while the Bottom plot specifically focuses on the voltage-regulated buses (bus has voltage violations that are fixed by the proposed approach). The proposed method restores all violated voltages within a safe range: some exactly at the lower bound and others strictly within bounds.
• Figure 3: Histogram of the 200 slack sources $\bm{n}$ for case2383wp (in Fig. \ref{['fig: sparse graph + VBound f']}): only a few buses require significant adjustments.
• Figure 4: Runtime and scalability. Left plot tests on high demand conditions (load factors: 1.4$\sim$1.6 for case30, 1.05$\sim$1.25 for case118, 1.25$\sim$1.45 for case1354pegase, and 1.00$\sim$1.20 for case2383wp) where systems remain feasible (power balanced) but have voltage violations. Under these conditions, the baseline method quickly returns zero compensations, but the proposed method needs longer time because it needs extra loops to return the sparse compensations for fixing voltage. Right plot further increases demand (load factors: 4.20$\sim$4.40 for case30, 1.40$\sim$1.60 for case118, 2.00$\sim$2.20 for case1354pegase, and 1.34$\sim$1.54 for case2383wp) to make systems infeasible (blackout collapsed) and voltage-violated. Under such conditions, our proposed method runs faster than the baseline, as it restores both power balance and voltage profile, resulting in slightly denser compensations than restoring balance alone, and therefore requiring fewer sparsity-enforcing iterations. This overall indicates that actionable compensations are slightly denser yet converge faster.
• Figure 5: High demand makes systems collapse (infeasible). Top Row (baseline): The prior work of sparse diagnosis restores only power balance by compensating at a few identified locations. Bottom Row (proposed): Our proposed approach identifies sparse compensations that restore both power balance and voltage stability, yielding more actionable solutions.