PMU-based Distributed Non-iterative Algorithm for Real-time Voltage Stability Monitoring

TL;DR

This paper addresses real-time voltage stability monitoring by eliminating reliance on centralized, Jacobian-based indices. It introduces a PMU-based distributed non-iterative voltage stability index (VSI) that emerges from recasting power-flow equations as intersecting circles at each bus, with local centers and radii computed from neighboring PMU data. The VSI is formulated via a determinant-based distance measure between the real- and reactive-power circles, normalized by its no-load value to yield a bounded, interpretable metric in [0,1], and is computed non-iteratively at each bus using only adjacent measurements. Simulations on IEEE test systems demonstrate robustness to measurement noise, missing data, and topology changes, and show advantages over centralized and iterative distributed approaches in speed, interpretability, and outage localization, making it suitable for scalable, secure WAMPAC-style operation.

Abstract

The Phasor measurement unit (PMU) measurements are mandatory to monitor the power system's voltage stability margin in an online manner. Monitoring is key to the secure operation of the grid. Traditionally, online monitoring of voltage stability using synchrophasors required a centralized communication architecture, which leads to high investment cost and cyber-security concerns. The increasing importance of cyber-security and low investment cost have recently led to the development of distributed algorithms for online monitoring of the grid that are inherently less prone to malicious attacks. In this work, a novel distributed non-iterative voltage stability index (VSI) is proposed by recasting the power flow equations as circles. The online computations of VSI are simultaneously performed by the processors embedded at each bus in the smart grid with the help of PMUs and communication of voltage phasors between neighboring buses. The distributed nature of the index enables the real-time identification of the critical bus of the system with minimal communication infrastructure. The effectiveness of the proposed distributed index is demonstrated on IEEE test systems and contrasted with existing methods to show the benefits of the proposed method in speed, interpretability, identification of outage location, and low sensitivity to noisy measurements.

Figures (13)

• Figure 1: Cyber-physical form of a futuristic power system with communication links. The PMUs cover all nodes in this cyber layer and only communicate between neighbours. This is when VCPI of every node needs to be computed. In a scenario where the operator would like monitor only a few critical nodes that are important, only a few PMUs are needed as shown in Fig. \ref{['fig:cyber_physical_system_2']}.
• Figure 2: Cyber-physical form of the power system to monitor the VCPI of bus $3$ in the network using proposed method. To monitor the margin at bus $3$ in an online fashion, we only need the PMU measurements from its adjacent buses i.e., buses $2$, $4$ and branch admittance of lines joining bus $3$ to $2$ and $4$. We do not need the admittance matrix of entire system.
• Figure 3: Power flow circles at bus $3$ with the voltage solutions for increasing loads.
• Figure 4: Family of circles corresponding to the power flow circles (arbitrary loading condition) at bus $3$ of the $3$-bus system described in Section \ref{['subsec:impact_load_incr_on_pf_circles']}.
• Figure 5: Effect of noisy measurements with different noise levels on decentralized (LTI) and proposed distributed index. LTI is more sensitive to noise due to its approximation errors.

Theorems & Definitions (1)

• Remark 1