Mode Participation and Inter-Area-Observability Blocking Controllers for Power Networks

TL;DR

The paper tackles the problem of adversarial manipulation of modal content in interconnected power systems by blocking mode participation and inter-area observability using a surgical eigenstructure assignment framework. It derives a static state-feedback law $u=F x$ that preserves the eigenvalues of the open-loop system while reshaping eigenvectors to suppress participation factors $p_{ki}=w_{ik}v_{ki}$ and to make selected inter-area modes unobservable in tie-line measurements via $A+BF$. The authors provide two algorithms, one to block participation (Algorithm 1) and another to block observability (Algorithm 2), and validate them on a 3-machine, 9-bus system and a 16-machine, 68-bus system, revealing both the potential and limits of the approach (e.g., localization vs. redistribution of participation). The work highlights fundamental limits of modal-based diagnostics under strong centralized control and points to future research directions in output-feedback or decentralized strategies to achieve similar security objectives in practice, with implications for cyber-physical power-system security and stability monitoring.

Abstract

In recent papers [1] and [2], the second author developed full-state feedback controllers for networked systems to block the observability and controllability of certain remote nodes. In this paper, we build on these control schemes to an interconnected power system with the aims of blocking (i) mode participation factors and (ii) inter-area mode observability in tie-line power flow measurements. Since participation factors depend on both controllable and observable eigenvectors, the control techniques from the cited works must be carefully tailored to this setting. Our research is motivated by cyber-security concerns in power systems, where an adversary aims to deceive the operator by tampering the system's modal content. We present extensive numerical results on a 3-machine, 9-bus system and a 16-machine, 68-bus system.

Figures (3)

• Figure 1: Blocking participation of states 1 and 4 of of 3 machine 9 bus power system using Algorithm 1. Refer main text for details.
• Figure 2: Norm of $\mathbf{C}\mathbf{v}_i$ for each eigenvector $\mathbf{v}_i$ of 3 machine 9 bus power system before (left) and after (right) inter-area blocking.
• Figure 3: Participation factors of the modes 6 (and associate conjugate mode 7) for each state of 16 machine 68 bus power system.