Residual-Evasive Attacks on ADMM in Distributed Optimization

TL;DR

The paper addresses the vulnerability of ADMM-based distributed optimization, particularly in optimal power flow (OPF), to residual-based detection through residual-evasive attacks that keep the primary residual $r=\|Ax+Bz-c\|$ unchanged. It develops two main strategies: (i) random-start attacks with Gram-Schmidt orthogonalization to produce undetectable perturbations, and (ii) a voltage-control attack that can yield financial gains by nudging the system toward the upper voltage limit while maintaining stealth. A formal Residual Evasion Criterion $a^T(a-2y)=0$ guides attack construction, with explicit methods for generating attack vectors $a$ through $a=\lambda y+b$ where $b\perp y$, and for targeted optimization to balance stealth and impact. Simulation on the IEEE 14-bus system demonstrates the trade-offs between detectability and effectiveness, showing that residual-evasive approaches can achieve meaningful disruption and financial incentives without triggering standard residual-based monitors, underscoring the need for more robust ADMM defenses in power systems.

Abstract

This paper presents two attack strategies designed to evade detection in ADMM-based systems by preventing significant changes to the residual during the attacked iteration. While many detection algorithms focus on identifying false data injection through residual changes, we show that our attacks remain undetected by keeping the residual largely unchanged. The first strategy uses a random starting point combined with Gram-Schmidt orthogonalization to ensure stealth, with potential for refinement by enhancing the orthogonal component to increase system disruption. The second strategy builds on the first, targeting financial gains by manipulating reactive power and pushing the system to its upper voltage limit, exploiting operational constraints. The effectiveness of the proposed attack-resilient mechanism is demonstrated through case studies on the IEEE 14-bus system. A comparison of the two strategies, along with commonly used naive attacks, reveals trade-offs between simplicity, detectability, and effectiveness, providing insights into ADMM system vulnerabilities. These findings underscore the need for more robust monitoring algorithms to protect against advanced attack strategies.

Figures (12)

• Figure 1: Our contribution: Evasion through minimal residual changes.
• Figure 2: Voltage control for active role. $U_{\text{ist}}$ is the actual voltage and $U_{\text{soll}}$ is the target voltage at the feed-in node. $\Delta U_{\text{Tol}}$ is the billing tolerance, and $\Delta U_{\text{Frei}}$ is the free conformity band. $W_Q$ is the net reactive power exchange for the quarter-hour. The left side represents capacitance-like behavior (delivering reactive power), while the right side represents inductance-like behavior (consuming reactive power). Source: Swissgrid swissgrid2020
• Figure 3: IEEE 14-bus test case and the split in TSO and DSO.
• Figure 4: Financial impact of the attacks.
• Figure 5: Reactive power at boundary bus 4 during ADMM, depicting a notable drop under attack.

Theorems & Definitions (6)

• Theorem 1: Residual Evasion Criterion
• Proposition 1
• Theorem 2
• Theorem 3
• Lemma 1
• Lemma 2