[Paper Review] Robustness of Distributed Averaging Control in Power Systems: Time Delays & Dynamic Communication Topology

Johannes Schiffer, Florian Dörfler+1 more|arXiv (Cornell University)|Jul 26, 2016

Power System Optimization and Stability5 citations

TL;DR

This paper proposes delay-dependent stability conditions for distributed averaging-based integral (DAI) controllers in power systems under heterogeneous time delays, link failures, and dynamic communication topologies. Using a common strictly decreasing Lyapunov-Krasovskii functional, it establishes robustness guarantees independent of equilibrium points, revealing a trade-off between performance and robustness, with tightness confirmed in simulations on Kundur’s four-machine system under varying stress levels.

ABSTRACT

Distributed averaging-based integral (DAI) controllers are becoming increasingly popular in power system applications. The literature has thus far primarily focused on disturbance rejection, steady-state optimality and adaption to complex physical system models without considering uncertainties on the cyber and communication layer nor their effect on robustness and performance. In this paper, we derive sufficient delay-dependent conditions for robust stability of a secondary-frequency-DAI-controlled power system with respect to heterogeneous communication delays, link failures and packet losses. Our analysis takes into account both constant as well as fast-varying delays, and it is based on a common strictly decreasing Lyapunov-Krasovskii functional. The conditions illustrate an inherent trade-off between robustness and performance of DAI controllers. The effectiveness and tightness of our stability certificates are illustrated via a numerical example based on Kundur's four-machine-two-area test system.

Motivation & Objective

• To address the lack of robustness analysis for DAI controllers under cyber-layer uncertainties such as time delays, packet losses, and link failures.
• To derive sufficient stability conditions for nonlinear DAI-controlled power systems that are independent of the operating equilibrium point.
• To analyze the impact of both constant and fast-varying delays on system stability using a unified Lyapunov-Krasovskii framework.
• To evaluate the performance-robustness trade-off inherent in DAI control under dynamic communication topologies.
• To validate the theoretical conditions through numerical simulations on a real-world test system, demonstrating tightness under stressed operating conditions.

Proposed method

• A common strictly decreasing Lyapunov-Krasovskii functional (LKF) is constructed to analyze stability under heterogeneous time delays.
• The method accounts for both constant and fast-varying delays, modeling them as time-varying delays with upper bounds.
• Stability conditions are derived using linear matrix inequalities (LMIs), ensuring feasibility without prior knowledge of the equilibrium point.
• The approach incorporates dynamic communication topologies via arbitrary switching, modeling link failures and packet losses as time-varying network structures.
• The analysis is validated using Kundur’s four-machine-two-area test system with random topology switching every 0.5 seconds.
• The conditions are evaluated for different operating points to assess conservativeness and tightness across varying stress levels.

Experimental results

Research questions

• RQ1 How do heterogeneous time delays affect the robust stability of DAI-controlled power systems with dynamic communication topologies?
• RQ2 Can delay-dependent stability conditions be derived that are independent of the system’s equilibrium point?
• RQ3 What is the performance-robustness trade-off in DAI control under time-varying delays and topology changes?
• RQ4 How tight are the proposed stability conditions compared to actual system behavior under different operating conditions?
• RQ5 To what extent does the largest eigenvalue of the Laplacian matrix influence the feasibility of the stability conditions?

Key findings

• For the nominal operating point (z∗,1), the simulation maximum feasible gain (κfeas,sim = 6.330) is 4.1 times higher than the theoretical bound (κfeas = 1.544), indicating moderate conservatism.
• Under more stressed conditions (z∗,2), the simulation gain (κfeas,sim = 2.856) is 1.85 times higher than the theoretical bound, showing reduced conservatism.
• Under highly stressed conditions (z∗,3), the simulation gain (κfeas,sim = 1.698) is only 1.1 times higher than the theoretical bound, indicating near-tightness of the conditions.
• The stability conditions are equilibrium-independent and guarantee local stability for any equilibrium with angle differences within an arc of length π/2.
• The DAI controller demonstrates strong robustness to dynamic communication topology changes, with no significant performance degradation under random switching every 0.5 seconds.
• The feasibility of the stability conditions is highly dependent on the largest eigenvalue of the Laplacian matrix, confirming the theoretical insight from Remark 10 and [31].