Load frequency control (LFC) requires transmitting measurements from remote RTUs to control center and control signals from the control center to plant side. Constant delays exist in the conventional dedicated communication channels, while the future usage of open communication networks will introduce time-varying delays. Those delays would degrade the dynamic performance of LFC and in the worst case, cause instability. The maximal delay time which allows an LFC scheme embedded with controllers to retain stable is defined as the delay margin. This paper investigates the delay-dependent stability of the LFC scheme by using Lyaponuv-theory based delay-dependent criterion and linear matrix inequalities (LMIs) techniques. Case studies are carried out based on one-area and multi-area LFC schemes installed with proportional-integral (PI) controllers, respectively. Relationship between the gains of PI controller and the delay margin of the LFC scheme are investigated and results obtained can be used to tune the PI controllers to achieve a compromise between the dynamic performance and the delay margin. Both constant and time-varying delays are considered. The effectiveness of the criterion used is verified by simulation studies.

The usage of remote signals obtained from a wide-area measurement system (WAMS) introduces time delays to a wide-area damping controller (WADC), which would degrade system damping and even cause system instability. The time-delay margin is defined as the maximum time delay under which a closed-loop system can remain stable. In this paper, the delay margin is introduced as an additional performance index for the synthesis of classical WADCs for flexible ac transmission systems (FACTS) devices to damp inter-area oscillations. The proposed approach includes three parts: a geometric measure approach for selecting feedback remote signals, a residue method for designing phase-compensation parameters, and a Lyapunov stability criterion and linear matrix inequalities (LMI) for calculating the delay margin and determining the gain of the WADC based on a tradeoff between damping performance and delay margin. Three case studies are undertaken based on a four-machine two-area power system for demonstrating the design principle of the proposed approach, a New England ten-machine 39-bus power system and a 16-machine 68-bus power system for verifying the feasibility on larger and more complex power systems. The simulation results verify the effectiveness of the proposed approach on providing a balance between the delay margin and the damping performance.