The usage of communication channels introduces time delays into load frequency control (LFC) schemes. Those delays may degrade dynamic performance, and even cause instability, of a closed-loop LFC scheme. In this paper, a delay-dependent robust method is proposed for analysis/synthesis of a PID-type LFC scheme considering time delays. The effect of the disturbance on the controlled output is defined as a robust performance index (RPI) of the closed-loop system. At first, for a preset delay upper bound, controller gains are determined by minimizing the RPI. Secondly, calculation of the RPIs of the closed-loop system under different delays provides a new way to assess robustness against delays and estimate delay margins. Case studies are based on three-area LFC schemes under traditional and deregulated environments, respectively. The results show that the PID-type controller obtained can guarantee the tolerance for delays less than the preset upper bound and provide a bigger delay margin than the existing controllers do. Moreover, its robustness against load variations and parameter uncertainties is verified via simulation studies.

The bounding inequalities and the Lyapunov-Krasovskii functionals (LKFs) are important for the stability analysis of time-delay systems. Much attention has been paid to develop tighter inequalities for improving stability criteria, while the contribution of the LKFs has not been considered when discussing the relationship between the tightness of inequalities and the conservatism of criteria. This note is concerned with this issue. Firstly, it is proved that, when a simple LKF is applied, the stability criteria obtained by the Wirtinger-based inequality and the Jensen inequality are equivalent although the Wirtinger-based inequality is tighter. It means that the tighter inequality does not always lead to a less conservative criterion. Secondly, it is found that a suitable augmented LKF with necessary integral vectors in its derivative is required to achieve the advantage of the Wirtinger-based inequality. Based on this observation, two delay-product-type terms are introduced into the LKF to establish new stability criteria. Finally, a numerical example is given to verify the equivalence statements and to show the benefit of the proposed criteria.

Uncertain transmission delays and sampling periods, parameters uncertainties regarding the power system, load fluctuations, and the intermittent generation of renewable energy sources (RESs) will significantly influence a power system's frequency. This paper designs a robust delay-dependent PI-based load frequency control (LFC) scheme for a power system based on sampled-data control. First, a sampled-data-based delay-dependent LFC model of power system is constructed. Then, by applying the Lyapunov theory and the linear matrix inequality technique, a novel stability criterion is developed for the LFC of the power system by considering the sampling period and transmission delay of the communication network, which ensures that the proposed scheme operates in large sampling periods and under transmission delays. Next, an exponential decay rate (EDR) is introduced to guide the design of a robust PI-based LFC scheme. The LFC scheme with robustness is designed by setting a small EDR. The values of EDR are adjusted by the given robust performance evaluation conditions of parameter uncertainties and $H_\infty$ performance. Finally, case studies are carried out based on a one-area power system and a three-area power system with RESs. Simulation results show that the proposed LFC scheme performs strong robustness against parameter uncertainties regarding the power system and communication network, load fluctuations, and the intermittent generation of RESs.