Computation of stability boundary locus of robust PID controller for time delayed LFC system

The open communication network in the secondary loop of the load frequency control (LFC) scheme introduces the time delay while transmitting the control signals. The communication time delays (CTDs) affect the load frequency control (LFC) system's performance, leading to system instability. This paper proposes a robust method for analysis using a graphical technique for proportional integral derivative (PID)-based LFC systems considering CTD for single-area and multi-area. Moreover, the LFC system with CTD is expressed by its transfer function. Then, stability regions are plotted using the stability boundary locus method to compute the set of stabilized PID controller parameters for the LFC systems having delays. The notable features of the proposed approach are determined using frequency response, maximum sensitivity, and H-infinity criteria in the presence of CTD. The communication time delay is assumed to be additive uncertainty weight. Finally, stability regions are depicted in the controller parameter spaces. Finally, case studies are carried out for LFC systems considering CTD of a single-area and three area isolated power systems. Simulation results as stability regions have demonstrated as (k(p), k(i)), (k(p), k(d)), and (k(d), k(i)) planes for LFC system with the delay of a single-area and three-area isolated power system. These results illustrate the effectiveness of the proposed method for LFC system with CTD and provide robust performance.