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This paper presents a comprehensive stability analysis of a single-area load frequency control (LFC) system with constant communication delays. First, an exact method that takes into account both gain and phase margins is proposed to determine stability delay margins in terms of system and controller parameters. The method implements an elimination procedure to transform transcendental characteristic equation into a standard polynomial of the crossing frequency. The real roots of this new standard polynomial exactly match with the purely imaginary roots (crossing frequencies) of the original characteristic equation with transcendental terms. Secondly, an effective and simple graphical method is implemented to compute all stabilizing Proportional Integral (PI) controller gains for a given time delay. The approach is based on extracting stability region and the stability boundary locus in the PI controller parameter space having user defined gain and phase margins, and relative stability. The time-domain simulation studies indicate that the proposed scheme improves dynamic performance gain and phase margins are included in delay-dependent stability analysis of single-area LFC with communication delays.

This paper studies the impact of load increase and a power system stabilizer (PSS) on the stability delay margin of a single-machine-infinite-bus system including an automatic voltage regulator. An analytical method is proposed to determine the stability delay margin of the excitation control system. The proposed method first eliminates transcendental terms in the characteristic equation of the excitation system without making any approximation and transforms the transcendental characteristic equation into a regular polynomial. The key result of the elimination process is that the real roots of the new polynomial correspond to the imaginary roots of the transcendental characteristic equation. With the help of the new polynomial, it is also possible to determine the delay dependency of system stability and the root tendency with respect to the time delay. Delay margins are computed for various loading conditions and PSS gains. It is observed that the delay margin generally decreases as the PSS gain and load demand increase, resulting in a less stable system.