Gain and phase margins based delay-dependent stability analysis of single-area load frequency control system with constant communication time delay

Abstract

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.

Delay-dependent Stability Analysis of Microgrid with Constant and Time-varying Communication Delays

“…Hence it is very difficult to determine all the roots. However, to analyze the stability of a time-delay system, it is sufficient to determine the variation of roots of the characteristic equation with respect to time delay, as illustrated in Figure 6 [13].…”

“…In the frequency-domain approach, Macana et al proposed an analytical method based on the Rekasius substitution and sum of squares decomposition to find the time-delay margin in MGs [12]. Sonmez et al analyzed the stability of singlearea LFC with communication delay using Routh-Hurwitz criterion [13], where the analysis is performed assuming the communication delays are constant; however, communication delays are mostly time varying.…”

Delay-dependent stability analysis of power system considering communication delays

“…[12][13][14][15][16][17] While the time domain methods are adequate for synthesizing robust controllers, they suffer from the lack of necessary and sufficient stability conditions. The computational burden in solving the Linear Matrix Inequality (LMI) problem in time domain approach is more, whereas in frequency domain approach, 18,19 the computational burden is reduced by finding only the reduced set of roots that have positive real part and it gives more accurate delay margin results compared with time domain approaches.…”

“…In frequency domain approach, Sahin Sonmez et al 19 proposed a method to analyze the delay-dependent stability of single-area LFC system using Routh's stability criterion. But the authors have not extended the analysis to the deregulated multiarea power system that more commonly experiences the communication delays.…”

An Improved Stability Criterion for Load Frequency Control of Power Systems with Time-Varying Delays

“…Finally, case studies for one-area and two-area LFC systems are carried out to show the relationship between delay margins ensuring the stability and the PI gains of the LFC, and also verify the superiority of proposed stability criterion compared with the previous ones.Energies 2020, 13, 2101 2 of 14 regular polynomial [11]. Furthermore, the method proposed in [12] realized the elimination process of transforming the transcendental characteristic equation into the cross frequency standard polynomial. The frequency-domain method can acquire accurate stability margins under the case of constant delays, while it cannot process the case of time-varying delays and has certain limitations.…”