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This paper aims at developing a novel stability criterion to access the influence of the time-varying delay on the stability of power systems equipped with a proportional-integral (PI)-based load frequency control (LFC). The model of the LFC scheme considering time-varying communication delays is established at first. Then, an improved stability condition related to the information of delay bounds is deduced by constructing an augmented Lyapunov-Krasovski functional and using a matrix inequality, and it is expressed as linear matrix inequalities (LMIs) for easily checking. 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. For the time-varying delays, the time-domain method based on the Lyapunov stability theory is more available.The delay margin of the traditional multi-area LFC scheme [14] and the deregulated market environment [15] as well as the relationship between the delay margin and the proportional-integral (PI) gain were discussed. However, since the stability analysis that produces these standards rely on a large number of free weighted matrix variables, the amount of calculation is huge. In [5,16], by taking into account both the random delays and the data packet, the stability of LFC scheme was discussed, but they did not put forward any way based on the delay stability margin to estimate the performance of the control system. In order to obtain more accurate stability margins, the delay correlation stability for a deregulated LFC system with probabilistic interval delays [17] or two additive time-varying delays [18] were analyzed through developing less conservative stability criteria. In [19], for the multi-area power systems, the exponential stability problem was investigated based on a transformed switching system with multiple time delays. By modeling the load disturbances as bounded perturbations, the authors in [20] analyzed the delay-and disturbance-dependent stability of the LFC system. Moreover, several stability criteria established via the double integral inequality in the form of auxiliary function [21], the truncated B-L inequality [22], and improved integral inequality [23] were used to improve the results.Although the aforementioned criteria were developed via different methods, the existing research results still have room for improvement. More specifically, the criteria developed are used to understand the influence of the delay on the stability of the...

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