New Stability Criteria of Delayed Load Frequency Control Systems via Infinite-Series-Based Inequality

A new approach is proposed for the stability problem of delayed load frequency control (LFC) scheme with fixed and time-varying delay cases included in the current paper. New stability criteria with delay dependence in terms of linear matrix inequalities for LFC systems are derived by a novel augmented Lyapunov-Krasovski (L-K) functional. Our proof deployment for system stability of power grids employs the further improved integral inequality in the form of infinite series, which turns out to be less conservative than Wirtinger's inequality that encompasses Jensen inequality. Simulation case studies are carried out to show the effectiveness and superiority of the presented delay-dependent PI-type LFC design scheme.

I. Introduction

Frequency stability is critical in the safe and stable operation of power systems, which reflects the basic position of power systems in supply and demand. The fluctuation of load frequency would bring serious consequences to the safety operation of power systems, plants, and users: it can cause the generator and auxiliary engine to deviate from operation status, thus reduces mechanical efficiency, makes power plant operation deviate from economic efficiency, and also has an adverse effect on the entire economic operation of the power grid. In addition, when the frequency is too low, the frequency fluctuations can even threaten the security of the entire network operation. Therefore, research on the load frequency analysis and control of power systems is considered to be the important elements necessary to ensure the safe operation of power systems. Load frequency control (LFC) strategies have been employed effectively in distributed power systems for the development of smart grid [1] , [2]. Maintaining frequency and power interchanges at the scheduled values with neighborhood areas is the significant aim of LFC.