Further Improvement on Stability Results for Delayed Load Frequency Control System via Novel LKFs and Proportional-Integral Control Strategy

In this work, novel stability results for load frequency control (LFC) system considering time-varying delays, nonlinearly perturbed load, and time-varying disturbance of system parameters are proposed by using proportional-integral control strategy. Considering the nonlinearly exogenous load disturbance and system parameters disturbance, an improved stability criterion in the form of linear matrix inequalities (LMIs) is derived by novel simple Lyapunov–Krasovskii functionals (LKFs). The delay-dependent matrix in quadratic term, cross terms of variables, and quadratic terms multiplied by 1st, 2nd, and 3rd degrees of scalar functions are included in the new simple LKF. Taking the single-area and two-area LFC system installed with proportional-integral (PI) controller as example, our results surpass the previous maximum allowable size of time delay. Meanwhile, the relationship between time delay varying rate, load disturbance degree, gains of PI controller, and delay margin of the LFC system is researched separately. The results can provide guidance to tune the PI controller for achieving maximum delay margin, in which the LFC system can withstand without losing stability. At last, the simulation results verify the effectiveness and superiority of the proposed stability criterion.