Stability Criteria for Nonlinearly Perturbed Load Frequency Systems With Time-Delay

In this paper, new criteria are presented for ascertaining delay-dependent stability of networked multi-area load frequency control (LFC) systems with feedback loop delay in presence of unknown and time-varying exogenous load disturbance. The proposed stability criteria are based on Lyapunov-Krasovskii (LK) functional approach, and they are expressed in linear matrix inequality (LMI) framework. Since the unknown exogenous load disturbance in the power system (cause) ultimately affects the evolution of the state variables of the system (effect), in the reported stability criteria, the load disturbance is mathematically modelled as a norm-bounded nonlinear time-varying function of current and delayed state vectors, and subsequently incorporated into the delay-dependent stability analysis. Two cases of time-delays are considered in the stability analysis: time-varying single feedback-loop delay element and time-invariant multiple feedback-loop delay elements. In addition, to realize less conservative stability criteria with minimal number of decision variables, in the stability analysis, tighter integral inequalities, viz., reciprocal convex combination lemma (for time-varying delay case) and Jenson integral inequality (for time-invariant delay case) are employed. The proposed results are illustrated on standard benchmark LFC systems, and supported suitably by simulation results.