Certain investigations on the stability of networked micro grid load frequency control system

Abstract

In this research work, delay-dependent stability problem of networked micro-grid load frequency control systems with time-invariant delays and time varying delays with and without nonlinear norm-bounded load perturbation is addressed using Lyapunov-Krasovskii functional approach, Wirtinger inequality and Reciprocal convex combination lemma. In the networked micro-grid control systems, it is observed that transfer of incremental frequency variable (feedback variable an indication of the imbalance between the generation and the demand) from the sensor to centralized controller, and the control effort from controller back to the actuator through communication links introduces time-delays in the feedback path. The time-delays invariably affect the overall performance of the closed-loop system to a considerable extent paving way to system instability. In addition, the uncertainties in the time- delayed micro-grid system brought about by the penetration of fluctuating power generators, viz., solar and wind power also affect the performance of the system. To assess the impact on the micro-grid system stability to these uncertainties, they are included in the mathematical model of the system as a bounded nonlinear perturbation term. Subsequently, the stated problem is solved in a less conservative manner by employing the classical Lyapunov-Krasovskii functional approach combined with Wirtinger inequality. The analysis results in a delay-dependent stability criterion in linear matrix inequality (LMI) framework. In the sequel, the presented stability criterion is validated on a standard benchmark system and supported with extensive simulation results newline