Stability Analysis of Network Controlled Micro-Grid Systems with Communication Delays and Nonlinear Perturbations

In this paper, the problem of delay-dependent stability of micro-grid load frequency control systems under networked environment with time-invariant delays and bounded nonlinear perturbations has been addressed using the Lyapunov-Krasovskii functional approach. In the networked control environment, it is observed that transfer of feedback variable 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 adversely affect the overall performance of the closed-loop system paving way to system instability. In addition, in distributed generation scenario, the uncertainties in the time-delayed microgrid system brought about by the penetration of fluctuating power generators, viz., solar and wind power combined with perturbations in the system load also affect the performance of the overall system. To assess the impact of these time-varying uncertainties to the closed-loop stability of the micro-grid system, they are included in the mathematical model of the system as a norm-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.