The Lyapunov-based stability analysis of reduced order micro-grid via uncertain LMI condition

This paper proposed a new three-step method for studying dynamic stability of an islanded micro-grid (MG). In conventional methods, state-space model linearization around an operating point and modal analysis are utilized. Due to lower inertia and operation of MG in islanding mode, MG is more sensitive to changes of parameters and contingencies. Therefore, small signal stability (sss) analysis has a very limited validity range and large signal studies should be also performed to get an appropriate perception of the system stability. In this paper, beside sss study to determine network stability status around a dominant operating point, an algorithm based on multi-time scale systems theory is suggested to detect slow and fast modes which can be used for system decomposition into fast and slow subsystems. Fast modes have large negative real values and/or damping ratios, which can be eliminated in large signal stability analysis with an appropriate approximation. Therefore, singular perturbation theory is used to reduce the model order and extract the network slow subsystem. Then, the Lyapunov function can be applied to reduced model. In addition, continuous load and the renewable distributed generators power variations in the system cause to wide range of changes in the operating point and state space model of the system. Therefore, the copula distribution is proposed to model the uncertainties. Then, the uncertain LMI condition based on scenarios extracted from the copula is used to determination of the Lyapunov function and the attraction domain. Finally, the attraction domain sensitivity to MG parameters change is studied to achieve sufficient insight about the system stability margins.