Dynamic stability analysis of a reduced order micro-grid by multi-time scale theory

In the islanded micro-grids the power cannot be exchanged by the upstream network and the system inertia level is low. Therefore, the network sensitivity to disturbances and load changes is more than the connected mode. In such situation, the system states can behave with more degree of freedom and have less dependency to total system dynamic. The variety of equipment with different dynamics and the load level uncertainty leads to continuous changes in the islanded micro-grid operating point. These changes are more considerable in the islanded micro-grid due to lack of inertia and limited stability margins. Therefore, the determination of appropriate model order for system in such way that the reduced order model keeps the essential dynamic behavior and neglects the less effective modes, is critical. Therefore, in this paper a three-step method based on multi-time scale theory and singular perturbation method is proposed for optimum model order reduction in islanded micro-grid. The proposed method is applied to a typical micro-grid with different types of DGs and loads. The load level uncertainty is modeled by probability density function (PDF) and reduced order model of system is validated in different operating scenarios by sensitivity analysis, participation factor investigation and time domain simulation.