Mathematical Modeling and Stability Analysis of a Microgrid in Island Operation

The paper presents the dynamic modeling and stability analysis of Low Voltage (LV) microgrids in island operation using simplified electrical models for Distributed Generations (DGs). These simplified models are used to simulate electrical (excluding switching) as well as control dynamics for each DG to setup and facilitate system level simulations. The paper focuses on the operation of components in grid forming mode using a droop based primary control. This approach is applied on a real microgrid which is set up within the IREN2 research project framework. The demonstrator incorporates a Li-Ion based Battery Energy Storage System (BESS), a plant oil driven generator as well as a BESS emulator. First, a brief overview of the detailed model for each DG including its simplification is discussed. Next, the microgrid is set up using simplified models for transient simulations and the comparison with real measurements is shown for different microgrid topologies. Later, overall microgrid stability i.e. various instability aspects in LV island grids are discussed. In this regard, an analytical method based on Eigenvalue analysis for identification of stability limits for relevant electrical and control parameters and under various loading conditions is presented. Finally, the complete microgrid model is simulated for potential instable conditions and a comparison with the analytical solution is shown.