## 2 Frequency Variations in Weak Power Systems with High Penetration of RES  
Microgrids have been identified as the best option to integrate distributed generation (DG) units in terms of flexibility and reliability [14; 15; 16]. The microgrids can be operated in three possible modes: grid-connected, islanded, or isolated. A microgrid is said to have been islanded when a microgrid that is grid-connected disconnects from the grid, either in a planned fashion or due to a fault/disturbance in the main grid. In the isolated mode of operation, the microgrid is designed such that it is never connected to the grid. Regardless, these microgrid systems represent weak power systems and the high penetration of inertia-less PV and wind energy systems has a severe effect on the frequency stability. The rapid changes in the generation can cause frequency variations in the system that are outside standard limits and compromise the stability of the system.  
Figure 3: Multiple time-frame frequency response in a power system following a frequency event.  
Figure 4 shows the recommended standard frequency range for grid-connected and isolated/islanded microgrids. In the grid-connected mode, the frequency is controlled by the main grid and the frequency deviations are relatively small. However, this scenario is slowly changing with increased integration of large-scale inertia-less generation. The Institute of Electrical and Electronic Engineers (IEEE) recommends a tight frequency operating standard of \(\pm\)0.036 Hz for grid-connected systems. The North American Reliability Corporation (NERC) recommends triggering the first level of UFLS when the system frequency drops below 59.3 Hz (for a nominal frequency of 60 Hz for the US power grid). The activation of UFLS is the last automated reliability measure to counteract frequency drop and re-balance the system [17]. NERC recommended control actions include disconnecting the generator if the frequency drops below 57 Hz or rises above 61.8 Hz [18]. The European Norm EN50160 also imposes similar tight ranges for grid-connected microgrid systems [19]. There are no specific standards defined for frequency limits for isolated microgrid systems. This is highly dependent on the generation and the load mix in a particular microgrid system. From a generator point-of-view, frequency standards like the ISO 8528-5 standard [20] can provide a guideline for the frequency limits. With the small amount of SGs in isolated microgrids, the frequency excursions and ROCOF are greater and the need for virtual inertia is of high importance. In such isolated microgrids, to implement virtual inertia, either dedicated energy storage systems (ESSs) can be used [21; 22], or inertia can be emulated by operating PV/wind below their maximum power point (MPP) [23; 24]. However, the allowable frequency nadirs and ROCOFs in the microgrids in islanded/isolated conditions may be relaxed compared to grid-connected operation. This will be especially vital for the design of virtual inertia systems for isolated microgrids as these microgrids often have limited energy resources and relaxing the frequency operating region would result in significant energy saving and reduction in power ratings of virtual inertia systems.  
Figure 4: Frequency standards for microgrid systems [18; 19; 20].