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Power system inertia is falling as more energy is supplied by renewable generators, and there are concerns about the frequency controls required to guarantee satisfactory system performance. The majority of research into the negative effect of low inertia has focused on poor dynamic response following major disturbances, when the transient frequency dip can become unacceptable. However, another important practical concernkeeping average frequency deviations within acceptable limits -was mainly out of the sight of the research community. In this manuscript we present a method for finding the frequency probability density function (PDF) for a given power system. We pass from an initial stochastic dynamic model to deterministic equations for the frequency PDF, which are analyzed to uncover key system parameters influencing frequency deviations. We show that system inertia has little effect on the frequency PDF, making virtual inertia services insufficient for keeping frequency close to nominal under ambient load fluctuations. We establish, that aggregate system droop and deadband width are the only parameters that have major influence on the average frequency deviations, suggesting that energy storage might be an excellent solution for tight frequency regulation. We also show that changing the governor deadband width does not significantly affect generator movement..

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Proper modeling of inverter-based microgrids is crucial for accurate assessment of stability boundaries. It has been recently realized that the stability conditions for such microgrids are significantly different from those known for largescale power systems. While detailed models are available, they are both computationally expensive and can not provide the insight into the instability mechanisms and factors. In this paper, a computationally efficient and accurate reduced-order model is proposed for modeling the inverter-based microgrids. The main factors affecting microgrid stability are analyzed using the developed reduced-order model and are shown to be unique for the microgrid-based network, which has no direct analogy to large-scale power systems. Particularly, it has been discovered that the stability limits for the conventional droop-based system (ω − P/V − Q) are determined by the ratio of inverter rating to network capacity, leading to a smaller stability region for microgrids with shorter lines. The theoretical derivation has been provided to verify the above investigation based on both the simplified and generalized network configurations. More importantly, the proposed reduced-order model not only maintains the modeling accuracy but also enhances the computation efficiency. Finally, the results are verified with the detailed model via both frequency and time domain analyses.

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