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The drive towards renewable energy generation is causing fundamental changes in both the structure and dynamics of power grids. Their topology is becoming increasingly decentralized due to distributed, embedded generation, and the emergence of microgrids. Grid dynamics are being impacted by decreasing inertia, as conventional generators with massive spinning cores are replaced by dc renewable sources. This leads to a risk of destabilization and places an upper limit on the volume of renewable power sources that can be installed. A wide variety of different control schemes have been proposed to overcome this problem. Such schemes fall into two broad categories: so-called “grid-following” controllers that seek to match output ac power with grid frequency, and “grid-forming” systems that seek to boost grid stability. The latter frequently work by providing synthetic inertia, enabling dc renewable sources to emulate conventional generators. This paper uses the master stability function methodology to analyze the stability of synchrony in microgrids of arbitrary size and containing arbitrary control systems. This approach provides a powerful and computationally efficient framework in which to benchmark the impact of any number of renewable sources on grid stability and thereby to support microgrid design strategies. The method is demonstrated by computing stability bounds for two different grid-forming systems, providing bounds on the feasible number of generators that can be accommodated. In addition, we contrast our results with predictions from a simplistic but widely used phase-oscillator model, finding that such descriptions significantly over estimate the grid stability properties. Published by the American Physical Society 2024
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