High renewable power (RP) penetration in a microgrid (MG) reduces the inertia of the MG. As a result, small load perturbation, or weather dependent fluctuations in RP generation, causes a high rate of change of frequency (RoCoF) and severe frequency instability problems. To cope with such issues, virtual inertia (VI) needs to be emulated in the MG for RoCoF and frequency control of a low-inertia MG. An MG consisting of thermal, wind, and solar photovoltaic power plants has been considered for the present study. In the proposed work, Genetic Algorithm (GA) optimized derivative-type VI control system has been designed considering both inertia and damping in the VI loop along with an energy storage device. The RoCoF and frequency responses of the MG using the proposed VI control strategy have been studied for variations in loads, weather dependent inputs, and MG parameters. Additionally, mathematical analysis has been provided to highlight the significance of adding a VI loop on steady-state stability and sensitivity of the MG. Furthermore, the performance of the proposed controller has been examined by comparing it with numerous pre-existing VI control topologies from recent literature for the same MG.

微电网（MG）中的高可再生能源（RP）渗透率降低了MG的惯性。结果，较小的负载扰动或RP生成中与天气有关的波动会导致较高的频率变化率（RoCoF）和严重的频率不稳定性问题。为了解决这些问题，需要在MG中模拟虚拟惯性（VI），以实现RoCoF和低惯性MG的频率控制。对于本研究，已经考虑了由火力，风能和太阳能光伏电站组成的MG。在拟议的工作中，设计了遗传算法（GA）优化的微分型VI控制系统，该系统同时考虑了VI回路中的惯性和阻尼以及储能装置。研究了使用建议的VI控制策略的MG的RoCoF和频率响应，以应对负载变化，天气相关输入和MG参数。此外，已经提供了数学分析，以突出说明添加VI环路对MG的稳态稳定性和灵敏度的重要性。此外，已通过将其与来自最近文献的同一MG的众多先前存在的VI控制拓扑进行比较，对所提出的控制器的性能进行了检查。