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Chemical battery energy storage systems (BESS) providing frequency compensation techniques such as virtual inertia response (VIR) can be a solution to tackle the frequency volatility ac-island grids suffer when inverter-based generation such as PV is integrated. However, the inverter connecting the BESS may suffer performance and stability issues when due to a low short circuit ratio (SCR) the inverter phase-locked loop (PLL) and the grid impedance negatively interact. To address this issue this work proposes a robust proportional-integral controller (R-PI) for the inverter inner-loop current control. The R-PI is synthesized by the structured H-infinity method using MATLAB and the performance is compared with a regular proportional-integral controller (PI) designed by the conventional frequency shaping method. A sensitivity analysis that includes the dynamic impact of the PLL is conducted for varying SCR. The analysis is verified by time domain simulations in MATLAB and shows that both the R-PI and the PI maintained the inverter stability under the worst-case SCR of 2. However, the benchmarked transient performance of the regular PI was compromised under the simulated SCR variation of 7.2 to 2, while the R-PI was capable of maintaining this performance throughout the SCR variation.
Passman et al. (Sat,) studied this question.