Robust and Adaptive Tuning of PI Current Controllers for Grid-Forming Inverters

In recent years, grid forming (GFM) inverters have become an increasingly active research interest, due to their ability to form autonomous grids and to maintain synchronism also in purely power electronics-based environments. The main building blocks of these machines are several pulsewidth modulation (PWM) controlled switches, receiving energy from the dc side, followed by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$LC$</tex-math></inline-formula> or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$LCL$</tex-math></inline-formula> output filters to produce nearly sinusoidal currents injected into the power grid. The filter inductances are usually small, to avoid high costs, such that tiny voltage measurement-, delay-, or PWM timing-errors can cause large deviations in the output currents. This is mitigated by employing fast output current controllers (OCCs), which allow us to correct the effect of measurement errors and delays and accurately track the reference currents. These controllers can be implemented as proportional integral (PI) controllers in a rotating reference frame or proportional resonant controllers or even more complex structures. GFM inverters usually employ virtual impedances to obtain the reference currents for the OCCs. While very efficient in strong grids, such control architectures face stability problems if the grid short-circuit ratio becomes low. While for grid following (GFL) inverters, this problem has been well researched in the past years, and various solutions have been proposed, for GFM inverters, the adequate tuning of the virtual impedances and the current controller parameters has yet to be fully understood. In this paper we investigate the influence of the grid impedance, and various control parameters of a GFM inverter with PI current controllers and virtual impedances, and give recommendations for the tuning of all the parameters to achieve stability in a wide range of grid conditions. We further suggest an updated procedure to select <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$LCL$</tex-math></inline-formula> filter values and demonstrate the suggested tuning in an experimental setup. To enable automatic tuning online, we employ a method for measuring the grid impedance by injecting a small probing current into the grid, at a frequency that is close but different from the grid frequency.