Passivity-Based Stabilization of LCL-Type Grid-Connected Inverters via a General Admittance Model

For LCL-type grid-connected inverters, inverter-side current, grid-side current, capacitor current and voltage are four commonly used variables in the control serving as different roles, such as control objective, active damping, synchronization, etc. This article builds a general admittance model, in which the total output admittance is decomposed into four paralleled subadmittance corresponding to the above four variables in the control law, to facilitate the passivity-based stability assessment and controller parameter optimization for different control objectives and schemes. Based on the passivity analysis, an appropriate combination scheme of subadmittance and a simple unified analytical controller parameter design method are proposed to obtain a passive output admittance from 0 Hz up to Nyquist frequency for either inverter-side or grid-side current control. Therefore, it can not only ensure the stable operation of LCL-type inverters regardless of grid impedance (either inductive or capacitive) but also avoid the conventional design constraints of an LCL filter, i.e., f r <; or > f s /6 is required for the single-loop inverter-side or the grid-side current control. Finally, experiments verify the theoretical results.