Passive damping is the most adopted method to guarantee the stability of LCL-filter based grid-converters. The method is simple and, if the switching and sampling frequencies are sufficiently high, the damping losses are negligible. This letter proposes the tuning of different passive damping methods and an analytical estimation of the damping losses allowing the choice of the minimum resistor value resulting in a stable current control and not compromising the LCL-filter effectiveness. Stability, including variations in the grid inductance, is studied through root locus analysis in the z-plane. The analysis is validated both with simulation and with experiments.

Three-phase active rectifiers guarantee sinusoidal input currents and unity power factor at the price of a high switching frequency ripple. To adopt an LCL-filter, instead of an L-filter, allows using reduced values for the inductances and so preserving dynamics. However, stability problems can arise in the current control loop if the present resonance is not properly damped. Passive damping simply adds resistors in series with the LCL-filter capacitors. This simplicity is at the expense of increased losses and encumbrances. Active damping modifies the control algorithm to attain stability without using dissipative elements but, sometimes, needing additional sensors. This solution has been addressed in many publications. The lead-lag network method is one of the first reported procedures and continues being in use. However, neither there is a direct tuning procedure (without trial and error) nor its rationale has been explained. Thus, in this paper a straightforward procedure is developed to tune the lead-lag network with the help of software tools. The rationale of this procedure, based on the capacitor current feedback, is elucidated. Stability is studied by means of the root locus analysis in z-plane. Selecting the lead-lag network for the maximum damping in the closed-loop poles uses a simple optimization algorithm. The robustness against the grid inductance variation is also analyzed. Simulations and experiments confirm the validity of the proposed design flow.

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LCL-filters are a cost-effective solution to mitigate harmonic current content in grid-tie converters. In order to avoid stability problems, the resonance frequency of LCL-filters can be damped with active techniques that remove dissipative elements but increase control complexity. A notch filter provides an effective solution, however tuning the filter requires considerable design effort and the variations in the grid impedance limit the LCL-filter robustness. This paper proposes a straightforward tuning procedure for a notch filter self-commissioning. In order to account for the grid inductance variations, the resonance frequency is estimated and later used for tuning the notch filter. An estimation for the maximum value of the proportional gain to excite the resonance is provided. The resonance frequency is calculated using the Goertzel algorithm, which requires little extra computational resources in the existing control processor. The Discrete Fourier Transform (DFT) coefficients are therefore obtained, with less calculations than the running sum implementation and less memory requirements than with the Fast Fourier Transform (FFT). Thus, the self-commissioning technique is robust to grid impedance variations due to its ability to tune the grid-tie inverter on-site. Finally, the analysis is validated with both simulation and experiments.

Grid connected converters employ LCL-filters, instead of simple inductors, because they allow lower inductances while reducing cost and size. Active damping, without dissipative elements, is preferred to passive damping for solving the associated stability problems. However, large variations in the grid inductance may compromise system stability, and this problem is more severe for parallel converters. This situation, typical of rural areas with solar and wind resources, calls for robust LCL-filter design. This paper proposes a design procedure with remarkable results under severe grid inductance variation. The procedure considers active damping using lead-lag network and capacitor current feedback. Passive damping is also discussed. The design flow, with little iteration and no complex algorithms, selects the proper ratios between the switching and resonance frequency, the grid and converter inductance, and the filter capacitance and total inductance. An estimation for the grid current THD is also proposed. Simulation and experiments validate the proposals.Index Terms-grid connected converter, LCL-filter, stability, robust design, active damping, weak grid. Active damping modifies the control algorithm without using dissipative elements [8].References [9], [10] established the basic guidelines for the selection of the LCL-filter parameters using an iterative process. The converter-side inductor is sized based on the current ripple at the switching frequency. The capacitor rating is limited by the fundamental reactive power. The grid side