Systematic design of the lead-lag network method for active damping in LCL-filter based three phase converters

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

Robust active damping in LCL-filter based medium-voltage parallel grid-inverters for wind turbines

LCL-filter based grid-tie inverters require damping for current-loop stability. There are only software modifications in active damping, whereas resistors are added in passive damping. Although passive damping incurs in additional losses, it is widely used because of its simplicity. This article considers the active damping in medium-voltage parallel inverters for wind turbines. Due to cost reasons, only minimal software changes are allowed and no extra sensors can be used. The procedure must be robust against line-inductance variations in weak grids. Double-update mode is needed so the resonance frequency is under the Nyquist limit. The bandwidth reduction when using active damping is also required to be known beforehand. Moreover, the design procedure should be simple without requiring numerous trial-and-error iterations. In spite of the abundant literature, the options are limited under these circumstances. Filter-based solutions are appropriate and a new procedure for tuning the notch-filter is proposed. However, this procedure requires that the resistance of the inductors is known and a novel filter-based solution is proposed that uses lag-filters. The lag-filters displace the phase angle at the resonance frequency so that the Nyquist stability criterion is fulfilled. Simulations and experiments with a 100 kVA prototype validate the analysis