Stability analysis of grid-connected voltage source inverters with LCL-filters using partial state feedback

Abstract

This paper addresses the stability of discrete controlled grid connected voltage source inverters with LCL-filter usually found in wind power generation systems. First a theorem that relates the controllability of the discrete dynamic equation with the LCL-filter parameters and the sampling frequency is derived. Then, a robust partial state feedback design on the linear matrix inequalities framework guarantee the stability damping the LCL-filter resonance for a large set of grid conditions without requiring tuning procedures. Finally, an internal model controller is added to ensure asymptotic reference tracking and disturbance rejection, therefore reducing significantly the impact of grid background voltage distortion on the line currents. Simulation and experimental results are presented to support the theoretical analysis carried out and to demonstrate the system performance.

Robust loop-shaping H<inf>&#x221E;</inf> control of LCL-connected grid converters

“…Few designs follow a robustness motivation: The Internal Model Control (IMC) [8], that is well know to present good robustness properties although is difficult to apply in LCL structures, Linear-Quadratic controllers [9] [10], that present interesting robustness properties provided a state estimator is not used. In the non-linear plane, several interesting approaches are reported making use of the sliding controllers paradigm with successful results [11], [12], [13], the application of Linear Matrix Inequalities has also been reported in several recent approaches [14] [15]. H ∞ approaches, up to this moment have been proposed few times, mostly for simpler topologies as L connected VSCs [16].…”

A general active damping method based on capacitor voltage detection for grid-connected inverter

“…Active damping methods includes virtual resistance method [4], lead-lag method [5], notch filter method [6], double current loop control [7], state feedback [8] etc. In order to increase the system damping, these methods require additional sensors to detect the state variables.…”

Multirate state estimator applied to the current control of PWM-VSI connected to the grid

“…This structure allows the stabilization of G f by a proper reallocation of the oscillatory poles of the LCL-filter. In [7] a partial robust state feedback is proposed. For a given set of grid impedances, it is possible to obtain feedback gains in a linear matrix inequalities framework that assure robust stability for the system for all impedances in the set.…”