Stability Analysis and Improvement of the Capacitor Current Active Damping of the LCL Filters in Grid-Connected Applications

Abstract

For grid-connected LCL-filtered inverters, dual-loop current control with an inner-loop active damping (AD) based on capacitor current feedback is generally used for the sake of current quality. However, existing studies on capacitor current feedback AD with a control delay do not reveal the mathematical relation among the dual-loop stability, capacitor current feedback factor, delay time and LCL parameters. The robustness was not investigated through mathematical derivations. Thus, this paper aims to provide a systematic study of dual-loop current control in a digitally-controlled inverter. At first, the stable region of the inner-loop AD is derived. Then, the dual-loop stability and robustness are analyzed by mathematical derivations when the inner-loop AD is stable and unstable. Robust design principles for the inner-loop AD feedback factor and the outer-loop current controller are derived. Most importantly, ensuring the stability of the inner-loop AD is critical for achieving high robustness against a large grid impedance. Then, several improved approaches are proposed and synthesized. The limitations and benefits of all of the approaches are identified to help engineers apply capacitor current feedback AD in practice.

LCL-resonance damping strategies for grid-connected inverters with LCL filters: a comprehensive review

“…For instance, with one-sample delay (i.e., T d = T s ), the resonance still exists if a is between 1/6 and 1/2, as also analyzed in [26][27][28][29][30][31][32]34]. If (10) is fulfilled, the feedback AD in Fig.…”

“…Besides delay, in practical application the filter parameters may vary from their design values and the grid at the PCC has non-negligible impedance. The studies in [6,[27][28][29][30][31][32], and [64][65][66][67][68] showed that the resonance frequency is significantly reduced when the filter parameters and the grid impedance are varied.…”

“…If (10) is fulfilled, the feedback AD in Fig. 4 produces two unstable poles in the open-loop transfer function from i ref to i L1 or i L2 , yielding some difficulties for robust design [27,31].…”

“…AD strategies based on feedback compensation are in essence the same while their differences mainly lie in the choice of states for feedback. Typical applications of proportional i C1 feedback can be found in [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. For 1 storder derivative feedback of u C1 , a high-pass filter (HPF) with a similar response is an alternative solution [35].…”

“…Filter-based AD improves stability by adding a digital filter next to the current controller [11][12][13][14][15][16]. For feedbackbased AD, the state used for feedback can be the capacitor current [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], the capacitor voltage [33][34][35][36], the inverterside current [37], the grid current [38][39][40][41] or a combination of multiple states [42][43][44][45][46][47][48][49][50]. Among the feedback-based AD methods, proportional feedback of capacitor current is widely studied during last decade due to its simple implementation.…”