Delay-Dependent Stability of Single-Loop Controlled Grid-Connected Inverters with LCL Filters

LCL filters have been widely used for grid-connected inverters. However, the problem that how time delay affects the stability of digitally controlled grid-connected inverters with LCL filters has not been fully studied. In this paper, a systematic study is carried out on the relationship between the time delay and stability of single-loop controlled grid-connected inverters that employ inverter current feedback (ICF) or grid current feedback (GCF). The ranges of time delay for system stability are analyzed and deduced in the continuous s-domain and discrete z-domain. It is shown that in the optimal range, the existence of time delay weakens the stability of the ICF loop, whereas a proper time delay is required for the GCF loop. The present work explains, for the first time, why different conclusions on the stability of ICF loop and GCF loop have been drawn in previous studies. To improve system stability, a linear predictor-based time delay reduction method is proposed for ICF, while a time delay addition method is used for GCF. A controller design method is then presented that guarantees adequate stability margins. The delay-dependent stability study is verified by simulation and experiment

Improvement of Stability of a Grid-Connected Inverter with an LCL filter by Robust Strong Active Damping and Model Predictive Control

This study addresses development and implementation of robust control methods for a three-phase grid-connected voltage source inverter (VSI) accompanied by an inductive-capacitive-inductive (LCL) filter. A challenge of current control for the VSI is LCL filter resonance near to the control stability boundary, which interacts with the inverter control switching actions and creates the possibility of instability. In general, active damping is needed to stabilize the system and ensure robust performance in steady-state and dynamic responses. While many active damping methods have been proposed to resolve this issue, capacitor-current-feedback active damping has been most widely used for its simple implementation. There has been no clear consensus regarding design of a control system including capacitor-current-feedback active damping. This is due to the fact that simulation/experiment results are not congruent with the design analyses on which the control is designed. This study explains the incoherence between theory and practice when it comes to a capacitor-currents-feedback active damping system. Proposed capacitor-current-estimate active damping utilizing a developed posteriori Kalman estimator gives coherent simulation results as expected from the design analyses. This reveals that the highly oscillatory capacitor currents containing the inverter switching effects bring about uncertainty in the system performance. The switching effects are not incorporated in the analyses and control system design. Therefore, it is required to remove the switching noise from the capacitor currents in order to yield consistent results. It has been confirmed that the proportional-negative feedback of the capacitor current is equivalent to virtual impedance connected in parallel with the filter capacitor. In a digitally controlled system, the computation delay causes the equivalent resistance of the virtual impedance to become negative in the frequency range of fs/6 to fs/2, which produces a pair of open-loop unstable poles in RHP. This happens when the displaced resonance peak by active damping is in that region. Thus, an a priori Kalman estimator has been developed to generate one-sample-ahead state variable estimates to reconstruct the capacitor currents for active damping, which can compensate for the delay. The one-sample-ahead capacitor-current estimates are computed from the inverter-side and grid-side current estimates. The proposed method provides extended limits of the active damping gain that improve robustness against system parameter variation. It also allows strong active damping which can sufficiently attenuate the resonance. Grid condition is another significant factor affecting the stability of the system. In particular, a weak grid tends to provide high impedance. The system employing the proposed active damping method stably operates in a weak grid, ensuring robustness under grid impedance variation. The developed Kalman estimators offer an effective and easy way of determining the stability status of a system in addition to the functions of filtering and estimation. Stability analysis can be easily made since state variable estimates go to infinity when a system is unstable. As a promising approach, model predictive control (MPC) has been designed for the system. This study suggests that MPC including active damping can be employed for a grid-connected VSI with an LCL filter with good dynamic performance

Resonance Damping of LCL Filters Using Capacitor-Current Proportional-Integral Positive Feedback Method for Grid-Integrated Fuel Cell System

Nowadays, the use of grid-integrated inverter proton exchange membrane fuel cell (PEMFC) systems is becoming more prevalent due to their efficiency and favorable environmental effects. Switching the grid-connected inverters causes high-frequency harmonics, which are eliminated using LCL filters. These filters are susceptible to instability when their resonant frequency is affected by changes in network impedance. Active damping methods are used to weaken the resonance of LCL filters. However, the grid-connected inverter is prone to be unstable under grid impedance variations due to the negative equivalent resistance resulting by digital control delays. As a solution to this problem, the capacitor-current proportional-integral (PI) positive feedback active damping approach is suggested in this study. It can provide a positive equivalent resistance almost within the Nyquist frequency, i.e., the entire controllable frequency range. As a result of the proposed method, the grid-connected inverter achieves strong stability against grid impedance variations. In this study, a PEMFC stack is used to produce and inject power into the weak grid using the proposed controller. MATLAB/Simulink simulation results are presented to verify the validity of the proposed method. The simulation results show that the proposed method is stable against changes in grid impedance and PEMFC parameters, and provides a good performance

Damping Methods for Resonances Caused by LCL-Filter-Based Current-Controlled Grid-Tied Power Inverters: An Overview

Grid-tied voltage source inverters using LCL filter have been widely adopted in distributed power generation systems (DPGSs). As high-order LCL filters contain multiple resonant frequencies, switching harmonics generated by the inverter and current harmonics generated by the active/passive loads would cause the system resonance, and thus the output current distortion and oscillation. Such phenomenon is particularly critical when the power grid is weak with the unknown grid impedance. In order to stabilize the operation of the DPGS and improve the waveform of the injected currents, many innovative damping methods have been proposed. A comprehensive overview on those contributions and their classification on the inverter- and grid-side damping measures are presented. Based on the concept of the impedance-based stability analysis, all damping methods can ensure the system stability by modifying the effective output impedance of the inverter or the effective grid impedance. Classical damping methods for industrial applications will be analyzed and compared. Finally, the future trends of the impedance-based stability analysis, as well as some promising damping methods, will be discussed