This paper addresses the harmonic stability caused by the interactions among the wideband control of power converters and passive components in an ac power-electronics-based power system. The impedance-based analytical approach is employed and expanded to a meshed and balanced three-phase network which is dominated by multiple current-and voltage-controlled inverters with LCL-and LC-filters. A method of deriving the impedance ratios for the different inverters is proposed by means of the nodal admittance matrix. Thus, the contribution of each inverter to the harmonic stability of the power system can be readily predicted through Nyquist diagrams. Time-domain simulations and experimental tests on a three-inverter-based power system are presented. The results validate the effectiveness of the theoretical approach.

This paper presents a new topology of higher order power filter for grid-tied voltage-source inverters, named the LLCL filter, which inserts a small inductor in the branch loop of the capacitor in the traditional LCL filter to compose a series resonant circuit at the switching frequency. Particularly, it can attenuate the switching-frequency current ripple components much better than an LCL filter, leading to a decrease in the total inductance and volume. Furthermore, by decreasing the inductance of a grid-side inductor, it raises the characteristic resonance frequency, which is beneficial to the inverter system control. The parameter design criteria of the proposed LLCL filter is also introduced. The comparative analysis and discussions regarding the traditional LCL filter and the proposed LLCL filter have been presented and evaluated through experiment on a 1.8-kW-single-phase grid-tied inverter prototype.

A higher order passive power filter (LLCL-filter) for the grid-tied inverter is becoming attractive for industrial applications due to the possibility to reduce the cost of the copper and the magnetic material. However, similar to the conventional LCL-filter, the grid-tied inverter is facing control challenges. An active or a passive damping measure can be adopted to suppress the possible resonances between the grid and the inverter. For an application with a stiff grid, a passive damping method is often preferred for its simpleness and low cost. This paper introduces a new passive damping scheme with low power loss for the LLCL-filter. Also a simple engineering design criterion is proposed to find the optimized damping resistor value, which is both effective for the LCL-filter and the LLCL-filter. The control analysis and the power loss comparison for different filter cases are given. All these are verified through the experiments on a 2 kW single-phase grid-tied inverter prototype using proportional resonant controllers. It is concluded that compared with the LCL-filter, the proposed passive damped LLCL-filter can not only save the total filter inductance and reduce the volume of filter, but also reduce the damping power losses for a stiff grid application.

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. Index terms-LCL-filter, current-controlled, grid-tied inverter, distributed power generation system, stability, damping, generalized Nyquist stability criterion, impedance-based stability analysis. I. INTRODUCTION HE rapid evolution of society and technology brings a vast increase in energy demand. Fossil fuels will soon be running out. The environmental problems caused by the fossil fuel consumption make the society pay more attentions

In order to minimize the effect of the grid harmonic voltages, harmonic compensation is usually adopted for a gridtied inverter. However, a large variation of the grid inductance challenges the system stability in case a high-order passive filter is used to connect an inverter to the grid. Although in theory, an adaptive controller can solve this problem, but in such case the grid inductance may need to be detected on-line, which will complicate the control system. This paper investigates the relationship between the maximum gain of the controller that still keeps the system stable and the Q-factor for a grid-tied inverter with an RL series or an RC parallel damped high-order power filter. Then, a robust passive damping method for LLCL-filter based grid-tied inverters is proposed, which effectively can suppress the possible resonances even if the grid inductance varies in a wide range. Simulation and experimental results are in good agreement with the theoretical analysis.