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This letter investigates the resonance characteristics and stability problem caused by the interactions of multi-parallel LCL-filtered inverters. Compared to single grid-connected inverter, the multi-inverter system presents a more challenging resonance issue, where the inverter interactions may excite multiple resonances at various frequencies. This letter proposes a modeling and analysis method based on the current separation scheme. It reveals that an interactive resonant current that circulates between the paralleled three-phase inverters may arise, depending on the current distribution and the system resonance characteristics. This is different from the common resonant current injected into the grid and has yet been discussed before. The analysis with the root loci in the discrete z-domain are carried out with two stability constraints identified, which correspond to the conditions of triggering the interactive resonant current and common resonant current, respectively. Simulations and experimental results verify the theoretical analysis.Index Terms-Multi-parallel inverters, LCL-filter, resonance interaction, stability analysis.

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This paper comprehensively analyzes the stability of a grid-interfacing inverter with LCL-filter in the discrete domain, where the LCL-filter, along with the controller, are modeled in a polar coordinate. System open-loop and closed-loop poles are analytically studied and expressed in the z-domain.Through the poles movement and distribution analysis, the relationship between system stability and the ratio of resonance frequency over sampling frequency is mathematically revealed and calculated as well as the system control gain limit. Moreover, this paper demonstrates that grid-voltage feedforward regulator would significantly alter the inverter stability in a weak power system. By means of Jury stability criterion, the stability status under different filter resonance frequency is given. The selection of resonance frequency and filter parameters makes a considerable difference on system behavior. Finally, to improve the robustness against grid inductance variation, a conservative design recommendation of filter parameters and control gain is given. Through the tests on a laboratory-scale prototype, the theoretical analysis is validated by experimental results.

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In modern power systems, the increasing penetration of renewables and power electronics, particularly inverter-based wind and solar power generation, is altering power system dynamics and bringing new stability concerns. One challenging issue that is attracting considerable attention is the wide range of power oscillations associated with multiple parallel grid-connected inverters. In such systems, the characteristics in terms of resonance and oscillation are significantly different from single-inverter systems. This paper investigates the mutual interaction and stability issues of multiple grid-interfacing inverters with LCL-filters in power electronics-based power systems under various grid conditions. The investigation reveals that such interactions between power inverters and the grid may excite multiple resonances at various frequencies under certain grid conditions. The nodal admittance matrix concept, which was originally from power systems engineering, is adopted here. Moreover, this paper further develops an Interaction-Admittance model that can effectively describe these mutual interactions in terms of a physical network admittance. We apply our model to various scenarios such as stiff grid conditions and inductive grids with/without Power Factor Correction (PFC) capacitors. The results with the proposed framework demonstrate an intuitive interpretation of multi-inverter system resonance and instabilities. Finally, simulations and experiments on a lab-scale system are provided to verify the theoretical analysis.

A new concept is introduced to model the main effect of tool wear on system dynamics during stable cutting. Audible sound generated from the cutting process is analyzed as a source for monitoring tool wear during turning, assuming adhesive wear as the predominant wear mechanism. The analysis incorporates the dynamics of the cutting process. In modeling the interaction on the flank surface, the asperities on the surfaces are represented as a trapezoidal series function with normal distribution. The effect of changing asperity height, size, spacing, and the stiffness of the asperity interaction is investigated and compared with experimental data.