Analysis of Harmonic Disturbance Response of Multi-Inverter Grid-Connected System Combining Characteristic Root and Modal Analysis Method
Li Rong1, Li Jianwen1, Li Yonggang1, Sun Wei2
1. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power University Baoding 071003 China; 2. Baoding Power Supply Subsidiary Company of State Grid Hebei Electric Power Supply Co. Ltd Baoding 071000 China
Abstract：The broadband oscillation caused by the interaction of a high proportion of new energy connected to the grid, grid impedance and load is a typical system stability problem. In recent years, some overvoltage phenomena have been difficult to classify into the classical stability problems. The electromagnetic transient process driving this phenomenon differs from the power-angle relationship on the rotor-side generator models using phase-locked loops (PLLs). To explain the dynamic behavior of inverter grid-connected systems disturbed by broadband harmonics, this paper derives a mathematical expression that characterizes the system's response to harmonic disturbances and analyzes the response's characteristics. Furthermore, the feasibility of analyzing harmonic responses using characteristic roots is verified by an example of a single inverter connected to the grid. The relationship between the characteristic root and the resonance mode is clarified for multi-inverter grid-connected systems. Finally, the dynamic behavior analysis is verified by simulation and experiments. The harmonic disturbance response expression is derived according to the characteristic roots and the harmonic disturbance. It is found that the system's response comprises two waveforms: the steady-state response and the transient response. The resonance characteristics of these two responses differ, with the magnitude of the resonance peak closely related to the damping coefficient ξ. A large peak occurs when ξ is close to 0, gradually decreasing as ξ increases, and no steady-state response resonance peak is observed when ξ>0.7. The characteristic root can effectively describe the harmonic disturbance response of inverter grid-connected systems. The dynamic behavior of the system after disturbance can be quantitatively analyzed by calculating the damping coefficient value. When multiple inverters are connected to the grid, the impedance-based system modeling method provides convenience for analyzing the stability of the inverter grid-connected system. The series and parallel resonance points in high-order networks are obtained by modal analysis. Accordingly, the characteristic roots of the system are obtained by converting the memory elements in the matrix from the frequency domain to the s domain, offering a simple and reusable approach to characterize coupling relationships within high-order networks and analyze system stability. The proposed method is verified using a single inverter connected to the grid and three inverters with different parameters to be connected to the grid. It is found that the parameter design of a single inverter can meet grid-connected harmonic requirements. However, when multiple inverters are connected to the grid, the damping coefficient of a single inverter decreases with the number of parallel inverters. A smaller damping coefficient makes the system less capable of actively suppressing harmonic oscillations. The slow attenuation of transient components results in a significantly increased waveform distortion rate over a short period of time. The following conclusions can be obtained through simulation and experiments: (1) As an analytical tool for finding system characteristic roots and traversing system resonance frequencies, the modal analysis method can provide numerical solutions and modal impedance curves simply and quickly. (2) The characteristic roots of the system can effectively describe the dynamic behavior of the system after disturbance. (3) A small damping coefficient renders the system susceptible to severe harmonic oscillations and deepens waveform distortion in a short period.
李戎, 李建文, 李永刚, 孙伟. 结合特征根及模态分析法的逆变器多机并网系统谐波扰动响应分析[J]. 电工技术学报, 2024, 39(14): 4519-4534.
Li Rong, Li Jianwen, Li Yonggang, Sun Wei. Analysis of Harmonic Disturbance Response of Multi-Inverter Grid-Connected System Combining Characteristic Root and Modal Analysis Method. Transactions of China Electrotechnical Society, 2024, 39(14): 4519-4534.
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2024, Vol. 39 
