Single-Input Single-Output Impedance Modeling and Analysis of Three-Phase Grid-Tied Converter Based on Symmetric Control
Wang Zhen1, Cheng Peng1, Jia Limin1,2
1. China Institute of Energy and Transportation Integrated Development North China Electric Power University Beijing 102206 China; 2. State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Beijing 100044 China
Abstract：With the development of renewable energy power systems, three-phase grid-tied converters (GTCs) are widely used as grid-tied interfaces of wind, solar, and battery systems. Because renewable sources are distributed in remote areas, long-distance transmission lines result in a weak grid. In the weak grid, the asymmetric control structure of a three-phase gird-tied converter leads to frequency coupling, which is not conducive to the stability of the system and the design of the controller. Therefore, a symmetric control strategy is proposed to compensate for the asymmetry of the dq axis caused by the phase-locked loop (PLL) and DC-link voltage control (DVC). Then, the frequency coupling effect is eliminated, and GTCs are modeled as a single-input and single-output (SISO) admittance complex vector. The stability analysis based on the SISO admittance can reveal the inducement of system oscillation and simplify the parameters design of the controller. Firstly, the dq-frame admittance model of the DVC-embedded GTC with the conventional control strategy is developed, and the instantaneous power balance of the filter is considered for accuracy. Then, the unified impedance modeling approach transforms the real admittance matrix into the complex admittance. Since the dq axis is asymmetric, the complex conjugate components of the PCC voltage and current are introduced, and the frequency coupling effect is inevitable. Consequently, the symmetric PLL (SPLL) and the q-axis compensation of DVC are introduced. Compared with the synchronous reference frame PLL (SRF-PLL), SPLL controls the q-axis and d-axis of common coupling (PCC) voltage points. Therefore, the output of the SPLL is a complex vector angle that tracks the amplitude and phase of the PCC voltage. For DVC, to compensate for the asymmetry of q-axis control, q-axis voltage feedforward compensation and q-axis current feedback compensation are introduced, respectively, effectively eliminating the conjugate components of the DVC. Moreover, the accuracy of the symmetric control model is verified by the sweep frequency method. The sweep frequency results show that the diagonal elements are equal, and the off-diagonal elements are opposite in the dq-frame admittance matrix. In other words, GTC becomes a symmetric system, and the frequency coupling is suppressed. The simulation results demonstrate that the proposed scheme does not affect the dynamic and steady-state performance of the system. Besides, based on the SISO model, the admittance characteristics of GTC are analyzed. The influencing factors of the admittance characteristics are divided into two parts, namely, the control parameters and the operating conditions. In the control system, high-bandwidth SPLL can cause the system to oscillate, while the DVC parameter changes have little effect on stability. Furthermore, oscillations are triggered when inductive reactive power is injected into the system, while the opposite is true when capacitive reactive power is injected. Further analysis shows that the SPLL dominates the GTC phase characteristics in the low-frequency band. The parallel admittance introduced by the SPLL dynamics has a negative resistance effect, significantly reducing the system stability margin. The experimental results verify the effectiveness of the proposed symmetric control strategy and the accuracy of the theoretical analysis. The conclusions of this paper can be summarized as follows: (1) By introducing the SPLL and q-axis compensation of DVC, the frequency coupling effect of GTC is eliminated. (2) Based on the analysis of SISO admittance characteristics, SPLL dominates the frequency characteristics of GTC in the low-frequency band, and its negative resistance characteristics lead to system instability. (3) Different operating conditions affect the admittance characteristics of GTC. The injection of inductive reactive power is detrimental to system stability, and the injection of capacitive reactive power is the opposite.
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2024, Vol. 39 
