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| Weak Robustness Analysis of Close Subsynchronous Oscillation Modes' Participation Factors in Multiple Direct-Drive Wind Turbines with the VSC-HVDC System |
| Shao Bingbing1, Zhao Zheng2, Xiao Qi1, Yang Zhiqing1, Meng Xiaoxiao1 |
1. Anhui Province Key Laboratory of Renewable Energy Utilization and Energy Saving Hefei University of Technology Hefei 230009 China;
2. State Grid Economic and Technological Research Institute Co. Ltd Beijing 102209 China |
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Abstract Direct-drive wind farms with the VSC-HVDC (DDWFV) system face the risk of sub-synchronous oscillations (SSOs), and multiple similar permanent magnet synchronous generators (PMSGs) grid-connected system contain multiple close SSO modes. Recently, the strong resonance, weak resonance and open-loop mode resonance when the SSO modes approach were analyzed. However, the research was about the change of SSO modes, while the change of close SSO modes' participation factors (PFs) was rarely studied. Certain research showed that the PF of SSO modes was sensitive to parameter changes, but the phenomenon was not explained theoretically and under which condition does the phenomenon happen was unknown. The PF reflects the participation of system state variables in the SSO modes, which determines the optimal location of damping controllers. Generally, the damping controller is preferred installed on the PMSGs with the largest PF. Therefore, the PF has a great impact on the performance of damping controllers, and it is necessary to reveal the reason why the PFs of close SSOs are sensitive to parameter changes, and appropriate tools need to be proposed to analyze this phenomenon. For the convenience of description, the phenomenon that the PF is sensitive to parameter changes is defined as the PFs weak robustness.
Firstly, the dynamic model of the DDWFV is built, which includes the dynamic models of PMSG power generation system, VSC-HVDC, and their interface model. Secondly, the PFs weak robustness phenomenon is presented with the homogeneous wind farms, heterogeneous wind farms and large-scale wind farms. The homogeneous and heterogeneous wind farms are based on the three-machine model, and the large-scale wind farms are based on the 160-machine model. After presenting the PFs weak robustness phenomenon, the PFs weak robustness mechanism is revealed with the matrix perturbation method, which explains the little change of SSO modes and large change of PFs under the parameter perturbation. Thirdly, the PFs weak robustness hazards are presented with the three-machine system. The performances of SSO damping controllers before and after the parameter perturbation are compared, and the results show that the optimal location of damping controllers before the perturbation does not mean the optimal location after the perturbation. Therefore, the parameter perturbation has a great impact on the performance of damping controllers when PFs weak robustness happens. Finally, to reduce the hazards of PFs weak robustness, three methods about the PMSGs design and damping controllers design are proposed. Meanwhile, the design of damping controllers under the perturbation of wind speeds is discussed.
The following conclusions can be drawn from the analysis: ① Where there are similar PMSGs, the DDWFV may contain multiple close modes. Under the parameter perturbation, the change of SSO modes is less, while the PFs of close SSO modes experience a great change. ② Under the parameter perturbation, the dominant PMSGs of close SSO modes may change, which affects the optimal location of damping controllers and their damping performances. ③ To reduce the hazards of PFs weak robustness, three methods can be adopted: increasing the differences between the PMSGs and dynamically adjusting the damping controller location according to the numerical solution/analytical solution of the PFs under the parameter perturbation, so as to improve the robustness of SSO damping controllers.
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Received: 06 September 2022
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2023, Vol. 38 
