# Power Stability Analysis and Evaluation Criteria of Dual-Infeed HVDC with LCC-HVDC and VSC-HVDC
###### Abstract  
This paper analyzes the power stability of the hybrid dual-infeed high-voltage direct-current (HVDC) system containing a line commutated converter-based HVDC (LCC-HVDC) and a voltage source converter-based HVDC (VSC-HVDC). First, the concept and the calculation method of power stability for the hybrid dual-infeed HVDC system are introduced. Second, the influence of VSC-HVDC on the power stability of the system is investigated. Third, the relationship between the power stability and the effective short circuit ratio (ESCR) is discussed under different system parameters. Then, the value range of the critical effective short circuit ratio is determined. Finally, the evaluation criteria of power stability are proposed. The results show that the evaluation criteria of the single-infeed LCC-HVDC system can still be used, if the VSC-HVDC is in constant AC voltage control mode; if the VSC-HVDC is in constant reactive power control mode, the hybrid dual-infeed HVDC system cannot operate stably when the ESCR is less than 2.0 and can operate stably with high power stability margin when the ESCR is greater than 3.0. The ESCR index can still be used to measure the power stability of the hybrid dual-infeed HVDC system. high-voltage direct current (HVDC); line-commutated converter (LCC); voltage source converter (VSC); power stability; effective short circuit ratio (ESCR); evaluation criteria +
Footnote †: journal: Applied Sciences  
short circuit ratio (MIESCR) index considering the interaction between HVDCs [14]. The effectiveness and application scope of ESCR and MIESCR in the dual-infeed LCC-HVDC system are analyzed in [15]. The results show that the MIESR index can be used to evaluate the power stability of the HVDC system in all DC current synchronous increase mode; while in the single DC current increase mode, the ESCR index should be used to evaluate the power stability of the HVDC system rather than the MIESR index and its threshold value can follow the threshold in single-infeed LCC-HVDC systems. For hybrid dual-infeed HVDC systems, a large number of references have studied the influence of VSC-HVDC on the operating characteristics of LCC-HVDC [16; 17; 18]. In [16], the receive-end-system voltage strength factor (RVSF) index was proposed based on the voltage sensitivity to evaluate the influence of VSC-HVDC on the strength of LCC-HVDC receiving end systems. In [17], the apparent increase in short circuit ratio (AISCR) index was proposed based on the concept of the maximum available power of LCC-HVDC, which was used to quantitatively evaluate the performance improvement of LCC-HVDC by VSC-HVDC. In [18], an equivalent single-infeed LCC-HVDC model of the hybrid dual-infeed HVDC system was derived to evaluate the voltage support capability of LCC-HVDC receiving-end systems. However, little research has been carried out on the power stability of the hybrid dual-infeed HVDC system in the above literature. The power stability evaluation of the hybrid dual-infeed HVDC system still lacks a unified quantitative standard. Additionally, as mentioned above, the research on the effectiveness of ESCR is generally based on the power system with one or two LCC-HVDC links. Such research is insufficient in the hybrid dual-infeed HVDC situation. There is no effective research to verify whether the ESCR index can still be used to quantitatively evaluate the power stability of the HVDC system in the new situation. Therefore, it is imperative to study the effectiveness of ESCR in the hybrid dual-infeed HVDC system. This paper establishes the mathematical model of the hybrid dual-infeed HVDC system. Based on the proposed mathematical model, the power stability of the HVDC system is analyzed from two aspects: the control mode and the transmission power of the VSC-HVDC. Furthermore, the relationship between the power stability and the effective short-circuit ratio is studied in the hybrid dual-infeed HVDC system. The contributions of this paper are summarized as follows:  
1.