###### Abstract  
Since thyristor cannot turn off automatically, line commutated converter based high voltage direct current (LCC-HVDC) will inevitably fail to commutate and therefore auxiliary controls or voltage control devices are needed to improve the commutation failure immunity of the LCC-HVDC system. The voltage control device, a synchronous condenser (SC), can effectively suppress the commutation failure of the LCC-HVDC system. However, there is a need for a proper evaluation index that can quantitatively assess the ability of the LCC-HVDC system to resist the occurrence of commutation failures. At present, the main quantitative evaluation indicators include the commutation failure immunity index and the commutation failure probability index. Although they can reflect the resistance of the LCC-HVDC system to commutation failures to a certain extent, they are all based on specific working conditions and cannot comprehensively evaluate the impact of SCs on suppressing the commutation failure of the LCC-HVDC system under certain fault ranges. In order to more comprehensively and quantitatively evaluate the influence of SCs on the commutation failure susceptibility of the LCC-HVDC system under certain fault ranges, this paper proposes the area ratio of commutation failure probability. The accuracy of this new index was verified through the PSCAD/EMTDC. Based on the CIGRE benchmark model, the effects of different synchronous condensers on LCC-HVDC commutation failure were analyzed. The results showed that the new index could effectively and more precisely evaluate the effect of SCs on commutation failures. Moreover, the proposed index could provide a theoretical basis for the capacity allocation of SCs in practical projects and it could also be utilized for evaluating the impact of other dynamic reactive power compensators on the commutation failure probability of the LCC-HVDC system under certain fault ranges. **Keywords:** commutation failure probability; line commutated converter; high voltage direct current (HVDC); synchronous condenser (SC); quantitative evaluation +
Footnote †: journal: Applied Soft  
alternating current (AC) grids [1]. However, due to the use of thyristor technology, the LCC-HVDC system can exhibit the commutation failure during various system disturbances [2]. One of the main reasons for commutation failure is the AC busbar voltage drop that occurs during fault conditions [3,4]. Therefore, it is necessary to quickly and effectively regulate the AC busbar voltage during faulty conditions so that the probability of commutation failure can be reduced. Dynamic reactive power compensators can be installed at the inverter side to achieve quick voltage regulation of the AC busbar by supplying a surplus of reactive power and thus decreasing the probability of commutation failure [5]. The synchronous condenser (SC), a type of dynamic reactive power compensator, can increase the AC system's strength due to the shunting effect of the transient reactance during steady and transient states [6]. It is therefore widely used in real-world LCC-HVDC systems to effectively regulate the AC voltage and thus avoid commutation failure. Recently, SCs have been installed in several LCC-HVDC projects in China to enhance the system's strength and mitigate commutation failures. Hence it is necessary to present an index that can quantitatively and comprehensively assess the influence of SCs on the commutation failure of the LCC-HVDC systems. Several works have focused on evaluating the commutation failure of the LCC-HVDC system. An area of vulnerability (AOV) was discussed and a mechanism for the optimal allocation of dynamic VAR sources was proposed in [7] in order to decrease the commutation failure probability of the LCC-HVDC system at the inverter end. However, due to the use of steady-state equations for calculating the probability of commutation failure, the transient behavior of the extinction angle and phase shift in the AC voltage were not considered, which could lead to a decrease in the accuracy of the results.