In a multi-infeed DC system

if a fault occurs on a certain line and propagates through the AC power grid to the inverter buses of the DC systems

it may lead to commutation failure in multiple DC systems. To effectively assess the risk of commutation failure in multi-infeed DC systems

this paper constructs a synthetical commutation security margin (SCSM) index

and proposes a method for synchronous condenser placement based on this. Firstly

considering the installation location and power voltage sensitivity of synchronous condensers

the interaction factors of voltage in multi-infeed DC systems are derived. Secondly

under different nodes' grounding faults in the AC system

the sum of the distances between the voltage drops of the single DC inverter buses and the critical voltage drop for commutation failure is taken as the commutation security margin (CSM) of the LCC-HVDC system. Furthermore

taking into account the different DC capacities and interaction degrees

a comprehensive assessment method for the CSM of multi-infeed LCC-HVDC systems

termed synthetical CSM (SCSM)

is constructed. Finally

based on this

a method for selecting locations of synchronous condensers is proposed. Using a modified IEEE 39-bus system in PSCAD/EMTDC

simulations are conducted to study commutation failure risk level in multi-infeed DC systems under three-phase and single-phase ground faults. The results demonstrate that the proposed method for synchronous condenser placement can effectively enhance the SCSM and reduce the commutation failure risk in multi-infeed DC systems

thereby providing guidance for the deployment of reactive power compensation devices such as synchronous condensers in practical engineering.