Building a secure and reliable high-voltage direct current transmission system with grid support capability has become an urgent requirement for the development of modern power systems. The hybrid commutated converter (HCC) based on the reverse blocking integrated gate commutated thyristor (IGCT) inherits the technical advantages of the line commutated converter (LCC) while fundamentally eliminating the issue of commutation failure. And theoretically

the reactive power and voltage support for the AC grid can be achieved to a certain extent by reducing the advancing firing angle. However

as the advancing firing angle decreases

the HCC exhibits different operation modes

leading to varying commutation loop characteristics

which leads to complex analytical calculations for the multi-mode power factor angle and unclear reactive power regulation capability. Therefore

based on the equivalent commutation circuit of the HCC

this paper refines the commutation modes and their boundary conditions

derives the nonlinear mapping relationship between the advance firing angle and the power factor angle

and proposes an approximate analytical calculation method for the power factor angle under different operating modes of the HCC. Building on this

a reactive power control and parameter design method for the HCC is further developed

with validation conducted in PSCAD/EMTDC

which offers theoretical and methodological support for understanding and improving the transient performance of the HCC during AC faults.