In the UHVDC hierarchical connection system

the reactive power regulation and voltage stability problem are more complicated.This is because there is an electrical coupling relationship between AC and DC systems

between the high and low converter valve groups and the two ends of the AC system with different voltage levels.Consequently

we proposed a multi-infeed voltage stability index（MVSI） based on traditional single-infeed voltage stability index（VSI）.Moreover

combined with the UHVDC hierarchical access mathematical model

calculation equation of multi infeed voltage stability index was derived.Based on these equations

the influences of the system parameters at the receiving systems and the operating state of the DC system on the static voltage stability of the converter bus were studied.The analysis results show that the static voltage stability of the converter bus can be effectively improved by reducing the receiving system parameters

reducing equivalent connection impedance of two AC systems

reducing the transmission power of UHVDC hierarchical connection system

and increasing the arc extinguishing angle.And the equivalent impedance angle of the AC system at the receiving end will also affect the static voltage stability of the converter bus.