Abstract: With the integration of renewable power and the lack of ancillary service, the static voltage stability of the power system is reduced. The eigenvalue analysis and the L index are the common methods to study the static voltage stability. There has been rare study on how to compare the stability indices obtained by the two methods and how to determine the threshold of the latter according to the stability margin of the former. By combining with the power flow equations, the sensitivity model of the L index to the bus loads is proposed. With these loads as the bridge, the exchange relation between the L index and the eigenvalues is proposed. With the above sensitivities, the load buses are sorted to find the measures to improve the static voltage stability. The threshold of the L index is proposed according to the stability margin of the eigenvalues and the exchange relation. The simulation results verify the accuracy and effectiveness of the proposed methods.