Transient stability domain estimation of AC/DC systems considering HVDC switching characteristics based on the polynomial Lyapunov function method

•The AC/DC system can be modeled as a switched nonlinear system.•The equations representing the transient characteristics of a DC system are reflected in the process of transient stability domain estimation.•The continuous piecewise Lyapunov function and stability domain estimation algorithm for the AC/DC system are proposed.•The effects of different SOS approximation methods on the results are shown under the influence of numerical problems.