Power flow is basic for studying the steady-state operation of flexible DC systems

and its efficiency is the core problem. Consequently

we compared and analyzed the efficiency of several high-order Newton methods suitable for power flow calculation of flexible DC systems. First

we analyzed the Newton method and its improvement higher-order convergence forms such as 2.414-order

third-order

and sixth-order

and proposed a new combined high-order algorithm based on the 2.414-order Newton and the simplified Newton. Then

we put forward an efficiency formula of the iterative methods suitable for VSC-HVDC power flow

and discussed the problem of unequal calculation of function value and Jacobian matrix in the efficiency formula. Finally

based on the modified IEEE examples

the pros and cons of efficiency for the above-mentioned methods are compared. Simulation verifies the applicability and effectiveness of the proposed combined high-order algorithm and efficiency index.