This paper presents an Expanding Annular Domain (EAD) algorithm combined with Sum of Squares (SOS) programming to estimate and maximize the domain of attraction (DA) of power systems. The proposed algorithm can systematically construct polynomial Lyapunov functions for power systems with transfer conductance and reliably determine a less conservative approximated DA

which are quite difficult to achieve with traditional methods. With linear SOS programming

we begin from an initial estimated DA

then enlarge it by iteratively determining a series of so-called annular domains of attraction

each of which is characterized by level sets of two successively obtained Lyapunov functions. Moreover

the EAD algorithm is theoretically analyzed in detail and its validity and convergence are shown under certain conditions. In the end

our method is tested on two classical power system cases and is demonstrated to be superior to existing methods in terms of computational speed and conservativeness of results.