Energy function method can provide fast evaluation on system stability after the transients. The boundary of attraction region is very important for application of the energy function method. However

how to approximate the boundary of attraction region remains unsolved. Based on the semi-tensor theory

a novel boundary approximation algorithm is presented

which is derived from the topological characteristics of the stability boundary. In the proposed algorithm

through matrix operations

the high rank approximation expression is obtained. It does not make any nonlinear transformation of the dynamic system

does not require calculating all the eigenvalues and eigenvectors of the dynamic system and also need not time domain integral. Thus

the nonlinear nature of the power system is fully preserved. Another advantage of the proposed algorithm is its easy implementation by the digital computer

since only the matrix calculation is involved in the algorithm.