Research on the algorithm of connectivity analysis for power system based on spectral graph theory

Power system model is described by graph in this paper. A new judging approach to the network connectivity is proposed, it is based on properties of Laplacian matrix eigenvalues in spectral graph theory, the property is that a network is connected if and only if the second smallest eigenvalue over zero. Note that computation of the spectrum of a matrix has worst-case complexityO(n
³
), the memory space needed isO(n
²
), where n is the size of the matrix. In order to improve operation efficiency of the judgment of network connectivity and reduce the memory space, a polynomial matrix is constructed based on the polynomial acceleration methods, the limited eigenvalues we needed are computed through matrix-vector multiplication and real backward FFT. Finally, the network connectivity is judged by the size of eigenvalues. This method is suitable for the judgment of network connectivity for large-scale power system, requires O(n) operations and the spending of memory space can be reduced effectively.