Fundamental concepts of a Krylov subspace power flow methodology

The well established power flow methods-Gauss-Seidel, Newton-Raphson, and fast decoupled load flow-are all based an major, classical methodologies of applied mathematics. The Krylov subspace power flow (KSPF) method presented in this paper uses a newer, very successful approach-the Krylov subspace methodology-developed in applied linear algebra for the iterative solution of large, sparse systems of linear equations. The method has been adapted to nonlinear equations and used for the solution of the power flow problem with either an approximation of the Jacobian, as in the fast decoupled load flow, or in a direct Newton-like manner but without explicitly forming the Jacobian. Convergence rates are from linear to almost quadratic. The general methodology is described as well as its application to the power flow problem. The main advantage of KSPF is that no matrix factorizations, only sparse matrix-vector multiplications or evaluations of residuals, are used. Preliminary tests suggest that KSPF may become a competitive alternative to existing methods, especially in the case of large power systems.