Spectral norm in the convergence of the fast decoupled load flow

The authors present a new formulation for the convergence of the fast decoupled load flow algorithm in terms of spectral norms. The fast decoupled load flow equations are written in a fixed point iterative form around the initial point, and the spectral norm of the resulting iteration matrix is calculated. The formulation differs from those proposed earlier in that the angles are updated during the second half of the iterations, and the power loading of the system is taken into account, yielding more realistic figures for the norm. A series of tests are carried out on IEEE test systems to demonstrate the correlation between the spectral norm and the convergence performance of the algorithm. It is shown that the algorithm tends to convergence more rapidly when this norm is reduced in magnitude.