On the convergence of the implicit Z-Bus power flow method for distribution systems

Abstract

In this paper, the convergence properties of the implicit Z-Bus power flow method for distribution systems are analyzed. First, the formulation of implicit Z-Bus method is simplified to obtain its expressions in real vector space. Second, two fundamental convergence problems are respectively discussed and derived. And the results obtained with regard to the implicit Z-Bus method include: it is inevitably convergent in the entire power flow solvability region (excluding the boundary which is comprised of all the saddle node bifurcation points), and it has reliable convergence property in the aspect of the basin of attraction. Finally, an accelerating strategy based on the Aitken–Steffensen formula is proposed to accelerate the implicit Z-Bus method. Numerical tests are implemented to illustrate the convergence characteristics.