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Block diagonal dominance for systems of nonlinear equations with application to load flow calculations in power systems

Abstract

AbstractThe concept of a pointwise strict (or Ω) diagonally dominant nonlinear function, first introduced by Moré, is generalized to the blockwise case. A sufficient condition is obtained for the convergence of underrelaxed block Jacobi and block Gauss– Seidel iterations for a nonlinear system of equations in terms of the strict (or Ω) diagonal dominance of an associated matrix. A new formulation for the determination of the steady-state load flow in lossless electric power systems is described and it is shown that this formulation leads to the solution of a system of quadratic equations in the unknown (complex-valued) voltages. Under suitable assumptions on the power system the sufficient condition is satisfied. Numerical examples, consisting of an illustrative three bus system and a realistic thirty bus system, are presented. Results of our block Gauss–Seidel iteration are compared with those of Newton–Raphson iteration

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