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This paper presents a modified version of the weighted least-square (WLS) estimator, using the Levenberg-Marquardt (L-M) algorithm for application to Ill-conditioned power systems. This algorithm essentially amounts to modifying the Gauss-Newton normal equations by adding a scalar to each element of the main diagonal of the information matrix. The L-M method reduces to either Gauss-Newton or Steepest Descent approach, according as the scalar tends to zero or infinity. Digital simulation results are presented on a structurally ill-conditioned (singular Jacobian) sample power system to illustrate the range of application of the method. It is found that the introduction of a scalar (Marquardt-Constant) achieves convergence to a solution in spite of the presence of ill-conditioning. In the event that this solution does not correspond to the true solution because of local singularities, the additional use of a Householder orthogonal transforma- tion leads to the true solution.
Date of Publication: March 1980