Abstract
The development of a robust state estimator for ill-conditioned systems based upon the Levenberg-Marquardt algorithm in connection with Givens orthogonal row processing technique is described. The estimator works in two stages: the square-root-free Givens transformation is applied to the measurement Jacobian matrix to reduces it to the product of a unit upper triangular matrix and a diagonal matrix, then the square-root-free Givens transformation is again used to transform a diagonal matrix whose diagonal element is equal to the Levenberg-Marquardt parameter. The Levenberg-Marquardt parameter is adjusted so that the reduction in quadratic cost function is downhill in successive iterations and rapid convergence of the estimator is ensured. An observability analysis algorithm is also developed which is simple and easy to implement. Both description and implementation of the square-root-free Givens transformation are presented. The estimator is applied to a 250 MW, double-flow, single reheat steam turbine which has seven feedwater heaters. Tests results show that the estimator performs well under a wide range of measurement errors and measurement redundancy ratios. A sample of estimated results for rated loading condition are presented. In the appendix, the turbine modelling procedure is discussed.
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