State estimation using augmented blocked matrices

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Abstract
A novel method of blocking the Hachtel formulation for power system state estimation is proposed. The key idea is organization of the Hachtel formulation into a submatrix block structure that conforms to that of the incidence matrix of the network. This leads to the normal first-neighbor topological structure of the blocked matrix, which is processed in the same sparsity-preserving order as the nodal admittance matrix. Explicit inversion of diagonal submatrix blocks overcomes former difficulties with small or zero diagonals and further enhances numerical stability. Equality constraints are enforced exactly instead of as measurements with artificially large weighting factors. Another feature of the method is that it can accommodate a more realistic covariance matrix having nonzero off-diagonal weighting factors corresponding to correlations between the active and reactive power measurements at a bus. In fact, any covariance terms that fall within the submatrix blocks (in locations that are now zeros) can be accommodated with no effects on computational burden. As indicated by its large reduction in the numerical condition number of three representation test problems, the proposed method should be able to overcome the usual causes of ill-conditioning of power system state estimation. As shown by comparisons of its computational requirements with those of other methods, there is no sacrifice in speed to achieve robustness.