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15 to 30. These values are simply added to the corresponding elements of sub-matrices Hpij, δi, Hpij, δj, Hpij, Vi, Hpij, Vj, Hpji, δi, Hpji, δj, Hpji, Vi, Hpji, Vj, Hqij, δi, Hqij, δj, Hqij, Vi, Hqij, Vj, Hqji, δi, Hqji, δj, Hqji, Vi and Hqji, Vj. Sub-matrices HP,δ, HP,V, HQ, δ and HQ,V are now considered. Partial derivatives of bus powers can be expressed in terms of partial derivatives of line flows. To illustrate this let i-j, i-k and i-m be the elements connected at bus i. Then the bus powers Pi and Qi are given by Therefore Pi  pi j  pi k  pi m (31) Qi  qi j  qi k  qi m (32) Pi pi j pi k pi m     i  i  i  i (33) Qi qi j qi k qi m     i  i  i  i (34) Similar expressions can be written for other partial derivatives of Pi and Qi with respect to j, Vi and Vj.

I Vi  i j Transmission line / Transformer V j  j gsh i  j bs h i gsh j  j bs h j Fig. 2. Transmission network element between buses i and j The transmission line is represented by the series impedance rij+ jxij or by the corresponding admittance gij + jbij. Transformer with series impedance rij + jxij and off-nominal tap setting “a” with tap setting facility at bus i is represented by the series admittance 1 (gij + jbij) and a  a1 shunt admittances  1  a  (gij + jbij) and   (gij + jbij) at buses i and j respectively.

1981), A robust numerical technique for power system state estimation, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-100, No. 2, pp. 691-698. A. Simoes-Costa & V. H. Quintana (August 1981), An orthogonal row processing algorithm for power system sequential state estimation, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-100, No. 8, pp. 3791-3800. W. F. Tinney, Orthogonal Sparse Vector Methods, IEEE Transactions on Power Systems, Vol. 7, No. 2, pp. 926-932. E (1988), Comparison of different methods for state estimation, IEEE Transactions on Power Systems, Vol.

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