A Cartesian Coordinate Algorithm for Power System State Estimation

This paper presents a new steady-state estimator based on the Cartesian coordinate formulation of nodal and line flow equations and minimization of weighted least squares (WLS) of the residuals. The fact that the rectangular coordinate version of network Performance equations is completely expressible in a Taylor series and contains terms up to the second order derivatives only, results in a fast exact second order state (FESOS) estimator. In this estimator, the Jacobian and information matrices are constant, and hence need to be computed once only. The size of the mathematical model for the new estimator is the same as that of the widely used fast decoupled state (FDS) estimator, and hence characterized by comparable computational requirements (storage and time per iteration). Digital simulation results are presented on several sample power systems (well-conditioned/ill-conditioned) under normal as well as unusual operating modes to illustrate the range of application of the method vis-a-vis the FDS estimator. It is found that the exactness of the FESOS algorithm provides an accurate solution during all modes of system operation, and assures convergence to the right solution in spite of network ill-conditioning. In particular, the convergence behaviour and accuracy of solution of the FESOS estimator approach those of the FDS estimator for lightly loaded and well- conditioned power systems during normal modes of operation, but are vastly superior during unusual modes of system operation or in relation to ill-conditioned networks.