A Complex Variable Perturbed Gauss-Newton Method for Tracking Mode State Estimation

The recent power systems literature has witnessed an intensified interest in state estimation methods that can handle a vast array of measurements from large-scale networks while maintaining performance that is commensurate with real-time requirements. When measurements are from the Supervisory Control and Data Acquisition (SCADA) system and Phasor Measurement Units (PMUs), an elegant formulation of the weighted least squares problem can be cast in complex variables and solved via the Gauss-Newton (GN) method. This paper presents a Perturbed Gauss-Newton (PGN) method in complex variables that is suitable for real-time tracking of the network's state vector. The proposed PGN method is built around an entirely linear measurement model expressed in function of the complex phasor voltages, and its iterative solution scheme requires one factorization of the coefficient matrix followed by repeated forward/backward substitutions. The complex variable PGN method for state estimation can be therefore seen as the counterpart of the classical implicit bus impedance method for power flow. The paper reports numerical results of the PGN method on large-scale transmission networks having up to 9241 nodes and contrasts the proposed method with the equality constrained GN method in complex variables and a recent two-stage estimator also operating in the complex domain.