Time domain transient state estimation using singular value decomposition Poincare map and extrapolation to the limit cycle

Abstract

This paper proposes an alternative methodology based on the Singular Value Decomposition (SVD) to evaluate the Transient State Estimation (TSE) in the time domain of a power system. Transient phenomena such as faults, sags and load changes can be estimated with the TSE, covering over, normal and under-determined cases, according to the number of measurements and state variables related through the measurement state estimation equation; proposed as being a function of measurements and their derivatives. The system observability can be determined by means of SVD. If the system is unobservable the SVD can determine which parts of the network are observable. The TSE takes partial measurements, calculates the best estimated state variables and completely determines the system state representing a transient condition. The periodic steady state following a transient condition is obtained through a Newton method based on a Numerical Differentiation (ND) process, Poincaré map and extrapolation to the limit cycle; this method is applied before and after the simulated transient. The TSE results are validated through direct comparison against those obtained with the Power Systems Computer Aided Design/Electromagnetic Transients Program including Direct Current (PSCAD/EMTDC) simulator.