Parameter estimation by solving polynomial eigenproblem: A synchronous machine example

Abstract

This paper describes a parameter estimation algorithm applicable for a model structure in the form of an overdetermined polynomial eigenproblem. An example of a third-order synchronous machine dynamic model is used to explain the contribution. The dynamic model is reformulated as the polynomial eigenproblem which provides algebraic (polynomial) relations between unknown generator parameters and terminal measurements. Time-varying (not measured) input is represented as a series expansion in the Chebyshev polynomials. The expansion coefficients are added to the set of unknown parameters and size of the polynomial eigenproblem is increased accordingly. The polynomial eigenproblem is reformulated as the equivalent linear generalized eigenproblem and solved using the shift-and-invert power method. Simulation examples are presented to demonstrate robustness of the algorithm in terms of sensitivity to the power of recorded signals (i.e. excitation power) and round-off errors.