Estimating the nonlinear oscillation frequency of a power system using the harmonic balanced method

This paper proposes a new approach to estimate the non-constant nonlinear frequency of a power system electro-mechanical oscillation mode by deriving an approximate, analytic expression about the oscillation amplitude-frequency dependency. The approach uses the Harmonic Balance Method (HBM) together with one of three representative function approximation techniques, i.e. Taylor Expansion (TE), Chebyshev Polynomials (CHEB-POL), and Padé approximants (PADE). Detailed tests are conducted on a Single-Machine-Infinite-Bus system and a 2-area system. The TE, CHEB-POL, and PADE are each applied to the swing equation in order to reformulate it into a general polynomial form. Then, the HBM is applied to derive an approximate, analytical expression describing the oscillation frequency by considering multiple oscillation components. A numerical integration method is used as a base line when comparing the function approximation techniques. The results demonstrate that CHEB-POL is the superior technique for both systems.