Analysis of power system oscillation frequency using Differential Groebner Basis and the Harmonic Balance Method

For analysis of non-constant electro-mechanical oscillation frequency with a power system, this paper proposes an analytical approach integrating Differential Groebner Basis (Diff-GB) and the Harmonic Balance Method (HBM). This approach is illustrated in detail on a single-machine-infinite-bus system, whose oscillation frequency fluctuates with time due to its nonlinear-system nature. The Diff-GB is first applied to convert the original swing equation into a higher order polynomial differential equation that eliminates explicit sine nonlinearity from its form. Then, the HBM is utilized to derive an approximate analytical expression about oscillation frequency, whose fluctuating nature is then studied by considering multiple oscillation components. The proposed approach is compared with other approaches including small signal analysis, a Taylor Expansion based approach and a numerical approach in terms of oscillation frequency estimation, and demonstrates its superiority.