Inertia Estimation of Synchronous Generators Using PMU Ambient Data in the Frequency Domain

A frequency-domain method for estimating inertia of synchronous generators (SGs) from PMU ambient data is proposed based on the SG swing equation model, whose inputs are the mechanical and electrical powers. The model output is the rotor speed, which is expressed with the electrical frequency plus the load angle derivative. Due to low-frequency dynamics of the governor-turbine system, the spectral density function (SDF) of the mechanical power is negligible except the vicinity of dc. In a low-frequency rage, the SDF of the load angle derivative is also negligible compared with the SDF of the electrical frequency. The transfer function of the model from the electrical power input to the electrical frequency output can be established in a frequency range where the SDFs of the mechanical power and rotor speed, which are unmeasurable by PMUs, are excluded. In this paper, SG inertia is estimated via a linear least square method by curve-fitting the SDFs of the input and output to the transfer function. The SDFs are calculated by averaging periodograms of PMU ambient data. The usefulness of the proposed method is validated through simulations of the IEEE 39-bus system under the ambient conditions.