Approximation of the Frequency-Amplitude Curve Using the Homotopy Analysis Method

Min Xiong, Xin Xu, Kai Sun, Bin Wang

Research output: Contribution to conferencePaper

1 Scopus Citations


The Frequency-Amplitude (F-A) curve on power system oscillation under a large disturbance characterizes how a natural oscillation mode transitions to nonlinear oscillations with growing amplitudes and decaying frequencies. The existing formulation of the F-A curve is derived by solving elliptical integrals on oscillation of a single-machine-infinite-bus equivalent about the targeted oscillation mode. The formula is in a form of infinite series and needs to sum a large number of terms for satisfactory accuracy. This paper introduces an explicit, approximate expression obtained from the Homotopy Analysis Method on the F-A curve. The proposed F-A curve expression is derived from an SMIB system and verified on the IEEE 3-machine 9-bus system to show how the oscillation frequency of a dominant mode varies with oscillation amplitude under large disturbances.
Original languageAmerican English
Number of pages5
StatePublished - 2021
Event2021 IEEE Power & Energy Society General Meeting (PESGM) - Washington, D.C.
Duration: 26 Jul 202129 Jul 2021


Conference2021 IEEE Power & Energy Society General Meeting (PESGM)
CityWashington, D.C.

NREL Publication Number

  • NREL/CP-5D00-78388


  • frequency-amplitude (F-A) curve
  • Homotopy Analysis Method
  • power system oscillation
  • rotor angle stability


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