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In this paper, the Cram\'{e}r-Rao Bounds (CRB) for the simultaneousestimation of power system electromechanical modes and forced oscillations (FO)are derived. Two cases are considered; in the first case only the steady-stateresponse to the FO is present in the measured system output used by estimationalgorithms. In the second, the startup transient of the FO is present inaddition to the steady-state response. The CRBs are analyzed numerically toexplore sensitivities to FO frequency, signal-to-noise ratio (SNR) andobservation window length. It is demonstrated that 1) the CRB of FO parametersis not affected by the presence of the transient response, 2) the CRB of thesystem modes is not affected by the presence of an FO in steady-state and 3)the CRB of the system modes can be drastically reduced by the presence of a FOstartup transient.

Cram\'er-Rao Bounds for the Simultaneous Estimation of Power System Electromechanical Modes and Forced Oscillations