A framework for assessing methods of deriving frequency data from PMU voltage angles in the presence of measurement noise

This paper examines the effects of using the derivative of a voltage angle signal to derive a frequency signal from Phasor Measurement Unit (PMU) data in the presence of measurement noise. By expressing the Signal-to-Noise Ratio (SNR) of the angle signal and the derived frequency signals in terms of correlation functions, the asymptotic behavior of numerical derivatives are studied. This provides insight as to how the derivative operation will potentially damage noise-corrupted PMU data to be analyzed by a mode meter. In particular the commonly used first order backwards difference (the `diff' function in MATLAB), the first order central difference, the second order backwards difference, and an angle differencing approach are studied. Data measured from PMUs in the WECC system are analyzed as are data simulated form a reduced-order model of the WECC system in order to better understand the correlation-based SNR expressions. The results presented herein provide a framework for the incorporation of measurement noise effects in mode meter algorithm performance and certification studies, and can provide a theoretical basis for the selection of a derivative filter for use in the preprocessing step of a mode meter algorithm.