Update on Removing Forced Oscillation Bias from the Mode Meter Luke Dosiek Union College Jim Follum PNNL John Pierre University of Wyoming Dan Trudnowski Montana Tech presented at WECC Joint Synchronized Information Subcommittee Meeting Session: Oscillation Detection and Analysis Tools October 13, 2017

Forced Oscillations Here an FO shall be characterized as the system response to a deterministic input that is periodic in nature (sine, square, etc.) Typical mode meter algorithms assume the system response is due to one or more random inputs. Thus, traditional mode meters have no way to directly model the effects of a FO

Mode Meter Bias Mode meters assume the FO in the measured data is a natural oscillation due to random noise exciting a system mode with 0% damping! In practice, this tends to bias the estimates of the system modes towards 0%. The amount of bias depends on the following, all of which relate to overall energy of the FO relative to the ambient data: Amplitude of FO at system input Fundamental frequency of FO (proximity to natural mode) Duration of the FO in the data analysis window

Traditional Mode Meter Measured Data (may include FO) Fit a Linear Model (assumes all system inputs are random) Mode Estimates (biased in the presence of FO near modal frequency)

FO-Ready Mode Meter Measured Data (may include FO) Detect FOs and Optional Detect FOs and Estimate Frequency Estimate start and stop of FO Fit a Linear Model (includes sinusoidal system inputs) Estimated FO Amplitudes Mode Estimates (unbiased)

Forced Oscillation Conditions WECC Example September 2014 Event Highly observable in Grand Coulee MW data Ambient Conditions Forced Oscillation Conditions

WECC Results The mode meters analyze the angle difference between John Day and Malin The FO is not visible to the naked eye in this signal Ambient only (no known FO present) No FOs detected Ambient with FO present throughout FO detected at 0.34 Hz – near a major mode! Mode Meter Frequency Damping FO Amp. Traditional 0.38 Hz 9.48 % N/A FO-Ready Mode Meter Frequency Damping FO Amp. Traditional 0.35 Hz 2.95 % N/A FO-Ready 0.34 Hz 6.51 % 1.5 mrad/s

miniWECC Simulation Analysis signal is a voltage angle difference Mode of interest: 0.3719 Hz, 4.66 % damping Simulated FO as square wave mechanical power input at a single generator FO fundamental frequency is very close to modal frequency FO amplitude is very small 20 minutes of data generated with FOs lasting, 2, 10, and 20 minutes. 300 Monte Carlo trials of each case True power spectral density (PSD) of simulated system output with FO fundamental frequency circled Major NS Mode at 0.3719 Hz FO Frequency is 0.35 Hz

Example Data FO start: 5 minutes FO stop: 15 minutes

Simulation Results Under ambient conditions, no FOs were detected, so the FO-ready mode meter performed identically to the traditional mode meter When the FO was present, the traditional mode meter was biased to varying degrees. The FO-Ready meter was able to incorporate the detected oscillations and correct the biasing.

Unmodeled Dynamics Malfunctioning or poorly tuned equipment, hydro rough zones, etc can introduce oscillations These are not necessarily Forced Oscillations in the classical sense They may be noise that is filtered by an extremely narrowband process These are like high energy local modes that may be observable across the system The detection algorithm will flag these as forced oscillations and attempt to model them as sinusoids Fundamental disagreement with model and reality E.g., detection algorithm may return multiple FOs

miniWECC Simulation True power spectral density (PSD) of simulated system output with FO fundamental frequency circled Simulated FO as noise run through an extremely narrowband filter Center frequency of filter is very close to modal frequency 20 minutes of data generated with FOs lasting, 2, 10, and 20 minutes. 300 Monte Carlo trials of each case Major NS Mode at 0.3719 Hz FO Frequency is 0.35 Hz

Example Data FO start: 5 minutes FO stop: 15 minutes

Simulation Results When the disturbance was present, the traditional mode meter was biased The detection algorithm typically estimated 3 FOs – one corresponding to the center frequency of the narrowband filter, and one on either side The FO-Ready meter was able to incorporate the detected oscillations and correct the biasing, although the improvement was not as dramatic as when the FOs were actually sinusoidal.

Thank You Questions?