1. 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

2. 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

3. 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

4. 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)

5. 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)

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

7. 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

8. miniWECC Simulation Analysis signal is a voltage angle difference
Mode of interest:
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 Hz
FO Frequency is 0.35 Hz

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

10. 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.

11. 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

12. 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 Hz
FO Frequency is 0.35 Hz

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

14. 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.

15. Thank You
Questions?