John Pierre, U of Wyoming pierre@uwyo Dan Trudnowski , Montana Tech dtrudnowski@mtech
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Transcript of John Pierre, U of Wyoming pierre@uwyo Dan Trudnowski , Montana Tech dtrudnowski@mtech
![Page 1: John Pierre, U of Wyoming pierre@uwyo Dan Trudnowski , Montana Tech dtrudnowski@mtech](https://reader035.fdocuments.us/reader035/viewer/2022062408/56813757550346895d9ee74d/html5/thumbnails/1.jpg)
Forced Oscillation Detection Fundamentalsand Simultaneous Estimation of Forced Oscillations and Modes
John Pierre, U of [email protected]
Dan Trudnowski, Montana [email protected]
Jim Follum, PNNL (formerly at U of Wyoming)
JSIS Meeting
September 9-11, 2014
Salt Lake City, UT
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Outline
• Fundamental of Forced vs Modal Oscillations• Simultaneous Estimation of Forced Oscillations and
Electromechanical Modes• Oscillation Detection – just an old Radar/Sonar Problem• Forced Oscillation Detection and Estimation• Why is knowing the Underlying Noise Spectrum is
Important? Setting the threshold• Approaches to Identifying Forced Oscillations• Power and Oscillation Detectors
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Fundamentals of Forced Oscillations vs Modal Oscillations
• Remember back to your second circuits course(1)
3 different classification of a response– Total Response = Forced Response + Natural (Modal) Response– Total Response = Zero State Response + Zero Input Response– Total Response = Steady State Response + Transient Response
• Also have a stochastic problem– part of the response is a random process (e.g. ambient noise)
(1) Lathi’s book Linear Systems and Signals
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Forced Response vs Natural (Modal) Response
• Forced Response – portion of response associated with the driving excitation of the system– Forced Oscillation: approximately sinusoidal forced response,
possibly with harmonics
• Natural (Modal) Response – portion of response associated with the modes (poles) of the system
• Problem: From measured synchrophasor data need to – Estimate modes– Detect when forced oscillations are occurring– These two require being able to distinguish between forced and
modal oscillations
• We obviously care about the large forced oscillations but what about the small ones?
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Simultaneous Estimation of Forced Oscillations and Electromechanical Modes
• LS-ARMA-S (Least Squares-Autoregressive Moving Average-Plus Sinusoid)Algorithm: a method to detect forced oscillations and simultaneously estimate the modes and force oscillation parameters– First detects forced oscillation– Then estimates:
• Frequency• Start-time• Duration
– Then simultaneously estimate• Mode Frequency and Damping• Forced Oscillation Amplitude
• So the Forced Oscillation is incorporated into the Mode Estimation
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Impact of FO on Standard Mode Meters
• Green Stars – True Modes
• Blue X’s estimated modes under ambient conditions
• What if a sinusoidal FO is present in the data?
• The estimated mode can be biased toward the forced oscillation!
S-plane
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Example WECC Data
72.5 72.52 72.54 72.56 72.58 72.6-6
-4
-2
0
2
4
6x 10
-3
Time (min)
Fre
quen
cy D
evia
tion
(Hz)
1.28 Hz0.845 Hz
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Mode Estimation ResultsFrequency Damping Ratio
0 10 20 30 40 50 60 70 80 90
0.8
0.845
0.9
1
1.1
1.2
1.28
Time (min)
Fre
quen
cy (
Hz)
0 10 20 30 40 50 60 70 80 900
2
4
6
8
10
12
14
16
18
20
22
Time (min)
Dam
ping
Rat
io (
%)
Two-Stage LSLS-ARMA+SDetected FO
False drop in DRdue to forcedoscillation
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Oscillation Detection – Old Radar/Sonar Problem
• Oscillation Detection is not a new problem. Other disciplines like Radar/Sonar have been doing this for decades.
• Really it is a detection of oscillations in noise problem• A major difference is that in the Power System case, the
oscillation is usually in highly colored (ambient) noise• Colored noise vs white noise
– For white noise the power is evenly spread across frequency– For colored noise it is not.
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Important Detection Terms and Concepts
• “Probability of Detection” – the probability of correctly identifying that an oscillation is occurring.
• “Probability of a False Alarm” – probability of concluding an oscillation is occurring when it is not.
• “Probability of a Miss” – probability of saying there is no oscillation when there actually is. (Pm=1-Pd)
• “Threshold” – a value set by the user defining the cutoff between saying Present or Not Present!
• There is a trade off between the Probability of Detection and False Alarm.– Can always make Probability of Detection higher but at the cost
of also making Probability of False Alarm higher
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Probability of Detection vs False Alarm
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Forced Oscillation Detection and Estimation• Identifying a forced oscillation is both a Detection and
Estimation Problem.• What needs to be detected and estimated
– Detect: the presence of an oscillation– Estimated:
• Amplitude or mean square value (MSV or Power) of the oscillation• Start time and duration of oscillation• Frequency of the oscillation• Possibly harmonics• Location of the oscillation• Etc.
• What drives the performance of the detector/estimator?• How do you set the threshold?
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What Drives the Detector/Estimator Performance
• Amplitude or mean square value of oscillation– Obviously the larger the oscillation the easier to detect/estimate
• Start time and duration of oscillation– The longer the time duration the easier to detect/estimate
• Ambient Noise– The more noise the more difficult to detect/estimate, we’ll say
more in a minute
• Analysis Method
Also, knowing the power spectral density allows one to set the Threshold for a given probability of false alarm!
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Ambient Noise Power Spectral DensityWhat does it tell us?
Mean Square Value = 3.3
What is the area under the PSD? It is the total Mean Square Value or power of the signal
Mean Square Value = 3.3
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Why knowing the Underlying Ambient Noise Spectrum is Important!
This area is the power in the frequency band
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Approaches to Identifying Forced Oscillations
• Energy Detector
• Oscillation Detectors
• Multi-Channel Methods – coherency detectors
• Matched Filter Detectors
• Etc.
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Oscillation vs Power Detectors
• Power Detectors – detects the power (MSV) in a frequency band, and possibly start-time and duration.
• Oscillation Detectors – detects oscillations including frequency, amplitude (or MSV), and possibly start-time, and duration.
• What are the advantages and disadvantages of each?– Remember narrower the band, the less noise!
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Oscillation Detector
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Power Detector
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Oscillation and Energy Detector
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Take Aways
• Forced Oscillation and Modal Oscillations are different phenomenon
• Can simultaneously estimate modes and forced oscillations
• Even small forced oscillations are problematic because they can mislead standard mode meters
• Knowing or having a good estimate of the ambient power spectral density can help set detection thresholds
• Both power and oscillation detectors have advantages, some combination may provide useful insights