and Simultaneous Estimation of Forced Oscillations and Modes John Pierre U of Wyoming pierreuwyoedu Dan Trudnowski Montana Tech dtrudnowskimtechedu Jim Follum PNNL formerly at U of Wyoming ID: 1031564
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1. Forced Oscillation Detection Fundamentalsand Simultaneous Estimation of Forced Oscillations and ModesJohn Pierre, U of Wyomingpierre@uwyo.eduDan Trudnowski, Montana Techdtrudnowski@mtech.eduJim Follum, PNNL (formerly at U of Wyoming)james.follum@pnnl.govJSIS MeetingSeptember 9-11, 2014Salt Lake City, UT
2. OutlineFundamental of Forced vs Modal OscillationsSimultaneous Estimation of Forced Oscillations and Electromechanical ModesOscillation Detection – just an old Radar/Sonar ProblemForced Oscillation Detection and EstimationWhy is knowing the Underlying Noise Spectrum is Important? Setting the thresholdApproaches to Identifying Forced OscillationsPower and Oscillation Detectors
3. Fundamentals of Forced Oscillations vs Modal OscillationsRemember back to your second circuits course(1) 3 different classification of a responseTotal Response = Forced Response + Natural (Modal) ResponseTotal Response = Zero State Response + Zero Input ResponseTotal Response = Steady State Response + Transient ResponseAlso have a stochastic problempart of the response is a random process (e.g. ambient noise)(1) Lathi’s book Linear Systems and Signals
4. Forced Response vs Natural (Modal) ResponseForced Response – portion of response associated with the driving excitation of the systemForced Oscillation: approximately sinusoidal forced response, possibly with harmonicsNatural (Modal) Response – portion of response associated with the modes (poles) of the systemProblem: From measured synchrophasor data need to Estimate modesDetect when forced oscillations are occurringThese two require being able to distinguish between forced and modal oscillationsWe obviously care about the large forced oscillations but what about the small ones?
5. Simultaneous Estimation of Forced Oscillations and Electromechanical ModesLS-ARMA-S (Least Squares-Autoregressive Moving Average-Plus Sinusoid)Algorithm: a method to detect forced oscillations and simultaneously estimate the modes and force oscillation parametersFirst detects forced oscillationThen estimates:FrequencyStart-timeDurationThen simultaneously estimateMode Frequency and DampingForced Oscillation AmplitudeSo the Forced Oscillation is incorporated into the Mode Estimation
6. Impact of FO on Standard Mode MetersGreen Stars – True ModesBlue X’s estimated modes under ambient conditionsWhat if a sinusoidal FO is present in the data?The estimated mode can be biased toward the forced oscillation!S-plane
7. Example WECC Data71.28 Hz0.845 Hz
8. 8Mode Estimation ResultsFrequencyDamping Ratio
9. Oscillation Detection – Old Radar/Sonar ProblemOscillation 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 problemA major difference is that in the Power System case, the oscillation is usually in highly colored (ambient) noiseColored noise vs white noiseFor white noise the power is evenly spread across frequencyFor colored noise it is not.
10. 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
11. Probability of Detection vs False Alarm
12. Forced Oscillation Detection and EstimationIdentifying a forced oscillation is both a Detection and Estimation Problem.What needs to be detected and estimatedDetect: the presence of an oscillationEstimated:Amplitude or mean square value (MSV or Power) of the oscillationStart time and duration of oscillationFrequency of the oscillationPossibly harmonicsLocation of the oscillationEtc.What drives the performance of the detector/estimator?How do you set the threshold?
13. What Drives the Detector/Estimator PerformanceAmplitude or mean square value of oscillationObviously the larger the oscillation the easier to detect/estimateStart time and duration of oscillationThe longer the time duration the easier to detect/estimateAmbient NoiseThe more noise the more difficult to detect/estimate, we’ll say more in a minuteAnalysis MethodAlso, knowing the power spectral density allows one to set the Threshold for a given probability of false alarm!
14. Ambient Noise Power Spectral DensityWhat does it tell us?Mean Square Value = 3.3What is the area under the PSD? It is the total Mean Square Value or power of the signalMean Square Value = 3.3
15. Why knowing the Underlying Ambient Noise Spectrum is Important!This area is the power in the frequency band
16. Approaches to Identifying Forced OscillationsEnergy DetectorOscillation DetectorsMulti-Channel Methods – coherency detectorsMatched Filter DetectorsEtc.
17. Oscillation vs Power DetectorsPower 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!
18. Oscillation Detector
19. Power Detector
20. Oscillation and Energy Detector
21. Take AwaysForced Oscillation and Modal Oscillations are different phenomenonCan simultaneously estimate modes and forced oscillationsEven small forced oscillations are problematic because they can mislead standard mode metersKnowing or having a good estimate of the ambient power spectral density can help set detection thresholdsBoth power and oscillation detectors have advantages, some combination may provide useful insights