Locating Power System Oscillation Sources by Extracting Interharmonics from Synchrophasor Data

I. INTRODUCTION

• Identifying an oscillation source is a prerequisite for mitigation, while heuristic source-location methods can be difficult to validate beyond case studies.A waveform-based interharmonic approach links phasor oscillations to beating waves and offers a mathematically proven source-location method.Source: §I · p. 1
• Phasor data are more available than waveform data, motivating the question of whether interharmonics can be extracted from phasors for similar applications.The paper reports that extraction is possible for certain oscillation phenomena.Source: §I · p. 1

A. Beating Wave Phnomenon Unlying Oscillating Phasor

• A wind-farm current waveform contains interharmonic components at 63.5 Hz and 56.5 Hz, defined as spectral components between harmonic frequencies.The corresponding phasor appears as an oscillating curve.Source: A. Beating Wave Phnomenon Unlying… · p. 1
• When fundamental and interharmonic peaks add or subtract across cycles, their beating makes the phasor magnitude oscillate at the beating frequency.Interharmonics carry oscillatory energy that can propagate through the grid and give rise to system-wide oscillations.Source: A. Beating Wave Phnomenon Unlying… · pp. 1–2, Figure 2 · p. 2

B. New Insights on Power System Oscillations

• A near-zero-damped grid natural frequency can sustain ringing that beats with the fundamental, with interharmonic-producing energy sources interacting with grid RLC components.Equivalent negative resistances in IBRs are one example of an interharmonic energy-producing component.Source: B. New Insights on Power System… · p. 2
• 30 Hz is the highest reportable phasor oscillation frequency in a 60 Hz system, and 15 Hz, 45 Hz, and 75 Hz interharmonics can each yield a 15 Hz oscillation frequency.The shared reported frequency follows from aliasing when PMUs represent one waveform cycle with one phasor.Source: B. New Insights on Power System… · p. 2
• A magnitude-modulated phasor corresponds to two equal-magnitude, equal-phase interharmonics symmetrically placed around the fundamental; unequal interharmonics or a single sustained natural ringing frequency are not properly represented.Small-disturbance stability-related natural oscillations typically have only one sustained ringing frequency.Source: B. New Insights on Power System… · p. 2
• Modulated phasors work well for synchronous-generator oscillations typically below 2 Hz, but the model is unreliable for higher-frequency events, especially IBR-related oscillations above 10 Hz.At higher oscillation frequencies, the underlying interharmonics can differ substantially from 60 Hz.Source: B. New Insights on Power System… · p. 2

C. Oscillation Source Location Using Interharmonic Power

• Facilities producing interharmonic power can be identified as oscillation sources, and comparing their contributions can locate multiple sources and rank them.The method relies on the premise that phasor oscillations indicate interharmonics and that interharmonic-frequency power drives their flow through the system.Source: C. Oscillation Source Location Using… · p. 2
• Tests using synchronous generators, solar farms, wind farms, and variable-frequency-drive loads successfully located and ranked oscillation sources using interharmonic power.The study also found that interharmonic power represents the sensitivity of the critical eigenvalue to a monitored facility's equivalent resistance.Source: C. Oscillation Source Location Using… · p. 2

III. USING PHASOR DATA FOR SOURCE LOCATION

• The proposed method seeks to apply interharmonic-power source location when waveform data are unavailable by extracting interharmonics from synchrophasor data.The section introduces this as a method for using phasor data for source location.Source: §III · p. 3

A. Problem definition

• The source-location problem is to identify generating or load facilities responsible for oscillations using synchrophasors at facility-grid interconnection points.Interconnection measurements capture facility-specific information; additional PMUs on interties and major transmission lines are not required for source identification.Source: A. Problem definition · p. 3
• A PMU phasor is calculated for a cycle using waveform samples, with the sample count N covering one fundamental-frequency cycle.The timestamp, first waveform-sample time, weighting function, and sampling interval are also specified as phasor-calculation quantities.Source: A. Problem definition · p. 3

B. The Proposed Method

• Phasor-magnitude data spanning multiple oscillation periods can estimate the oscillation frequency adequately using a simple FFT.The paper reports that sensitivity analysis supports this approach.Source: B. The Proposed Method · p. 3
• The method assumes two interharmonic frequencies related to oscillation frequency, an assumption that may not fit variable-frequency drives or SSR.The assumed range is described as valid for oscillations involving synchronous generators, wind farms, solar farms, and cyclic loads; different frequency assumptions can be chosen using engineering judgment.Source: B. The Proposed Method · p. 3
• Once interharmonic frequencies are known, the method constructs a waveform from fundamental and interharmonic components.The waveform model is used to derive phasor data for each cycle.Source: B. The Proposed Method · p. 3
• Least-squares fitting estimates six unknown coefficients from phasor data; reliable solutions should use at least six samples covering one or two oscillation periods.Three complex phasor samples suffice in theory, but the paper recommends at least six for adequate redundancy.Source: B. The Proposed Method · p. 3

C. Implementation Steps

• The workflow estimates oscillation frequency with an FFT, selects interharmonic frequencies, then fits coefficients and calculates interharmonic powers for each period.It can compare interharmonic powers across facilities to quantify their contribution levels.Source: C. Implementation Steps · pp. 3–4
• A generating facility is a source when fundamental and interharmonic power signs match; for a load facility, opposite signs indicate a source.The workflow checks interharmonic power signs against fundamental-frequency power.Source: C. Implementation Steps · p. 4
• Assuming more than two interharmonic components makes the least-squares matrix ill-conditioned because phasor data lack enough information.An assumed component absent from the waveform receives very small estimated coefficients.Source: C. Implementation Steps · p. 4

IV. VERIFICATION AND SENSITIVITY STUDIES

• Close agreement between waveform- and phasor-derived wind-farm estimates indicates acceptable source-location performance.Fig. 4 compares extracted interharmonic currents and three-phase interharmonic powers.Source: A. Verification Study · p. 4, Figure 4 · p. 4
• Solar-farm phasor accuracy is reduced, but results remain practically acceptable when PMU data are the only available measurements.Differences are more evident at the higher interharmonic frequency and with stronger beating patterns; the main interharmonic is 75 Hz, corresponding to a 15 Hz oscillation.Source: A. Verification Study · p. 4, Figure 6 · p. 4
• Positive interharmonic powers indicate that both the wind- and solar-farm cases are oscillation sources.Utilities confirmed this conclusion through field experience and other troubleshooting analysis.Source: A. Verification Study · p. 4

B. Sensitivty Study

• 5–6% error plateau follows overestimating the actual PMU sampling rate, while underestimating it causes noticeable error when the assumed rate is too low.When the actual rate is unknown, the study recommends assuming N=16 or 32.Source: B. Sensitivty Study · p. 4
• Timestamp choice has a large impact on accuracy, so use the PMU's timestamp convention or assume the standard midpoint, m=50%.The PMU standard assigns the timestamp to the midpoint of the waveform samples used for each phasor.Source: B. Sensitivty Study · p. 5
• The weighting function does not significantly affect estimation results in the simulated-waveform sensitivity study.The section identifies weighting function as a PMU implementation detail that may be unknown to users.Source: B. Sensitivty Study · p. 5
• When fos exceeds 20 Hz, corresponding to interharmonic frequency above 80 Hz, phasor data are not adequate for interharmonic estimation or source location.The estimation error begins increasing above 80 Hz.Source: Figure 9 · p. 5, B. Sensitivty Study · p. 5
• FFT estimation is sufficient because the relative error in fIH2 estimation is very small, and the expected analysis window is at least 5 seconds.The paper notes that oscillation events should last at least 5 seconds to be considered events.Source: B. Sensitivty Study · p. 5
• When actual system frequency f1 deviates from f0, the impact is significant, although more advanced estimation algorithms can address the issue.The paper omits further discussion of this issue due to space limitations.Source: B. Sensitivty Study · p. 5

C. Summary

• If fos exceeds 20 Hz, implying fIH2 exceeds 80 Hz, phasor data are not adequate for interharmonic estimation.The summary points to Fig. 9 for this result.Source: C. Summary · p. 5
• Simple FFT analysis is sufficient to determine fos, with no need for sophisticated algorithms.Source: C. Summary · p. 5
• Estimation accuracy is very sensitive to PMU timestamp and deriving actual frequency from f0, but only mildly sensitive to weighting function and PMU sampling rate.Source: C. Summary · p. 5
• Estimation accuracy is not sensitive to the presence of one or two interharmonics.Source: C. Summary · p. 5

V. SOURCE LOCATION APP “OS OCATOR”

• The proposed method is implemented in the cloud-based OSLocator app for public testing and use.The app is hosted by Vercel.Source: §V · p. 5

A. Input and Output Data

• Input phasor data use the IEEE PES Task Force on Forced Oscillations Excel format, and output workbooks contain voltage, current, power, and user-entered parameter sheets.The app does not use the input file's frequency data.Source: A. Input and Output Data · p. 5, Figure 10 · p. 6

B. Application Example

• In the ISO-NE-Case5 example, users set the data segment, timestamp anchor, and PMU sampling rate; the app finds the strongest-oscillation location and displays downloadable interharmonic results.Timestamp anchor defaults to 50%, and sampling rate defaults to 32.Source: B. Application Example · p. 6, Figure 12 · p. 6

• The method locates power system oscillation sources by extracting interharmonic information from synchrophasor data.Source: §VI · p. 6
• The method extends interharmonic-power-based source location to monitoring environments where waveform data are not routinely available.Source: §VI · p. 6
• Field-data tests and sensitivity studies indicate PMU phasor data can support useful interharmonic extraction and source-location analysis under appropriate conditions.Source: §VI · p. 6
• OSLocator provides an initial cloud application for applying the method to field PMU data.Source: §VI · p. 6