**5. Actual Oscillation Incident**

In this section, estimated Floquet multiplier is calculated to actual oscillation event observed in New England ISO in 17 June 2016. The oscillation was system wide and the frequency of 0.27 Hz, 27 MW peak-to-peak. The location of the source was far away outside of interested area. PMU data was acquired for 3 min, and actual event kept going for 140 s. For data preprocessing, original current data was subtracted to its averaged value. Average values are calculated by 162 samples of moving window considering a period is approximately 8 samples and its quarter at sampling rate of 0.033 s. So the signal oscillates around zero for the current PMU data of 35 locations. And the oscillation is clearly observable at 24 locations. Figure 12a shows example actual current minus average current value with noise at transmission line near substation 6. The local maxima have been well detected but still the peak values are fluctuations of Floquet multiplier of 1.045. Figure 12b shows a simple map of New England ISO with all estimated Floquet multiplier marked on it. It is clear that area marked in yellow has high value than other line currents. Even the line connected substation 9 and external area has the highest value of all. So the oscillation source for this incident can be traced through external area. Overall estimated Floquet multiplier is 1.0396, which can be judged that the system wide oscillation is unstable periodic solution mathematically. However, considering the real power system, Floquet multiplier of the oscillation can be shown slightly higher than 1.0 due to load fluctuation or generator excitor operation.

average current value with noisetransmissionline nearsubstation6.

with all estimated Floquet multiplier

**Figure 12.** An estimation of Floquet multiplier at actual power system oscillation event.

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