Systems and methods to detect poorly damped oscillation modes

1. A device for detecting poorly damped oscillation modes in an electric power delivery system, the device comprising:

a communications interface configured to receive a plurality of measurement signals comprising real-time electric power delivery system information;

a frequency transform calculator configured to compute a frequency transform of at least one of the plurality of measurement signals;

an oscillation mode detector configured to determine an oscillation mode of interest based on the frequency transform;

an amplitude calculator configured to:

determine a sliding window size based on a predetermined multiple of a period of the oscillation mode of interest;

determine a step size for the sliding window based on a predetermined multiple of the period of the oscillation mode of interest;

determine a static window size based on a predetermined multiple of the period of the oscillation mode of interest;

calculate amplitudes of the oscillation mode of interest over the sliding window;

and, a damping calculator configured to compute a damping of the oscillation mode of interest based on changes over time in the amplitudes of the oscillation mode of interest in the plurality of measurement signals, wherein the frequency transform calculator is further configured to compute the amplitudes over the sliding window during the static window, and wherein the changes over time in the amplitudes are determined by shifting the sliding window by the step size, and computing updated amplitudes; and

the device configured to take a control action when the poorly damped oscillation modes are detected, wherein the control action comprises one of: connecting a capacitor bank, disconnecting the capacitor bank, tripping a relay, or tripping a breaker.

2. The device of claim 1 , further comprising a signal screener configured to select a plurality of valid measurement signals from among the plurality of measurement signals.

3. The device of claim 2 , wherein the damping is computed based on the plurality of valid measurement signals only.

4. The device of claim 2 , wherein the signal screener is configured to determine which of the plurality of measurement signals are valid based on a statistical measure of validity.

5. The device of claim 1 , wherein the damping calculator uses a common set of time points to determine the changes over time in the amplitudes.

6. The device of claim 1 , wherein the damping calculator solves a linearized system of equations comprising the amplitudes to determine the damping of the oscillation mode of interest.

7. The device of claim 6 , wherein the linearized system of equations includes as unknown values the damping of the oscillation mode of interest and a distinct offset for each of the plurality of measurement signals.

8. The device of claim 6 , wherein the damping calculator solves the linearized system of equations by determining a least square estimate for the damping of the oscillation mode of interest.

9. The device of claim 1 , wherein the amplitudes-and updated amplitudes are computed using a common set of measurement signals.

10. A non-transitory computer readable storage medium comprising program code configured to cause a processor to perform a method of detecting poorly damped oscillation modes in an electric power delivery system, the method comprising:

receiving a plurality of measurement signals comprising real-time electric power delivery system information;

computing a frequency transform of at least one of the plurality of measurement signals;

determining an oscillation mode of interest from the frequency transform;

computing a sliding window size based on a predetermined multiple of a period of the oscillation mode of interest;

computing a step size for the sliding window based on a predetermined multiple of the period of the oscillation mode of interest;

computing a static window size based on a predetermined multiple of the period of the oscillation mode of interest;

computing a plurality of amplitudes of the oscillation mode of interest corresponding to a plurality of time points, each amplitude of the plurality of amplitudes computed over a sliding window during the static window, the sliding window being shifted by the step size to compute another amplitude of the plurality of amplitudes; and

calculating a damping of the oscillation mode of interest based on the plurality of amplitudes computed for each of the plurality of measurement signals; and

taking a control action when the poorly damped oscillation modes are detected, wherein the control action comprises one of: connecting a capacitor bank, disconnecting the capacitor bank, tripping a relay, or tripping a breaker.

11. The non-transitory computer readable storage medium of claim 10 , wherein the method further comprises initial steps of removing a center mean from each of the plurality of measurement signals and normalizing each of the plurality of the measurement signals.

12. The non-transitory computer readable storage medium of claim 10 , wherein the method further comprises an initial step of detrending each of the plurality of measurement signals.

13. The non-transitory computer readable storage medium of claim 12 , wherein detrending comprises representing trending as a low-order polynomial and removing the trending.

14. The non-transitory computer readable storage medium of claim 10 , wherein calculating the damping comprises solving a linearized system of equations comprising the plurality of amplitudes for each of the plurality of measurement signals.

15. The non-transitory computer readable storage medium of claim 14 , wherein solving the linearized system of equations comprises setting up the linearized system of equations to include as unknown values the damping of the oscillation mode of interest and a distinct offset for each of the plurality of measurement signals.

16. The non-transitory computer readable storage medium of claim 14 , wherein solving the linearized system of equations comprises determining a least square estimate for the damping of the oscillation mode of interest.

17. The non-transitory computer readable storage medium of claim 14 , wherein a common set of measurement signals are used to compute sequential amplitudes of the plurality of amplitudes.

18. A method for detecting poorly damped oscillation modes in an electric power delivery system, the method comprising:

receiving, at an intelligent electronic device (IED), a plurality of measurement signals comprising real-time electric power delivery system information from a plurality of phasor measurement units;

the IED computing a frequency transform from at least one of the plurality of measurement signals;

determining an oscillation mode of interest from the frequency transform;

determining a sliding window size based on a predetermined multiple of a period of the oscillation mode of interest;

determining a step size for the sliding window based on a predetermined multiple of the period of the oscillation mode of interest;

determining a static window size based on a predetermined multiple of the period of the oscillation mode of interest;

the IED computing changes over time in amplitudes of the oscillation mode of interest in the plurality of measurement signals, each change in amplitude calculated for adjacent sliding windows shifted by the step size during the static window; and

the IED calculating a damping of the oscillation mode of interest based on the changes over time in the amplitudes; and

the IED taking a control action when the poorly damped oscillation modes are detected, wherein the control action comprises one of: connecting a capacitor bank, disconnecting the capacitor bank, tripping a relay, or tripping a breaker.