Power system disturbance localization using recurrence quantification analysis and minimum-volume-enclosing ellipsoid

1. A method for determining a location of a disturbance in a power system, comprising:

receiving data from a plurality of sensors distributed across the power system;

identifying, based on the data from the plurality of sensors, a number of sensors that are closest to the disturbance;

constructing a plurality of minimum-volume-enclosing ellipsoids based on and enclosing the data received from the identified sensors;

extracting one or more parameters from the plurality of ellipsoids;

inputting the one or more parameters into a regression algorithm to determine the location of the disturbance; and

modifying an operation of at least one element in the power system to mitigate an impact of the disturbance on the power system based on the determined location of the disturbance.

2. The method of claim 1 , wherein the data comprise frequency data.

3. The method of claim 1 , wherein the identifying the number of sensors comprises performing a recurrence quantification analysis on the received data.

4. The method of claim 3 , wherein the identifying the number of sensors by performing a recurrence quantification analysis on the received data comprises:

identifying, from the data, an occurrence time of the disturbance;

calculating, about the occurrence time, step changes in subsequent samples of the data;

calculating, based on the step changes, a distance matrix for each of the plurality of sensors;

calculating a space diameter based on the distance matrix for each of the plurality of sensors;

determining a recurrence rate, for each of the plurality of sensors, based on the corresponding distance matrix and the corresponding space diameter; and

identifying the number of sensors as a subset of the plurality of sensors with the highest recurrence rates.

5. The method of claim 1 , wherein the one or more parameters comprise volumes of the plurality of ellipsoids, centers of the plurality of ellipsoids, orientations of the plurality of ellipsoids, time derivatives of the volumes, time derivatives of the centers, or time derivatives of the orientations.

6. The method of claim 1 , wherein the regression algorithm is a multivariate-random-forest regression algorithm.

7. The method of claim 1 , further comprising, prior to the inputting the one or more parameters into the regression algorithm, training the regression algorithm with historical data from the plurality of sensors.

8. The method of claim 1 , wherein the inputting the one or more parameters into the regression algorithm comprises determining a power mismatch corresponding to the disturbance.

9. The method of claim 8 , further comprising presenting, on one or more display units, the determined location of the disturbance and the determined power mismatch.

10. A system, comprising:

a power system;

a plurality of sensors distributed across the power system; and

a computer system including one or more processors, one or more display units, and memory storing instructions adapted to be executed by the plurality of processors to perform operations comprising:

receiving data from the plurality of sensors;

identifying, based on the data and from the plurality of sensors, a number of sensors that are closest to a disturbance in the power system;

constructing a plurality of minimum-volume-enclosing ellipsoids based on and enclosing the data received from the identified sensors;

extracting one or more parameters from the plurality of ellipsoids;

inputting the one or more parameters into a regression algorithm to determine the location of the disturbance; and

modifying an operation of at least one element in the power system to mitigate an impact of the disturbance on the power system based on the determined location of the disturbance.

11. The system of claim 10 , wherein the data comprise frequency data.

12. The system of claim 10 , wherein the operation of identifying the number of sensors comprises performing a recurrence quantification analysis on the received data.

13. The system of claim 12 , wherein the operation of identifying the number of sensors by performing a recurrence quantification analysis on the received data comprises:

identifying, from the data, an occurrence time of the disturbance;

calculating, about the occurrence time, step changes in subsequent samples of the data;

calculating, based on the step changes, a distance matrix for each of the plurality of sensors;

calculating a space diameter based on the distance matrix for each of the plurality of sensors;

determining a recurrence rate, for each of the plurality of sensors, based on the corresponding distance matrix and the corresponding space diameter; and

identifying the number of sensors as a subset of the plurality of sensors with the highest recurrence rates.

14. The system of claim 10 , wherein the one or more parameters comprise volumes of the plurality of ellipsoids, centers of the plurality of ellipsoids, orientations of the plurality of ellipsoids, time derivatives of the volumes, time derivatives of the centers, or time derivatives of the orientations.

15. The system of claim 10 , wherein the regression algorithm is a multivariate-random-forest regression algorithm.

16. The system of claim 10 , the operations further comprising, prior to the operation of inputting the one or more parameters into the regression algorithm, training the regression algorithm with historical data from the plurality of sensors.

17. The system of claim 10 , wherein the operation of inputting the one or more parameters into the regression algorithm comprises determining a power mismatch corresponding to the disturbance.

18. The system of claim 17 , wherein the operations further comprises presenting, on one or more display units, the determined location of the disturbance and the determined power mismatch.

19. A computer program product, comprising:

a tangible computer readable storage medium comprising computer readable program code embodied in the medium that when executed by a processor causes the processor to perform operations comprising:

receiving data from a plurality of sensors distributed across the power system;

identifying, based on the data from the plurality of sensors, a number of sensors that are closest to the disturbance;

constructing a plurality of minimum-volume-enclosing ellipsoids based on and enclosing the data received from the identified sensors;

extracting one or more parameters from the plurality of ellipsoids;

inputting the one or more parameters into a regression algorithm to determine the location of the disturbance; and

modifying an operation of at least one element in the power system to mitigate an impact of the disturbance on the power system based on the determined location of the disturbance.

20. The computer program product of claim 19 , wherein the one or more parameters comprise volumes of the plurality of ellipsoids, centers of the plurality of ellipsoids, orientations of the plurality of ellipsoids, time derivatives of the volumes, time derivatives of the centers, or time derivatives of the orientations.