Power system inertia estimation using synchrophasor frequency measurements

1. A method comprising:

performing by a processor:

receiving a first plurality of power system frequency measurements from a plurality of phasor measurement units (PMUs) in the power system over a first time interval;

generating a first plurality of multi-dimensional ellipsoids based on the first plurality of power system frequency measurements;

extracting a first plurality of values for each of a plurality of graphic parameters from the first plurality of multi-dimensional ellipsoids, respectively, the first graphic parameter being one of the plurality of graphic parameters;

performing a regression analysis on the first plurality of values for each of the plurality of graphic parameters to generate a predictive relationship between the first plurality of values for each of the plurality of graphic parameters and the inertia values of the power system;

receiving a second plurality of power system frequency measurements from the plurality of PMUs over a second time interval;

generating a second plurality of multi-dimensional ellipsoids based on the second plurality of power system frequency measurements;

extracting a second plurality of values for each of the plurality of graphic parameters from the second plurality of multi-dimensional ellipsoids, respectively; and

estimating a current inertia value of the power system based on the second plurality of values for each of the plurality of graphic parameters by using the predictive relationship between the first plurality of values for each of the plurality of graphic parameters and the inertia values of the power system.

2. The method of claim 1 , wherein a dimension number of each of the first plurality of multi-dimensional ellipsoids and a dimension number of each of the second plurality of multi-dimensional ellipsoids corresponds to a number of the plurality of PMUs.

3. The method of claim 1 , wherein performing the regression analysis comprises performing a multivariate random forest regression analysis.

4. The method of claim 1 , further comprising:

subtracting a first common frequency component from the first plurality of power system frequency measurements; and

subtracting a second common frequency component from the second plurality of power system frequency measurements;

wherein generating the first plurality of multi-dimensional ellipsoids comprises:

generating the first plurality of multi-dimensional ellipsoids responsive to subtracting the first common frequency component from the first plurality of power system frequency measurements; and

wherein generating the second plurality of multi-dimensional ellipsoids comprises:

generating the second plurality of multi-dimensional ellipsoids responsive to subtracting the second common frequency component from the second plurality of power system frequency measurements.

5. The method of claim 1 , further comprising:

adjusting an assignment of a power generator to a load in the power system based on the current inertia value of the power system.

6. The method of claim 1 , wherein the plurality of graphic parameters comprises ellipsoid volume, ellipsoid eccentricity, ellipsoid center vector, or a projection vector of a longest semi-axis of the respective ellipsoid.

7. The method of claim 6 , wherein the plurality of graphic parameters further comprises a plurality of ellipsoid center vectors corresponding to the plurality of PMUs, respectively, and a plurality projection vectors of the longest semi-axis of the respective ellipsoids corresponding to the plurality of PMUs, respectively.

8. A system, comprising:

a processor; and

a memory coupled to the processor and comprising computer readable program code embodied in the memory that is executable by the processor to perform operations comprising:

receiving a first plurality of power system frequency measurements from a plurality of phasor measurement units (PMUs) in the power system over a first time interval;

generating a first plurality of multi-dimensional ellipsoids based on the first plurality of power system frequency measurements;

extracting a first plurality of values for each of a plurality of graphic parameters from the first plurality of multi-dimensional ellipsoids, respectively, the first graphic parameter being one of the plurality of graphic parameters;

performing a regression analysis on the first plurality of values for each of the plurality of graphic parameters to generate a predictive relationship between the first plurality of values for each of the plurality of graphic parameters and the inertia values of the power system;

receiving a second plurality of power system frequency measurements from the plurality of PMUs over a second time interval;

generating a second plurality of multi-dimensional ellipsoids based on the second plurality of power system frequency measurements;

extracting a second plurality of values for each of the plurality of graphic parameters from the second plurality of multi-dimensional ellipsoids, respectively; and

estimating a current inertia value of the power system based on the second plurality of values for each of the plurality of graphic parameters by using the predictive relationship between the first plurality of values for each of the plurality of graphic parameters and the inertia values of the power system.

9. The system of claim 8 , wherein a dimension number of each of the first plurality of multi-dimensional ellipsoids and a dimension number of each of the second plurality of multi-dimensional ellipsoids corresponds to a number of the plurality of PMUs.

10. The system of claim 8 , wherein performing the regression analysis comprises performing a multivariate random forest regression analysis.

11. The system of claim 8 , wherein the operations further comprise:

subtracting a first common frequency component from the first plurality of power system frequency measurements; and

subtracting a second common frequency component from the second plurality of power system frequency measurements;

wherein generating the first plurality of multi-dimensional ellipsoids comprises:

generating the first plurality of multi-dimensional ellipsoids responsive to subtracting the first common frequency component from the first plurality of power system frequency measurements; and

wherein generating the second plurality of multi-dimensional ellipsoids comprises:

generating the second plurality of multi-dimensional ellipsoids responsive to subtracting the second common frequency component from the second plurality of power system frequency measure.

12. The system of claim 8 , wherein the operations further comprise:

adjusting an assignment of a power generator to a load in the power system based on the current inertia value of the power system.

13. The system of claim 8 , wherein the plurality of graphic parameters comprises ellipsoid volume, ellipsoid eccentricity, ellipsoid center vector, or a projection vector of a longest semi-axis of the respective ellipsoid.

14. The system of claim 13 , wherein the plurality of graphic parameters further comprises a plurality of ellipsoid center vectors corresponding to the plurality of PMUs, respectively, and a plurality projection vectors of the longest semi-axis of the respective ellipsoids corresponding to the plurality of PMUs, respectively.

15. A computer program product, comprising:

a non-transitory computer readable storage medium comprising computer readable program code embodied in the medium that is executable by a processor to perform operations comprising:

receiving a first plurality of power system frequency measurements from a plurality of phasor measurement units (PMUs) in the power system over a first time interval;

generating a first plurality of multi-dimensional ellipsoids based on the first plurality of power system frequency measurements;

extracting a first plurality of values for each of a plurality of graphic parameters from the first plurality of multi-dimensional ellipsoids, respectively, the first graphic parameter being one of the plurality of graphic parameters;

performing a regression analysis on the first plurality of values for each of the plurality of graphic parameters to generate a predictive relationship between the first plurality of values for each of the plurality of graphic parameters and the inertia values of the power system;

receiving a second plurality of power system frequency measurements from the plurality of PMUs over a second time interval;

generating a second plurality of multi-dimensional ellipsoids based on the second plurality of power system frequency measurements;

extracting a second plurality of values for each of the plurality of graphic parameters from the second plurality of multi-dimensional ellipsoids, respectively; and

estimating a current inertia value of the power system based on the second plurality of values for each of the plurality of graphic parameters by using the predictive relationship between the first plurality of values for each of the plurality of graphic parameters and the inertia values of the power system.

16. The computer program product of claim 15 , wherein the operations further comprise:

subtracting a first common frequency component from the first plurality of power system frequency measurements; and

subtracting a second common frequency component from the second plurality of power system frequency measurements;

wherein generating the first plurality of multi-dimensional ellipsoids comprises:

generating the first plurality of multi-dimensional ellipsoids responsive to subtracting the first common frequency component from the first plurality of power system frequency measurements; and

wherein generating the second plurality of multi-dimensional ellipsoids comprises:

generating the second plurality of multi-dimensional ellipsoids responsive to subtracting the second common frequency component from the second plurality of power system frequency measurements.

17. The computer program product of claim 15 , wherein the operations further comprise:

adjusting an assignment of a power generator to a load in the power system based on the current inertia value of the power system.

18. The computer program product of claim 15 , wherein the plurality of graphic parameters comprises ellipsoid volume, ellipsoid eccentricity, ellipsoid center vector, or a projection vector of a longest semi-axis of the respective ellipsoid.

19. The computer program product of claim 18 , wherein the plurality of graphic parameters further comprises a plurality of ellipsoid center vectors corresponding to the plurality of PMUs, respectively, and a plurality projection vectors of the longest semi-axis of the respective ellipsoids corresponding to the plurality of PMUs, respectively.