Systems and methods for improved stability of power systems

1. A system, comprising:

a processor configured to:

select at least one grid system contingency from a plurality of grid system contingencies;

derive one or more eigen-sensitivity values based on the at least on grid system contingency;

derive one or more control actions at least partially based on the eigen-sensitivity values;

apply a quadratic programming to solve an optimization problem to derive the one or more control actions, wherein the optimization problem comprises min J=Σ i=1 N g ΔP i 2 where N g is a total number of generator systems included in the grid system, min J is a representative of a minimum generation re-dispatch and ΔP i is an amount of re-dispatch power for each generator system i of the generator systems; and

apply the one or more control actions for generation re-dispatch of a grid system, wherein the grid system is controlled based on the one or more control actions.

2. The system of claim 1 , wherein the processor is configured to derive the one or more eigen-sensitivity values by perturbing a power of a generator system included in a plurality of generator systems via a perturbation and to distribute the perturbation among a remainder of the plurality of generator systems.

3. The system of claim 2 , wherein the perturbation is distributed equally among the remainder of the plurality of generator systems.

4. The system of claim 1 , wherein a first eigenvalue of the one or more eigenvalues comprises a base case σ base representative of a base case settling time for a specific oscillation mode of the grid system.

5. The system of claim 1 , wherein a second eigenvalue of the one or more eigen/values comprises a post-contingency case σ post having a settling time after the grid system contingency for a specific oscillation mode of the grid system.

6. The system of claim 4 , wherein the processor is configured to move the base case σ base so that a settling time corresponding to a post-redispatch post-contingency condition lies beyond a threshold representative of a desired damping ratio, a desired settling time, or a combination, thereof.

7. The system of claim 4 , wherein a third eigenvalue of the one or more eigenvalues comprises a σ target and wherein the processor is configured to derive the σ target by using the σ base and a Δσ target .

8. The system of claim 7 , wherein the processor is configured to derive the Δσ target by applying a σ post-target and a σ post , wherein the σ post-target is representative of a target settling time after the grid system contingency and wherein the σ post comprises a settling time after the grid system contingency.

9. The system of claim 1 , comprising simulating the one or more control actions to determine if the one or more control actions are acceptable, and if acceptable, to apply the control actions for the generation re-dispatch.

10. A method, comprising:

selecting, via a processor, at least one grid system contingency from a plurality of grid system contingencies;

deriving, via the processor, one or more eigen-sensitivity values based on the at least on grid system contingency;

deriving, via the processor, one or more control actions at least partially based on the eigen-sensitivity values;

applying a quadratic pro ramming to solve an optimization problem to derive the one or more control actions, wherein the optimization problem comprises min J=Σ i=1 N g ΔP i 2 where N g is a total number of generator systems included in the grid system, min J is a representative of a minimum generation re-dispatch and ΔP i is an amount of re-dispatch power for each generator system i of the generator systems; and

applying, via the processor, the one or more control actions for generation re-dispatch of a grid system.

11. The method of claim 10 , wherein deriving, via the processor, the one or more eigen-sensitivity values comprises perturbing a power of a generator system included in a plurality of generator systems via a perturbation and to distribute the perturbation among a remainder of the plurality of generator systems.

12. The method of claim 10 , comprising creating, via the processor, a simulation model of the grid system, wherein the simulation model comprises one or more generation systems, one or more loads, and one or more power lines electrically coupling the one or more generation systems to the one or more loads, wherein deriving, via the processor, the one or more eigen-sensitivity values comprises perturbing a power of a generator system included in a plurality of generator systems via a perturbation and to distribute the perturbation among a remainder of the plurality of generator systems, and wherein perturbing the power comprises executing a simulation of the simulation model.

13. The method of claim 9 , wherein deriving, via the processor, one or more eigen-sensitivity values comprises deriving, via the processor, one or more load-based eigen-sensitivity values, and wherein the one or more control actions comprises a control of one or more loads configured to receive power from the grid system.

14. A non-transitory computer readable medium storing instructions that when executed by a processor cause the processor to:

select at least one grid system contingency from a plurality of grid system contingencies;

derive one or more eigen-sensitivity values based on the at least on grid system contingency;

derive one or more control actions at least partially based on the eigen-sensitivity values;

to apply a quadratic programming to solve an optimization problem to derive the one or more control actions, wherein the optimization problem comprises min J=Σ i=1 N g ΔP i 2 where N g is a total number of generator systems included in the grid system, min J is a representative of a minimum generation re-dispatch and ΔP i is an amount of re-dispatch power for each generator system i of the generator systems; and

apply the one or more control actions for generation re-dispatch of a grid system.

15. The non-transitory computer readable medium of claim 14 , wherein the instructions that cause the processor to derive the one or more eigen-sensitivity values comprise instructions that cause the processor to perturb a power of a generator system included in a plurality of generator systems via a perturbation and to distribute the perturbation among a remainder of the plurality of generator systems.

16. The non-transitory computer readable medium of claim 14 , wherein the one or more eigen-sensitivity values comprise a base case σ base representative of a base case settling time for a specific oscillation mode of the grid system, and wherein the instructions comprise instructions that cause the processor to move the base case σ base so that the base case σ base lies beyond a threshold representative of a desired damping ratio, a desired settling time, or a combination, thereof.

17. The non-transitory computer readable medium of claim 14 , comprising instructions that cause the processor to simulate the one or more control actions to determine if the one or more control actions are acceptable, and if acceptable, to apply the control actions for the generation re-dispatch.