Reducing corrective actions in security-constrained optimal power flow via sparsity regularization

1. A method for determining a generation schedule with contingency constraints for controlling power output levels for a plurality of generators in an electric power system comprising:

determining a measure of a sparse, corrective model, security-constrained optimal power flow (C-SCOPF) using a penalty term which reduces a number of post-contingency rescheduling operations for each of a plurality of contingencies and reduces an amount of total power rescheduled for each of the plurality of contingencies;

wherein the penalty term is defined Σ cεC ∥p c −p 0 ∥ 1 where C is a contingency index set which includes the plurality of contingencies, P c is a post-contingency power generation level for a corresponding contingency c, P 0 is a power generation level for a normal state of the electric power system; and

adjusting a power output level of at least one of the plurality of generators according to the measure of the sparse C-SCOPF upon detecting a contingency in the electric power system.

2. The method of claim 1 , number of post-contingency rescheduling operations for each of the plurality of contingencies is determined according to a ramping capability of at least one of the plurality of generators.

3. The method of claim 1 , further comprising decomposing the determination of the measure of the sparse C-SCOPF into a master problem and a plurality of sub-problems, each of the plurality of sub-problems corresponding to one of the plurality of contingencies.

4. The method of claim 3 , wherein each of the plurality of sub-problems is independent, the method further comprising solving the plurality of sub-problems by distributed and parallel computation.

5. The method of claim 3 , further comprising an acceleration of a convergence rate of the decomposition.

6. The method of claim 3 , where the power output is a direct current output.

7. The method of claim 3 , where the power output is an alternating current output.

8. A non-transitory computer readable storage medium for determining power output levels with contingency constraints for a plurality of generators in an electric power system, the non-transitory computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause the processor to perform a method comprising:

determining a measure of a sparse, corrective model, security-constrained optimal power flow (C-SCOPF) using a penalty term which reduces a number of post-contingency rescheduling operations for each of a plurality of contingencies and reduces an amount of total power rescheduled for each of the plurality of contingencies;

wherein the penalty term is defined Σ cεC ∥p c −p 0 ∥ 1 where C is a contingency index set, which includes the plurality of contingencies, P c is a post-contingency power generation level for a corresponding contingency c, P 0 is a power generation level for a normal state of the electric power system; and

adjusting a power output level of at least one of the plurality of generators according to the measure of the sparse C-SCOPF upon detecting a contingency in the electric power system.

9. The non-transitory computer readable storage medium of claim 8 , number of post-contingency rescheduling operations for each of the plurality of contingencies is determined according to a ramping capability of at least one of the plurality of generators.

10. The non-transitory computer readable storage medium of claim 8 , further comprising decomposing the determination of the measure of the sparse C-SCOPF into a master problem and a plurality of sub-problems, each of the plurality of sub-problems corresponding to one of the plurality of contingencies.

11. The non-transitory computer readable storage medium of claim 10 , wherein each of the plurality of sub-problems is independent, the method further comprising solving the plurality of sub-problems by distributed and parallel computation.

12. The non-transitory computer readable storage medium of claim 10 , further comprising an acceleration of a convergence rate of the decomposition.

13. The non-transitory computer readable storage medium of claim 10 , where the power output is one of a direct current output and an alternating current output.

14. An apparatus configured to determine power output levels with contingency constraints for a plurality of generators in an electric power system comprising:

a non-transitory computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor of the apparatus to cause the apparatus to:

determining a measure of a sparse, corrective model, security-constrained optimal power flow (C-SCOPF) using a penalty term which reduces a number of post-contingency rescheduling operations for each of a plurality of contingencies and reduces an amount of total power rescheduled for each of the plurality of contingencies;

wherein the penalty term is defined Σ cεC ∥p c −p 0 ∥ 1 where C is a contingency index set, which includes the plurality of contingencies, P c is a post-contingency power generation level for a corresponding contingency c, P 0 is a power generation level for a normal state of the electric power system; and

adjusting a power output level of at least one of the plurality of generators according to the measure of the sparse C-SCOPF upon detecting a contingency in the electric power system.

15. The apparatus of claim 14 , wherein a number of post-contingency rescheduling operations for each of the plurality of contingencies is determined according to a ramping capability of at least one of the plurality of generators.

16. The apparatus of claim 14 , wherein the system operator decomposes the determination of the measure of the sparse C-SCOPF into a master problem and a plurality of sub-problems, each of the plurality of sub-problems corresponding to one of the plurality of contingencies.

17. The apparatus of claim 16 , wherein each of the plurality of sub-problems is independent, the apparatus solving the plurality of sub-problems by distributed and parallel computation.

18. The apparatus of claim 16 , wherein the apparatus is configured to accelerate a convergence rate of the decomposition.

19. The apparatus of claim 14 , wherein the at least one of the plurality of generators outputs one of a direct current output and an alternating current output.