Systems and methods for determining gas turbine operating space

1. A system comprising:

a gas turbine, the gas turbine having an operating space during operation and a current operating point during operation; and

a computing device communicatively coupled to said gas turbine and configured to:

determine the current operating point of said gas turbine based on sensed inputs from said gas turbine;

calculate, based on the current operating point of said gas turbine, the operating space for said gas turbine by solving for a plurality of corner points that define the operating space by iteratively solving for the plurality of corner, wherein iteratively solving for the plurality of corner points includes:

setting an initial state vector;

calculating a difference vector;

assembling a Jacobian matrix; and

generating an updated state vector based on the initial state vector, the difference vector, and the Jacobian matrix;

display, to a user, a graph that includes the calculated operating space and the current operating point;

receive, from the user, a command to transition the gas turbine to a new operating point based on graph of the calculated operating space; and

transition the gas turbine to the new operating point.

2. A system in accordance with claim 1 , wherein the current operating point is defined by a current exhaust temperature and a current output power for said gas turbine.

3. A system in accordance with claim 1 , wherein solving for a plurality of corner points includes iteratively solving for the plurality of corner points using the current operating point as an initial guess.

4. A system in accordance with claim 3 , wherein iteratively solving for the plurality of corner points includes:

setting the current operating point as the initial state vector;

calculating the difference vector as a difference between the initial state vector and the plurality of corner points;

perturbing the current operating point to estimate partial derivatives of the current operating point;

assembling the Jacobian matrix from the estimated partial derivatives;

inverting the Jacobian matrix;

multiplying the inverted Jacobian matrix by the difference vector to generate a change vector; and

adding the change vector to the initial state vector to generate the updated state vector.

5. A system in accordance with claim 4 , wherein perturbing the current operating point includes perturbing the current operating point to estimate partial derivatives of the current operating point with respect to fuel flow and an inlet guide vane angle of said gas turbine.

6. A system in accordance with claim 1 , wherein said computing device is configured to calculate the operating space during operation of said gas turbine.

7. A system in accordance with claim 1 , wherein to display a graph, said computing device is further configured to display a graph that includes an emissions boundary and an exhaust flow boundary for said gas turbine.

8. A computing device comprising:

a communications device configured to communicatively couple the computing device to a gas turbine having an operating space during operation and a current operating point during operation;

a memory device configured to store the current operating point of the gas turbine derived from sensed inputs from the gas turbine;

a processor communicatively coupled to said memory device and configured to calculate, based on the current operating point, the operating space for the gas turbine by solving for a plurality of corner points that define the operating space by iteratively solving for the plurality of corner points, wherein iteratively solving for the plurality of corner points includes:

setting an initial state vector;

calculating a difference vector;

assembling a Jacobian matrix; and

generating an updated state vector based on the initial state vector, the difference vector, and the Jacobian matrix;

a display device communicatively coupled to said processor, said display device configured to display a graph that includes the calculated operating space and the current operating point, wherein said processor is configured to:

receive, from a user, a command to transition the gas turbine to a new operating point based on graph of the calculated operating space; and

transition the gas turbine to the new operating point.

9. A computing device in accordance with claim 8 , wherein the current operating point is defined by a current exhaust temperature and a current output power for the gas turbine.

10. A computing device in accordance with claim 8 , wherein solving for a plurality of corner points includes iteratively solving for the plurality of corner points using the current operating point as an initial guess.

11. A computing device in accordance with claim 10 , wherein iteratively solving for the plurality of corner points includes:

setting the current operating point as the initial state vector;

calculating the difference vector as a difference between the initial state vector and the plurality of corner points;

perturbing the current operating point to estimate partial derivatives of the current operating point;

assembling the Jacobian matrix from the estimated partial derivatives;

inverting the Jacobian matrix;

multiplying the inverted Jacobian matrix by the difference vector to generate a change vector; and

adding the change vector to the initial state vector to generate the updated state vector.

12. A computing device in accordance with claim 11 , wherein perturbing the current operating point includes perturbing the current operating point to estimate partial derivatives of the current operating point with respect to fuel flow and an inlet guide vane angle of the gas turbine.

13. A computing device in accordance with claim 8 , wherein said processor is configured to calculate the operating space during operation of the gas turbine.

14. A computing device in accordance with claim 8 , wherein to display a graph, said display device is further configured to display a graph that includes an emissions boundary and an exhaust flow boundary for the gas turbine.

15. A method for operating a gas turbine having an operating space during operation and a current operating point during operation, said method comprising:

determining, using a computing device communicatively coupled to the gas turbine, the current operating point of the gas turbine based on sensed inputs from the gas turbine;

calculating, using the computing device, based on the current operating point, the operating space for the gas turbine by solving for a plurality of corner points that define the operating space by iteratively solving for the plurality of corner, wherein iteratively solving for the plurality of corner points includes:

setting an initial state vector;

calculating a difference vector;

assembling a Jacobian matrix; and

generating an updated state vector based on the initial state vector, the difference vector, and the Jacobian matrix;

displaying to a user, using the computing device, a graph that includes the calculated operating space and the current operating point;

receive, from the user, a command to transition the gas turbine to a new operating point based on graph of the calculated operating space; and

transition the gas turbine to the new operating point.

16. A method in accordance with claim 15 , wherein determining the current operating point comprises determining the current operating point defined by a current exhaust temperature and a current output power for the gas turbine.

17. A method in accordance with claim 15 , wherein solving for a plurality of corner points comprises iteratively solving for the plurality of corner points using the current operating point as an initial guess.

18. A method in accordance with claim 17 , wherein iteratively solving for the plurality of corner points comprises:

setting the current operating point as the initial state vector;

calculating the difference vector as a difference between the initial state vector and the plurality of corner points;

perturbing the current operating point to estimate partial derivatives of the current operating point;

assembling the Jacobian matrix from the estimated partial derivatives;

inverting the Jacobian matrix;

multiplying the inverted Jacobian matrix by the difference vector to generate a change vector; and

adding the change vector to the initial state vector to generate the updated state vector.

19. A method in accordance with claim 18 , wherein perturbing the current operating point comprises perturbing the current operating point to estimate partial derivatives of the current operating point with respect to fuel flow and an inlet guide vane angle of the gas turbine.

20. A method in accordance with claim 15 , wherein calculating the operating space comprises calculating the operating space during operation of the gas turbine.