Method and apparatus for determining optimal control settings of a pipeline

• US 6,701,223 B1
• Filed: 09/11/2000
• Issued: 03/02/2004
• Est. Priority Date: 09/11/2000
• Status: Active Grant

• Current Assignee: Advantica Incorporated
• Original Assignee: Advantica Incorporated
• Inventors: Rachford, Henry R. Jr., Carter, Richard G.
• Primary Examiner(s): Patel, Ramesh
• Assistant Examiner(s): PHAM, THOMAS K
• Application Number:
  US09/659,497
• Time in Patent Office: 1,268 Days
• Field of Search: 700/28, 700/46, 700/36, 700/301, 700/304, 700/299, 700/281, 700/282, 700/289, 702/100, 702/45, 702/47, 137/8, 137/45, 137/47
• US Class Current: 700/301
• CPC Class Codes: F16K 37/0075 For recording or indicating the functioning of a valve in combination with test equipment
• CPC Class Codes: G05B 13/021 in which a variable is automatically adjusted to optimise the performance
• CPC Class Codes: Y10T 137/0357 For producing uniform flow
• CPC Class Codes: Y10T 137/0923 By pendulum or swinging member
• CPC Class Codes: Y10T 137/0971 Speed responsive valve control

Abstract

Pipelines are controlled by specifying operations along them. Control specifies sequential control values defining operations at each station to control the pipeline state. The time-dependent state is determinable by software calculations using continuous measurements along the pipeline. Forecasted deliveries dictate that the current pipeline state must change by future time (T). Control sequences are determined at pipeline stations to exercise optimum pipeline control while achieving predetermined goals from the current state to a sustainable target state which supports future deliveries by simulating current pipeline states through time interval T, while satisfying time-dependent forecast deliveries. An initial computable control set is iteratively improved and evaluated by computing the gradient of pipeline operational cost, costs of missing target(s), and costs of violating constraints by solving an adjoint problem each time the simulation is made. The gradient information, using second-order approximations to the N-dimensional cost, rapidly produces optimizing solutions using an accelerated iteration.

Claims

1. A method of formulating an optimal set of controls to transit a pipeline from an initial state to a sustainable target state over a preselected time period, the pipeline comprising a plurality of control devices and the preselected time period having a plurality of discrete intermediate times, said method comprising the steps of:

generating a set of controls capable of transitioning the pipeline from the initial state to the sustainable target state, the set of controls having a plurality of control values for each control device of the plurality of control devices and each control value of the plurality of control values for each control device corresponds to a discrete intermediate time of the plurality of discrete intermediate times;

simulating a state of the pipeline using the set of controls for each of the plurality of discrete intermediate times from the start of the preselected time period to the end of the preselected time period, each state of the pipeline including a plurality of state variables representing conditions of the pipeline at discrete points along the pipeline;

calculating a total cost for the simulation of the set of controls with a cost functional;

modifying the set of controls to generate an updated set of controls having a lower calculated total cost; and

repeating said steps of simulating, calculating, and modifying with updated sets of controls until the updated set of controls is an optimal set of controls, wherein the optimal set of controls has a minimum total cost.

2. The method of claim 1, further comprising the step of calculating the sustainable target state externally with steady-state optimization software.

3. The method of claim 1, further comprising the step of calculating the sustainable target state by computing control values to obtain a state of the pipeline that does not change during the discrete intermediate time occurring immediately before the end of the preselected time period.

4. The method of claim 1, wherein the total cost for the simulation of the pipeline using the set of controls includes aggregate operational costs during the preselected time period and penalties for failing to achieve the target state at the end of the preselected time period.

5. The method of claim 1, further comprising the step of calculating an intermediate cost increment for each discrete intermediate time of the plurality of discrete intermediate times.

6. The method of claim 4, wherein the aggregate operational costs includes at least one of fuel costs, power costs and gas emission costs.

7. The method of claim 6 further comprising the step of evaluating and saving a derivative of the intermediate cost increment with respect to the plurality of state variables for each discrete intermediate time of the plurality of discrete intermediate times.

8. The method of claim 7, further comprising the steps of:

calculating a final cost increment for the state of the pipeline at the end of the preselected time period;

evaluating, at the end of the preselected time period, derivatives of the final cost increment with respect to the plurality of state variables, wherein the derivatives at the end of the preselected time period are non-zero if the simulated state differs from the target state;

evaluating an adjoint solution for each of the plurality of intermediate times with the evaluated derivatives, beginning at the end of the preselected time period and proceeding back to the start of the preselected time period time by incorporating the saved derivatives for each discrete intermediate time of the plurality of intermediate times; and

combining the adjoint solutions developed at all discrete intermediate times from the end of the preselected time period to the start of the preselected time period to generate a gradient.

9. The method of claim 8, wherein said step of modifying the set of controls includes the step of changing the plurality of control values using the gradient.

10. The method of claim 8, further comprising the steps of:

evaluating a second derivative with respect to the plurality of state variables for each cost increment; and

said step of modifying the set of controls includes the step of modifying the plurality of control values using the gradient and the evaluated second derivatives.

11. A method for computing a cost gradient for a control set for use in generating an optimal control set to transit a pipeline from an initial state to a sustainable target state over a preselected time period having a plurality of discrete intermediate times, said method comprising the steps of:

simulating a state of the pipeline at each of the plurality of discrete intermediate times from the start of the preselected time period to the end of the preselected time period using the set of controls, the state of the pipeline having a plurality of state variables representing conditions of the pipeline at discrete points along the pipeline;

calculating a cost associated with the state of the pipeline at each of the plurality of discrete intermediate times and at the end of the preselected time period;

evaluating, with respect to the plurality of state variables, derivatives of the cost associated with the state of the pipeline at each of the plurality of discrete intermediate times and with the state of the pipeline at the end of the preselected time period;

evaluating an adjoint solution for each of the plurality of discrete intermediate times with the evaluated derivatives beginning at the end of the preselected time period and proceeding back to the start of the preselected time period time by incorporating the evaluated derivatives from each of the plurality of discrete intermediate times; and

combining the adjoint solutions evaluated at the plurality of discrete intermediate times from the end of the preselected time period to the start of the preselected time period to generate a cost gradient.

12. The method of claim 11, further comprising the step of storing the evaluated derivatives of the cost.

13. The method of claim 11, wherein the step of evaluating an adjoint solution includes the step of generating a LaGrange Multiplier for each of the plurality of discrete intermediate times starting with the end of the preselected time period.

14. The method of claim 11, wherein the cost associated with the state of the pipeline includes at least one of fuel costs, power costs and gas emission costs.

15. A method of transitioning a pipeline from a first state to a second state over a predetermined time period comprising the steps of:

dividing the predetermined time period into a plurality of discrete time segments;

calculating a first state of the pipeline at the start of the predetermined time period, the state of the pipeline having a plurality of state variables representing conditions of the pipeline at discrete points along the pipeline;

calculating a second state of the pipeline to be achieved at the end of the predetermined time period;

generating a valid and feasible set of controls capable of transitioning the pipeline from the first state of the pipeline to a final state of the pipeline at the end of the predetermined time period;

simulating a state of the pipeline at each of the plurality of discrete time segments from the first state of the pipeline at the start of the predetermined time period to the final state of the pipeline at the end of the predetermined time period using the valid and feasible set of controls;

calculating a cost associated with the state of the pipeline at each of the plurality of discrete time segments and with the final state of the pipeline at the end of the predetermined time period and summing each of the calculated costs to determine a total cost for the valid and feasible set of controls;

evaluating, with respect to the plurality of state variables, first derivatives and second derivatives of the cost associated with the state of the pipeline at each of the plurality of discrete time segments and with the final state of the pipeline at the end of the predetermined time period;

evaluating an adjoint solution for each of the plurality of discrete time segments with the evaluated first derivatives beginning at the end of the predetermined time period and proceeding back to the start of the predetermined time period time by incorporating the evaluated first derivatives from each of the plurality of discrete time segments;

combining the adjoint solutions evaluated at the plurality of discrete time segments from the end of the predetermined time period to the start of the predetermined time period to generate a gradient;

modifying the set of controls using the gradient and the second derivatives to generate an updated set of controls having a lower total cost; and

repeating said steps of simulating, calculating, evaluating first and second derivatives, evaluating an adjoint solution, combining the adjoint solutions and modifying with updated sets of controls until the updated set of controls is an optimal set of controls, wherein the optimal set of controls has a minimum total cost.

16. The method of claim 15, wherein the second state of the pipeline is a sustainable second state and comprising the step of computing the sustainable second state with steady-state optimization software.

17. The method of claim 15, wherein the second state of the pipeline is a sustainable second state and comprising the step of calculating the sustainable second state by determining a state of the pipeline that does not change during the discrete time segment occurring immediately before the end of the predetermined time period.

18. The method of claim 15, wherein the total cost for the valid and feasible set of controls includes aggregate operational costs during the predetermined time period and penalties for failing to achieve the target state at the end of the predetermined time period.

19. The method of claim 15, wherein said step of modifying the set of controls includes the steps of:

generating a modification step from the gradient and the second derivatives; and

adding the modification step to the set of controls to generate the updated set of controls.

20. The method of claim 15, wherein said step of simulating a state of the pipeline includes satisfying any designated loads occurring at stated points on the pipeline.

21. The method of claim 18, wherein the aggregate operational costs includes at least one of fuel costs, power costs and gas emission costs.

22. The method of claim 19, wherein said step of generating a modification step includes the step of generating the modification step with a Trust Region Method.

23. A computer program product embodied on a computer readable medium and executable by a computer for determining an optimal set of controls for devices in a pipeline to transition the pipeline from a first state to a sustainable second state over a preselected time period, said computer program product comprising instructions for executing the steps of:

dividing the preselected time period into a plurality of discrete intermediate times;

generating a valid and feasible set of controls capable of transitioning the pipeline from the first state of the pipeline to a final state of the pipeline at the end of the preselected time period;

simulating a state of the pipeline at each of the plurality of discrete intermediate times from the first state of the pipeline at the start of the preselected time period to the final state of the pipeline at the end of the preselected time period using the valid and feasible set of controls, the state of the pipeline including a plurality of state variables representing conditions of the pipeline at discrete points along the pipeline;

calculating a total cost for the simulated set of controls using a cost functional;

computing a gradient of the cost functional;

modifying the set of controls using the gradient to generate an updated set of controls having a lower calculated total cost; and

repeating said steps of simulating, calculating, computing and modifying with updated sets of controls until the updated set of controls is an optimal set of controls, wherein the optimal set of controls has a minimum total cost.

24. The computer program product of claim 23, further comprising instructions for executing the step of calculating the sustainable second state with steady-state optimization software.

25. The computer program product of claim 23, further comprising instructions for executing the step of calculating the sustainable target state by determining a state of the pipeline that does not change during the discrete intermediate time occurring immediately before the end of the preselected time period.

26. The computer program product of claim 23, wherein the total cost for the simulated set of controls includes aggregate operational costs during the preselected time period and penalties for failing to achieve the second state at the end of the preselected time period.

27. The computer program product of claim 23, further comprising instructions for executing the step of calculating an intermediate cost increment for each discrete intermediate time of the plurality of discrete intermediate times.

28. The computer program product of claim 26, wherein the aggregate operational costs includes at least one of fuel costs, power costs and gas emission costs.

29. The computer program product of claim 28, further comprising instructions for executing the step of evaluating and saving a derivative of the intermediate cost increment with respect to the plurality of state variables for each discrete intermediate time of the plurality of discrete intermediate times.

30. The computer program product of claim 29, further comprising instructions for executing the steps of:

calculating a final cost increment for the final state of the pipeline at the end of the preselected time period;

evaluating, at the end of the preselected time period, derivatives of the final cost increment with respect to the plurality of state variables, wherein the derivatives at the end of the preselected time period are non-zero if the final state of the pipeline at the end of the preselected time differs from the second state;

evaluating an adjoint solution for each of the plurality of discrete intermediate times with the evaluated derivatives beginning at the end of the preselected time period and proceeding to the start of the preselected time period time by incorporating the saved derivatives for each discrete intermediate time of the plurality of discrete intermediate times; and

combining the adjoint solutions developed at all discrete intermediate times from the end of the preselected time period to the start of the preselected time period to generate the gradient.

31. The computer program product of claim 29, further comprising instructions for executing the steps of:

evaluating a second derivative of the cost functional with respect to the plurality of state variables;

generating a modification step from the gradient and the second derivative; and

adding the modification step to the set of controls to generate the updated set of controls.

32. A system for determining an optimal set of control values for control devices in a pipeline to transition the pipeline from a first state to a second state over a predetermined time period, said system comprising:

a plurality of sensors located on the pipeline to measure characteristics of the pipeline;

a control and data acquisition system to receive measurements from said plurality of sensors and to apply control values to the control devices of the pipeline;

a pipeline state calculator to generate the first state of the pipeline at the start of the predetermined time period using said measurements received by said control and data acquisition system;

a load forecaster to predict future loads at specific points along the pipeline;

a control set optimizer to generate an optimal control set for the control devices of the pipeline, said control set optimizer using a starting control set, the first state of the pipeline from said pipeline state calculator, the second state of the pipeline and said predicted future loads from said load forecaster to generate said optimal control set, and said control set optimizer comprising;

means for dividing the predetermined time period into a plurality of discrete time segments;

means for generating a valid and feasible set of controls capable of transitioning the pipeline from the first state of the pipeline to a final state of the pipeline at the end of the predetermined time period; and

means for iteratively modifying said valid and feasible set of controls until the optimal set of controls is obtained; and

said optimal control set being transmitted to said control and data acquisition system for application to the control devices of the pipeline.

33. The system of claim 32 further comprising a steady-state optimizer to generate the second state of the pipeline using said predicted future loads from said load forecaster.

34. The system of claim 32 further comprising a predictive simulation system to simulate application of said optimal control set from said control set optimizer on the pipeline.

35. The system of claim 32 wherein said means for iteratively modifying said valid and feasible set of controls comprises:

means for simulating a state of the pipeline at each of the plurality of discrete time segments from the first state of the pipeline at the start of the predetermined time period to the final state of the pipeline at the end of the predetermined time period using said valid and feasible set of controls, said state of the pipeline having a plurality of state variables representing conditions of the pipeline at discrete points along the pipeline;

means for calculating a cost associated with said state of the pipeline at each of said plurality of discrete time segments and with said final state of the pipeline at the end of the predetermined time period and summing each of said calculated costs to determine a total cost for said valid and feasible set of controls;

means for evaluating, with respect to said plurality of state variables, first derivatives and second derivatives of the cost associated with said state of the pipeline at each of said plurality of discrete time segments and with said final state of the pipeline at the end of the predetermined time period;

means for evaluating an adjoint solution for each of the plurality of discrete time segments with the evaluated first derivatives beginning at the end of the predetermined time period and proceeding back to the start of the predetermined time period time by incorporating the evaluated first derivatives from each of the plurality of discrete time segments;

means for combining the adjoint solutions evaluated at the plurality of discrete time segments from the end of the predetermined time period to the start of the predetermined time period to generate a gradient; and

means for modifying the set of controls using the gradient and the second derivatives to generate an updated set of controls having a lower total cost.

36. The system of claim 35, wherein said total cost for said valid and feasible set of controls includes aggregate operational costs during the predetermined time period and penalties for failing to achieve the second state at the end of the predetermined time period.

37. The system of claim 35, wherein said means for modifying the set of controls comprises:

means for generating a modification step from the gradient and the second derivatives; and

means for adding said modification step to said valid and feasible set of controls to generate said updated set of controls.

38. The system of claim 35, wherein said means for evaluating an adjoint solution includes means for generating a LaGrange Multiplier for each of said plurality of discrete time segments starting with the end of the predetermined time period.

39. The system of claim 36, wherein the aggregate operational costs includes at least one of fuel costs, power costs and gas emission costs.