Warranty and Maintenance Decision Making for Gas Turbines

1. Warranty and Maintenance Decision Making for Gas Turbines Susan Y. Chao*, Zu-Hsu Lee†, and Alice M. Agogino‡ University of California, Berkeley Berkeley, CA 94720 *chao@garcia.me.berkeley.edu †leez@ieor.berkeley.edu ‡aagogino@euler.me.berkeley.edu

2. Acknowledgments • Many thanks to General Electric Corporate Research and Development and the University of California MICRO Program. • Special thanks to Louis Schick and Mahesh Morjaria of General Electric Corporate Research and Development for their guidance and intellectual input.

3. Gas Turbine Basics • Complex system: large number of parts subject to performance degradation, malfunction, or failure. • Turbine, combustion system, hot-gas path equipment, control devices, fuel metering, etc. • Condition information available from operators, sensors, inspections.

4. Gas Turbine Maintenance • Enormous number of candidates for maintenance, so ideally focus on most cost-effective items. • Maintenance planning (optimized, heuristic, ad hoc) determines: • Inspection activities • Maintenance activities • Intervals between inspection and maintenance activities.

5. Maintenance Planning On-line Statistical Analysis Expert Subjective Probabilities On-line Machine Learning Knowledge Extraction Diagnosis Sensor Fusion Maintenance Planning Sensor Validation Sensor Readings Inspection Results Repair or Replace Parts Order Inspections

6. Gas Turbine Warranty • Warranty/service contract for gas turbine would transfer all necessary maintenance and repair responsibilities to the manufacturer for the life of the warranty. • Fixed warranty period determined by manufacturer. • Gas turbine customer pays fixed price for warranty.

7. 4 Key Issues • Types of maintenance and sensing activities (current focus) • Price of a gas turbine and service contract • Length of service contract period • Number of gas turbines for consumer

8. Consumer Profit Maximization How many gas turbines should the customer purchase, if any? • Maximize Rj (nj,w)–(p1 + p2) *nj* - n(w/m) * shutdown loss

9. Producer Profit Maximization How much should the manufacturer charge for a gas turbine engine and warranty? How long should the warranty period be? • Maximize (p1 + p2 - m) *Snj* p1,p2,w Subject To m=F0 (xt, s, ts) .

10. Optimal Maintenance What types of maintenance and sensing activities should the manufacturer pursue? How often? • Derive an optimal maintenance policy via stochastic dynamic programming to minimize maintenance costs, given a fixed warranty period. • Solve for F0 (xt, s, ts).

11. Gas Turbine Water Wash Maintenance • Focus on a specific area of gas turbine maintenance: compressor water washing. • Compressor degradation results from contaminants (moisture, oil, dirt, etc.), erosion, and blade damage. • Maintenance activities scheduled to minimize expected maintenance cost while incurring minimum profit loss caused by efficiency degradation.

12. Compressor Efficiency • Motivation: if fuel is 3¢/KWHr, then 1% loss of efficiency on a 100MW turbine = $30/hr or $263K/yr. • On-line washing with or without detergents (previously nutshells) relatively inexpensive; can improve efficiency ~1%. • Off-line washing more expensive, time consuming; can improve efficiency ~2-3%.

13. On-line wash Major scouring Off-line wash Blade replacement Do nothing Major inspection Do nothing Decision Alternatives

14. Influence Diagram Current Engine State, s´ Total Maintenance Cost, v Decision, d Average Efficiency, xt Last Measured Engine State, s

15. Stochastic Dynamic Programming • Computes minimum expected costs backwards, period by period. • Final solution gives expected minimum maintenance cost, which can be used to determine appropriate warranty price. • Given engine status information for any period, model chooses optimal decision for that period.

16. Stochastic Dynamic Programming Assumptions • Problem divided into periods, each ending with a decision. • Finite number of possible states associated with each period. • Decision and engine state for any period determine likelihood of transition to next state. • Given current state, optimal decision for subsequent states does not depend on previous decisions or states.

17. Other Assumptions • Compressor working performance is main determinant of engine efficiency level. • Working efficiency and engine state can be represented as discrete variables. • Current efficiency can be derived from temperature and pressure statistics. • Intra-period efficiency transition probability depends on maintenance decision and engine state.

18. Dynamic Program Constraints

19. Dynamic Program Constraints

20. Dynamic Program Constraints Ft (xt, s, ts) = min [ c1, c2, c3, c7 ]

21. User/Other Inputs Service Contract period Cost of each decision Losses incurred at each efficiency level Transition probabilities for state and efficiency changes Program Outputs Expected minimum maintenance cost Optimal action for any period Dynamic Program Simulation

22. Turbine Performance Degradation Curves* *Source: GE

23. Turbine Performance Degradation Curves* *Source: GE

24. Online Water Wash Effects* *Source: GE

25. Online Water Wash Effects* *Source: GE

26. Efficiency Transition Probabilities

27. Conclusions • Analyzed maintenance and warranty decision making for gas turbines used in power plants. • Described and modeled economic issues related to warranty. • Developed a dynamic programming approach to optimize maintenance activities and warranty period length suited in particular to compressor maintenance.

28. Future Research • Sensitivity analysis of all user-input costs . • Sensitivity analysis of the efficiency and state transition probabilities.