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

2. Acknowledgments n Many thanks to General Electric Corporate Research and Development and the University of California MICRO Program. n 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 n Complex system: large number of parts subject to performance degradation, malfunction, or failure. n Turbine, combustion system, hot-gas path equipment, control devices, fuel metering, etc. n Condition information available from operators, sensors, inspections.

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

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

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

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

8. Consumer Profit Maximization How many gas turbines should the customer purchase, if any? Maximize R j (n j,w)–(p 1 + p 2 ) *n j * - n(w/ * 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 (p 1 + p 2 - m) * n j * p 1,p 2,w Subject Tom=F 0 (x t, s, t s ).

10. Optimal Maintenance What types of maintenance and sensing activities should the manufacturer pursue? How often? n Derive an optimal maintenance policy via stochastic dynamic programming to minimize maintenance costs, given a fixed warranty period. n Solve for F 0 (x t, s, t s ).

11. Gas Turbine Water Wash Maintenance n Focus on a specific area of gas turbine maintenance: compressor water washing. n Compressor degradation results from contaminants (moisture, oil, dirt, etc.), erosion, and blade damage. n 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. n On-line washing with or without detergents (previously nutshells) relatively inexpensive; can improve efficiency ~1%. n Off-line washing more expensive, time consuming; can improve efficiency ~2-3%.

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

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

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

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

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

18. Dynamic Program Constraints

20. F t (x t, s, t s ) = min [ c1, c2, c3, c7 ]

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

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

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