Warranty

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Warranty

  1. 1. Warranty and Maintenance Decision Making for Gas Turbines <ul><li>Susan Y. Chao*, Zu-Hsu Lee † , and Alice M. Agogino ‡ </li></ul><ul><li>University of California, Berkeley </li></ul><ul><li>Berkeley, CA 94720 </li></ul><ul><li>*chao@garcia.me.berkeley.edu † [email_address] ‡ [email_address] </li></ul>
  2. 2. Acknowledgments <ul><li>Many thanks to General Electric Corporate Research and Development and the University of California MICRO Program. </li></ul><ul><li>Special thanks to Louis Schick and Mahesh Morjaria of General Electric Corporate Research and Development for their guidance and intellectual input. </li></ul>
  3. 3. Gas Turbine Basics <ul><li>Complex system: large number of parts subject to performance degradation, malfunction, or failure. </li></ul><ul><li>Turbine, combustion system, hot-gas path equipment, control devices, fuel metering, etc. </li></ul><ul><li>Condition information available from operators, sensors, inspections. </li></ul>
  4. 4. Gas Turbine Maintenance <ul><li>Enormous number of candidates for maintenance, so ideally focus on most cost-effective items. </li></ul><ul><li>Maintenance planning (optimized, heuristic, ad hoc) determines: </li></ul><ul><ul><li>Inspection activities </li></ul></ul><ul><ul><li>Maintenance activities </li></ul></ul><ul><ul><li>Intervals between inspection and maintenance activities. </li></ul></ul>
  5. 5. Maintenance Planning On-line Statistical Analysis Expert Subjective Probabilities On-line Machine Learning Knowledge Extraction Diagnosis Sensor Fusion Sensor Validation Maintenance Planning Repair or Replace Parts Order Inspections Sensor Readings Inspection Results
  6. 6. Gas Turbine Warranty <ul><li>Warranty/service contract for gas turbine would transfer all necessary maintenance and repair responsibilities to the manufacturer for the life of the warranty. </li></ul><ul><li>Fixed warranty period determined by manufacturer. </li></ul><ul><li>Gas turbine customer pays fixed price for warranty. </li></ul>
  7. 7. 4 Key Issues <ul><li>Types of maintenance and sensing activities ( current focus ) </li></ul><ul><li>Price of a gas turbine and service contract </li></ul><ul><li>Length of service contract period </li></ul><ul><li>Number of gas turbines for consumer </li></ul>
  8. 8. Consumer Profit Maximization <ul><li>How many gas turbines should the customer purchase, if any? </li></ul><ul><li>Maximize R j (n j ,w)–(p 1 + p 2 ) *n j * - n (w/  * shutdown loss </li></ul>
  9. 9. Producer Profit Maximization <ul><li>How much should the manufacturer charge for a gas turbine engine and warranty? </li></ul><ul><li>How long should the warranty period be? </li></ul><ul><li>Maximize (p 1 + p 2 - m) *  n j * </li></ul><ul><li> p 1 ,p 2 ,w </li></ul><ul><li>Subject To m=F 0 (x t , s, t s ) . </li></ul>
  10. 10. Optimal Maintenance <ul><li>What types of maintenance and sensing activities should the manufacturer pursue? How often? </li></ul><ul><li>Derive an optimal maintenance policy via stochastic dynamic programming to minimize maintenance costs, given a fixed warranty period. </li></ul><ul><li>Solve for F 0 (x t , s, t s ). </li></ul>
  11. 11. Gas Turbine Water Wash Maintenance <ul><li>Focus on a specific area of gas turbine maintenance: compressor water washing. </li></ul><ul><li>Compressor degradation results from contaminants (moisture, oil, dirt, etc.), erosion, and blade damage. </li></ul><ul><li>Maintenance activities scheduled to minimize expected maintenance cost while incurring minimum profit loss caused by efficiency degradation. </li></ul>
  12. 12. Compressor Efficiency <ul><li>Motivation: if fuel is 3 ¢/KWHr, then 1% loss of efficiency on a 100MW turbine = $30/hr or $263K/yr. </li></ul><ul><li>On-line washing with or without detergents (previously nutshells) relatively inexpensive; can improve efficiency ~1%. </li></ul><ul><li>Off-line washing more expensive, time consuming; can improve efficiency ~2-3%. </li></ul>
  13. 13. Decision Alternatives Blade replacement Major scouring Do nothing On-line wash Do nothing Off-line wash Major inspection
  14. 14. Influence Diagram Current Engine State, s´ Average Efficiency, x t Decision, d Total Maintenance Cost, v Last Measured Engine State, s
  15. 15. Stochastic Dynamic Programming <ul><li>Computes minimum expected costs backwards, period by period. </li></ul><ul><li>Final solution gives expected minimum maintenance cost, which can be used to determine appropriate warranty price. </li></ul><ul><li>Given engine status information for any period, model chooses optimal decision for that period. </li></ul>
  16. 16. Stochastic Dynamic Programming Assumptions <ul><li>Problem divided into periods, each ending with a decision. </li></ul><ul><li>Finite number of possible states associated with each period. </li></ul><ul><li>Decision and engine state for any period determine likelihood of transition to next state. </li></ul><ul><li>Given current state, optimal decision for subsequent states does not depend on previous decisions or states. </li></ul>
  17. 17. Other Assumptions <ul><li>Compressor working performance is main determinant of engine efficiency level. </li></ul><ul><li>Working efficiency and engine state can be represented as discrete variables. </li></ul><ul><li>Current efficiency can be derived from temperature and pressure statistics. </li></ul><ul><li>Intra-period efficiency transition probability depends on maintenance decision and engine state. </li></ul>
  18. 18. Dynamic Program Constraints
  19. 19. Dynamic Program Constraints
  20. 20. Dynamic Program Constraints <ul><li>F t (x t , s, t s ) = min [ c1, c2, c3, c7 ] </li></ul>
  21. 21. Dynamic Program Simulation <ul><li>User/Other Inputs </li></ul><ul><li>Service Contract period </li></ul><ul><li>Cost of each decision </li></ul><ul><li>Losses incurred at each efficiency level </li></ul><ul><li>Transition probabilities for state and efficiency changes </li></ul><ul><li>Program Outputs </li></ul><ul><li>Expected minimum maintenance cost </li></ul><ul><li>Optimal action for any period </li></ul>
  22. 22. Turbine Performance Degradation Curves* *Source: GE
  23. 23. Turbine Performance Degradation Curves* *Source: GE
  24. 24. Online Water Wash Effects* *Source: GE
  25. 25. Online Water Wash Effects* *Source: GE
  26. 26. Efficiency Transition Probabilities
  27. 27. Conclusions <ul><li>Analyzed maintenance and warranty decision making for gas turbines used in power plants. </li></ul><ul><li>Described and modeled economic issues related to warranty. </li></ul><ul><li>Developed a dynamic programming approach to optimize maintenance activities and warranty period length suited in particular to compressor maintenance. </li></ul>
  28. 28. Future Research <ul><li>Sensitivity analysis of all user-input costs . </li></ul><ul><li>Sensitivity analysis of the efficiency and state transition probabilities. </li></ul>

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