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Dr. Julian Feuchtwang Prof. David Infield

The offshore access problem and turbine availability probabilistic modelling of expected delays to repairs. Dr. Julian Feuchtwang Prof. David Infield. Background:

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Dr. Julian Feuchtwang Prof. David Infield

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  1. The offshore access problem and turbine availability probabilistic modelling of expected delays to repairs Dr. Julian Feuchtwang Prof. David Infield

  2. Background: • Aim: Estimate expected delay times to turbine repairs due to sea-state (and/or wind) and how they are influenced by key factors, especially vessel access limits and time required • Contributes as part of a ‘Cost of Energy’ model including risks

  3. Why use a probabilistic method? • Monte Carlo approach needs: • Long, continuous, time series data (real or synthesised?) • Many runs (for statistical validity) • Probabilistic approach needs: • Time series data (best but scant) • or duration statistics • or simple wave height statistics (less accurate) • Allows trends and sensitivities to be explored quickly and easily

  4. Estimating subsystem down-times Site wind & wave data / stats Access limit conditions Statistical model of access and repair O & M cost Failure types Failure rates Expected down-time Lost revenue Repair times

  5. Event tree fault is access possible? wait for next ‘weather window’ no no is there enough access time left? yes carry out repair yes Assumption:No travel without forecast

  6. Sea-state conditions & Event tree 0: repair can go ahead required duration 1: waves too high 2b: fault too late 2a: period too short After 1, 2a or 2b, low sea-state periods may again be too short leading to more delays

  7. exceedence probability is Wave height distribution For a given threshold wave height Hth the wave height probability density function is p( Hth)

  8. Wave height –Maximum likelihood Weibull fit • For a given threshold wave height Hth • the wave height exceedence probability H0location parameter HC scale parameter k shape parameter

  9. the storm duration exceedence probability is found by integration: the mean storm duration Wave height duration joint distributions the storm duration probability density function is q( H > Hth , t ) = qx( t ) • For a given threshold wave height Hth and a ‘storm or calm’ duration treq

  10. the calm duration exceedence probability is τn is the mean calm duration αn is the shape factor is a normalisation factor Duration exceedence - M.L. Weibull fit

  11. Wave-height Non-exceedence-Duration curves

  12. Estimating delay times O&M cost Wave-height data Storm / calm time series Storm & calm duration distns qx(H,t) qn(H,t) Partial Moments etc. ∫dt Expected delay time E(tdel(Hthr)) Access limits Hthr& treq Lost revenue

  13. Estimating delay timesif no time-series data& no duration statistics:Kuwashima & Hogben method Wave-height Weibull parameters K&H Expected delay time E(tdel(Hthr)) Partial Moments etc. ∫dt Storm & calm duration distns qx(H,t) qn(H,t) Access limits Hthr& treq Kuwashima & Hogben method based on data correlations mostly from North Sea from H0 HC & k → gives estimates of τn & αn

  14. Expected 1st delays of different types: 1st order:Wave height above threshold P(H) is the storm probability τx is the mean storm duration Mqqx(H) is the 2nd moment (non-dim) of the storm distribution

  15. Expected 1st delays of different types: 2nd order (a):Wave height below threshold, insufficient duration Mqn(H,t) is the 1st moment (non-dim) of the calm distribution Mqqn(H,t) is the 2nd moment (non-dim) of the calm distribution 2nd order (b):Wave height below threshold, insufficient time left Qn(H,t) is the calm duration probability

  16. Further delays of different types: After 2nd order (a or b):Wave height is above threshold After 1st and 3rd order:Wave height is below threshold but duration may be short • all these components can be calculated: • directly from time-series data by numerical integration • from Weibull parameters from duration data (uses exponential and Gamma functions) • or from estimated Weibull parameters (K&H)

  17. Estimated delay times

  18. In order to use this model, we need: • Failure rate data per fault type • Tavner et al (D & DK) • Hahn Durstewitz & Rohrig (D & DK) • DOWECS (D & DK) • Ribrant & Bertling (SE – includes gearbox components) • All the above are land-based data. No offshore data available • Repair times • ditto • Vessel Operational limits • 2 types of vessel modelled • Site climate data • in UK: CEFAS, BOCD, NEXT (parameters only) • in NL: Rijkswaterstaat • elsewhere: ?

  19. Baseline Case Data

  20. Baseline Case Results: annual down-time by subsystem

  21. Influence of repair time on availability

  22. Influence of site on availability

  23. Influence of large vessel threshold on availability

  24. Influence of small vessel threshold on availability

  25. Nacelle Crane Vestas V39-500 Enercon E66 Tacke TW600 Enercon E40 Nordex N52/54 dataset failure rate Drive-train reliability scaled Individual Turbine Models Influence of failure rate on availability

  26. Conclusions: • Probabilistic method allows rapid exploration of sensitivity to different factors • vessel operability • site climate • reliability • repair times • Offshore exacerbates differences in • reliability • time to repair • accessibility • Highly dependent on access to data but so are other methods

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