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Fault Tree — Offshore Turbine Unavailability

Loss of export from a single offshore wind turbine over a year, combining drivetrain and converter faults with an array cable branch and a two-of-three pitch system vote that keeps the rotor controllable.

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Loss of export from an offshore wind turbineFault tree (IEC 61025) · 12 basic events · 6 gates · depth 3topTurbine exports nopower0.199156turbine_faultTurbine unable togenerate0.1583drivetrainDrivetrain failure0.08466gearboxGearbox failurerequiring a jack-up…0.043main_bearingMain bearing failure0.018generatorGenerator windingfailure0.026converterFull-power converterfails0.071pitch_lostPitch controlunavailable2/30.008742pitch_1Pitch drive blade 1fails0.055pitch_2Pitch drive blade 2fails0.055pitch_3Pitch drive blade 3fails0.055yaw_lostYaw systemunavailable0.001444yaw_drive_aYaw drive group Afails0.038yaw_drive_bYaw drive group Bfails0.038export_path_lostExport pathunavailable0.04854array_cableArray cable fault orabrasion at the…0.012switchgear33 kV switchgearfault in the tower…0.030195transformerTurbine transformerfault0.007Top event probability (exact)0.199156Minimal cut sets11Smallest cut set order1Single points of failure7Mission time8760 hExact top-event probability 0.199156 · rare-event sum ΣP(cut set) 0.217714The usual approximation overstates this tree by 9.32% — that gap is the overlap between cut sets, which only the exact evaluation removes.Minimal cut sets — by order, then probability1. {converter} order 1 P 0.071 35.7% of the top ← single point of failure2. {gearbox} order 1 P 0.043 21.6% of the top ← single point of failure3. {switchgear} order 1 P 0.030195 15.2% of the top ← single point of failure4. {generator} order 1 P 0.026 13.1% of the top ← single point of failure5. {main_bearing} order 1 P 0.018 9% of the top ← single point of failure6. {array_cable} order 1 P 0.012 6% of the top ← single point of failure7. {transformer} order 1 P 0.007 3.5% of the top ← single point of failure8. {pitch_1, pitch_2} order 2 P 0.003025 1.5% of the top9. {pitch_1, pitch_3} order 2 P 0.003025 1.5% of the top10. {pitch_2, pitch_3} order 2 P 0.003025 1.5% of the top+ 1 further cut sets not listedImportance — Fussell–Vesely (share of current risk) and Birnbaum (potential swing)converter — Full-power converter fails q 0.071 FV 35.7% B 0.862049 CR 30.7%gearbox — Gearbox failure requiring a jack-up vessel q 0.043 FV 21.6% B 0.836827 CR 18.1%switchgear — 33 kV switchgear fault in the tower base q 0.030195 FV 15.2% B 0.825778 CR 12.5%generator — Generator winding failure q 0.026 FV 13.1% B 0.822222 CR 10.7%main_bearing — Main bearing failure q 0.018 FV 9% B 0.815523 CR 7.4%array_cable — Array cable fault or abrasion at the J-tube q 0.012 FV 6% B 0.810571 CR 4.9%transformer — Turbine transformer fault q 0.007 FV 3.5% B 0.806489 CR 2.8%pitch_1 — Pitch drive blade 1 fails q 0.055 FV 3% B 0.083982 CR 2.3%Rectangle intermediate event · dome AND · shield OR · shield with k/n voting · hexagon INHIBIT with its oval condition · circle basic · diamond undeveloped · triangle transfer

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title "Loss of export from an offshore wind turbine"
mission 8760h

top "Turbine exports no power" = OR(turbine_fault, export_path_lost)

gate turbine_fault "Turbine unable to generate" = OR(drivetrain, converter, pitch_lost, yaw_lost)
gate drivetrain "Drivetrain failure" = OR(gearbox, main_bearing, generator)
gate pitch_lost "Pitch control unavailable" = KOFN(2, pitch_1, pitch_2, pitch_3)
gate yaw_lost "Yaw system unavailable" = AND(yaw_drive_a, yaw_drive_b)
gate export_path_lost "Export path unavailable" = OR(array_cable, switchgear, transformer)

event gearbox "Gearbox failure requiring a jack-up vessel" p=0.043
event main_bearing "Main bearing failure" p=0.018
event generator "Generator winding failure" p=0.026
event converter "Full-power converter fails" p=0.071
event pitch_1 "Pitch drive blade 1 fails" p=0.055
event pitch_2 "Pitch drive blade 2 fails" p=0.055
event pitch_3 "Pitch drive blade 3 fails" p=0.055
event yaw_drive_a "Yaw drive group A fails" p=0.038
event yaw_drive_b "Yaw drive group B fails" p=0.038
event array_cable "Array cable fault or abrasion at the J-tube" p=0.012
event switchgear "33 kV switchgear fault in the tower base" rate=3.5e-6
undeveloped transformer "Turbine transformer fault" p=0.007