# A Decision-making Model for Corrective Maintenance of Offshore Wind Turbines Considering Uncertainties

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## Abstract

**:**

## 1. Introduction

## 2. Problem Description

^{th}ranked failure classification is defined as “the combination of maintenance personnel, spare parts and vessels which can solve component failures under the rank “1 to n” failure classifications”. From the definition, it is understood that, if a B-type RC is sent to address the n

^{th}ranked failure classification it cannot solve component failures under rank “n + 1 to N” failure classifications.

## 3. Mathematical Model

_{i}denotes the probability of occurrence of the i

^{th}failure classification. The probabilities of occurrences of all the failure classifications are assumed known.

^{th}failure classification, is sent to address the unknown failure, the trip is successful when the failure classification is $i$ and the trip is a failure when the failure classification is not i. For A-type RC, the probability of the maintenance trip to be a success is P

_{i}and the probability of the maintenance trip to be a failure is 1−P

_{i}. If the failure classification is not i, we are able to identify that the failure is k and a single next trip with an A-type RC for k will solve the failure. When a B-type RC that is dedicated for the n

^{th}failure classification is sent to address the unknown failure, the trip is successful when the failure classification is $1,2,3,\dots ,n$ and, trip is a failure when the failure classification is k (k > n). For B-type RC, the probability of the maintenance trip to be a success is ${P}_{1}+{P}_{2}+{P}_{3}+\dots +{P}_{n}$ and the probability of the maintenance trip to be a failure is ${P}_{n+1}+{P}_{n+2}+{P}_{n+3}+\dots +{P}_{N}$. A single next trip with an A-type RC for k will solve the failure.

- Z Expected total maintenance cost for S
_{ij} - g
_{ij}Weight of spares for S_{ij}in tons - D Cost per tonnage of spares
- H
_{ij}Cost of special vessel for S_{ij} - t
_{ij}Travel time for S_{ij}in hours - C
_{ij}Cost of vessel, maintenance personnel, and revenue loss per hour for S_{ij} - V
_{ij}Vessel cost per hour for S_{ij} - n
_{ij}Number of maintenance personnel for S_{ij} - M Maintenance personnel cost per hour
- R Revenue loss per hour
- r
_{ij}Repair time for S_{ij}in hours - α
_{ij}Probability of trip success for S_{ij} - B
_{ij}Probability of trip failure for S_{ij} - P
_{i}Probability that the failure is of classification i - A Fixed additional trip cost of sending an A-type RC to solve known failure, which includes vessel cost, personnel cost, spare parts cost, and revenue loss due to downtime

_{ij}to address the unknown failure. The first two terms in the model, is the sum of the spare parts cost and fixed special vessel cost of S

_{ij}. The third term in the model is the total cost including vessel cost, personnel cost and revenue loss incurred because of the travel to and from the turbine using S

_{ij}. The fourth term in the model is the trip success using S

_{ij}. The trip success considers the total cost including the vessel cost, personnel cost ad revenue loss incurred because of the repair activity at the turbine using S

_{ij}and, the probability that the turbine failure could be solved by S

_{ij}. The fifth term in the model is the trip failure using S

_{ij}. The trip failure considers the total cost including the vessel cost, personnel cost ad revenue loss to solve the known failure using an appropriate A-type RC and, the probability that the turbine failure could not be solved by S

_{ij}. The waiting time and failure identification time are constants in our proposed model and both the time elements does not affect the decision and the results. Therefore, the waiting time and failure identification time are not included in the model. In the Equations (6)–(9), j = 1 represents the A-type RC and j = 2 represents the B-type RC.

## 4. Case Study

#### 4.1. Wind Farm Models

**S**

_{11}and

**S**have identical resource elements, which means both A-type and B-type RC’s are identical for imperfect maintenance in this study.

_{12}#### 4.2. Time and Cost Inputs

#### 4.3. Results

_{n}for the wind farm model n represents the optimal solution, that is, the corresponding resource combination is identified to be the cost-effective resource combination.

_{11}(which is same as S

_{12}in this study) is the cost-effective option to address the corrective maintenance for turbines that are in operation for less than 10 years (base case model and wind farm model 1). In addition, S

_{22}is the cost-effective option to address the corrective maintenance for turbines that are in operation for more than 10 years (wind farm model 2 and 3). Comparing the results of the proposed model with the traditional practice, the proposed model produces very high cost savings of 82.12% for the base case model and a considerable cost savings for the other three different wind farm models. It has to be noted that the proposed model is for one corrective maintenance trip and when there are multiple corrective maintenance problem instances with no information from CM systems, the cost savings will be more for the wind farm models 1, 2 and 3.

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Table 1.**Failure classifications for a 3 MW offshore wind turbine [11].

Maintenance Rank | Failure Classification | Definition |
---|---|---|

1 | Imperfect maintenance | An imperfect maintenance operation where there is no requirement for spare parts. |

2 | Minimal replacement | A minimal replacement of small sized sub-components with a maximum weight of 1 tonne. |

3 | Perfect replacement I | A perfect replacement of medium weight sub-components with a maximum weight of 50 tonnes. |

4 | Perfect replacement II | A perfect replacement of medium or large sized sub-components, with weight 50 tonnes to 100 tonnes. |

Resource Combination | Resource Elements |
---|---|

${S}_{11}$ | No Spare part + Access Vessel (Crew Transfer Vessel -small) + 2 maintenance personnel |

${S}_{21}$ | Required Spare part + Access Vessel (Crew Transfer Vessel -small) + 3 maintenance personnel. (Use of permanent internal crane for replacement). |

${S}_{31}$ | Required Spare part + Crane Vessel + Access Vessel (Crew Transfer Vessel small) + 6 maintenance personnel. |

${S}_{41}$ | Required Spare part + Access Vessel (Crew Transfer Vessel -small) + Access Vessel (Jack- Up Vessel) + 6 maintenance personnel. |

${S}_{12}$ | No Spare part + Access Vessel (Crew Transfer Vessel - small) + 2 maintenance personnel |

${S}_{22}$ | All Class B Spare parts + Access Vessel (Crew Transfer Vessel-Large) + 3 maintenance personnel (Use of permanent internal crane for replacement). |

${S}_{32}$ | All Class B and C Spare parts + build-up crane with a vessel + Access Vessel (SUVs) + 6 maintenance personnel. |

${S}_{42}$ | All Class B, C and D spare parts + Access Vessel (SUVs) + Access Vessel (Jack- Up barge) + 6 maintenance personnel |

**Table 3.**Probabilities of failure classifications for different OWF models [11].

Failure Classification | Probability | |||
---|---|---|---|---|

Base Case Model | Wind Farm Model 1 | Wind Farm Model 2 | Wind Farm Model 3 | |

Imperfect maintenance | 0.995165258 | 0.002353569 | 0.000995862 | 0.000995862 |

Minimal replacement | 0.002353569 | 0.995165258 | 0.001485311 | 0.001485311 |

Perfect replacement I | 0.000995862 | 0.001485311 | 0.995165258 | 0.002353569 |

Perfect replacement II | 0.001485311 | 0.000995862 | 0.002353569 | 0.995165258 |

Resource Combination | Travel Speed (km/h) | Travel Time (h) | Repair Time (h) | Access Vessel Cost/hour | Crane/Jack up Vessel Cost | Weight of Spare Parts (tonnes) |
---|---|---|---|---|---|---|

${S}_{11}$ | 37.04 | 0.76 | 4 | $62.5 | N/A | 0 |

${S}_{21}$ | 37.04 | 0.76 | 48 | $62.5 | N/A | 1 |

${S}_{31}$ | 37.04 | 0.76 | 48 | $62.5 | $105,259.5 | 50 |

${S}_{41}$ | 37.04 | 0.76 | 48 | $62.5 | $119,294.1 | 100 |

${S}_{12}$ | 37.04 | 0.76 | 4 | $62.5 | N/A | 0 |

${S}_{22}$ | 46.3 | 0.6 | 48 | $93.75 | N/A | 11 |

${S}_{32}$ | 18.52 | 1.5 | 48 | $93.75 | $105,259.5 | 600 |

${S}_{42}$ | 18.52 | 1.5 | 48 | $93.75 | $119,294.1 | 600 |

Parameter | Values |
---|---|

Maintenance Personnel cost/hour | 70 |

Cost/tonnage of spares | 29.72 |

Revenue Loss/hour | $18,684 |

Fixed cost for corrective maintenance trip for offshore wind turbine | $500,000 |

**Table 6.**Cost-effective resource combination for different wind farm models given in Table 3.

Wind Farm Model | Cost-Effective Resource Combination | Expected Total Maintenance Cost (in $’s) | Cost Savings (in Comparison with Traditional Practice) |
---|---|---|---|

Base case | ${S}_{11}$ | 91591 | 82.12% |

Model 1 | ${S}_{11}$ | 513354 | 0.19% |

Model 2 | ${S}_{22}$ | 512740 | 0.31% |

Model 3 | ${S}_{22}$ | 512740 | 0.31% |

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**MDPI and ACS Style**

Nachimuthu, S.; Zuo, M.J.; Ding, Y.
A Decision-making Model for Corrective Maintenance of Offshore Wind Turbines Considering Uncertainties. *Energies* **2019**, *12*, 1408.
https://doi.org/10.3390/en12081408

**AMA Style**

Nachimuthu S, Zuo MJ, Ding Y.
A Decision-making Model for Corrective Maintenance of Offshore Wind Turbines Considering Uncertainties. *Energies*. 2019; 12(8):1408.
https://doi.org/10.3390/en12081408

**Chicago/Turabian Style**

Nachimuthu, Sathishkumar, Ming J. Zuo, and Yi Ding.
2019. "A Decision-making Model for Corrective Maintenance of Offshore Wind Turbines Considering Uncertainties" *Energies* 12, no. 8: 1408.
https://doi.org/10.3390/en12081408