# Assessing the Factors Impacting on the Reliability of Wind Turbines via Survival Analysis—A Case Study

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Survival Analysis

#### 3.1.1. Non-Parametric Survival Analyses: Kaplan–Meier and Nelson–Aalen Estimators

_{j}is the number of individuals that have an event at time t

_{j}where j = 1, …, k; m

_{j}is the number of individuals censored in the interval [t

_{j}, t

_{j}

_{+ 1}); and n

_{j}= (m

_{j}+ d

_{j})+ … + (m

_{k}+ d

_{k}) is the number of individuals at risk just prior to t

_{j}[24].

_{i}is the number of individuals that have an event at time t

_{i}and n

_{i}is the total individuals at risk at time t

_{i}.

#### 3.1.2. Log-Rank Test for the Significance of Survival

^{2}/E for each group where O is observed, and E is the expected number of events. The obtained test statistical value is checked in a Chi-distribution table and the corresponding p-value represents the probability of the event occurring by chance [23].

#### 3.1.3. Semi-Parametric Survival Analysis: Cox Proportional Hazard Model

_{0}(t)e

^{zB}

_{0}(t) is the baseline function, z is the variable and B is the hazard coefficient for the variable. The hazard ratio between the two groups (z

_{1}and z

_{2}) in a factor can be estimated using Equation (9).

_{1}, z

_{0}) = e

^{B}

^{(z1−z2)}

- Standard error (SE): the SE of the estimate shows the accuracy of the estimation for the observed value.
- Wald statistic: The Wald statistic is the ratio of the regression coefficient B to SE. It is used to evaluate the significance of the B coefficients of factors.
- Degrees of freedom: df represents the number of sub-factors that are compared against a factor. For example, design type has two sub-factors, direct and geared, thus the df is 2 − 1 = 1.
- Significance level (sig.): The probability of the coefficient occurring by chance for a specific factor.
- Exp (B): The hazard ratio from the Cox regression is given as Exp (B).
- Confidence intervals (CI) of 95%: 95% upper and lower levels of coefficients resulting from the regression.

## 4. Case Study Based on WMEP Data

#### 4.1. Survival Analysis Factors

#### 4.1.1. Koppen–Geiger Climatic Regions

- Cfa: Temperate—without dry season—hot summer
- Cfb: Temperate—without dry season—warm summer
- Dfb: Cold—without dry season—warm summer
- Dfc: Cold—without dry season—cold summer

#### 4.1.2. Elevational Location

#### 4.1.3. Distance to Coast

#### 4.1.4. Mean Annual Wind Speed (MAWS)

#### 4.1.5. Turbine Age

#### 4.1.6. Turbine Type

#### 4.1.7. Number of Previous Failures (NOPF)

#### 4.1.8. Scheduled Maintenance History

#### 4.2. Selected Turbine Aspects

## 5. Results

#### 5.1. Wind Turbine System Approach

#### 5.2. Survival Analysis of the Electrical Subsystem

#### 5.3. Survival Analysis for Components of the Electrical Subsystems

#### 5.3.1. Survival Analysis for Fuses

#### 5.3.2. Survival Analysis for Switches

## 6. Conclusions

- Geared-drive wind turbines and their electrical systems were observed to have 1.3- and 1.4- times higher survival rates, respectively, compared to direct-drive wind turbines and their electrical systems. This distinction in survival was also true for fuses, while switches showed the exact opposite trend—switches in direct-drive turbines were less likely to fail compared to switches in geared-drive wind turbines. The geared-drive type of wind turbines might improve the survival of certain components while reducing the survival of other components. For example, the survival of fuses was two times higher in direct-drive turbines than in geared-drive turbines, whereas the survival of switches was reduced by 66%.
- Although the survival probability graphs show some differences between the climatic regions, these were not significant to the survival of wind turbines, the electrical subsystem and components of the electrical systems. However, this significance is related to the number of data points and the relative number of data points among the factors as well as the investigated subsystems and components. The lack of expected significance for the climatic regions in this study may be attributed to data scarcity, specifically for the Dfc region with a cold climate in the summer.
- The impact of turbine age on the survival of turbine systems and electrical subsystems varied with time. However, fuses had a 60% lower survival in the “mature” age group (4–14 years) than in their early years.
- Scheduled maintenance reporting significantly improved the survival of wind turbines; our data and analysis showed a 2.8- and 3.8-times improvement in survival for wind turbines as a system and for the electrical subsystems, respectively. In other words, at any time there was 2.8 times higher probability of survival for a wind turbine and a 3.8 times higher probability of survival for an electrical subsystem with a history of scheduled maintenance than one without such a history.
- Distance to the coast was not found to be a significant reliability factor for wind turbine systems and electrical subsystems. However, the shorter distance to the coast increased the survival of switches by 39%. A potential explanation for this is that wind patterns in coastal regions fluctuate less than ones on land.
- Elevational location was found not to be a significant factor for the survival of turbine systems, electrical subsystems and fuse and switch components. It must be noted that the maximum elevation of the considered turbines in this study was 800 m.
- Although the hazard rate cannot be quantified due to the violation of proportionality, it was found that a high number of previous failures (NOPF) reduced the survival of wind turbines as a system and of the electrical systems compared to low NOPF. It was also found that a high NOPF showed a lower survival rate for wind turbine components, however in order to determine the significance more data are required.
- MAWS was not shown to be a significantly reliable factor for wind turbine systems and electrical subsystems. However, higher MAWS increased the survival of switches by 35%, which can be attributed to more consistent wind patterns.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Nelson–Aalen cumulative hazard functions of wind turbines based on the operational, climatic and geographical factors. (

**a**) Design type (

**b**) Climatic regions (

**c**) Turbine age (

**d**) Scheduled maintenance history (

**e**) Distance to coast (

**f**) Elevational location (

**g**) NOPF (

**h**) MAWS.

**Figure 4.**Kaplan–Meier survival functions of electrical subsystems based on the operational, climatic and geographic factors. (

**a**) Design type (

**b**) Climatic regions (

**c**) Turbine age (

**d**) Scheduled maintenance history (

**e**) Distance to coast (

**f**) Elevational location (

**g**) NOPF (

**h**) MAWS.

**Figure 5.**Kaplan–Meier survival functions for fuses based on the operational, climatic and geographic factors. (

**a**) Design type (

**b**) Climatic regions(

**c**) Turbine age (

**d**) Distance to coast (

**e**) Elevational location (

**f**) MAWS (

**g**) NOPF.

**Figure 6.**Kaplan–Meier survival functions of switches based on the operational, climatic and geographic factors. (

**a**) Design type (

**b**) Climatic regions (

**c**) Distance to coast (

**d**) Turbine age (

**e**) Elevational location (

**f**) MAWS (

**g**) NOPF.

Geographical and Environmental Factors | Operational Factors |
---|---|

1. Koppen–Geiger Climatic Regions: Cfb, Dfb, Dfc | 5. Turbine age (years): 0–3, 4–14 |

2. Elevational location: High land (>100 m), Low land (≤100 m) | 6. Turbine type: Geared-drive, Direct-drive |

3. Distance to coast: Coastal (0–20 km), Inland (>20 km) | 7. Number of previous failures (NOPF) Varies |

4. Mean annual wind speed (MAWS)High (>6.25 m/s), Low (≤6.25 m/s) | 8. Scheduled maintenance history: Yes, No |

1st | 2nd | 3rd | Description | Criteria * |
---|---|---|---|---|

C | Temperate | T_{hot} ≥ 10 & 0 < T_{cold} < 18 | ||

s | - Dry Summer | P_{sdry} < 40 & P_{sdry} < P_{wwet}/3 | ||

w | - Dry Winter | P_{wdry} < P_{swet}/10 | ||

f | - Without dry season | Not (Cs) or (Cw) | ||

a | - Hot Summer | T_{hot} ≥ 22 | ||

b | - Warm Summer | Not (a) & T_{mon10} ≥ 4 | ||

c | - Cold Summer | Not (a or b) & 1 ≤ T_{mon10} < 4 | ||

D | Cold | T_{hot} ≥ 10 & T_{cold} ≤ 0 | ||

s | - Dry Summer | P_{sdry} < 40 & P_{sdry} < P_{wwet}/3 | ||

w | - Dry Winter | P_{wdry} < P_{swet}/10 | ||

f | - Without dry season | Not (Ds) or (Dw) | ||

a | - Hot Summer | T_{hot} ≥ 22 | ||

b | - Warm Summer | Not (a) & T_{mon10} ≥ 4 | ||

c | - Cold Summer | Not (a, b or d) | ||

d | - Very Cold Winter | Not (a or b) & T_{cold} < −38 |

_{hot}= temperature of the hottest month, T

_{cold}= temperature of the coldest month, T

_{mon10}= number of months where the temperature is above 10, P

_{dry}= precipitation of the driest month, P

_{sdry}= precipitation of the driest month in summer, P

_{wdry}= precipitation of the driest month in winter, P

_{swet}= precipitation of the wettest month in summer, P

_{wwet}= precipitation of the wettest month in winter.

Turbine Model | Time to Failure (days) | Status | Design Type | Climatic Regions | Turbine Age (years) | Distance to Coast | Elevational Location | MAWS |
---|---|---|---|---|---|---|---|---|

Model A | 675 | Failed | Geared | Cfb | 0–3 | Coastal | Low | High |

Model A | 2978 | Censored | Geared | Cfb | 0–3 | Coastal | Low | High |

Model A | 1572 | Failed | Geared | Cfb | 0–3 | Inland | Low | Low |

Model B | 3849 | Censored | Direct | Dfb | 0–3 | Coastal | Low | Low |

Characteristics | Wind Turbine System Study | Electrical Subsystem Study | Component Study | |||||
---|---|---|---|---|---|---|---|---|

Fuses | Switches | |||||||

Turbine type | Geared | Direct | Geared | Direct | Geared | Direct | Geared | Direct |

Number of participants | 1477 | 3334 | 269 | 704 | 47 | 123 | 157 | 126 |

**Table 5.**Log-rank test results for comparison of the effect of factors impacting on wind turbine system failures.

Factors | Groups | Test Statistics | |
---|---|---|---|

Chi-Square | Sig. | ||

Design type | Direct vs. Geared | 53.01 | 0.000 |

Scheduled maintenance history | No vs. Yes | 991.01 | 0.000 |

Factors | B | SE | Wald | Df | Sig. | Exp (B) | 95.0% CI for Exp (B) | |
---|---|---|---|---|---|---|---|---|

Lower | Upper | |||||||

Design type | 0.22 | 0.035 | 39.3 | 1 | 0.000 | 1.25 | 1.16 | 1.34 |

Scheduled (Y/N) | 1.02 | 0.033 | 935.2 | 1 | 0.000 | 2.77 | 2.59 | 2.95 |

**Table 7.**Log-rank test results for the comparison of the factors impacting on electrical subsystem failures.

Factors | Groups | Test Statistics | |
---|---|---|---|

Chi-Square | Sig. | ||

Design type | Direct vs. Geared | 22.77 | 0.000 |

Scheduled maintenance history | No vs. Yes | 351.76 | 0.000 |

Factors | B | SE | Wald | df | Sig. | Exp (B) | 95.0% CI for Exp (B) | |
---|---|---|---|---|---|---|---|---|

Lower | Upper | |||||||

Design type | 0.35 | 0.080 | 18.99 | 1 | 0.000 | 1.42 | 1.21 | 1.66 |

Scheduled (Y/N) | 1.34 | 0.075 | 319.29 | 1 | 0.000 | 3.81 | 3.30 | 4.42 |

Elevational location | 0.06 | 0.077 | 0.68 | 1 | 0.408 | 1.07 | 0.916 | 1.24 |

Distance to coast | 0.04 | 0.087 | 0.20 | 1 | 0.652 | 1.04 | 0.88 | 1.23 |

Factors | B | SE | Wald | Df | Sig. | Exp (B) | 95.0% CI for Exp (B) | |
---|---|---|---|---|---|---|---|---|

Lower | Upper | |||||||

Design type | 1.13 | 0.381 | 8.73 | 1 | 0.003 | 3.09 | 1.46 | 6.52 |

Turbine age | −0.95 | 0.329 | 8.35 | 1 | 0.004 | 0.39 | 0.203 | 0.74 |

Factors | B | SE | Wald | df | Sig. | Exp (B) | 95.0% CI for Exp (B) | |
---|---|---|---|---|---|---|---|---|

Lower | Upper | |||||||

Design type | −1.08 | 0.167 | 41.48 | 1 | 0.000 | 0.34 | 0.25 | 0.47 |

Distance to coast | −0.50 | 0.177 | 8.04 | 1 | 0.005 | 0.61 | 0.43 | 0.86 |

MAWS | −0.43 | 0.178 | 5.89 | 1 | 0.015 | 0.65 | 0.46 | 0.92 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ozturk, S.; Fthenakis, V.; Faulstich, S. Assessing the Factors Impacting on the Reliability of Wind Turbines via Survival Analysis—A Case Study. *Energies* **2018**, *11*, 3034.
https://doi.org/10.3390/en11113034

**AMA Style**

Ozturk S, Fthenakis V, Faulstich S. Assessing the Factors Impacting on the Reliability of Wind Turbines via Survival Analysis—A Case Study. *Energies*. 2018; 11(11):3034.
https://doi.org/10.3390/en11113034

**Chicago/Turabian Style**

Ozturk, Samet, Vasilis Fthenakis, and Stefan Faulstich. 2018. "Assessing the Factors Impacting on the Reliability of Wind Turbines via Survival Analysis—A Case Study" *Energies* 11, no. 11: 3034.
https://doi.org/10.3390/en11113034