**4. Wind turbine reliability analysis**

The reliability definition is the probability that subassembly will meet its required function under a stated condition for a specified period of time. For an unrepairable system, the rating scale is reliability; for a repairable system, the rating scale is availability. Wind turbines consist of both unrepairable systems and repairable systems like gears, bearings, bolts and electronic components. So both reliability and availability should be considered to assess the wind turbines. **Figure 10** shows the failure rates of different subassemblies and its downtime after failure. The results in **Figure 10** show that the lower the subassembly's reliability, the longer is the downtime of the corresponding subassembly.

The reliability of wind turbine system is becoming more and more important with the continued growth and expansion of markets for wind turbine technology. In addition, wind turbines with reduced repair and maintenance (R&M) requirements and higher reliability are needed emergently. However, wind turbines produced by different companies have different reliability. There is no unified evaluation criterion. The current reliability analysis methods mainly focus on gear transmission systems of wind turbines and ignore the influences of other systems. The effects of the reliability model are limited if the system is simplified and seen as a series or parallel connection. Due to high costs of repair and maintenance, it is essential to study the health management systems of wind turbines and develop maintenance strategies in order to improve reliability and reduce unexpected repair and maintenance. The high-reliability systems can be achieved from three aspects, as shown in **Figure 11**.

#### **4.1. Reliability analysis methods**

There are two kinds of reliability analysis methods: statistical method based on database and stress-strength interference theory based on loads.

#### *4.1.1. Statistical method based on database*

**Figure 8.** Generator failure: (a) bearing, (b) magnetic wedge loss and (c) contamination.

**4. Wind turbine reliability analysis**

**Items Failure modes**

176 Stability Control and Reliable Performance of Wind Turbines

**Table 3.** Failure modes of the generator.

**Figure 9.** Failure modes of the blades. (a) Trailing edge crack; (b) leading edge failure and (c) blade fracture.

Design issues (1) Electrical insulation inadequate; (2) loose components (wedges, banding); (3)

Operations issues (1) Improper installation; (2) voltage irregularities; (3) improper grounding; (4) overspeed conditions and (5) transient damage Maintenance practices (1) ignoring alignment; (2) cooling system failures leading to heat related failure; (3) bearing failure and (4) rotor lead failures Environmental condition (1) Wind leading; (2) thermal cycling; (3) moisture/arid; (4) contamination and (5)

complex structure

electrical storms

crimped lead connections; (4) transient shaft voltages; (5) rotor lead failures and (6)

The reliability definition is the probability that subassembly will meet its required function under a stated condition for a specified period of time. For an unrepairable system, the rating scale is reliability; for a repairable system, the rating scale is availability. Wind turbines consist of both unrepairable systems and repairable systems like gears, bearings, bolts and electronic components. So both reliability and availability should be considered to assess the The failure rates of wind turbines are time-varying during its lifetime, but the failure rates of repairable systems follow a bathtub curve. With a service life of around 20 years, wind turbine failure rates are assumed to follow the famous bathtub curve, as shown in **Figure 12**. Weibull

**Figure 10.** Failure rates and downtime for different subassemblies (DFIG).

**Figure 11.** The requirements for developing the high-reliability systems.

distribution, gamma distribution and lognormal distribution are three commonly used methods in wind turbine reliability analysis. A method with mixtures of Weibull distribution with increasing hazard rates is written as follows [11]:

$$F(t) = \lambda \left[ 1 - \exp\left(-\left(\frac{t - t\_0}{\eta\_1}\right)^{\beta\_1}\right) \right] + (1 - \lambda) \left[ 1 - \exp\left(-\left(\frac{t - t\_0}{\eta\_2}\right)^{\beta\_1}\right) \right] \tag{1}$$

rates are obvious higher at these two peaks. When the weighting factor equals 0.1, 0.2 and 0.3, the differences just happen at the peaks. Therefore, a proper weighting factor should be selected to meet the failure rate changes of wind turbines in different working environments. **Figure 14** shows the change of failure rates over time. The results in **Figure 14** show that a wind turbine is at running-in stage where its wear is large, and the failure rates are fluctuating and then stable. The failure rates of wind turbines will become higher and higher at the wear-out stage. Failure rate function curves with different weighting factors just show a difference at peak values, which has something to do with capacity and conditions. **Figure 15** shows the reliability function diagram which has three phases. The reliability in Phase I decreases sharply because newly installed wind turbines need to adapt to the environment. The reliability in Phase II is stable. There is a sharp decline in Phase III, which represents that the wind turbine has entered into wear-out failures, and its failure rates are high. Above all, it can be found that the bathtub

Random loads and fatigue strength of wind turbine subassemblies follow a normal distribution. The probability density function of stress and strength is expressed by the following

> exp(−\_\_1 2 ( *<sup>S</sup>* <sup>−</sup> *<sup>u</sup>* \_\_\_\_*<sup>s</sup> σ<sup>s</sup>* ) 2

exp(−\_\_1 2 ( *<sup>δ</sup>* <sup>−</sup> *<sup>u</sup>* \_\_\_\_*<sup>δ</sup> σδ* ) 2

**Figure 16** is a common practice to represent stress-strength interference. The figure shows the probability density function of stress and strength and their interference (overlap) over time.

) (2)

Reliability Analysis of Wind Turbines http://dx.doi.org/10.5772/intechopen.74859 179

) (3)

are the standard devia-

, *u<sup>δ</sup>*

are the

, *σδ*

curve can simulate the failure rate change among its service life as well.

√ \_\_\_ 2*π σ<sup>s</sup>*

√ \_\_\_ 2*π σδ*

tion of stress random variable and strength random variable, respectively; and *us*

expectation of stress random variable and strength random variable, respectively.

where *S*, *<sup>δ</sup>* are stress and strength random variables, respectively; *<sup>σ</sup><sup>s</sup>*

*4.1.2. Stress-strength interference theory based on loads*

**Figure 13.** Fault probability density function.

*<sup>f</sup>*(*S*) <sup>=</sup> \_\_\_\_ <sup>1</sup>

*<sup>g</sup>*(*δ*) <sup>=</sup> \_\_\_\_ <sup>1</sup>

equations:

where *t* is time, *t* > 0, *β*<sup>1</sup> · *β*<sup>2</sup> > 1, *β*<sup>1</sup> · *β*<sup>2</sup> are shape parameters, *β*<sup>1</sup> , *β*<sup>2</sup> are scale parameters and *<sup>λ</sup>* is the mixing parameter, *t* <sup>0</sup> = 0, *η*<sup>1</sup> = 10, *η*<sup>2</sup> = 100, *β*<sup>1</sup> = 5, *β*<sup>2</sup> = 5.

**Figure 13** shows the fault probability density function. The results in **Figure 13** show that there are two peaks which represent early failures and wear out failures, respectively, and the failure

**Figure 12.** Bathtub curve of failure rates for repairable system.

**Figure 13.** Fault probability density function.

rates are obvious higher at these two peaks. When the weighting factor equals 0.1, 0.2 and 0.3, the differences just happen at the peaks. Therefore, a proper weighting factor should be selected to meet the failure rate changes of wind turbines in different working environments. **Figure 14** shows the change of failure rates over time. The results in **Figure 14** show that a wind turbine is at running-in stage where its wear is large, and the failure rates are fluctuating and then stable. The failure rates of wind turbines will become higher and higher at the wear-out stage. Failure rate function curves with different weighting factors just show a difference at peak values, which has something to do with capacity and conditions. **Figure 15** shows the reliability function diagram which has three phases. The reliability in Phase I decreases sharply because newly installed wind turbines need to adapt to the environment. The reliability in Phase II is stable. There is a sharp decline in Phase III, which represents that the wind turbine has entered into wear-out failures, and its failure rates are high. Above all, it can be found that the bathtub curve can simulate the failure rate change among its service life as well.

#### *4.1.2. Stress-strength interference theory based on loads*

**Figure 12.** Bathtub curve of failure rates for repairable system.

increasing hazard rates is written as follows [11]:

178 Stability Control and Reliable Performance of Wind Turbines

**Figure 11.** The requirements for developing the high-reliability systems.

*F*(*t*) = *λ*[1 − exp(−(

where *t* is time, *t* > 0, *β*<sup>1</sup> · *β*<sup>2</sup> > 1, *β*<sup>1</sup> · *β*<sup>2</sup>

is the mixing parameter, *t*

distribution, gamma distribution and lognormal distribution are three commonly used methods in wind turbine reliability analysis. A method with mixtures of Weibull distribution with

)] + (1 − *λ*)

<sup>0</sup> = 0, *η*<sup>1</sup> = 10, *η*<sup>2</sup> = 100, *β*<sup>1</sup> = 5, *β*<sup>2</sup> = 5. **Figure 13** shows the fault probability density function. The results in **Figure 13** show that there are two peaks which represent early failures and wear out failures, respectively, and the failure

are shape parameters, *β*<sup>1</sup>

[1 − exp(−(

*<sup>t</sup>* <sup>−</sup> *<sup>t</sup>* \_\_\_0 *η*<sup>2</sup> ) *β*2

)] (1)

, *β*<sup>2</sup> are scale parameters and *<sup>λ</sup>*

*<sup>t</sup>* <sup>−</sup> *<sup>t</sup>* \_\_\_0 *η*<sup>1</sup> ) *β*1

> Random loads and fatigue strength of wind turbine subassemblies follow a normal distribution. The probability density function of stress and strength is expressed by the following equations:

$$f(\mathbf{S}) = \frac{1}{\sqrt{2\pi}} \exp\left(-\frac{1}{2} \left(\frac{\mathbf{S} - \boldsymbol{u}\_{\ast}}{\sigma\_{\ast}}\right)^{2}\right) \tag{2}$$

$$\mathbf{g}(\delta) = \frac{1}{\sqrt{2\pi}} \exp\left(-\frac{1}{2} \left(\frac{\delta - u\_s}{\sigma\_\delta}\right)^2\right) \tag{3}$$

where *S*, *<sup>δ</sup>* are stress and strength random variables, respectively; *<sup>σ</sup><sup>s</sup>* , *σδ* are the standard deviation of stress random variable and strength random variable, respectively; and *us* , *u<sup>δ</sup>* are the expectation of stress random variable and strength random variable, respectively.

**Figure 16** is a common practice to represent stress-strength interference. The figure shows the probability density function of stress and strength and their interference (overlap) over time.

**Figure 14.** Failure rate function.

The interference is failure probability. The larger the area of the interference, the higher is the failure probability. Moreover, the interference area will become larger and larger over time in service life. The reliability of the system is:

$$\text{Reliability} = 1 - \text{Interference} \tag{4}$$

A new random variable *z* can be introduced, which is defined by

$$z = \delta - \mathcal{S}\tag{5}$$

The dynamic reliability of gears can be calculated by the reliability calculation equation with the mean and standard deviation of gear fatigue stress and fatigue strength. **Figure 17** shows the reliability of high-speed stage gear. The figure shows that the reliability declines heavily before

Reliability Analysis of Wind Turbines http://dx.doi.org/10.5772/intechopen.74859 181

High-performance gearboxes with large transmission ratios are available, which have been used in many areas. However, wind turbine gearboxes have more challenging and a greater

20,000 h.

**4.2. Current gearbox reliability analysis**

**Figure 17.** Reliability of high-speed stage gear.

**Figure 16.** Graphical representation of stress-strength interference.

Then, the random variable *z* also follows normal distribution, so the reliability of stressstrength interference theory model is:

$$R = \int\_0^\omega \frac{1}{\sqrt{2\pi}} \exp\left(-\frac{(z - u\_\circ)^2}{2\sigma\_\circ^2}\right) dz \tag{6}$$

where *<sup>σ</sup><sup>z</sup>* is the standard deviation of *z* and *uz* is the expectation of *z.*

**Figure 15.** Reliability function.

**Figure 16.** Graphical representation of stress-strength interference.

The dynamic reliability of gears can be calculated by the reliability calculation equation with the mean and standard deviation of gear fatigue stress and fatigue strength. **Figure 17** shows the reliability of high-speed stage gear. The figure shows that the reliability declines heavily before 20,000 h.

#### **4.2. Current gearbox reliability analysis**

The interference is failure probability. The larger the area of the interference, the higher is the failure probability. Moreover, the interference area will become larger and larger over time in

Reliability = 1 − Interference (4)

*z* = *δ* − *S* (5)

Then, the random variable *z* also follows normal distribution, so the reliability of stress-

exp(−

(*z* − *uz*) 2 \_\_\_\_\_\_ 2 *σ<sup>z</sup>*

is the expectation of *z.*

<sup>2</sup> )*dz* (6)

service life. The reliability of the system is:

180 Stability Control and Reliable Performance of Wind Turbines

**Figure 14.** Failure rate function.

strength interference theory model is:

*R* = ∫

is the standard deviation of *z* and *uz*

where *<sup>σ</sup><sup>z</sup>*

**Figure 15.** Reliability function.

A new random variable *z* can be introduced, which is defined by

0 <sup>∞</sup> \_\_\_\_ 1 √ \_\_\_ 2*π σ<sup>z</sup>*

High-performance gearboxes with large transmission ratios are available, which have been used in many areas. However, wind turbine gearboxes have more challenging and a greater

**Figure 17.** Reliability of high-speed stage gear.

number of technical requirements, like high reliability, safety and up to 25 years of operating life. Due to its complex structure and variable conditions, gearboxes have been and still are a source of failure and so have been paid more attention in the industry. Nowadays, the capacity of the multistage planetary wind turbines that are installed is up to the megawatt power classes. Hence, it is important to point out that the reliability of wind turbine gearboxes has great influences on wind turbines.

The current reliability research methods of the wind turbine gearbox include finite element method (FEM), lumped mass method (LMM), statistical methods based on database, experiment method (EM), simulation with software, and so on. Statistical methods based on database are most commonly used.

The researchers in national renewable energy laboratory (NREL) have done much milestone work. Generator and gearbox models have been produced in Matrix Laboratory (MATLAB) and NREL's Fatigue, Aerodynamics, Structures and Turbulence (FAST) [12]. NREL proposed that it is essential to bring all the parties involved in the gearbox-design process together to achieve the common goal of improving the reliability and lifetime of gearboxes [13]. The effects of different constant rotor torque and moment conditions and intentional generator misalignment on gearbox motion and high-speed shaft loads are examined [14].

The condition monitoring and fault diagnosis based on condition monitoring system (CMS) and supervisory control and data acquisition (SCADA) are also popular in wind turbine industry. The whole condition monitoring and assessment process within the system boundary include hard platform, condition monitoring and administrators of wind farms. Hard platform for wind farms includes the wind turbines, meteorological stations and monitoring data

via CMS and SCADA. Condition monitoring can be divided into remote monitoring system (RMS) and field management information system (FMIS); where, the FMIS includes data port, field engineer, uninterruptible power system (UPS) and human-machine interaction (HMI), and the RMS includes remote replication and a data center. The boundaries of the condition monitoring and assessment process for the wind turbine gearboxes are shown in **Figure 18**.

Reliability Analysis of Wind Turbines http://dx.doi.org/10.5772/intechopen.74859 183

The condition monitoring systems of the CMS and SCADA can reflect the real-time running status of the wind turbine gearbox. The framework of the indices and project layers for the assessment of the wind turbine gearbox are established based on the CMS and SCADA. The goal layer can be classified into five project layers, and simultaneously, each project layer consists of the monitoring indices. For example, the goal layer can be divided into main shaft bearing (MSB), planetary stage (PS), low-speed stage (LSS), intermediate-speed stage (IMS), high-speed stage (HSS) and external factors (EF). The monitoring objects mainly consist of the nacelle, main shaft, bearing, cooling system, lubrication system and other related variables.

In order to solve reliability problems in wind power industry, scholars all over the world proposed many methods. But these reliability analysis methods mainly focus on gear transmission systems of wind turbines and ignore the influences of other systems. The effects of the reliability analysis are limited if the system is simplified and seen as a series or parallel connection. Based on the abovementioned analysis and field research, some key conclusions

**Figure 19** shows the location distribution of the sensors.

**5. Conclusions**

**Figure 19.** The distributions of the sensors.

are proposed:

**Figure 18.** Flowchart of the condition monitoring and assessment process.

**Figure 19.** The distributions of the sensors.

via CMS and SCADA. Condition monitoring can be divided into remote monitoring system (RMS) and field management information system (FMIS); where, the FMIS includes data port, field engineer, uninterruptible power system (UPS) and human-machine interaction (HMI), and the RMS includes remote replication and a data center. The boundaries of the condition monitoring and assessment process for the wind turbine gearboxes are shown in **Figure 18**.

The condition monitoring systems of the CMS and SCADA can reflect the real-time running status of the wind turbine gearbox. The framework of the indices and project layers for the assessment of the wind turbine gearbox are established based on the CMS and SCADA. The goal layer can be classified into five project layers, and simultaneously, each project layer consists of the monitoring indices. For example, the goal layer can be divided into main shaft bearing (MSB), planetary stage (PS), low-speed stage (LSS), intermediate-speed stage (IMS), high-speed stage (HSS) and external factors (EF). The monitoring objects mainly consist of the nacelle, main shaft, bearing, cooling system, lubrication system and other related variables. **Figure 19** shows the location distribution of the sensors.
