**5. Simulation results**

The reliability model and its implementation procedure described in the preceding sections are performed to determine probability distribution parameters as well as the reliability of the various subsystems in the wind generation system for stochastically varying wind speed condition. Such reliability estimation is then utilized to determine MSR in various operating modes of the microgrid. The power generation wind speed region of the selected turbine is *vciw* = 4 m/s and *vcow* = 25 m/s. The reliability of HGU and utility grid are selected as 85%, since they are regarded as highly reliable power generation sources. The reliability of the storage unit is assumed to be the same as the IPE system (=0.8144), because these are commonly interfaced through power electronics inverter systems. One-year wind speed data is used for the field data modeling process. Assume that three WT systems can be connected to the isolated microgrid system due to the stability issue.

**Figure 10** shows the hourly wind speed field data collected over a 1-year period. Such data is utilized to identify the distribution using probability plot techniques. The probability plots of wind speed field data are shown in **Figure 11**, revealing that the probability of wind speed follows Weibull and Rayleigh distributions closely. However, the Weibull distribution follows the probability of wind speed closer than the Rayleigh distribution. Thus, the Weibull distribution is identified as the best-fit distribution for wind speed data in this study. In order to select Weibull distribution, a goodness-of-fit test is also carried out, and the probability density function of Weibull distribution is shown in **Figure 12**.

*βws* = 1.92, and the scale parameter *θws* = 13.1. These parameters are used to generate random wind speed data for reliability evaluation of different subsystems in a wind

The results of the reliability calculation for different subsystems in a wind generation system are presented in **Table 1**. The outcomes reveal that the resulting reliability of the wind turbine rotor is 0.9068, while the reliability of gearbox and generator are 0.9107 and 0.9266, respectively. However, the reliability of generating power for the IPE sub-system is only 0.8144. These findings indicate that the IPE sub-system in a variable-speed wind generator system is less reliable than the other subsystems. **Table 2** presents the reliability results of DG units such as WT system, WPGS, HGU, SU, and utility grid. The reliability of a WT system and a WPGS is calculated based on the model derived in this study; however, the reliability of HGU, SU, and utility grid is assumed based on their availability in operation. The overall reliability of a wind turbine system is 0.6232. Since nine WT systems are connected in parallel in the WPGS, the calculated reliability of WPGS is signifi-

The reliability estimation results of the microgrid system during various operational modes are presented in **Table 3**. The MSR during grid-connected mode is

turbine system.

**Figure 13.**

**Figure 11.**

**Figure 12.**

*Probability plots for distribution identification.*

*Microgrid System Reliability*

*DOI: http://dx.doi.org/10.5772/intechopen.86357*

*Probability density function of wind speed data.*

*Least-squares plot for parameter estimation.*

cantly high.

**185**

A least-squares method is performed to estimate the Weibull distribution parameter, which is shown in **Figure 13**. The shape parameter for wind speed

**Figure 10.** *Wind speed field data.*

• Estimating parameter of failure rate distribution of IPE system

• MSR calculation using Eqs. (36)–(39) for various operational modes

The reliability model and its implementation procedure described in the preceding sections are performed to determine probability distribution parameters as well as the reliability of the various subsystems in the wind generation system for stochastically varying wind speed condition. Such reliability estimation is then utilized to determine MSR in various operating modes of the microgrid. The power generation wind speed region of the selected turbine is *vciw* = 4 m/s and *vcow* = 25 m/s. The reliability of HGU and utility grid are selected as 85%, since they are regarded as highly reliable power generation sources. The reliability of the storage unit is assumed to be the same as the IPE system (=0.8144), because these are commonly interfaced through power electronics inverter systems. One-year wind speed data is used for the field data modeling process. Assume that three WT systems can be connected to the isolated microgrid system due to the stability issue. **Figure 10** shows the hourly wind speed field data collected over a 1-year period. Such data is utilized to identify the distribution using probability plot techniques. The probability plots of wind speed field data are shown in **Figure 11**, revealing that the probability of wind speed follows Weibull and Rayleigh distributions closely. However, the Weibull distribution follows the probability of wind speed closer than the Rayleigh distribution. Thus, the Weibull distribution is identified as the best-fit distribution for wind speed data in this study. In order to select Weibull distribution, a goodness-of-fit test is also carried out, and the probability density function

A least-squares method is performed to estimate the Weibull distribution parameter, which is shown in **Figure 13**. The shape parameter for wind speed

• Reliability calculation of a WT system using Eq. (34)

• Determining reliability of WPGS using Eq. (35)

• Calculating reliability using Eq. (32)

*Reliability and Maintenance - An Overview of Cases*

• Assuming reliability for HGU and SU

Step 7: Reliability of microgrid system

of Weibull distribution is shown in **Figure 12**.

**Figure 10.**

**184**

*Wind speed field data.*

**5. Simulation results**

Step 6: Reliability of DG units

**Figure 11.** *Probability plots for distribution identification.*

**Figure 12.** *Probability density function of wind speed data.*

**Figure 13.** *Least-squares plot for parameter estimation.*

*βws* = 1.92, and the scale parameter *θws* = 13.1. These parameters are used to generate random wind speed data for reliability evaluation of different subsystems in a wind turbine system.

The results of the reliability calculation for different subsystems in a wind generation system are presented in **Table 1**. The outcomes reveal that the resulting reliability of the wind turbine rotor is 0.9068, while the reliability of gearbox and generator are 0.9107 and 0.9266, respectively. However, the reliability of generating power for the IPE sub-system is only 0.8144. These findings indicate that the IPE sub-system in a variable-speed wind generator system is less reliable than the other subsystems. **Table 2** presents the reliability results of DG units such as WT system, WPGS, HGU, SU, and utility grid. The reliability of a WT system and a WPGS is calculated based on the model derived in this study; however, the reliability of HGU, SU, and utility grid is assumed based on their availability in operation. The overall reliability of a wind turbine system is 0.6232. Since nine WT systems are connected in parallel in the WPGS, the calculated reliability of WPGS is significantly high.

The reliability estimation results of the microgrid system during various operational modes are presented in **Table 3**. The MSR during grid-connected mode is
