*3.2.4 Power electronics interfacing system*

An interfacing power electronics (IPE) system in a doubly fed induction generator-based WT consists of a back-to-back pulse width modulated (PWM) converter as shown in **Figure 7**. The components in the IPE system are diodes, IGBT switches, and a DC bus capacitor. The reliability model of such a system can be developed based on the relationship between the lifetime and failure rate of the components in the system. These are determined considering the junction temperature as a covariate. The junction temperature,*Tj*, of a semiconductor device can be calculated as [34]

$$T\_j = T\_a + P\_l R\_{ja} \tag{21}$$

*Pcl,d* <sup>¼</sup> <sup>1</sup>

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

*Ptl,d* <sup>¼</sup> *<sup>n</sup>* <sup>1</sup>

where:

<sup>8</sup> � *<sup>M</sup>*

*Microgrid System Reliability*

<sup>3</sup>*<sup>π</sup>* cos *<sup>φ</sup>* � �*RdI*

• *fs* is the switching frequency.

respectively.

be expressed as [37]

*Ptl,IGBT* <sup>¼</sup> *<sup>n</sup>* <sup>1</sup>

where:

**179**

8 þ *M* <sup>3</sup>*<sup>π</sup>* cos *<sup>φ</sup>* � �*RceI*

respectively.

*Pcl,IGBT* <sup>¼</sup> <sup>1</sup>

<sup>8</sup> � *<sup>M</sup>*

2 *mo* <sup>þ</sup> *<sup>n</sup>* <sup>1</sup>

• *Imo* is maximum output current of the inverter.

• *n* is the number of semiconductor components.

• *φ* is the angle between voltage and current.

8 þ *M* <sup>3</sup>*<sup>π</sup>* cos *<sup>φ</sup>* � �*RceI*

*Psl,IGBT* <sup>¼</sup> <sup>1</sup>

2 *mo* <sup>þ</sup> *<sup>n</sup>* <sup>1</sup>

• *M* is the modulation index (0 ≤ *M* ≤ 1).

<sup>3</sup>*<sup>π</sup>* cos *<sup>φ</sup>* � �*RdI*

*Psl,d* <sup>¼</sup> <sup>1</sup>

for the total number of switches in the system can be expressed as

2 *mo* þ

Total power losses of diodes, *Ptl,d*, in the IPE system can be expressed as the sum of the conduction loss, *Pcl,d*, for the total number of diodes. The switching loss, *Psl,d*,

> <sup>8</sup> cos *<sup>φ</sup>* � �*VFOImo* <sup>þ</sup> *<sup>n</sup>* <sup>1</sup>

*π fs Esr*

<sup>2</sup>*<sup>π</sup>* � *<sup>M</sup>*

• *VFO* and *Rd* are the diode threshold voltage and resistance, respectively.

• *Eer* is the rated switching loss energy given for the commutation voltage.

• *Vref,d* and *Iref,d*, *Vdc*, and *Idc* are the actual commutation voltage and current,

The conduction loss, *Pcl,IGBT*, and switching loss *Psl,IGBT* of an IGBT switch can

*<sup>π</sup> fs Eon* <sup>þ</sup> *Eoff* � � *VdcImo*

Total power losses of switches, *Ptl,IGBT*, in the IPE system can be expressed as the sum of the conduction loss, *Pcl,IGBT*, for total number of diodes. The switching loss,

1 <sup>2</sup>*<sup>π</sup>* <sup>þ</sup> *<sup>M</sup>*

!

<sup>8</sup> cos *φ*

*Vref,IGBTIref,IGBT*

2 *mo* þ

*Psl,IGBT*, for the total number of switches in the system can be expressed as

• *VCEO* and *Rce* are the IGBT threshold voltage and on-state resistance,

2*π* þ *M* <sup>8</sup> cos *<sup>φ</sup>* � �*VCEOImo* <sup>þ</sup> *<sup>n</sup>* <sup>1</sup>

1 <sup>2</sup>*<sup>π</sup>* � *<sup>M</sup>*

*VdcImo Vref,dIref,d*

<sup>8</sup> cos *<sup>φ</sup>*

� �*VFOImo* (23)

*π fs Esr*

*VdcImo Vref,dIref,d*

*VCEOImo* (26)

*<sup>π</sup> fs Eon* <sup>þ</sup> *Eoff* � � *VdcImo*

(27)

*Vref,IGBTIref,IGBT* (28)

(24)

(25)

where *Pl,Ta*, and *Rja* are the power loss of a component, the ambient temperature, and the junction resistance, respectively. A reliability model of a power conditioning system for a small (1.5 kW) wind energy conversion system is developed by considering power loss only at a rated wind speed operating condition.

However, it is to be noted that power losses in the semiconductor components vary according to the wind speed variation at the wind turbine input. Thus, a power loss variation in the semiconductor component is important to be considered as a stress factor in order to calculate the lifetime of the components instead of using power loss quantity for a single operating condition. Hence, Eq. (21) can be expressed as

$$T\_{j\_i} = T\_a + P\_{l\_i} R\_{ja} \tag{22}$$

where:


In an IPE system, there are two types of semiconductor components, namely, diode and IGBT switches. Two types of power losses such as conduction losses and switching losses occur in such components. The conduction loss, *Pcl,d*, and the switching loss, *Psl,d*, of a diode can be expressed as [35, 36]

**Figure 7.** *Interfacing power electronics system of a doubly fed induction generator-based wind turbine system.*

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

$$P\_{cl,d} = \left(\frac{1}{8} - \frac{M}{3\pi}\cos\varphi\right) R\_d I\_{mo}^2 + \left(\frac{1}{2\pi} - \frac{M}{8}\cos\varphi\right) V\_{FO} I\_{mo} \tag{23}$$

$$P\_{sl,d} = \frac{1}{\pi} f\_s E\_{sr} \frac{V\_{dc} I\_{mo}}{V\_{ref,d} I\_{ref,d}} \tag{24}$$

Total power losses of diodes, *Ptl,d*, in the IPE system can be expressed as the sum of the conduction loss, *Pcl,d*, for the total number of diodes. The switching loss, *Psl,d*, for the total number of switches in the system can be expressed as

$$P\_{t\!I,d} = n\left(\frac{1}{8} - \frac{M}{3\pi}\cos\varphi\right)R\_d I\_{mo}^2 + n\left(\frac{1}{2\pi} - \frac{M}{8}\cos\varphi\right)V\_{FO}I\_{mo} + n\frac{1}{\pi}f\_{s}E\_{r}\frac{V\_{dc}I\_{mo}}{V\_{r\!f,d}I\_{r\!f,d}}\tag{25}$$

where:

where *Pg,I* is the generator power at the *ith* wind speed in between cut-in and

An interfacing power electronics (IPE) system in a doubly fed induction generator-based WT consists of a back-to-back pulse width modulated (PWM) converter as shown in **Figure 7**. The components in the IPE system are diodes, IGBT switches, and a DC bus capacitor. The reliability model of such a system can be developed based on the relationship between the lifetime and failure rate of the components in the system. These are determined considering the junction temperature as a covariate. The junction temperature,*Tj*, of a semiconductor device can be

where *Pl,Ta*, and *Rja* are the power loss of a component, the ambient temperature, and the junction resistance, respectively. A reliability model of a power conditioning system for a small (1.5 kW) wind energy conversion system is developed

However, it is to be noted that power losses in the semiconductor components vary according to the wind speed variation at the wind turbine input. Thus, a power loss variation in the semiconductor component is important to be considered as a stress factor in order to calculate the lifetime of the components instead of using power loss quantity for a single operating condition. Hence, Eq. (21) can be

*<sup>i</sup>* ¼ *Ta* þ *Pli*

In an IPE system, there are two types of semiconductor components, namely, diode and IGBT switches. Two types of power losses such as conduction losses and switching losses occur in such components. The conduction loss, *Pcl,d*, and the

by considering power loss only at a rated wind speed operating condition.

*Tj*

• Junction resistance is assumed to be constant for all wind speed.

*Interfacing power electronics system of a doubly fed induction generator-based wind turbine system.*

• *Pli* is the power loss of a component at the *i*

*<sup>i</sup>* is the component junction temperature at the *i*

switching loss, *Psl,d*, of a diode can be expressed as [35, 36]

*Tj* ¼ *Ta* þ *PlRja* (21)

*Rja* (22)

*th* wind speed

*th* wind speed.

cut-out regions.

calculated as [34]

expressed as

where:

• *Tj*

**Figure 7.**

**178**

*3.2.4 Power electronics interfacing system*

*Reliability and Maintenance - An Overview of Cases*


The conduction loss, *Pcl,IGBT*, and switching loss *Psl,IGBT* of an IGBT switch can be expressed as [37]

$$P\_{d,IGBT} = \left(\frac{\mathbf{1}}{8} + \frac{M}{3\pi} \cos \rho\right) R\_{\epsilon\epsilon} I\_{mo}^2 + \left(\frac{\mathbf{1}}{2\pi + \frac{M}{8} \cos \rho}\right) V\_{CEO} I\_{mo} \tag{26}$$

$$P\_{sl,IGBT} = \frac{1}{\pi} f\_s \left( E\_{on} + E\_{off} \right) \frac{V\_{dc} I\_{mo}}{V\_{ref,IGBT} I\_{ref,IGBT}} \tag{27}$$

Total power losses of switches, *Ptl,IGBT*, in the IPE system can be expressed as the sum of the conduction loss, *Pcl,IGBT*, for total number of diodes. The switching loss, *Psl,IGBT*, for the total number of switches in the system can be expressed as

$$P\_{\rm tI,IGBT} = n\left(\frac{1}{8} + \frac{M}{3\pi}\cos\rho\right)R\_{\rm ef}I\_{\rm mo}^2 + n\left(\frac{1}{2\pi} + \frac{M}{8}\cos\rho\right)V\_{\rm CEO}I\_{\rm mo} + n\frac{1}{\pi}f\_i\left(E\_{\rm ou} + E\_{\rm eff}\right)\frac{V\_{\rm df}I\_{\rm mo}}{V\_{\rm ref,IGBT}I\_{\rm ref,IGBT}}\tag{28}$$

where:

• *VCEO* and *Rce* are the IGBT threshold voltage and on-state resistance, respectively.


The lifetime, *L*(*Tji*), of a component for *ith* wind speed can be expressed as

$$L\left(T\_{\vec{\mu}}\right) = L\_o \exp\left(-B\Delta T\_{\vec{\mu}}\right) \tag{29}$$

where:

*Microgrid System Reliability*

• *θIPEC* and *βIPEC* are defined as the shape parameter and the scale factor for the

In WPGS, all nine WTs are connected in parallel with identical configuration.

**Figure 4** shows the simplified RBD of the microgrid system, where all DG units are connected in parallel. In addition, SU is considered as a power-generating unit since it will supply power to the load during an isolated mode of operation of the microgrid. Assuming the reliability of the HGU as *RHGU* and utility grid as *RUG*, the

However, the microgrid system operates in three different modes, which are shown in **Figure 5**. The MSR can also be modeled according to their operating modes. **Figure 5a** shows the grid-connected mode of operation where all DG or generation units are connected with the utility grid. Thus, the MSR pertaining to the grid-connected mode of operation, *RMSRM*<sup>1</sup> , can be expressed by the similar model

**Figure 5b** represents an isolated microgrid system with WPGS. In addition, the storage unit is not working as a generation unit in this mode of operation. Thus, the

Furthermore, **Figure 5c** shows an isolated microgrid without WPGS mode where the SU operates as a generation unit. Assuming that the reliability of the SU is

MSR during isolated operation with WPGS, *RMSRM*<sup>2</sup> , can be defined as

*RSU*, hence, the MSR during this mode, *RMSRM*<sup>3</sup> , can be written as

*RMSR* <sup>¼</sup> <sup>1</sup> � ð Þ <sup>1</sup> � *Rwts <sup>N</sup>*ð Þ <sup>1</sup> � *RHGU* ð Þ <sup>1</sup> � *RUG* h i (36)

*RMSRM*<sup>1</sup> <sup>¼</sup> <sup>1</sup> � ð Þ <sup>1</sup> � *Rwts <sup>N</sup>*ð Þ <sup>1</sup> � *RHGU* ð Þ <sup>1</sup> � *RUG* h i (37)

*RMSRM*<sup>2</sup> <sup>¼</sup> <sup>1</sup> � ð Þ <sup>1</sup> � *Rwts <sup>N</sup>*ð Þ <sup>1</sup> � *RHGU* h i (38)

*RMSRM*<sup>3</sup> ¼ ½ � 1 � ð Þ 1 � *RHGU* ð Þ 1 � *RHGU* (39)

*Rwts* ¼ *Rtp* � *Rgb* � *Rg* � *RIPE* (34)

*RWPGS* <sup>¼</sup> <sup>1</sup> � ð Þ <sup>1</sup> � *Rwts <sup>N</sup>* h i (35)

• *τciwC* and *τcowC* are failure rates at cut-in and cut-out wind speeds for a

The reliability of a WT system, *Rwts*, can now be expressed as

Hence, the reliability of the WPGS, *RWPGS*, can be expressed as

where N is the number of WT system in a WPGS.

overall microgrid system reliability, *RMSR*, can be modeled as

failure rate distribution of a component.

component, respectively.

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

**3.3 Microgrid reliability model**

presented in Eq. (36). Therefore,

**181**

where:


$$
\Delta T\_{ji} = \frac{1}{T\_a} - \frac{1}{T\_{ji}} \tag{30}
$$

The failure rate of a component for *ith* wind speed can be defined as

$$\pi\_i = \frac{1}{L\left(T\_{ji}\right)}\tag{31}$$

Using Eq. (31), a distribution of failure rates for a set of wind speed data for a semiconductor component can be generated. The components in the IPE system are considered as an in-series connection from the reliability point of view, because the IPE system fails, if any one of the components breaks down in the IPE system. Thus, the failure rates for different components are added to determine the failure rate of the IPE system for the *ith* wind speed. Hence, a distribution of failure rates for the IPE system can be generated for a series of wind speed data.

A least-squares technique is then used to determine the distribution parameters. By knowing the distribution parameters, the reliability of the IPE system, *RIPE*, can be modeled as

$$R\_{IPE} = \exp\left[-\left(\frac{\tau\_{civ}}{\theta\_{IPE}}\right)^{\beta\_{IPE}}\right] - \exp\left[\left(\frac{\tau\_{cov}}{\theta\_{IPE}}\right)^{\beta\_{IPE}}\right] \tag{32}$$

Hence:


The reliability of a component in IPE system, *RIPEC*, can be expressed as

$$R\_{IPE\_C} = \exp\left[-\left(\frac{\tau\_{ciw\_C}}{\theta\_{IPE\_C}}\right)^{\beta\_{IPE\_C}}\right] - \exp\left[\left(\frac{\tau\_{cow\_C}}{\theta\_{IPE\_C}}\right)^{\beta\_{IPE\_C}}\right] \tag{33}$$

where:

• The reference commutation voltage and current are *Vref,IGBT* and *Iref,IGBT*.

The lifetime, *L*(*Tji*), of a component for *ith* wind speed can be expressed as

� � <sup>¼</sup> *Lo* exp �*B*Δ*Tji*

*<sup>K</sup>* , where *<sup>K</sup>* is the Boltzmann's constant (=8.6 � <sup>10</sup>�<sup>5</sup> eV/K) and *EA* is the

• *ΔTji* is the variation in junction temperature for the *ith* wind speed and can be

• *Lo* is the quantitative normal life measurement (assumed to be 10<sup>6</sup>

activation energy (= 0.2 eV) for typical semiconductor components.

<sup>Δ</sup>*Tji* <sup>¼</sup> <sup>1</sup> *Ta* � 1 *Tji*

The failure rate of a component for *ith* wind speed can be defined as

IPE system can be generated for a series of wind speed data.

*RIPE* <sup>¼</sup> exp � *<sup>τ</sup>ciw*

failure rate distribution of the IPE system.

*RIPEC* <sup>¼</sup> exp � *<sup>τ</sup>ciwC*

*θIPE* � �*<sup>β</sup>IPE* " #

• *θIPE* and *βIPE* are defined as the shape parameter and the scale factor for the

• *τciw* and *τcow* are failure rates of IPE system at cut-in and cut-out wind speeds,

The reliability of a component in IPE system, *RIPEC*, can be expressed as

*θIPEC* � �*<sup>β</sup>IPEC* " #

*<sup>τ</sup><sup>i</sup>* <sup>¼</sup> <sup>1</sup> *L Tji*

Using Eq. (31), a distribution of failure rates for a set of wind speed data for a semiconductor component can be generated. The components in the IPE system are considered as an in-series connection from the reliability point of view, because the IPE system fails, if any one of the components breaks down in the IPE system. Thus, the failure rates for different components are added to determine the failure rate of the IPE system for the *ith* wind speed. Hence, a distribution of failure rates for the

A least-squares technique is then used to determine the distribution parameters. By knowing the distribution parameters, the reliability of the IPE system, *RIPE*, can

� exp *<sup>τ</sup>cow*

� exp *<sup>τ</sup>cowC*

*θIPEC* � �*<sup>β</sup>IPEC* " #

*θIPE* � �*<sup>β</sup>IPE* " #

� � (29)

� � (31)

).

(30)

(32)

(33)

• *Eon* and *Eoff* are the turn-on and turn-off energies of IGBT.

*L Tji*

• *Vdc* is the actual commutation voltage.

*Reliability and Maintenance - An Overview of Cases*

where:

• *B* = *EA*

be modeled as

Hence:

**180**

respectively.

expressed as


The reliability of a WT system, *Rwts*, can now be expressed as

$$R\_{wts} = R\_{tp} \times R\_{gb} \times R\_{\text{g}} \times R\_{IPE} \tag{34}$$

In WPGS, all nine WTs are connected in parallel with identical configuration. Hence, the reliability of the WPGS, *RWPGS*, can be expressed as

$$R\_{\rm WPGS} = \left[\mathbf{1} - (\mathbf{1} - R\_{\rm wts})^N\right] \tag{35}$$

where N is the number of WT system in a WPGS.

## **3.3 Microgrid reliability model**

**Figure 4** shows the simplified RBD of the microgrid system, where all DG units are connected in parallel. In addition, SU is considered as a power-generating unit since it will supply power to the load during an isolated mode of operation of the microgrid. Assuming the reliability of the HGU as *RHGU* and utility grid as *RUG*, the overall microgrid system reliability, *RMSR*, can be modeled as

$$R\_{\rm MSR} = \left[\mathbf{1} - (\mathbf{1} - R\_{\rm wts})^N (\mathbf{1} - R\_{\rm HGU}) (\mathbf{1} - R\_{\rm UG})\right] \tag{36}$$

However, the microgrid system operates in three different modes, which are shown in **Figure 5**. The MSR can also be modeled according to their operating modes. **Figure 5a** shows the grid-connected mode of operation where all DG or generation units are connected with the utility grid. Thus, the MSR pertaining to the grid-connected mode of operation, *RMSRM*<sup>1</sup> , can be expressed by the similar model presented in Eq. (36). Therefore,

$$R\_{\rm MSR\_{M1}} = \left[\mathbf{1} - (\mathbf{1} - R\_{wts})^N (\mathbf{1} - R\_{HGU}) (\mathbf{1} - R\_{UG})\right] \tag{37}$$

**Figure 5b** represents an isolated microgrid system with WPGS. In addition, the storage unit is not working as a generation unit in this mode of operation. Thus, the MSR during isolated operation with WPGS, *RMSRM*<sup>2</sup> , can be defined as

$$R\_{\rm MSR\_{M2}} = \left[\mathbf{1} - (\mathbf{1} - R\_{\rm uts})^N (\mathbf{1} - R\_{\rm HGU})\right] \tag{38}$$

Furthermore, **Figure 5c** shows an isolated microgrid without WPGS mode where the SU operates as a generation unit. Assuming that the reliability of the SU is *RSU*, hence, the MSR during this mode, *RMSRM*<sup>3</sup> , can be written as

$$R\_{\rm MSR\_M} = \left[\mathbf{1} - (\mathbf{1} - R\_{HGU})(\mathbf{1} - R\_{HGU})\right] \tag{39}$$
