**3. Power electronic converters for wind turbine system**

A permanent magnet generator has no excitation control and output voltage is proportional to the rotor speed. Therefore, in control of wind turbine, the rotor speed is obtained via the output voltage measurement. The earliest and still most widely used power electronic cir‐ cuit for this application uses an AC/DC/AC technology in which the variable frequency, var‐ iable voltage from the generator is first rectified to DC and then converted to AC and fed to the grid or load. The continuous variation of wind speed will result in a DC link voltage varying in an uncontrolled manner. In order to get variable speed operation and stable dc bus voltage, a boost dc-dc converter could be inserted in the dc link [17]. As there is active power flows unidirectionally from the PMSG to the dc link through a power converter, only a simple diode rectifier can be applied to the generator side converter in order to obtain a cost-efficient solution [4,5].

#### **3.1. AC/DC/AC converters for power electronic interface**

#### *3.1.1. Three-Phase bridge rectifier*

A three-phase bridge rectifier is commonly used in wind power applications. This is a fullwave rectifier and gives six-pulse ripples on the output voltage. Each one of six diodes con‐ ducts for 120º. The pair of diodes which are connected between that pair of supply lines having the highest amount of instantaneous line-to-line voltage will conduct [18]. The threephase bridge rectifier is shown in Figure 3.

**Figure 3.** Three-phase bridge rectifier.

If *Vm* is the peak value of the phase voltage, then the average and rms output voltage is cal‐ culate with

$$V\_{dc} = \frac{2}{2\pi \times 6} \zeta\_0^{\pi/6} \sqrt{3} \text{ V}\_m \cos \omega t \text{ } d(\omega t) = \frac{3\sqrt{3}}{\pi} V\_m = 1.654 V\_m \tag{1}$$

$$V\_{rms} = \left[\frac{2}{2\pi/6} \xi\_0^{\pi/6} \text{\textdegree V}\_m \text{-}^2 \text{cos}^2 \text{ } \omega t \text{ } d \text{ (}\omega t\text{)}\right]^{1/2} = \left(\frac{3}{2} + \frac{9\sqrt{5}}{4\pi}\right)^{1/2} V\_m = 1.6554 V\_m \tag{2}$$

#### *3.1.2. DC/DC converters*

Dc converters can be used as switching-mode regulators to convert to dc voltage, normally unregulated, to a regulated dc output voltage. The regulation is normally achieved by PWM at a fixed frequency and the switching device is normally IGBT or MOSFET. The following range of DC-to-DC converters, in which the input and output share a common return line, are often referred to as "three-terminal switching regulators" [19].

The switching regulators will often replace linear regulators when higher efficiencies are re‐ quired. They are characterized by the use of a choke rather than a transformer between the input and output lines. The switching regulator differs from its linear counterpart in that switching rather than linear techniques are used for regulation, resulting in higher efficien‐ cies and wider voltage ranges. Further, unlike the linear regulator, in which the output volt‐ age must always be less than the supply. The switching regulator can provide outputs which are equal to, lower than, higher than, or of reversed polarity to the input. There are four basic topologies of switching regulators:

**1.** *Buck regulators:* In buck regulators, the output voltage will be of the same polarity but always lower than the input voltage. One supply line must be common to both input and output. This may be either the positive or negative line, depending on the regulator design.


## *3.1.2.1. Buck regulators*

**Figure 3.** Three-phase bridge rectifier.

*Vrms* <sup>=</sup> <sup>2</sup>

*3.1.2. DC/DC converters*

design.

*Vdc* <sup>=</sup> <sup>2</sup> <sup>2</sup>*<sup>π</sup>* / 6 *∫* 0

<sup>2</sup>*<sup>π</sup>* / 6 *∫* 0 *<sup>π</sup>*/63 *Vm*

four basic topologies of switching regulators:

culate with

310 Advances in Wind Power

If *Vm* is the peak value of the phase voltage, then the average and rms output voltage is cal‐

Dc converters can be used as switching-mode regulators to convert to dc voltage, normally unregulated, to a regulated dc output voltage. The regulation is normally achieved by PWM at a fixed frequency and the switching device is normally IGBT or MOSFET. The following range of DC-to-DC converters, in which the input and output share a common return line,

The switching regulators will often replace linear regulators when higher efficiencies are re‐ quired. They are characterized by the use of a choke rather than a transformer between the input and output lines. The switching regulator differs from its linear counterpart in that switching rather than linear techniques are used for regulation, resulting in higher efficien‐ cies and wider voltage ranges. Further, unlike the linear regulator, in which the output volt‐ age must always be less than the supply. The switching regulator can provide outputs which are equal to, lower than, higher than, or of reversed polarity to the input. There are

**1.** *Buck regulators:* In buck regulators, the output voltage will be of the same polarity but always lower than the input voltage. One supply line must be common to both input and output. This may be either the positive or negative line, depending on the regulator

<sup>2</sup> + 9 3 <sup>4</sup>*<sup>π</sup>* ) 1/2

*<sup>π</sup> Vm* =1.654*Vm* (1)

*Vm* =1.6554*Vm* (2)

*<sup>π</sup>*/6 <sup>3</sup>*Vm*cos *<sup>ω</sup><sup>t</sup> <sup>d</sup>*(*ωt*)= <sup>3</sup> <sup>3</sup>

2cos2 *<sup>ω</sup><sup>t</sup> <sup>d</sup>*(*ωt*) 1/2 =( <sup>3</sup>

are often referred to as "three-terminal switching regulators" [19].

The step-down dc-dc converter, commonly known as a buck converter, is shown in Figure 4. Its operation can be seen as similar to a mechanical flywheel and a one piston engine. The L-C filter, like the flywheel, stores energy between the power pulses of the driver. The input to the L-C filter (choke input filter) is the chopped input voltage. The L-C filter volt-time aver‐ ages this duty-cycle modulated input voltage waveform. The L-C filtering function can be approximated by

$$V\_{out} = V\_{in} \times \text{Duty cycle} \tag{3}$$

**Figure 4.** Basic circuit of a buck switching regulator

The output voltage is maintained by the controller by varying the duty cycle. The buck con‐ verter is also known as a step-down converter, since its output must be less than the input voltage [19,20].

The state of the converter in which the inductor current is never zero for any period of time is called the continuous conduction mode (CCM). It can be seen from the circuit that when the switch SW is commanded to the on state, the diode D is reverse-biased. When the switch SW is off, the diode conducts to support an uninterrupted current in the inductor [20].

Typical waveforms in the converter are shown in Figure 5 under the assumption that the in‐ ductor current is always positive.

**Figure 5.** The voltage and current waveforms for a buck converter

The operation of the buck regulator can be seen by breaking its operation into two periods (refer to Figure 5). When the switch is turned on, the input voltage is presented to the input of the L-C filter. The inductor current ramps linearly upward and is described as

$$\dot{\mathbf{i}}\_L \text{ (}\rho m\text{)} = \frac{(V\_{in} \cdot V\_{out})t\_{on}}{L\_{\odot}} + \dot{\mathbf{i}}\_{init} \tag{4}$$

The energy stored within the inductor during this period is

$$E\_{\text{stored}} = \frac{1}{2} \mathbf{L}\_{\odot} (\mathbf{i}\_{\text{peak}} - \mathbf{i}\_{\text{min}})^2 \tag{5}$$

When SW turns off, the inductor will try to maintain the forward current constant, and the input voltage to the inductor wants to fly below ground and the diode. The current in induc‐ tor will now continue to circulate in the same direction as before with diode and the load. However, since the voltage now impressed across inductor has reversed, the current in in‐ ductor will now decrease linearly to its original value during the "off" period. The current through the inductor is described during this period by

$$\mathbf{i}\_L \cdot \begin{pmatrix} \mathbf{0}f' \end{pmatrix} = \mathbf{i}\_{\text{peak}} \cdot \begin{array}{c} V\_{out}, t\_{\text{eff}} \\ \hline L\_{\odot} \end{array} \tag{6}$$

The current waveform, this time, is a negative linear ramp whose slope is -*Vout* / *L* . The dc output load current value falls between the peak and the minimum current values. In typi‐ cal applications, the peak inductor current is about 150 percent of the dc load current and the minimum current is about 50 percent [20].

*Condition for continuous inductor current and capacitor voltage:* The voltage across the inductor *L* is, in general

$$\mathbf{e}\_L = \mathbf{L} \begin{array}{c} \frac{di}{dt} \\ \end{array} \tag{7}$$

Assuming that the inductor current rises linearly from *Imin* to *I pk* in time *ton*.

$$t\_{on} = \frac{\Delta I \ L}{V\_{in} \cdot V\_{out}} \tag{8}$$

And the inductor currents falls linearly from *I pk* to *Imin* in time *toff* .

$$t\_{off} = \frac{\Delta I \ L}{V\_{out}} \tag{9}$$

The switching period *T* can be expressed as

The output voltage is maintained by the controller by varying the duty cycle. The buck con‐ verter is also known as a step-down converter, since its output must be less than the input

The state of the converter in which the inductor current is never zero for any period of time is called the continuous conduction mode (CCM). It can be seen from the circuit that when the switch SW is commanded to the on state, the diode D is reverse-biased. When the switch SW is off, the diode conducts to support an uninterrupted current in the inductor [20].

Typical waveforms in the converter are shown in Figure 5 under the assumption that the in‐

The operation of the buck regulator can be seen by breaking its operation into two periods (refer to Figure 5). When the switch is turned on, the input voltage is presented to the input

*<sup>L</sup> <sup>O</sup>* + *i*

*L <sup>O</sup>*(*ipeak* - *i*

*init* (4)

*min*)2 (5)

of the L-C filter. The inductor current ramps linearly upward and is described as

*iL* (*on*)= (*Vin* - *Vout*)*ton*

2

voltage [19,20].

312 Advances in Wind Power

ductor current is always positive.

**Figure 5.** The voltage and current waveforms for a buck converter

The energy stored within the inductor during this period is

*Estored* <sup>=</sup><sup>1</sup>

$$T = t\_{out} + t\_{off} = \frac{\Delta I \parallel L}{V\_{in} \cdot V\_{out}} + \frac{\Delta I \parallel L}{V\_{out}} = \frac{\Delta I \parallel L \cdot V\_{in}}{V\_{out}(V\_{in} \cdot V\_{out})} \tag{10}$$

Which gives the peak-to-peak ripple current as

$$
\Delta I = \frac{V\_{out} \left(V\_{in} \cdot V\_{out}\right)}{fL \cdot V\_{in}} = \frac{V\_{in}k \left(1 \cdot k\right)}{fL} \tag{11}
$$

If *I <sup>L</sup>* is the average inductor current, the inductor ripple current ∆*I* =2*I <sup>L</sup>* . Using equations (3) and (11), we get

$$\frac{V\_{in}k(1\cdot k)}{fL} = 2I\_L \ = 2I\_a = \frac{2k\ V\_{in}}{R} \tag{12}$$

Which gives the critical value of the inductor *L <sup>c</sup>* as

$$L\_c = \frac{(1 \cdot k)R}{2f} \tag{13}$$

The capacitor voltage is expressed as

$$
\upsilon\_c = \frac{1}{C} \dot{f}\_c dt + \upsilon\_c \begin{pmatrix} t = 0 \\ \end{pmatrix} \tag{14}
$$

If we assume that the load ripple current ∆*i <sup>o</sup>* is very small, ∆*iL* = ∆*i <sup>c</sup>*. The average capacitor current, which flows into *ton* <sup>2</sup> + *toff* <sup>2</sup> <sup>=</sup> *<sup>T</sup>* <sup>2</sup> , is

$$I\_c = \frac{\Delta I}{4} \tag{15}$$

From (14) and (15) the peak-to-peak ripple voltage of the capacitor is

$$
\Delta V\_c = \upsilon\_c - \upsilon\_c \text{(t=0)} = \frac{1}{C} \int\_0^{T/2} \frac{\Delta I}{4} dt = \frac{\Delta I \ T}{8C} = \frac{\Delta I}{8\beta C} \tag{16}
$$

From (11) and (16), we get

$$
\Delta V\_{c} = \frac{V\_{out} \left(V\_{in} \cdot V\_{out}\right)}{8LC \int \,^{2}V\_{in}} = \frac{V\_{in} k \left(1 \cdot k\right)}{8LC \int \,^{2}}\tag{17}
$$

If *Vc* is the average capacitor voltage, the capacitor ripple voltage ∆*Vc* =2*Vout*. Using equa‐ tions (3) and (17), we get

$$\frac{\left(\frac{V\_{in}k\left(1\cdot k\right)}{8\,\mathrm{LC}\,f\,\mathrm{}^{2}}\right)}{8\,\mathrm{LC}\,f\,\mathrm{}^{2}} = \mathfrak{D}V\_{out} = \mathfrak{D}k\,V\_{in} \tag{18}$$

Which gives the critical value of the capacitor *Cc* as

$$C\_c = C = \frac{1 \cdot k}{16L \cdot f^2} \tag{19}$$

The advantages of forward-mode converters are: they exhibit lower output peak-topeak ripple voltages than do boost-mode converters, and they can provide much high‐ er levels of output power. Forward-mode converters can provide up to kilowatts of power [18-20].

#### *3.1.2.2. Boost regulators*

*Vink* (1 - *k* )

*vc* <sup>=</sup> <sup>1</sup> *<sup>C</sup> ∫i*

From (14) and (15) the peak-to-peak ripple voltage of the capacitor is

(*<sup>t</sup>* =0)= <sup>1</sup> *C ∫* 0 *T* /2 ∆ *I*

<sup>∆</sup>*Vc* <sup>=</sup> *Vout*(*Vin* - *Vout*) 8*LC f* <sup>2</sup> *Vin*

*Vink* (1 - *k* )

*Cc* <sup>=</sup>*<sup>C</sup>* <sup>=</sup> 1 - *<sup>k</sup>*

Which gives the critical value of the inductor *L <sup>c</sup>* as

The capacitor voltage is expressed as

current, which flows into

314 Advances in Wind Power

From (11) and (16), we get

tions (3) and (17), we get

power [18-20].

If we assume that the load ripple current ∆*i*

*ton* <sup>2</sup> + *toff* <sup>2</sup> <sup>=</sup> *<sup>T</sup>* <sup>2</sup> , is

∆*Vc* =*vc* - *vc*

Which gives the critical value of the capacitor *Cc* as

*fL* =2*<sup>I</sup> <sup>L</sup>* =2*Ia* <sup>=</sup> <sup>2</sup>*<sup>k</sup> Vin*

*<sup>L</sup> <sup>c</sup>* <sup>=</sup> (1 - *<sup>k</sup>* )*<sup>R</sup>*

*<sup>c</sup>dt* + *vc*

*Ic* <sup>=</sup> <sup>∆</sup> *<sup>I</sup>*

*<sup>R</sup>* (12)

<sup>2</sup> *<sup>f</sup>* (13)

(*t* =0) (14)

<sup>4</sup> (15)

*<sup>c</sup>*. The average capacitor

<sup>8</sup> *fC* (16)

<sup>8</sup>*LC f* 2 (17)

*<sup>o</sup>* is very small, ∆*iL* = ∆*i*

<sup>4</sup> *dt* <sup>=</sup> <sup>∆</sup> *<sup>I</sup> <sup>T</sup>*

<sup>=</sup> *Vink* (1 - *<sup>k</sup>* )

If *Vc* is the average capacitor voltage, the capacitor ripple voltage ∆*Vc* =2*Vout*. Using equa‐

The advantages of forward-mode converters are: they exhibit lower output peak-topeak ripple voltages than do boost-mode converters, and they can provide much high‐ er levels of output power. Forward-mode converters can provide up to kilowatts of

<sup>8</sup>*<sup>C</sup>* <sup>=</sup> <sup>∆</sup> *<sup>I</sup>*

<sup>8</sup>*LC f* <sup>2</sup> =2*Vout* =2*kVin* (18)

<sup>16</sup>*L f* 2 (19)

In a boost regulator the output voltage is greater than the input voltage. Figure 6 shows the general arrangement of the power sections of a boost regulator. As one can notice, the boostmode converter has the same parts as the forward-mode converter, but they have been rear‐ ranged. This new arrangement causes the converter to operate in a completely different fashion than the forward-mode converter [19, 20]. When SW turns on, the supply voltage will be impressed across the series inductor L. Under steady-state conditions, the current in L will increase linearly in the forward direction. Rectifier D will be reverse-biased and not conducting. At the same time, current will be flowing from the output capacitor Cout into the load. Hence, Cout will be discharging. Figures 7 and 8 show the current waveforms. The inductor's current wave form is also a positive linear ramp and is described by

$$\begin{array}{c} \text{in} \quad \text{(on)} = \frac{\text{V}\_{in}\text{t}\_{on}}{\text{L}} \end{array} \tag{20}$$

When SW turns off the current in L will continue to flow in the same direction, rectifier di‐ ode D will conduct, and the inductor current will be transferred to the output capacitor and load. Since the output voltage exceeds the supply voltage, L will now be reverse-biased, and the current in L will decay linearly back toward its original value during the "off" period of SW. The inductor current during the power switch off period is described by

*iL* (*off* )=*ipeak* (*on*) - (*Vout* - *Vin*)*toff <sup>L</sup>* (21)

As with the buck regulator, for steady-state conditions, the forward and reverse volt-sec‐ onds across L must equate. The output voltage *Vout* is controlled by the duty ratio of the power switch and the supply voltage, as follows

$$V\_{in} \times t\_{out} = \begin{pmatrix} V\_{out} \ \cdot \ V\_{in} \end{pmatrix} \times t\_{off} \quad \rightarrow \ V\_{out} = V\_{in} \times \begin{pmatrix} \frac{t\_{off} \ \cdot \ t\_{in}}{t\_{off}} \end{pmatrix} \stackrel{\frac{t\_{off} \cdot t\_{in}}{t\_{off}} \cdot \frac{1}{1 \cdot t}}{\longrightarrow} \quad V\_{out} = \frac{1}{1 \cdot k} V\_{in} \tag{22}$$

**Figure 6.** Basic circuit of a boost switching regulator

When the core's flux is completely emptied prior to the next cycle, it is referred to as the dis‐ continuous-mode of operation. This is seen in the inductor current and voltage waveforms in Figure 7. When the core does not completely empty itself, a residual amount of energy remains in the core. This is called the continuous mode of operation and can be seen in Fig‐ ure 8. The majority of boost-mode converters operate in the discontinuous mode since there are some intrinsic instability problems when operating in the continuous mode. The energy stored within the inductor of a discontinuous-mode boost converter is described by

$$E\_{stored} = \frac{1}{2} \mathbf{L} \cdot \mathbf{i}\_{pk}^2 \tag{23}$$

The energy delivered per second (joules/second or watts) must be sufficient to meet the con‐ tinuous power demands of the load. This means that the energy stored during the ON time of the power switch must have a high enough Ipk to satisfy equation (24):

$$P\_{load} < P\_{out} = f\left[\frac{1}{2}L \parallel I\_{pk}^2\right] \tag{24}$$

**Figure 7.** Waveforms for a discontinuous-mode boost converter.

**Figure 8.** Waveforms for a continuous-mode boost converter.

*Condition for continuous inductor current and capacitor voltage:* Assuming that the inductor cur‐ rent rises linearly from *Imin* to *I pk* in time *ton*.

$$t\_{ov} = \frac{\Delta I \ L}{V\_{in}} \tag{25}$$

And the inductor currents falls linearly from *I pk* to *Imin* in time *toff* .

$$\mathbf{t}\_{off} = \frac{\Delta I \ L}{V\_{out} \cdot V\_{in}} \tag{26}$$

The switching period *T* can be expressed as

When the core's flux is completely emptied prior to the next cycle, it is referred to as the dis‐ continuous-mode of operation. This is seen in the inductor current and voltage waveforms in Figure 7. When the core does not completely empty itself, a residual amount of energy remains in the core. This is called the continuous mode of operation and can be seen in Fig‐ ure 8. The majority of boost-mode converters operate in the discontinuous mode since there are some intrinsic instability problems when operating in the continuous mode. The energy

stored within the inductor of a discontinuous-mode boost converter is described by

<sup>2</sup> *L ipk*

The energy delivered per second (joules/second or watts) must be sufficient to meet the con‐ tinuous power demands of the load. This means that the energy stored during the ON time

<sup>2</sup> *L I pk*

2 (23)

2 (24)

*Estored* <sup>=</sup> <sup>1</sup>

of the power switch must have a high enough Ipk to satisfy equation (24):

**Figure 7.** Waveforms for a discontinuous-mode boost converter.

316 Advances in Wind Power

**Figure 8.** Waveforms for a continuous-mode boost converter.

*Pload* <sup>&</sup>lt; *Pout* <sup>=</sup> *<sup>f</sup>* <sup>1</sup>

$$T = t\_{out} + t\_{off} = \frac{\Delta I \parallel L}{V\_{in}} + \frac{\Delta I \parallel L}{V\_{out} \cdot V\_{in}} = \frac{\Delta I \parallel L \parallel V\_{out}}{V\_{in}(V\_{out} \cdot V\_{in})} \tag{27}$$

Which gives the peak-to-peak ripple current as

$$
\Delta I = \frac{V\_{in} \left(V\_{out} \cdot V\_{in}\right)}{fL \cdot V\_{out}} = \frac{V\_{in}k}{fL} \tag{28}
$$

If *I <sup>L</sup>* is the average inductor current, the inductor ripple current ∆*I* =2*I <sup>L</sup>* . Using equations (22) and (28), we get

$$\frac{V\_{in}k}{\frac{fL}{fL}} = \mathfrak{D}I\_L \quad \mathfrak{D}I\_a = \overline{\mathfrak{D}I\_a} = \frac{2\,\,V\_{in}}{(1\,\,\,-k)R} \tag{29}$$

Which gives the critical value of the inductor *L <sup>c</sup>* as

$$L\_{\
u} = \frac{k \left(1 - k\right) R}{2f} \tag{30}$$

When the SW is on, the capacitor supplies the load current for *t* =*ton*. The average capacitor current during time *ton* is *Ic* = *Iout* and peak-to-peak voltage of the capacitor is

$$
\Delta V\_c = \upsilon\_c - \upsilon\_c(t=0) = \frac{1}{C} f\_0^{t\_{on}} I\_c dt = \frac{1}{C} f\_0^{t\_{on}} I\_{out} dt = \frac{I\_{out} t\_{on}}{C} \tag{31}
$$

Substituting *ton* =(*Vout* - *Vin*) / (*V out f* ) in (31) gives

$$
\Delta V\_c = \frac{I\_{out} \left(V\_{out} \cdot V\_{in}\right)}{V\_{out} f \text{C}} = \frac{I\_{out} k}{f \text{C}} \tag{32}
$$

If *Vc* is the average capacitor voltage, the capacitor ripple voltage ∆*Vc* =2*Vout*. Using equa‐ tions (32), we get

$$\frac{I\_{out}k}{fC} = 2V\_{out} = 2I\_{out}R\tag{33}$$

Which gives the critical value of the capacitor *Cc* as

$$\mathbf{C}\_c = \mathbf{C} = \frac{k}{2f\mathbb{R}}\tag{34}$$

To the boost regulator's advantage, the input current is now continuous (although there will be a ripple component depending on the value of the inductance L). Hence less input filter‐ ing is required, and the tendency for input filter instability is eliminated [18-20].

#### *3.1.2.3. Buck-boost regulators*

A buck-boost regulator provides an output voltage that may be less than or greater than the input voltage. The output voltage polarity is opposite to that of the input voltage. Figure 9 shows the power circuit of a typical buck-boost regulator which operates as discussed below [18-20]

When SW is on, current will build up linearly in inductor L. Diode D is reverse-biased and blocks under steady-state conditions. When SW turns off, the current in L will continue in the same direction, and diode D is brought into conduction, transferring the inductor cur‐ rent into the output capacitor C and load. During the off period, the voltage across L is re‐ versed, and the current will decrease linearly toward its original value. The output voltage depends on the supply voltage and duty cycle (*ton* / *toff* ), and this is adjusted to maintain the required output. The current waveforms are the same as those for the boost regulator shown in Figure 10. As previously, the forward and reverse volt-seconds on L must equate for steady-state conditions, and to meet this volt-seconds equality

$$V\_{in} \times t\_{on} = V\_{out} \times t\_{off} \quad \rightarrow \ V\_{out} = V\_{in} \times \left(\frac{t\_{on}}{t\_{off}}\right) \rightarrow \ V\_{out} = \cdot \frac{k}{1 \cdot k} V\_{in} \tag{35}$$

**Figure 9.** Basic circuit of a buck-boost switching regulator

**Figure 10.** The voltage and current waveforms for a buck-boost converter

If *Vc* is the average capacitor voltage, the capacitor ripple voltage ∆*Vc* =2*Vout*. Using equa‐

To the boost regulator's advantage, the input current is now continuous (although there will be a ripple component depending on the value of the inductance L). Hence less input filter‐

A buck-boost regulator provides an output voltage that may be less than or greater than the input voltage. The output voltage polarity is opposite to that of the input voltage. Figure 9 shows the power

When SW is on, current will build up linearly in inductor L. Diode D is reverse-biased and blocks under steady-state conditions. When SW turns off, the current in L will continue in the same direction, and diode D is brought into conduction, transferring the inductor cur‐ rent into the output capacitor C and load. During the off period, the voltage across L is re‐ versed, and the current will decrease linearly toward its original value. The output voltage depends on the supply voltage and duty cycle (*ton* / *toff* ), and this is adjusted to maintain the required output. The current waveforms are the same as those for the boost regulator shown in Figure 10. As previously, the forward and reverse volt-seconds on L must equate for

*toff*

) <sup>→</sup> *Vout* = - *<sup>k</sup>*

1 - *<sup>k</sup> Vin* (35)

*fC* =2*Vout* =2*IoutR* (33)

<sup>2</sup> *fR* (34)

*I out k*

*Cc* <sup>=</sup>*<sup>C</sup>* <sup>=</sup> *<sup>k</sup>*

ing is required, and the tendency for input filter instability is eliminated [18-20].

circuit of a typical buck-boost regulator which operates as discussed below [18-20]

steady-state conditions, and to meet this volt-seconds equality

*Vin* <sup>×</sup>*ton* <sup>=</sup>*Vout* <sup>×</sup>*toff* <sup>→</sup> *Vout* <sup>=</sup>*Vin* ×( *ton*

**Figure 9.** Basic circuit of a buck-boost switching regulator

Which gives the critical value of the capacitor *Cc* as

tions (32), we get

318 Advances in Wind Power

*3.1.2.3. Buck-boost regulators*

*Condition for continuous inductor current and capacitor voltage:* Assuming that the inductor cur‐ rent rises linearly from *Imin* to *I pk* in time *ton*.

$$t\_{on} = \frac{\Delta I \ L}{V\_{in}} \tag{36}$$

And the inductor currents falls linearly from *I pk* to *Imin* in time *toff* .

$$\text{At}\_{off} = \frac{-\Delta I \text{ L}}{V\_{out}} \tag{37}$$

The switching period *T* can be expressed as

$$T = t\_{out} + t\_{off} = \frac{\Delta I \ L}{V\_{in}} + \frac{\text{- }\Delta I \ L}{V\_{out}} = \frac{\Delta I \ L \ \left(V\_{out} \cdot V\_{in}\right)}{V\_{in} V\_{out}}\tag{38}$$

Which gives the peak-to-peak ripple current as

$$
\Delta I = \frac{V\_{in} V\_{out}}{f \text{L} \cdot (V\_{out} \cdot V\_{in})} = \frac{V\_{in} k}{f \text{L}} \tag{39}
$$

If *I <sup>L</sup>* is the average inductor current, the inductor ripple current ∆*I* =2*I <sup>L</sup>* . Using equations (35) and (39), we get

$$\frac{V\_{in}k}{\frac{fL}{fL}} = \mathbf{2}I\_L \ = \mathbf{2}I\_a = \frac{2k\ \mathbf{V}\_{in}}{(1\ \cdot\ \cdot\ \mathbf{k})R} \tag{40}$$

Which gives the critical value of the inductor *L <sup>c</sup>* as

$$L\_c = \frac{(1 - k)R}{2f} \tag{41}$$

When the SW is on, the capacitor supplies the load current for *t* =*ton*. The average capacitor current during time *ton* is *Ic* = *Iout* and peak-to-peak voltage of the capacitor is

$$
\Delta V\_c = \upsilon\_c - \upsilon\_c \text{(t=0)} = \frac{1}{C} f\_0^{t\_{on}} I\_c dt = \frac{1}{C} f\_0^{t\_{on}} I\_{out} dt = \frac{I\_{out} t\_{on}}{C} \tag{42}
$$

Substituting *ton* =*Vout* / (*V out* - *Vin*) *f* in (42) gives

$$
\Delta V\_c = \frac{I\_{out} V\_{out}}{(V\_{out} - V\_{in})/C} = \frac{I\_{out} k}{fC} \tag{43}
$$

If *Vc* is the average capacitor voltage, the capacitor ripple voltage ∆*Vc* =2*Vout*. Using equa‐ tions (43), we get

$$\frac{I\_{out}k}{fC} = 2V\_{out} = 2I\_{out}R\tag{44}$$

Which gives the critical value of the capacitor *Cc* as

$$\mathbf{C}\_c = \mathbf{C} = \frac{k}{2f\mathbb{R}}\tag{45}$$

Note that the output voltage is of reversed polarity but may be greater or less than *Vin*, de‐ pending on the duty cycle. In the inverting regulator, both input and output currents are discontinuous, and considerable filtering will be required on both input and output [18-21].

#### *3.1.2.4. Cuk regulators*

*<sup>T</sup>* <sup>=</sup>*ton* <sup>+</sup> *toff* <sup>=</sup> <sup>∆</sup> *<sup>I</sup> <sup>L</sup>*

Which gives the peak-to-peak ripple current as

(35) and (39), we get

320 Advances in Wind Power

tions (43), we get

*Vin* <sup>+</sup> - <sup>∆</sup> *<sup>I</sup> <sup>L</sup>*

*fL* (*<sup>V</sup> out*-*<sup>V</sup> in*) <sup>=</sup> *Vink*

*fL* =2*<sup>I</sup> <sup>L</sup>* =2*Ia* <sup>=</sup> <sup>2</sup>*<sup>k</sup> Vin*

*<sup>L</sup> <sup>c</sup>* <sup>=</sup> (1 - *<sup>k</sup>* )*<sup>R</sup>*

current during time *ton* is *Ic* = *Iout* and peak-to-peak voltage of the capacitor is

(*<sup>t</sup>* =0)= <sup>1</sup> *C ∫* 0 *tonIcdt* <sup>=</sup> <sup>1</sup> *C ∫* 0

<sup>∆</sup>*Vc* <sup>=</sup> *<sup>I</sup> outVout*

*I out k*

*Cc* <sup>=</sup>*<sup>C</sup>* <sup>=</sup> *<sup>k</sup>*

If *I <sup>L</sup>* is the average inductor current, the inductor ripple current ∆*I* =2*I <sup>L</sup>* . Using equations

When the SW is on, the capacitor supplies the load current for *t* =*ton*. The average capacitor

(*<sup>V</sup> out* - *Vin*) *fC* <sup>=</sup> *<sup>I</sup> out <sup>k</sup>*

If *Vc* is the average capacitor voltage, the capacitor ripple voltage ∆*Vc* =2*Vout*. Using equa‐

Note that the output voltage is of reversed polarity but may be greater or less than *Vin*, de‐ pending on the duty cycle. In the inverting regulator, both input and output currents are discontinuous, and considerable filtering will be required on both input and output [18-21].

<sup>∆</sup>*<sup>I</sup>* <sup>=</sup> *VinVout*

*Vink*

Which gives the critical value of the inductor *L <sup>c</sup>* as

∆*Vc* =*vc* - *vc*

Substituting *ton* =*Vout* / (*V out* - *Vin*) *f* in (42) gives

Which gives the critical value of the capacitor *Cc* as

*Vout* <sup>=</sup> <sup>∆</sup> *<sup>I</sup> <sup>L</sup>* (*Vout* - *Vin*)

*VinVout* (38)

*fL* (39)

(1 - *<sup>k</sup>* )*R* (40)

<sup>2</sup> *<sup>f</sup>* (41)

*<sup>C</sup>* (42)

*fC* (43)

*fC* =2*Vout* =2*IoutR* (44)

<sup>2</sup> *fR* (45)

*tonIoutdt* <sup>=</sup> *<sup>I</sup> outton*

Similar to the buck-boost regulator, the cuk regulator provides an output voltage that is less than or greater than input voltage, but the output voltage polarity is opposite to that of the input voltage. Figure 11 shows the general arrangement of the power sections of a cuk regu‐ lator. The voltage and current waveforms for the cuk regulator are shown in Figure 12.

**Figure 11.** Basic circuit of a cuk switching regulator

**Figure 12.** The voltage and current waveforms for a cuk converter

An important advantage of this topology is a continuous current at both the input and the output of the converter. Disadvantages of the cuk converter are a high number of reactive components and high current stresses on the switch, the diode, and the capacitor C1. When the switch is on, the diode is off and the capacitor C1 is discharged by the inductor L2 cur‐ rent. With the switch in the off state, the diode conducts currents of the inductors L1 and L2, whereas capacitor C1 is charged by the inductor L1 current [18-21].

To obtain the dc voltage transfer function of the converter, we shall use the principle that the average current through a capacitor is zero for steady-state operation. Let us assume that in‐ ductors L1 and L2 are large enough that their ripple current can be neglected. Capacitor C1 is in steady state if

$$I\_{L-2}kT = I\_{L-1} \text{(1-k)}T \tag{46}$$

For a lossless converter

$$P\_S = V\_S I\_{L\ \ 1} = \text{-}V\_O I\_{L\ \ 2} = P\_O \tag{47}$$

From (46) and (47), the dc voltage transfer function of the cuk converter is

$$\mathbf{V}\_{out} = -\frac{k}{1 - k} \mathbf{V}\_{in} \tag{48}$$

The critical values of the inductor *L <sup>c</sup>*1 and *L <sup>c</sup>*2 determined by

$$L\_{c1} = \frac{(1 \cdot k)^2 R}{2k^f} \tag{49}$$

$$L\_{-c2} = \frac{(1 - k)R}{2f} \tag{50}$$

And the critical values of the capacitor *Cc*1 and *Cc*2 determined by

$$C\_{c1} = \frac{k}{2f\text{R}}\tag{51}$$

$$C\_{c2} = \frac{1}{\frac{8}{\pi f R}}\tag{52}$$

#### *3.1.3. Inverters*

DC-to-ac converters are known as inverters. The function of inverter is to change a dc input voltage to symmetric ac output voltage of desired magnitude and frequency. The output voltage could be fixed or variable at a fixed or variable frequency. A variable output voltage can be obtained by varying the input dc voltage and maintaining the gain of inverter con‐ stant. The output voltage waveforms of ideal inverters should be sinusoidal. However, the waveforms of practical inverters are non-sinusoidal and contain certain harmonics [18, 22].

For sinusoidal ac outputs, the magnitude, frequency, and phase should be controllable. In‐ verters generally use PWM control signals for producing an ac output voltage. According to the type of ac output waveform, these topologies can be considered as voltage source inver‐ ters (VSIs), where the independently controlled ac output is a voltage waveform. These structures are the most widely used in small-scale wind power applications. Similarly, these topologies can be found as current source inverters (CSIs), where the independently control‐ led ac output is a current waveform. These structures are not widely used in small-scale wind power applications [18].

Inverters can be broadly classified into two types: single-phase inverters, and three-phase inverters.

#### *3.1.3.1. Single-phase bridge inverters*

An important advantage of this topology is a continuous current at both the input and the output of the converter. Disadvantages of the cuk converter are a high number of reactive components and high current stresses on the switch, the diode, and the capacitor C1. When the switch is on, the diode is off and the capacitor C1 is discharged by the inductor L2 cur‐ rent. With the switch in the off state, the diode conducts currents of the inductors L1 and L2,

To obtain the dc voltage transfer function of the converter, we shall use the principle that the average current through a capacitor is zero for steady-state operation. Let us assume that in‐ ductors L1 and L2 are large enough that their ripple current can be neglected. Capacitor C1

(1 - *k*)*T* (46)

1 - *<sup>k</sup> Vin* (48)

<sup>2</sup>*kf* (49)

<sup>2</sup> *<sup>f</sup>* (50)

<sup>2</sup> *fR* (51)

<sup>8</sup> *fR* (52)

*PS* =*VS I <sup>L</sup>* <sup>1</sup> =-*V <sup>O</sup>I <sup>L</sup>* <sup>2</sup> =*PO* (47)

whereas capacitor C1 is charged by the inductor L1 current [18-21].

*I <sup>L</sup>* <sup>2</sup>*kT* = *I <sup>L</sup>* <sup>1</sup>

From (46) and (47), the dc voltage transfer function of the cuk converter is

The critical values of the inductor *L <sup>c</sup>*1 and *L <sup>c</sup>*2 determined by

And the critical values of the capacitor *Cc*1 and *Cc*2 determined by

*Vout* = - *<sup>k</sup>*

*<sup>L</sup> <sup>c</sup>*<sup>1</sup> <sup>=</sup> (1 - *<sup>k</sup>* )2

*<sup>L</sup> <sup>c</sup>*<sup>2</sup> <sup>=</sup> (1 - *<sup>k</sup>* )*<sup>R</sup>*

*Cc*<sup>1</sup> <sup>=</sup> *<sup>k</sup>*

*Cc*<sup>2</sup> <sup>=</sup> <sup>1</sup>

DC-to-ac converters are known as inverters. The function of inverter is to change a dc input voltage to symmetric ac output voltage of desired magnitude and frequency. The output voltage could be fixed or variable at a fixed or variable frequency. A variable output voltage can be obtained by varying the input dc voltage and maintaining the gain of inverter con‐

*R*

is in steady state if

322 Advances in Wind Power

For a lossless converter

*3.1.3. Inverters*

A single-phase bridge voltage source inverter (VSI) is shown in Figure 13. It consists of four switches. When S1 and S2 are turned on, the input voltage *Vd* appears across the load. If S3 and S4 are turned on, the voltage across the load is -*Vd* . Table 1 shows five switch states. If these switches are off at the same time, the switch state is 0. The rms output voltage can be found from

$$V\_O = \sqrt{\left(\frac{2}{T\_0} \zeta\_0^{T\_0/2} V\_d^2 dt\right)} = V\_d \tag{53}$$

Output voltage can be represented in Fourier series. The rms value of fundamental compo‐ nent as

$$
\omega\_O = \sum\_{n=1,3,\dots}^{\infty} \frac{4V\_d}{n\pi} \sin n\omega t \stackrel{n=1}{\rightharpoonup} V\_1 = \frac{4V\_d}{\sqrt{2\pi}} = 0.90V\_d \tag{54}
$$

**Figure 13.** Single-phase full bridge inverter

When diodes D1 and D2 conduct, The energy is fed back to the dc source; so, they are known as feedback diodes. The instantaneous load current *i <sup>o</sup>* for an RL load becomes

$$\dot{q}\_o = \sum\_{n=1,3,\dots}^{\omega} \frac{4V\_d}{n\pi \cdot \sqrt{\mathcal{R}^2 + (n\omega L\_\circ)^2}} \sin\left(n\omega t \cdot \Theta\_n\right) \tag{55}$$


Where *θ<sup>n</sup>* =tan-1 (*nω<sup>L</sup>* / *<sup>R</sup>*).

**Table 1.** Switches states for a single-phase full-bridge inverter.

To control of the output voltage of inverters is often necessary to compensate the var‐ iation of dc input voltage, regulate the output voltage of inverter, and to adjust the output frequency to the desired value. There are various techniques to vary the inver‐ ter gain. The most operational method of controlling the gain and output voltage wave‐ form is sinusoidal pulse-width modulation (SPWM) technique. In SPWM approach, the width of each pulse is varied in proportion to the amplitude of sine wave compared at the center of the same pulse. The gating signals in this approach are shown in Fig‐ ure 14. The gating signals are generated by comparing a sinusoidal wave as reference signal with triangular carrier wave of frequency *f <sup>c</sup>*. The frequency of reference signal *f <sup>r</sup>* determines the output frequency *f <sup>o</sup>* of inverter, and the peak amplitude of it *Ar* specifies the modulation index M. Comparing the bidirectional carrier signal *vtri* with to sinusoidal reference signals *vcontrol* and -*vcontrol* results gating signals *g*1 and *g*4. The output voltage is *vo* =*Vd* (*g*<sup>1</sup> - *g*4). However, *g*1 and *g*4 can not be released at the same time. The same gating signals can be generate by using unidirectional triangular carri‐ er wave as shown in Figure 15. This method is easy to implementation [18,22,23].

When diodes D1 and D2 conduct, The energy is fed back to the dc source; so, they are known

State No. Output Voltage Level State of *(S1 , S2 , S3 , S4)* Components Conducting

(0, 0 , 0 , 0)

To control of the output voltage of inverters is often necessary to compensate the var‐ iation of dc input voltage, regulate the output voltage of inverter, and to adjust the output frequency to the desired value. There are various techniques to vary the inver‐ ter gain. The most operational method of controlling the gain and output voltage wave‐ form is sinusoidal pulse-width modulation (SPWM) technique. In SPWM approach, the width of each pulse is varied in proportion to the amplitude of sine wave compared at the center of the same pulse. The gating signals in this approach are shown in Fig‐ ure 14. The gating signals are generated by comparing a sinusoidal wave as reference signal with triangular carrier wave of frequency *f <sup>c</sup>*. The frequency of reference signal *f <sup>r</sup>* determines the output frequency *f <sup>o</sup>* of inverter, and the peak amplitude of it *Ar* specifies the modulation index M. Comparing the bidirectional carrier signal *vtri* with to sinusoidal reference signals *vcontrol* and -*vcontrol* results gating signals *g*1 and *g*4. The output voltage is *vo* =*Vd* (*g*<sup>1</sup> - *g*4). However, *g*1 and *g*4 can not be released at the same time. The same gating signals can be generate by using unidirectional triangular carri‐ er wave as shown in Figure 15. This method is easy to implementation [18,22,23].

*<sup>o</sup>* for an RL load becomes

*S*1 and *S*2 if *i*

*D*1 and *D*2 if *i*

*D*3 and *D*4 if *i*

*S*3 and *S*4 if *i*

*S*1 and *D*3 if *i*

*D*1 and *S*3 if *i*

*D*4 and *S*2 if *i*

*S*4 and *D*2 if *i*

*D*4 and *D*3 if *i*

*D*4 and *D*2 if *i*

*<sup>o</sup>* > 0

*<sup>o</sup>* < 0

*<sup>o</sup>* > 0

*<sup>o</sup>* < 0

*<sup>o</sup>* > 0

*<sup>o</sup>* < 0

*<sup>o</sup>* > 0

*<sup>o</sup>* < 0

*<sup>o</sup>* > 0

*<sup>o</sup>* < 0

*<sup>n</sup><sup>π</sup> <sup>R</sup>* <sup>2</sup> <sup>+</sup> (*nω<sup>L</sup>* )2 sin (*nω<sup>t</sup>* - *<sup>θ</sup>n*) (55)

as feedback diodes. The instantaneous load current *i*

<sup>∞</sup> 4*Vd*

*i <sup>o</sup>* = ∑ *n*=1,3,…

1 +*Vd* (1, 1 , 0 , 0)

2 −*Vd* (0, 0 , 1 , 1)

3 0 (1, 0 , 1 , 0)

4 0 (0, 1 , 0 , 1)

Where *θ<sup>n</sup>* =tan-1 (*nω<sup>L</sup>* / *<sup>R</sup>*).

324 Advances in Wind Power

<sup>5</sup> <sup>−</sup>*Vd*

+*Vd*

**Table 1.** Switches states for a single-phase full-bridge inverter.

#### *3.1.3.2. Multi-level inverters*

The voltage source inverters generate an output voltage levels either 0 or ±*V <sup>d</sup>* . They are called two-level inverter. To obtain a quality output voltage or a current waveform with a minimum amount of THD1 , they require high-switching frequency and various pulse-width modulation (PWM) techniques. However, Switching devices have some limitations in oper‐ ating at high frequency such as switching losses and device ratings [18].

<sup>1</sup> Total Harmonic Distortion

**Figure 15.** Unidirectional SPWM.

The most significant advantages of multilevel converters in comparison with two-level in‐ verters are incorporating an output voltage waveform from several steps of voltage with sig‐ nificantly improved harmonic content, reduction of output *dv dt* , electromagnetic interference, filter inductance, etc [24]. The general structure of multilevel converter is to synthesize a near sinusoidal voltage from several levels of dc voltages, typically obtained from capacitor voltage sources [18]. With increasing of levels, the output waveform has more steps, which produce a staircase wave that approaches a desired waveform. Also, as more steps are add‐ ed to the waveform, the total harmonic distortion (THD) of output wave decreases.

Multilevel converters can be classified into three general types which are diode-clamped multilevel (DCM) converters, cascade multicell (CM) converters, and flying capacitor multi‐ cell (FCM) converters and its derivative, the SM converters [24].

#### *3.1.3.2.1. Diode-clamped multilevel (DCM) converter*

The n-level diode-clamped multilevel inverter (DCMLI) produces n-levels on the phase volt‐ age and consists of (*n* - 1) capacitors on the dc bus, 2(*n* - 1) switching devices and (*n* - 1)(*n* - 2) clamping diodes. Figure 16 shows a 3-level diode-clamped converter. For a dc bus voltage *<sup>E</sup>*, the voltage across each capacitor is *<sup>E</sup>* <sup>2</sup> , and each switching device stress is limited to one capacitor voltage level *<sup>E</sup>* <sup>2</sup> through clamping diodes.

**Figure 16.** level diode-clamped converter.

**Figure 15.** Unidirectional SPWM.

326 Advances in Wind Power

The most significant advantages of multilevel converters in comparison with two-level in‐ verters are incorporating an output voltage waveform from several steps of voltage with sig‐

filter inductance, etc [24]. The general structure of multilevel converter is to synthesize a near sinusoidal voltage from several levels of dc voltages, typically obtained from capacitor voltage sources [18]. With increasing of levels, the output waveform has more steps, which produce a staircase wave that approaches a desired waveform. Also, as more steps are add‐

Multilevel converters can be classified into three general types which are diode-clamped multilevel (DCM) converters, cascade multicell (CM) converters, and flying capacitor multi‐

The n-level diode-clamped multilevel inverter (DCMLI) produces n-levels on the phase volt‐ age and consists of (*n* - 1) capacitors on the dc bus, 2(*n* - 1) switching devices and (*n* - 1)(*n* - 2) clamping diodes. Figure 16 shows a 3-level diode-clamped converter. For a dc bus voltage

ed to the waveform, the total harmonic distortion (THD) of output wave decreases.

*dt* , electromagnetic interference,

<sup>2</sup> , and each switching device stress is limited to one

nificantly improved harmonic content, reduction of output *dv*

cell (FCM) converters and its derivative, the SM converters [24].

<sup>2</sup> through clamping diodes.

*3.1.3.2.1. Diode-clamped multilevel (DCM) converter*

*<sup>E</sup>*, the voltage across each capacitor is *<sup>E</sup>*

capacitor voltage level *<sup>E</sup>*

To produce a staircase output voltage, for output voltage *Vout* <sup>=</sup> *<sup>E</sup>* <sup>2</sup> , *S*1 and *S*2 power switches must be turned on. When *S*<sup>1</sup> *'* and *S*<sup>2</sup> *'* power switches are turned on, the output voltage *Vout* = - *<sup>E</sup>* <sup>2</sup> appears across the load. For output voltage *Vout* =0, *S*<sup>1</sup> *'* and *S*2 power switches must be turned on [18,23].

The significant advantages of DCM inverter can be expressed as follows:


The significant disadvantages of DCM inverter can be expressed as follows:


#### *3.1.3.2.2. Cascade multilevel (CM) converter*

A cascade multilevel inverter consists of series of H-bridge inverter units. The general oper‐ ation of this multilevel inverter is to synthesize a desired voltage from several separate dc sources, which may be obtained from wind turbines, batteries, or other voltage sources. Fig‐ ure 17 shows the general structure of a cascade multilevel inverter with isolated dc voltage sources.

**Figure 17.** The 2n+1 levels cascade multilevel inverter: (a) with separated dc voltage sources. (b) with one dc voltage source and isolator transformers.

Each inverter can produce three different levels of voltage outputs, +*E*, 0, and –*E*, by con‐ necting the dc source to the ac output side by different states of four switches, *S*1, *S*2, *S* - 1, and *S* - 2. Table 1 shows five switch states for H-bridge inverter. The phase output voltage is ob‐

tain by the sum of inverter outputs. Hence, the CM inverter output voltage becomes

$$
\upsilon \upsilon\_{out} = \sum\_{i=1}^{n} \upsilon\_i \tag{56}
$$

where *n* is number of cells and *vi* is the output voltage of cell *i*.

*3.1.3.2.2. Cascade multilevel (CM) converter*

sources.

328 Advances in Wind Power

source and isolator transformers.

*S* -

A cascade multilevel inverter consists of series of H-bridge inverter units. The general oper‐ ation of this multilevel inverter is to synthesize a desired voltage from several separate dc sources, which may be obtained from wind turbines, batteries, or other voltage sources. Fig‐ ure 17 shows the general structure of a cascade multilevel inverter with isolated dc voltage

**Figure 17.** The 2n+1 levels cascade multilevel inverter: (a) with separated dc voltage sources. (b) with one dc voltage

Each inverter can produce three different levels of voltage outputs, +*E*, 0, and –*E*, by con‐

2. Table 1 shows five switch states for H-bridge inverter. The phase output voltage is ob‐


(56)

necting the dc source to the ac output side by different states of four switches, *S*1, *S*2, *S*

tain by the sum of inverter outputs. Hence, the CM inverter output voltage becomes

*vout* = ∑ *i*=1 *n vi* If *n* is number of cells, the output phase voltage level is 2*n* + 1. Thus, a five-level CM inverter needs 2 bridge inverters with separated dc voltage sources. Table 2 shows the switches states for five-level CM inverter [18,23].


**Table 2.** Switches states for a five-level CM inverter.

The significant advantages of the CM inverter can be expressed as follows:


The significant disadvantage of the CM inverter can be expressed as follows:

**•** It needs separate dc voltage sources for real power conversions [18,23].

#### *3.1.3.2.3. Flying capacitor multicell (FCM) converter*

The FCM converters consist of ladder connection of cells while each cell in FCM is made up of a flying capacitor and a pair of semiconductor switches with a complimen‐ tary state. The commutation between adjacent cells with their associated flying capaci‐ tors charged to the specific values generates different levels of chopped input voltage at the output side of converter [24]. The voltage balancing of flying capacitors which guarantees the safe operation of the converter is a important subject in these topolo‐ gies [23, 24]. The capacitors voltage balancing which is called self-balancing occurs if phase-shifted carrier pulse-width modulation (PSC-PWM) technique is applied to the converter control pattern [24]. Figure 18 and Figure 19 show the general structure of a flying capacitor multilevel (FCM) inverter and the phase-shifted carrier pulse-width modulation (PSC-PWM) technique for five-level FCM inverter, respectively.

**Figure 18.** The *n* cells (*n* + 1 levels) FCM inverter.

**Figure 19.** The phase-shifted carrier pulse-width modulation (PSC-PWM) technique for five-level FCM inverter.

The significant advantages of the FCM inverter can be expressed as follows:


The significant disadvantages of the FCM inverter can be expressed as follows:


Table 3 shows the switches states for five-level FCM inverter.


**Table 3.** Switches states for a five-level FCM inverter.

**Figure 18.** The *n* cells (*n* + 1 levels) FCM inverter.

330 Advances in Wind Power

**•** No need for clamping diodes.

age across flying capacitors.

**Figure 19.** The phase-shifted carrier pulse-width modulation (PSC-PWM) technique for five-level FCM inverter.

**•** Availability of redundant states balance and inherent self-balancing property of the volt‐

The significant advantages of the FCM inverter can be expressed as follows: **•** No need for isolation of dc links and transformerless operation capability.

The significant disadvantages of the FCM inverter can be expressed as follows:

**•** A large number of flying capacitors is required when the number of levels is high.

**•** Equal distribution of switching stress between power switches.

**•** The inverter control can be very complicated [18,23,24].

Table 3 shows the switches states for five-level FCM inverter.

### **4. Small-scale wind energy conversion system**

Small-scale wind conversion system may be integrated into loads or power systems with full rated power electronic converters. The wind turbines with a full scale power converter between the generator and load give the extra technical performance. Usually, a back-toback voltage source converter (VSC) is used in order to achieve full control of the active and reactive power. But in this case, the control of whole system would be a difficult task. Since the generator has been decoupled from electric load, it can be operated at wide range fre‐ quency (speed) condition and maximum power extract. Figure 20 shows two most used sol‐ utions with full-scale power converters. Both solutions have almost the same controllable characteristics since the generator is decoupled from the load by a dc link [1,17].

**Figure 20.** Small-scale wind energy conversion system. (a)self-excited induction generator with gearbox. (b)direct cou‐ pled permanent magnet synchronous generator.

The configuration shown in Figure 20(a) is characterized by having a gearbox. The wind tur‐ bine system with a SEIG and full rated power electronic converters is shown in Figure 20(a). Multipole systems with the permanent magnet synchronous generator without a gearbox is shown in Figure 20(b).

**Figure 21.** a) output regulated voltage of DC/DC boost converter. (b) output AC voltage and current of DC/AC 4 levels FCMC. (c) output AC voltage and current of DC/AC 5 levels FCMC [23].

The grid connected 1 KW small scale wind generation system has been modelled, designed and implemented in renewable energy research center of sahand university of technology. In this project the maximum power point tracking method has been used to control of varia‐ ble speed small scale wind turbine. Wind turbine consist of axial flux permanent magnet synchronous generator (AFPMSG), rectifier, DC/DC boost chopper, maximum power point tracking controller, inverter and load. Tracking system is embedded in boost chopper con‐ troller in order to regulate wind turbine shaft at optimum speed to extract maximum power from wind. Two inverters such as: 4 and 5 levels flying capacitor multi-cell converter (FCMC) have been implemented. The small scale wind generation system has been simulat‐ ed on MATLAB/Simulink platform. Simulation results clearly demonstrate that designed small scale wind generation system can operate correctly under various wind speeds. The regulated output DC voltage of DC/DC boost chopper has been converted to AC voltage with 4 and 5 levels flying capacitor multi-cell converter (FCMC). The DC/DC boost chopper and inverter include IGBT transistors, interfacing board, driver boards, voltage and current sensors and ATMEGA16 microcontroller board. The phase shifted pulse width modulation (PSPWM) and pulse width modulation (PWM) techniques have been implemented on mul‐ ticell inverters and DC/DC boost chopper respectively [23]. The experimental results of the 1 KW small scale wind generation system have been shown in Figure 21. Figure 21(a) shows the output regulated voltage of DC/DC boost converter. Whereas, Figure 21(b) shows the output AC voltage and current of DC/AC 4 levels FCMC, and Figure 21(b) shows the output AC voltage and current of DC/AC 5 levels FCMC.
