**4. Co-simulation (PSIM/Matlab) program for interconnecting wind energy system with electric utility**

In this study, the WECS is designed as PMSG connected to the grid via a back-to-back PWM-VSC as shown in Figure 21. MPPT control algorithm has been introduced using FLC to regulate the rotational speed to force the PMSG to work around its maximum power point in speeds below rated speeds and to produce the rated power in wind speed higher than the rated wind speed of the WT. Indirect vector-controlled PMSG system has been used for this purpose. The input to FLC is two real time measurements which are the change of output power and rotational speed between two consequent iterations (*ΔP*, and *Δωm*). The output from FLC is the required change in the rotational speed *Δωm-new\**. The detailed logic behind the new proposed technique is explained in details in the following sections. Two effective computer simulation software packages (PSIM and Simulink) have been used to carry out the simulation effectively where PSIM contains the power circuit of the WECS and Matlab/Simulink contains the control circuit of the system. The idea behind using these two different software packages is the effective tools provided with PSIM for power circuit and the effective tools in Simulink for control circuit and FLC.

**Figure 21.** Schematic diagram of the overall system.

of the grid side converter as shown in Figure 20. The phase angle of utility voltage is detected

Calculate an d

*Vabc abc i*

*Pout*

*nPnPP* -D-D=D )1()( *out out out*

*Qout*

*a inv m V*

> ç ç è æ D-÷ ÷ ø ö

*inccrease m QQif mdecrease QQif*

*m na* <sup>+</sup> )1(

)(

<

)(

>

÷ ÷ ø ö


*a out desired a out desired*

> d ÷ ÷ ø ö

*na ninv*

*m V*

Calculate

ç ç è æ D=÷ ÷ ø ö ç ç è æ D

*a inv*

*m V*

)( )(

*na ninv*

*m V*

*m na* <sup>+</sup> )1(

+

ddD+

*m*


*<sup>n</sup> m*

ç ç è <sup>æ</sup> <sup>=</sup>

*Cdc*

*Vdc\**

VC *Iq\** PFC *Id\**

*cosɸº*

CCd *Vq\**

*<sup>θ</sup>* 3 2

*Id*

*θ*

 CCdc :dc Current Control CCq :q-axis Current Control CCd :d-axis Current Control VC :Voltage Control PFC :Power Factor Control

3 2 *Eq Ed* PLL *θ*

*a b c*

*LF*

*Id Iq*

CCq *Vq\**

PWM SVPWM

*Iq*

*Vdc*

using Phased Locked Loop, *PLL*, in d-q synchronous reference frame [17].

**Figure 19.** Flowchart of the proposed maximum active power and reactive power control [1].

Table I

Dd

> d*n*+ )1(

*Vin Vdc*

CCdc *D*

*Idc\**

*Idc Ldc*

*Vin*

**Figure 20.** Block diagram of system control [17].

*Idc*

**SG**

178 New Developments in Renewable Energy

#### **4.1. Wind energy conversion system description**

Figure 22 shows a co-simulation (PSIM/Simulink) program for interconnecting WECS to electric utility. The PSIM program contains the power circuit of the WECS and Matlab/ Simulink program contains the control of this system. The interconnection between PSIM and Matlab/Simulink has been done via the SimCoupler block. The basic topology of the power circuit which has PMSG driven wind turbine connected to the utility grid through the ac-dcac conversion system is shown in Figure 21. The PMSG is connected to the grid through back– to-back bidirectional PWM voltage source converters VSC. The generator side converter is used as a rectifier, while the grid side converter is used as an inverter. The generator side converter is connected to the grid side converter through dc-link capacitor. The control of the overall system has been done through the generator side converter and the grid side converter. MPPT algorithm has been achieved through controlling the generator side converter using FLC. The grid-side converter controller maintains the dc-link voltage at the desired value by exporting active power to the grid and it controls the reactive power exchange with the grid.

For a fixed pitch angle, *β*, *CP* becomes a nonlinear function of tip speed ratio, λ, only. According to Equation (29), there is a relation between the tip speed ratio, *λ* and the rotational speed, *ωm*. Hence, at a certain wind speed, the power is maximum at a certain *ω<sup>m</sup>* called optimum rotational speed, *ωopt*. This speed corresponds to optimum TSR, *λopt* [15]. The value of the TSR is constant for all maximum power points. So, to extract maximum power at variable wind speed, the WT should always operate at *λopt* in speeds bellow the rated speed. This occurs by controlling the rotational speed of the WT to be equal to the optimum rotational speed. Figure 23 shows that the mechanical power generated by WT at the shaft of the generator as a function of the rotational speed, *ωm*. These curves have been extracted from PSIM support for the wind turbine used in this study. It is clear from this figure that for each wind speed the mechanical

Maximum Power Extraction from Utility-Interfaced Wind Turbines

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181

output power is maximum at particular rotational speed, *ωopt* as shown in Figure 23.

The generator is modeled by the following voltage equations in the rotor reference frame (dq

*sd sd s sd r sq*

w l

(32)

w l

*dt d*

l

l

*dt*

*<sup>d</sup> v Ri*

=+-

=++

*v Ri*

l

l

*sq sq s sq r sd*

Where *λsq,* and *λsd* are the stator flux linkages in the direct and quadrature axis of rotor which in the absence of damper circuits can be expressed in terms of the stator currents and the

> y

<sup>=</sup> (33)

*sd s sd F sq s sq L i L i*

= +

**Locus of** *Pmax*

Mechanical output power

**Figure 23.** Typical output power characteristics.

*4.1.2. PMSG model*

magnetic flux as [29].

axes) [29]:

**Figure 22.** Co-simulation block of wind energy system interfaced to electric utility.

#### *4.1.1. Wind turbine model*

Wind turbine converts the wind power to a mechanical power. This mechanical power generated by wind turbine at the shaft of the generator can be expressed as:

$$P\_m = \frac{1}{2} \mathcal{C}\_p \left(\mathcal{A}\_\prime \mathcal{B} \right) \rho A u^3 \tag{30}$$

where *ρ* is the air density (typically 1.225 kg/m3 ), *β* is the pitch angle (in degree), *A* is the area swept by the rotor blades (in m2 ); *u* is the wind speed (in m/s) and *Cp*(*λ, β*) is the wind-turbine power coefficient (dimensionless).

The turbine power coefficient, *Cp*(*λ, β*), describes the power extraction efficiency of the WT and is defined as the ratio between the mechanical power available at the turbine shaft and the power available in wind. A generic equation shown later in Equation (3) is used to model *Cp*(*λ, β*). *CP* is a nonlinear function of both tip speed ratio, λ and the blade pitch angle, *β*. The tip speed ratio, λ is the ratio of the turbine tip speed, *ωm\*R* to the wind speed, *u*. This tip speed ratio, *λ,* is defined as [28]:

$$
\mathcal{X} = \frac{\alpha\_m \, ^\ast R}{\mu} \tag{31}
$$

Where *ωm* is the rotational speed and *R* is the turbine blade radius, respectively.

For a fixed pitch angle, *β*, *CP* becomes a nonlinear function of tip speed ratio, λ, only. According to Equation (29), there is a relation between the tip speed ratio, *λ* and the rotational speed, *ωm*. Hence, at a certain wind speed, the power is maximum at a certain *ω<sup>m</sup>* called optimum rotational speed, *ωopt*. This speed corresponds to optimum TSR, *λopt* [15]. The value of the TSR is constant for all maximum power points. So, to extract maximum power at variable wind speed, the WT should always operate at *λopt* in speeds bellow the rated speed. This occurs by controlling the rotational speed of the WT to be equal to the optimum rotational speed. Figure 23 shows that the mechanical power generated by WT at the shaft of the generator as a function of the rotational speed, *ωm*. These curves have been extracted from PSIM support for the wind turbine used in this study. It is clear from this figure that for each wind speed the mechanical output power is maximum at particular rotational speed, *ωopt* as shown in Figure 23.

**Figure 23.** Typical output power characteristics.

#### *4.1.2. PMSG model*

MPPT algorithm has been achieved through controlling the generator side converter using FLC. The grid-side converter controller maintains the dc-link voltage at the desired value by exporting active power to the grid and it controls the reactive power exchange with the grid.

> From PSIM

Wind turbine converts the wind power to a mechanical power. This mechanical power

The turbine power coefficient, *Cp*(*λ, β*), describes the power extraction efficiency of the WT and is defined as the ratio between the mechanical power available at the turbine shaft and the power available in wind. A generic equation shown later in Equation (3) is used to model *Cp*(*λ, β*). *CP* is a nonlinear function of both tip speed ratio, λ and the blade pitch angle, *β*. The tip speed ratio, λ is the ratio of the turbine tip speed, *ωm\*R* to the wind speed, *u*. This tip speed

> \* *<sup>m</sup> R u* w l

Where *ωm* is the rotational speed and *R* is the turbine blade radius, respectively.

( ) <sup>1</sup> <sup>3</sup> , <sup>2</sup> *m P P C Au* <sup>=</sup> lb r

Generator-side controller

> Grid-side controller

Simuliink (control circuit )

(30)

), *β* is the pitch angle (in degree), *A* is the area

); *u* is the wind speed (in m/s) and *Cp*(*λ, β*) is the wind-turbine

= (31)

SimCoupler Block (Power circuit)

generated by wind turbine at the shaft of the generator can be expressed as:

**Figure 22.** Co-simulation block of wind energy system interfaced to electric utility.

where *ρ* is the air density (typically 1.225 kg/m3

swept by the rotor blades (in m2

ratio, *λ,* is defined as [28]:

power coefficient (dimensionless).

To PSIM

180 New Developments in Renewable Energy

*4.1.1. Wind turbine model*

The generator is modeled by the following voltage equations in the rotor reference frame (dq axes) [29]:

$$\begin{aligned} \upsilon\_{sd} &= \mathcal{R}\_s \dot{i}\_{sd} + \frac{d\mathcal{\lambda}\_{sd}}{dt} - \alpha\_r \,\dot{\mathcal{\lambda}}\_{sq} \\ \upsilon\_{sq} &= \mathcal{R}\_s \dot{i}\_{sq} + \frac{d\mathcal{\lambda}\_{sq}}{dt} + \alpha\_r \,\dot{\mathcal{\lambda}}\_{sd} \end{aligned} \tag{32}$$

Where *λsq,* and *λsd* are the stator flux linkages in the direct and quadrature axis of rotor which in the absence of damper circuits can be expressed in terms of the stator currents and the magnetic flux as [29].

$$\begin{aligned} \mathcal{A}\_{sd} &= L\_s \dot{\mathbf{i}}\_{sd} + \boldsymbol{\Psi}\_F\\ \mathcal{A}\_{sq} &= L\_s \dot{\mathbf{i}}\_{sq} \end{aligned} \tag{33}$$

Where *ψ<sup>F</sup>* is the flux of the permanent magnets.

The electrical torque *Te* of the three-phase generator can be calculated as follows [29, 30]:

$$T\_e = \frac{3}{2} P \left[ \mathcal{A}\_{sd} i\_{sq} - \mathcal{A}\_{sq} i\_{sd} \right] \tag{34}$$

Where *P* is the number of pole pairs. For a non-salient-pole machine the stator inductances *Lsd* and *Lsq* are approximately equal. This means that the direct-axis current *isd* does not contribute to the electrical torque. Our concept is to keep *isd* to zero in order to obtain maximal torque with minimum current. Then, the electromagnetic torque results:

$$T\_e = \frac{3}{2} P \,\psi\_F \, i\_{sq} = K\_c i\_{sq} \tag{35}$$

*Kc* is called the torque constant and represents the proportional coefficient between *Te* and *isq.*

#### **4.2. Control of the generator side converter (PMSG)**

The generator side controller controls the rotational speed to produce the maximum output power via controlling the electromagnetic torque according to Equation (33), where the indirect vector control is used. The proposed control logic of the generator side converter is shown in Figure 24. The speed loop will generate the q-axis current component to control the generator torque and speed at different wind speed via estimating the references value of *iα, iβ* as shown in Figure 24. The torque control can be achieved through the control of the *isq* current as shown in Equation (33). Figure 25 shows the stator and rotor current space phasors and the excitation flux of the PMSG. The quadrature stator current *isq* can be controlled through the rotor reference frame (*α, β* axis) as shown in Figure 25. So, the references value of *iα, i<sup>β</sup>* can be estimated easily from the amplitude of *isq\** and the rotor angle, *Өr*. Initially, to find the rotor angle, *Өr*, the relationship between the electrical angular speed, *ωr* and the rotor mechanical speed (rad/ sec), *ωm* may be expressed as:

$$
\alpha \alpha\_r = \frac{P}{2} \alpha\_m \tag{36}
$$

2

PWM

abc / α, β Clark's Trasformation

*i*<sup>α</sup> *i<sup>β</sup>*

**Figure 24.** Control block diagram of generator side converter.

CCq *CCd i<sup>q</sup> i<sup>d</sup>*

*Frfr Ii* =

*id*

**Figure 28.** Control block diagram of grid-side converter.

*r*

**Figure 25.** The stator and rotor current space phasors and the excitation flux of the PMSG [29].

*i<sup>a</sup> i<sup>b</sup> ic*

Speed control

*i*<sup>α</sup> *i<sup>β</sup>*

SVPWM

*ωm\* ω<sup>m</sup>*

 a b c q d

*ic*

Utility

d (rotor direct-axis)

*sα* (stator direct -axis)

*θ*

CCq : q- axis Current Controller CCd : d- axis Current Controller VC : Voltage Controller

*i<sup>a</sup> i<sup>b</sup>*

*i*α*\* iβ\**

*v*αs*\* vβs\**

*CCα*

PMSG

*CCβ: β-* axis current controller *CCα: α-* axis current controller

**Δ***P* FLC

VC

*<sup>i</sup>q\* id\**

*vq\* vd\** SVPWM

PWM converter *<sup>v</sup>dc*

*sβ*

*vdc\**

*vdc*

*αs*

*iq*

*sq i*

**Δ***ω<sup>m</sup>*

**Figure 24.** Control block diagram of generator side converter.

*q*

*si*

converter *<sup>v</sup>dc*

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183

*CCβ*

So, the rotor angle, *Өr*, can be estimated by integrating of the electrical angular speed, *ωr*. The input to the speed control is the actual and reference rotor mechanical speed (rad/sec) and the output is the (*α, β*) reference current components. The actual values of the (*α, β*) current components are estimated using Clark's transformation to the three phase current of PMSG. The FLC can be used to find the reference speed along which tracks the maximum power point.

2

**Figure 24.** Control block diagram of generator side converter.

**Figure 24.** Control block diagram of generator side converter.

Where *ψ<sup>F</sup>* is the flux of the permanent magnets.

182 New Developments in Renewable Energy

The electrical torque *Te* of the three-phase generator can be calculated as follows [29, 30]:

<sup>3</sup> [ ] <sup>2</sup> *<sup>e</sup> sd sq sq sd T Pi i* = l

with minimum current. Then, the electromagnetic torque results:

**4.2. Control of the generator side converter (PMSG)**

sec), *ωm* may be expressed as:

3

<sup>2</sup> *e F sq c sq T P i Ki* = = y

*Kc* is called the torque constant and represents the proportional coefficient between *Te* and *isq.*

The generator side controller controls the rotational speed to produce the maximum output power via controlling the electromagnetic torque according to Equation (33), where the indirect vector control is used. The proposed control logic of the generator side converter is shown in Figure 24. The speed loop will generate the q-axis current component to control the generator torque and speed at different wind speed via estimating the references value of *iα, iβ* as shown in Figure 24. The torque control can be achieved through the control of the *isq* current as shown in Equation (33). Figure 25 shows the stator and rotor current space phasors and the excitation flux of the PMSG. The quadrature stator current *isq* can be controlled through the rotor reference frame (*α, β* axis) as shown in Figure 25. So, the references value of *iα, i<sup>β</sup>* can be estimated easily from the amplitude of *isq\** and the rotor angle, *Өr*. Initially, to find the rotor angle, *Өr*, the relationship between the electrical angular speed, *ωr* and the rotor mechanical speed (rad/

> 2 *r m P*

 w

So, the rotor angle, *Өr*, can be estimated by integrating of the electrical angular speed, *ωr*. The input to the speed control is the actual and reference rotor mechanical speed (rad/sec) and the output is the (*α, β*) reference current components. The actual values of the (*α, β*) current components are estimated using Clark's transformation to the three phase current of PMSG. The FLC can be used to find the reference speed along which tracks the maximum power point.

w

 l

Where *P* is the number of pole pairs. For a non-salient-pole machine the stator inductances *Lsd* and *Lsq* are approximately equal. This means that the direct-axis current *isd* does not contribute to the electrical torque. Our concept is to keep *isd* to zero in order to obtain maximal torque

(34)

(35)

= (36)

**Figure 25.** The stator and rotor current space phasors and the excitation flux of the PMSG [29].

#### **4.3. Fuzzy logic controller for MPPT**

At a certain wind speed, the power is maximum at a certain *ω* called optimum rotational speed, *ωopt*. This speed corresponds to optimum tip speed ratio,*λopt* [15]. So, to extract maximum power at variable wind speed, the turbine should always operate at *λopt*. This occurs by controlling the rotational speed of the turbine. Controlling of the turbine to operate at optimum rotational speed can be done using the fuzzy logic controller. Each wind turbine has one value of *λopt* at variable speed but *ωopt* changes from a certain wind speed to another. From Equation (29), the relation between *ωopt* and wind speed, *u*, for constant *R* and *λopt* can be deduced as follow:

$$
\rho \alpha\_{\rm opt} = \frac{\mathcal{A}\_{\rm opt}}{R} \mu \tag{37}
$$

Time delay

Time delay

*ωm\**

P

**Figure 26.** Input and output of fuzzy controller.

**Figure 27.** Membership functions of fuzzy logic controller

Fuzzy Logic Controller

Δωm\*

ΔP


N ZE P


Output membership functions

N++ NB NM NS ZE PS PM PB P++


N++ NB NM NS ZE PS PM PB P++

Time delay

*ωm-new\** <sup>Δ</sup>*ωm-new\** 

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185

Maximum Power Extraction from Utility-Interfaced Wind Turbines

From Equation (35), the relation between the optimum rotational speed and wind speed is linear. At a certain wind speed, there is optimum rotational speed which is different at another wind speed. The fuzzy logic control is used to search (observation and perturbation) the rotational speed reference which tracks the maximum power point at variable wind speeds. The fuzzy logic controller block diagram is shown in Figure 26. Two real time measurements are used as input to fuzzy (ΔP, and Δ*ωm\**) and the output is (Δ*ωm-new\**). Membership functions are shown in Figure 27. Triangular symmetrical membership functions are suitable for the input and output, which give more sensitivity especially as variables approach to zero value. The width of variation can be adjusted according to the system parameter. The input signals are first fuzzified and expressed in fuzzy set notation using linguistic labels which are characterized by membership functions before it is processed by the FLC. Using a set of rules and a fuzzy set theory, the output of the FLC is obtained [22]. This output, expressed as a fuzzy set using linguistic labels characterized by membership functions, is defuzzified and then produces the controller output. The fuzzy logic controller doesn't require any detailed mathematical model of the system and its operation is governed simply by a set of rules. The principle of the fuzzy logic controller is to perturb the reference speed *ωm\** and to observe the corresponding change of power, Δ*P*. If the output power increases with the last increment, the searching process continues in the same direction. On the other hand, if the speed increment reduces the output power, the direction of the searching is reversed. The fuzzy logic controller is efficient to track the maximum power point, especially in case of frequently changing wind conditions [22].

Figure 27 shows the input and output membership functions and Table 2 lists the control rule for the input and output variable. The next fuzzy levels are chosen for controlling the inputs and output of the fuzzy logic controller. The variation step of the power and the reference speed may vary depending on the system. In Figure 27, the variation step in the speed reference is from -0.15rad/s to 0.15rad/s for power variation ranging over from -30W to 30W. The membership definitions are given as follows: N (negative), N++ (very big negative), NB (negative big), NM (negative medium), NS (negative small), ZE (zero), P (positive), PS (positive small), PM (positive medium), PB (positive big), and P++ ( very big positive ).

**Figure 26.** Input and output of fuzzy controller.

**4.3. Fuzzy logic controller for MPPT**

184 New Developments in Renewable Energy

follow:

conditions [22].

At a certain wind speed, the power is maximum at a certain *ω* called optimum rotational speed, *ωopt*. This speed corresponds to optimum tip speed ratio,*λopt* [15]. So, to extract maximum power at variable wind speed, the turbine should always operate at *λopt*. This occurs by controlling the rotational speed of the turbine. Controlling of the turbine to operate at optimum rotational speed can be done using the fuzzy logic controller. Each wind turbine has one value of *λopt* at variable speed but *ωopt* changes from a certain wind speed to another. From Equation (29), the relation between *ωopt* and wind speed, *u*, for constant *R* and *λopt* can be deduced as

> *opt opt u R* l

From Equation (35), the relation between the optimum rotational speed and wind speed is linear. At a certain wind speed, there is optimum rotational speed which is different at another wind speed. The fuzzy logic control is used to search (observation and perturbation) the rotational speed reference which tracks the maximum power point at variable wind speeds. The fuzzy logic controller block diagram is shown in Figure 26. Two real time measurements are used as input to fuzzy (ΔP, and Δ*ωm\**) and the output is (Δ*ωm-new\**). Membership functions are shown in Figure 27. Triangular symmetrical membership functions are suitable for the input and output, which give more sensitivity especially as variables approach to zero value. The width of variation can be adjusted according to the system parameter. The input signals are first fuzzified and expressed in fuzzy set notation using linguistic labels which are characterized by membership functions before it is processed by the FLC. Using a set of rules and a fuzzy set theory, the output of the FLC is obtained [22]. This output, expressed as a fuzzy set using linguistic labels characterized by membership functions, is defuzzified and then produces the controller output. The fuzzy logic controller doesn't require any detailed mathematical model of the system and its operation is governed simply by a set of rules. The principle of the fuzzy logic controller is to perturb the reference speed *ωm\** and to observe the corresponding change of power, Δ*P*. If the output power increases with the last increment, the searching process continues in the same direction. On the other hand, if the speed increment reduces the output power, the direction of the searching is reversed. The fuzzy logic controller is efficient to track the maximum power point, especially in case of frequently changing wind

Figure 27 shows the input and output membership functions and Table 2 lists the control rule for the input and output variable. The next fuzzy levels are chosen for controlling the inputs and output of the fuzzy logic controller. The variation step of the power and the reference speed may vary depending on the system. In Figure 27, the variation step in the speed reference is from -0.15rad/s to 0.15rad/s for power variation ranging over from -30W to 30W. The membership definitions are given as follows: N (negative), N++ (very big negative), NB (negative big), NM (negative medium), NS (negative small), ZE (zero), P (positive), PS (positive

small), PM (positive medium), PB (positive big), and P++ ( very big positive ).

= (37)

w

**Figure 27.** Membership functions of fuzzy logic controller


**Table 2.** Rules of fuzzy logic controller

#### **4.4. Control of the grid side converter**

The power flow of the grid-side converter is controlled in order to maintain the dc-link voltage at reference value, 600v. Since increasing the output power than the input power to dc-link capacitor causes a decrease of the dc-link voltage and vise versa, the output power will be regulated to keep dc-link voltage approximately constant. To maintain the dc-link voltage constant and to ensure the reactive power flowing into the grid, the grid side converter currents are controlled using the d-q vector control approach. The dc-link voltage is controlled to the desired value by using a PI-controller and the change in the dc-link voltage represents a change in the q-axis (*iqs*) current component. Figure 28 shows a control block diagram of the grid side converter.

The active power can be defined as;

$$P\_s = \frac{3}{2} \left( \upsilon\_{ds} i\_{ds} + \upsilon\_{qs} i\_{qs} \right) \tag{38}$$

The reactive power can be defined as:

$$Q\_s = \frac{3}{2} \left( v\_{qs} i\_{ds} - v\_{ds} i\_{qs} \right) \tag{39}$$

By aligning the q-axis of the reference frame along with the grid voltage position *vds*=0 and *vqs*= constant because the grid voltage is assumed to be constant. Then the active and reactive power can be obtained from the following equations:

$$P\_s = \frac{3}{2} \upsilon\_{qs} i\_{qs} \tag{40}$$

2

PWM converter

abc / α, β Clark's Trasformation

*i*<sup>α</sup> *i<sup>β</sup>*

**Figure 24.** Control block diagram of generator side converter.

CCq *CCd i<sup>q</sup> i<sup>d</sup>*

*id*

A co-simulation (PSIM/Simulink) program has been used where PSIM contains the power circuit of the WECS and Matlab/Simulink has the whole control system as described before. The model of WECS in PSIM contains the WT connected to the utility grid through back–toback bidirectional PWM converter. The control of whole system in Simulink contains the generator side controller and the grid side controller. The wind turbine characteristics and the parameters of the PMSG are listed in Appendix. The generator can be directly controlled by the generator side controller to track the maximum power available from the WT. The wind speed is variable and changes from 7 m/s to 13 m/s as input to WT. To extract maximum power at variable wind speed, the turbine should always operate at *λopt*. This occurs by controlling the rotational speed of the WT. So, it always operates at the optimum rotational speed. *ωopt* changes from a certain wind speed to another. The fuzzy logic controller is used to search the optimum rotational speed which tracks the maximum power point at variable wind speeds. Figure 29 (a) shows the variation of the wind speed which varies randomly from 7 m/s to13 m/s. On the other hand, Figure 29 (b) shows the variation of the actual and reference rotational speed as a result of the wind speed variation. At a certain wind speed, the actual and reference rotational speed have been estimated and this agree with the power characteristic of the wind turbine shown later in Figure 23. I.e. the WT always operates at the optimum rotational speed which is found using FLC; hence, the power extraction from wind is maximum at variable

*i<sup>a</sup> i<sup>b</sup> ic*

Speed control

*i*<sup>α</sup> *i<sup>β</sup>*

SVPWM

*CCβ*

*ωm\* ω<sup>m</sup>*

 a b c q d

*ic*

Utility

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187

*θ*

Maximum Power Extraction from Utility-Interfaced Wind Turbines

CCq : q- axis Current Controller CCd : d- axis Current Controller VC : Voltage Controller

*i<sup>a</sup> i<sup>b</sup>*

*i*α*\* iβ\**

*v*αs*\* vβs\**

*CCα*

PMSG

*CCβ: β-* axis current controller *CCα: α-* axis current controller

**Δ***P* FLC

VC

*<sup>i</sup>q\* id\**

**Figure 28.** Control block diagram of grid-side converter. **Figure 28.** Control block diagram of grid-side converter.

*vq\* vd\**

SVPWM

PWM converter *<sup>v</sup>dc*

*vdc\**

*vdc*

**4.5. Simulation results**

*iq*

**Δ***ω<sup>m</sup>*

*vdc*

$$Q\_s = \frac{\mathfrak{Z}}{2} v\_{qs} i\_{ds} \tag{41}$$

PWM converter

Speed control

*i*<sup>α</sup> *i<sup>β</sup>*

SVPWM

*CCβ*

*ωm\* ω<sup>m</sup>*

*i*α*\* iβ\**

*v*αs*\* vβs\**

*CCα*

*vdc*

2

abc / α, β Clark's Trasformation

*i*<sup>α</sup> *i<sup>β</sup>*

*i<sup>a</sup> i<sup>b</sup> ic*

**Figure 28.** Control block diagram of grid-side converter. **Figure 28.** Control block diagram of grid-side converter.

PMSG

*CCβ: β-* axis current controller *CCα: α-* axis current controller

**Δ***P* FLC

**Δ***ω<sup>m</sup>*

#### **4.5. Simulation results**

ΔP Δω<sup>m</sup>

converter.

**Table 2.** Rules of fuzzy logic controller

186 New Developments in Renewable Energy

**4.4. Control of the grid side converter**

The active power can be defined as;

The reactive power can be defined as:

can be obtained from the following equations:

**N++ NB NM NS ZE PS PM PB P++**

**N** P++ PB PM PS ZE NS NM NB N++

**ZE** NB NM NS NS ZE PS PM PM PB **P** N++ NB NM NS ZE PM PM PB PB

The power flow of the grid-side converter is controlled in order to maintain the dc-link voltage at reference value, 600v. Since increasing the output power than the input power to dc-link capacitor causes a decrease of the dc-link voltage and vise versa, the output power will be regulated to keep dc-link voltage approximately constant. To maintain the dc-link voltage constant and to ensure the reactive power flowing into the grid, the grid side converter currents are controlled using the d-q vector control approach. The dc-link voltage is controlled to the desired value by using a PI-controller and the change in the dc-link voltage represents a change in the q-axis (*iqs*) current component. Figure 28 shows a control block diagram of the grid side

( ) <sup>3</sup>

( ) <sup>3</sup>

By aligning the q-axis of the reference frame along with the grid voltage position *vds*=0 and *vqs*= constant because the grid voltage is assumed to be constant. Then the active and reactive power

3

3

<sup>2</sup> *s ds ds qs qs P vi vi* = + (38)

<sup>2</sup> *Q vi vi s qs ds ds qs* = - (39)

<sup>2</sup> *s qs qs P vi* <sup>=</sup> (40)

<sup>2</sup> *Q vi s qs ds* <sup>=</sup> (41)

A co-simulation (PSIM/Simulink) program has been used where PSIM contains the power circuit of the WECS and Matlab/Simulink has the whole control system as described before. The model of WECS in PSIM contains the WT connected to the utility grid through back–toback bidirectional PWM converter. The control of whole system in Simulink contains the generator side controller and the grid side controller. The wind turbine characteristics and the parameters of the PMSG are listed in Appendix. The generator can be directly controlled by the generator side controller to track the maximum power available from the WT. The wind speed is variable and changes from 7 m/s to 13 m/s as input to WT. To extract maximum power at variable wind speed, the turbine should always operate at *λopt*. This occurs by controlling the rotational speed of the WT. So, it always operates at the optimum rotational speed. *ωopt* changes from a certain wind speed to another. The fuzzy logic controller is used to search the optimum rotational speed which tracks the maximum power point at variable wind speeds. Figure 29 (a) shows the variation of the wind speed which varies randomly from 7 m/s to13 m/s. On the other hand, Figure 29 (b) shows the variation of the actual and reference rotational speed as a result of the wind speed variation. At a certain wind speed, the actual and reference rotational speed have been estimated and this agree with the power characteristic of the wind turbine shown later in Figure 23. I.e. the WT always operates at the optimum rotational speed which is found using FLC; hence, the power extraction from wind is maximum at variable wind speed. It is seen that according to the wind speed variation the generator speed varies and that its output power is produced corresponding to the wind speed variation. The fuzzy logic controller works well and it gives the good tracking performance for the maximum output power point. The fuzzy logic controller makes WT always operates at the optimum rotational speed. On the other hand, the grid-side controller maintains the dc-link voltage at the desired value, 600v, as shown in Figure 29 (c). The dc-link voltage is regulated by exporting active power to the grid as shown in Figure 29 (d). The reactive power transmitted to the grid is shown in Figure 29 (e).

**Figure 29.** Different simulation waveforms: (a) Wind speed variation (7-13) m/s. (b) Actual and reference rotational speed (rad/s). (c) dc-link voltage (v). (d) Active power (watt). (e) Reactive power (Var).

3

**5. Conclusions**

the whole control system.

**Table 3.** Parameters of wind turbine model and PMSG

**Appendix**

Wind energy conversion system has high priority among the various renewable energy systems. Maximum power extraction from wind energy system became an importantresearch topic due to the increase in output energy by using this technique. Wind speed sensorless MPPT control has been a very active area of research. In this study, a concise review of MPPT control methods has been presented for controlling WECS. On the other hand, there is a continuing effort to make converter and control schemes more efficient and cost effective in hopes of developing an economically viable solution of increasing environmental issues. Wind power generation has grown at a high rate in the past decade and will continue with power electronic technology advanced. The survey of MPPT algorithms have been classi‐ fied into MPPT algorithms with wind speed sensor and MPPT algorithms without wind speed sensor. A co-simulation (PSIM/Simulink) program has been proposed for WECS where PSIM contains the power circuit of the WECS and Matlab/Simulink has the control circuit of the system. The WT is connected to the grid via back–to-back PWM-VSC. The generator side controller and the grid side controller have been done in Simulink. The main function of the generator side controller is to track the maximum power from wind through controlling the rotational speed of the turbine using fuzzy logic controller. The fuzzy logic algorithm for the maximum output power of the grid-connected wind power generation system using a PMSG has been proposed and implemented above. The PMSG was controlled in indirect-vector field oriented control method and its speed reference was determined using fuzzy logic controller. The grid-side converter controls the dc-link voltage at a desired value, 600V, for the proposed system. Active and reactive power control has been achieved by controlling qaxis and d-axis grid current components respectively. The d-axis grid current is controlled to be zero for unity power factor and the q-axis grid current is controlled to deliver the power flowing from the dc-link to the grid. The simulation results prove the superiority of FLC and

Maximum Power Extraction from Utility-Interfaced Wind Turbines

http://dx.doi.org/10.5772/54675

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**Wind turbine PMSG** Nominal Output Power 19kw *Rs* (stator resistance) 1m Wind speed input 7:13 m/s (saw tooth) *Ld* (d-axis inductance) 1m Base Wind Speed 12 m/s *Lq* (q-axis inductance) 1m Base Rotational Speed 190 rpm No. of Poles P 30 Moment of inertia 1m Moment of inertia 100m Blade pitch angle input 0º Mech. Time Constant 1
