**2. Wind Energy Conversion Systems (WECS)**

rings. In addition, the performance of PM materials is improving, and the cost is decreasing in recent years. Therefore, these advantages make direct-drive PM wind turbine systems more

Robust controller has been developed in many literatures [5-15] to track the maximum power available in the wind. They include tip speed ratio (TSR) [5, 13], power signal feedback (PSF) [8, 14], and the hill-climb searching (HCS) [11-12] methods. The TSR control method regulates the rotational speed of the generator to maintain an optimal TSR at which power extracted is maximum [13]. For TSR calculation, both the wind speed and turbine speed need to be measured, and the optimal TSR must be given to the controller. The first barrier to implement TSR control is the wind speed measurement, which adds to system cost and presents difficul‐ ties in practical implementations. The second barrier is the need to obtain the optimal value of TSR, this value is different from one system to another. This depends on the turbine-generator characteristics results in custom-designed control software tailored for individual wind turbines [14]. In PSF control [8, 14], it is required to have the knowledge of the wind turbine's maximum power curve, and track this curve through its control mechanisms. The power curves need to be obtained via simulations or off-line experiment on individual wind turbines or from the datasheet of WT which makes it difficult to implement with accuracy in practical applications [7-8, 15]. The HCS technique does not require the data of wind, generator speeds and the turbine characteristics. But, this method works well only for very small wind turbine inertia. For large inertia wind turbines, the system output power is interlaced with the turbine mechanical power and rate of change in the mechanically stored energy, which often renders the HCS method ineffective [11-12]. On the other hand, different algorithms have been used for maximum power extraction from WT in addition to the three method mentioned above. For example, Reference [1] presents an algorithm for maximum power extraction and reactive power control of an inverter through the power angle, *δ* of the inverter terminal voltage and the modulation index, *m*a based variable-speed WT without wind speed sensor. Reference [16] presents an algorithm for MPPT via controlling the generator torque through q-axis current and hence controlling the generator speed with variation of the wind speed. These techniques are used for a decoupled control of the active and reactive power from the WT through q-axis and d-axis current respectively. Also, reference [17] presents a decoupled control of the active and reactive power from the WT, independently through q-axis and d-axis current but maximum power point operation of turbine system has been produced through regulating the input dc current of the dc/dc boost converter to follow the optimized current reference [17]. Reference [18] presents an algorithm for MPPT through directly adjusting duty ratio of the dc/ dc boost converter and modulation index of the PWM- VSC. Reference [19] presents MPPT control algorithm based on measuring the dc-link voltage and current of the uncontrolled rectifier to attain the maximum available power from wind. Finally, references [20-22] present MPPT control based on a fuzzy logic control (FLC). The function of FLC is to track the generator speed with the reference speed for maximum power extraction at variable speeds. The MPPT algorithms can be divided into two categories, the first one is MPPT algorithms for WT with wind speed sensor and the second one is MPPT algorithms without wind speed sensor (sensorless MPPT controller). Wind speed sensor normally used in conventional wind energy conversion systems, WECS [10, 23] for implementing MPPT control algorithm. This algorithm

attractive in application of small and medium-scale wind turbines [1, 3-4].

160 New Developments in Renewable Energy

Figure 1 shows the schematic diagram of the variable-speed wind energy conversion system based on a synchronous generator. This system is directly connected to the grid through power conversion system. There are two common types of the power conversion systems, the first configuration is a back-to-back PWM-VSC connected to the grid. This configuration has a lot of switches, which cause more losses and voltage stress in addition to the presence of Electro‐ magnetic Interference (EMI). The presence of a dc-link capacitor in PWM-VSC system provides a decoupling between the two converters, it separates the control between these two convert‐ ers, allowing compensation of asymmetry of both on the generator side and on the grid side, independently [16]. The second configuration consists of a diode-bridge rectifier, a boost converter and a PWM-VSC connected to the grid. This configuration is, simple, less expensive, robust, and rigid and needs simple control system. But, with this configuration the control of the generator power factor is not possible, which in turn, affects generator efficiency. Also, high harmonic distortion currents are obtained in the generator that reduce efficiency and produce torque oscillations [22].

**Figure 1.** Wind energy conversion system based on a synchronous generator [26].

Wind turbine converts the wind power to a mechanical power, which in turn, runs a generator to generate electrical power. The mechanical power generated by wind turbine can be expressed as [15]:

$$P\_m = \frac{1}{2} \mathcal{C}\_p \left(\mathcal{A}, \mathcal{J}\right) \rho A u^3 \tag{1}$$

where

*Cp*: Turbine power coefficient.

*ρ*: Air density (kg/m3 ).

*A*: Turbine sweeping area (m2 ).

*u*: wind speed (m/s).

*λ*: tip speed ratio of the wind turbine which is given by the following equation [1];

$$
\lambda = \frac{r\_m \,\alpha\_r}{\mu} \tag{2}
$$

20 0

In this arrangement both the generator and the grid-side converters are PWM-VSCs as shown in Figure 3. The output voltage of the generator is converted into dc voltage through a PWM-VSC. As the previous model the dc-link voltage is converted to constant frequency voltage using grid side PWM-VSC. The dc-link voltage is controlled by the modulation index (*m*a) and power angle (*δ*). Controlling the dc-link voltage and the bitch angle of the blades of WT will track the maximum power of WT in the case of variable pitch angle control. In the case of fixed pitch angle control the maximum power extraction is achieved by tracking the optimum shaft speed. The grid side PWM-VSC can be used to enhance the stability of the dc-link voltage and controls the active and reactive power from WT by controlling *m*a and *δ*. The generator can be directly controlled by the generator side converter (controller-1) while the grid-side converter (controller-2) maintains the dc-link voltage at the desired value by exporting active power to the grid. Controller-2 also controls the reactive power exchange with the grid [26]. So, the main target of controller-1 is to track the maximum power available from the WTG and the function of controller-2 is to control the dc-link voltage and the reactive power injected to the electric

Figure 4 shows the wind turbine with a diode-based rectifier as the generator-side converter. The diode bridge rectifier converts the generator output ac power to dc power and the PWM-VSC converts the dc power from the rectifier output to ac power. One method to control the operation of the wind turbine with this arrangement (assuming a PMSG) is illustrated in Figure 4. A dc–dc converter is employed to control the dc-link voltage (controller-1), the grid side converter controls the operation of the generator and the power flow to the grid (controller-2). With appropriate control, the generator and turbine speed can be adjusted as wind speed varies so that maximum energy is collected [26]. On the other hand, in most PMSG wind systems,

b

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163

l

*Cp*

**Figure 2.** Aerodynamic power coefficient variation against λ and β.

utility.

**2.1. Wind turbine arrangement with back-to-back PWM-VSCs**

**2.2. Wind turbine arrangement with diode-based rectifier**

Where *rm* is the turbine rotor radius, *ωr*is the angular velocity of turbine (rad/s).

The turbine power coefficient, *C*p, describes the power extraction efficiency of the wind turbine. It is a nonlinear function of both tip speed ratio, λ and the blade pitch angle, *β*. While its maximum theoretical value is approximately 0.59, it is practically between 0.4 and 0.45 [15]. There are many different versions of fitted equations for *C*<sup>p</sup> made in the literatures. A generic equation has been used to model *C*p(*λ, β*) and based on the modeling turbine characteristics as shown in the following equation [27]:

$$\mathbf{C}\_{p}\left(\lambda,\beta\right) = 0.5176 \left(116\,^{\circ}\frac{1}{\lambda\_{\text{i}}} - 0.4\,\beta - 5\right) e^{-\frac{21}{\lambda\_{\text{i}}}} + 0.0068\lambda\tag{3}$$

With

$$\frac{1}{\lambda\_i} = \frac{1}{\lambda + 0.08\beta} - \frac{0.035}{1 + \beta^3} \tag{4}$$

The Cp-λ characteristics, for different values of the pitch angle *β*, are illustrated in Figure 2. The maximum value of Cp is achieved for *β* = 0 degree and for *λ*opt. The particular value of *λ* is defined as the optimal value (*λ*opt). Continuous operation of wind turbine at this point guarantees the maximum available power which can be harvested from the available wind at any speed.

**Figure 2.** Aerodynamic power coefficient variation against λ and β.

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

*λ*: tip speed ratio of the wind turbine which is given by the following equation [1];

l

Where *rm* is the turbine rotor radius, *ωr*is the angular velocity of turbine (rad/s).

*m r r u* w

The turbine power coefficient, *C*p, describes the power extraction efficiency of the wind turbine. It is a nonlinear function of both tip speed ratio, λ and the blade pitch angle, *β*. While its maximum theoretical value is approximately 0.59, it is practically between 0.4 and 0.45 [15]. There are many different versions of fitted equations for *C*<sup>p</sup> made in the literatures. A generic equation has been used to model *C*p(*λ, β*) and based on the modeling turbine characteristics

<sup>1</sup> , 0.5176 116 \* 0.4 5 0.0068 *<sup>i</sup>*


b

*i*

1 1 0.035

 b*<sup>i</sup>* 0.08 1

The Cp-λ characteristics, for different values of the pitch angle *β*, are illustrated in Figure 2. The maximum value of Cp is achieved for *β* = 0 degree and for *λ*opt. The particular value of *λ* is defined as the optimal value (*λ*opt). Continuous operation of wind turbine at this point guarantees the maximum available power which can be harvested from the available wind at

l

*C e*

ll

21

l

3

b

where

With

any speed.

*Cp*: Turbine power coefficient.

162 New Developments in Renewable Energy

*A*: Turbine sweeping area (m2

).

as shown in the following equation [27]:

*P*

( )

l b ).

*ρ*: Air density (kg/m3

*u*: wind speed (m/s).

(1)

= (2)

l

= - <sup>+</sup> <sup>+</sup> (4)

(3)

### **2.1. Wind turbine arrangement with back-to-back PWM-VSCs**

In this arrangement both the generator and the grid-side converters are PWM-VSCs as shown in Figure 3. The output voltage of the generator is converted into dc voltage through a PWM-VSC. As the previous model the dc-link voltage is converted to constant frequency voltage using grid side PWM-VSC. The dc-link voltage is controlled by the modulation index (*m*a) and power angle (*δ*). Controlling the dc-link voltage and the bitch angle of the blades of WT will track the maximum power of WT in the case of variable pitch angle control. In the case of fixed pitch angle control the maximum power extraction is achieved by tracking the optimum shaft speed. The grid side PWM-VSC can be used to enhance the stability of the dc-link voltage and controls the active and reactive power from WT by controlling *m*a and *δ*. The generator can be directly controlled by the generator side converter (controller-1) while the grid-side converter (controller-2) maintains the dc-link voltage at the desired value by exporting active power to the grid. Controller-2 also controls the reactive power exchange with the grid [26]. So, the main target of controller-1 is to track the maximum power available from the WTG and the function of controller-2 is to control the dc-link voltage and the reactive power injected to the electric utility.

#### **2.2. Wind turbine arrangement with diode-based rectifier**

Figure 4 shows the wind turbine with a diode-based rectifier as the generator-side converter. The diode bridge rectifier converts the generator output ac power to dc power and the PWM-VSC converts the dc power from the rectifier output to ac power. One method to control the operation of the wind turbine with this arrangement (assuming a PMSG) is illustrated in Figure 4. A dc–dc converter is employed to control the dc-link voltage (controller-1), the grid side converter controls the operation of the generator and the power flow to the grid (controller-2). With appropriate control, the generator and turbine speed can be adjusted as wind speed varies so that maximum energy is collected [26]. On the other hand, in most PMSG wind systems,

the day, even though abundant. The Amount of power output from a WECS depends upon the accuracy of tracking the peak power points using the MPPT controller irrespective of the generator type used. The maximum power extraction algorithms can be classified into two categories. The two categories are MPPT algorithms with wind speed sensor and MPPT algorithms without wind speed sensor (sensor-less MPPT controller). These two algorithms

The TSR control method regulates the rotational speed of the generator to maintain an optimal TSR at which power extracted is maximum [13]. The target optimum power extracted from

3

*rm* \* *u*

Controller Wind Energy

Load Power

Generator Speed, Wind Speed

w*<sup>g</sup>* \* *R* system

w*g*

w*g*

(5)

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165

w

The power for a certain wind speed is maximum at a certain value of rotational speed called optimum rotational speed,*ω*opt. This optimum rotational speed corresponds to optimum tip speed ratio, *λ*opt. In order to track maximum possible power, the turbine should always operate at *λ*opt. This is achieved by controlling the rotational speed of the WT so that it always rotates at the optimum rotational speed. As shown in Figure 5, for TSR calculation, both the wind speed and turbine speed need to be measured, and the optimal TSR must be given to the controller. The first barrier to implement TSR control is the wind speed measurement, which adds to system cost and presents difficulties in practical implementations. The second barrier is the need to obtain the optimal value of TSR, this value is different from one system to another. This depends on the turbine-generator characteristics results in custom-designed control

max \* *opt opt P K*=

\* *CP*−max, and *ωopt* <sup>=</sup> *<sup>λ</sup>opt*

have been discussed in the following sections.

*3.1.1. Tip Speed Ratio (TSR) technique*

wind turbine can be written as [14]:

Where*Kopt* =0.5 \* *<sup>ρ</sup> <sup>A</sup>* \*( *rm*

l*opt*

Reference Tip-speed ratio

**3.1. MPPT algorithms for a WT with wind speed sensor**

*λopt* ) 3

software tailored for individual wind turbines [14].

l*act*

÷

**Figure 5.** The block diagram of the tip speed ratio control of WECS [15].

**Figure 3.** Wind turbine generator with back-to-back PWM-VSCs [26].

the output voltage of the generator is converted into dc voltage via a full-bridge diode rectifier and this dc voltage is adjusted to control the maximum power of turbine. The grid side converter is controlled by grid injected active and reactive power control method. The ac power output from PMSG is fed to a three-phase diode bridge forward by boost converter to effectively control the dc voltage level through the duty ratio of boost converter. The PWM-VSC is used to interface the WTG with the electrical utility also to track the maximum power available from PMSG. The modulation index of the PWM-VSC is controlled to enhance the stability of the dc link voltage as shown in Figure 4.

**Figure 4.** Wind turbine generator with a diode-based rectifier as the generator-side converter [26].

#### **3. MPPT control strategies for the WECS**

WECS has been attracting wide attention as a renewable energy source due to depleting fossil fuel reserves and environmental concerns as a direct consequence of using fossil fuel and nuclear energy sources. Wind energy varies continually as wind speed changes throughout the day, even though abundant. The Amount of power output from a WECS depends upon the accuracy of tracking the peak power points using the MPPT controller irrespective of the generator type used. The maximum power extraction algorithms can be classified into two categories. The two categories are MPPT algorithms with wind speed sensor and MPPT algorithms without wind speed sensor (sensor-less MPPT controller). These two algorithms have been discussed in the following sections.

#### **3.1. MPPT algorithms for a WT with wind speed sensor**

#### *3.1.1. Tip Speed Ratio (TSR) technique*

the output voltage of the generator is converted into dc voltage via a full-bridge diode rectifier and this dc voltage is adjusted to control the maximum power of turbine. The grid side converter is controlled by grid injected active and reactive power control method. The ac power output from PMSG is fed to a three-phase diode bridge forward by boost converter to effectively control the dc voltage level through the duty ratio of boost converter. The PWM-VSC is used to interface the WTG with the electrical utility also to track the maximum power available from PMSG. The modulation index of the PWM-VSC is controlled to enhance the

Controller -1 Controller -2

Controller -1 Controller -2

WECS has been attracting wide attention as a renewable energy source due to depleting fossil fuel reserves and environmental concerns as a direct consequence of using fossil fuel and nuclear energy sources. Wind energy varies continually as wind speed changes throughout

**Figure 4.** Wind turbine generator with a diode-based rectifier as the generator-side converter [26].

dc–dc converter

stability of the dc link voltage as shown in Figure 4.

**Figure 3.** Wind turbine generator with back-to-back PWM-VSCs [26].

164 New Developments in Renewable Energy

**3. MPPT control strategies for the WECS**

The TSR control method regulates the rotational speed of the generator to maintain an optimal TSR at which power extracted is maximum [13]. The target optimum power extracted from wind turbine can be written as [14]:

$$P\_{\text{max}} = K\_{\text{opt}} \, ^\ast \, \text{o} \, ^\ast\_{\text{opt}} \tag{5}$$

$$\text{Where}\\
K\_{opt} = 0.5 \,\text{\*}\,\rho \,\text{A} \,\text{\*}\,\left(\frac{r\_m}{\lambda\_{opt}}\right)^3 \,\text{\*}\,\text{C}\_{P-\text{max}\,\text{\*}}\,\text{and}\,\,\omega\_{opt} = \frac{\lambda\_{opt}}{r\_m} \,\text{\*}\,\mu$$

The power for a certain wind speed is maximum at a certain value of rotational speed called optimum rotational speed,*ω*opt. This optimum rotational speed corresponds to optimum tip speed ratio, *λ*opt. In order to track maximum possible power, the turbine should always operate at *λ*opt. This is achieved by controlling the rotational speed of the WT so that it always rotates at the optimum rotational speed. As shown in Figure 5, for TSR calculation, both the wind speed and turbine speed need to be measured, and the optimal TSR must be given to the controller. The first barrier to implement TSR control is the wind speed measurement, which adds to system cost and presents difficulties in practical implementations. The second barrier is the need to obtain the optimal value of TSR, this value is different from one system to another. This depends on the turbine-generator characteristics results in custom-designed control software tailored for individual wind turbines [14].

**Figure 5.** The block diagram of the tip speed ratio control of WECS [15].

#### *3.1.2. Power Signal Feedback (PSF) control*

In PSF control [14], it is required to have the knowledge of the wind turbine's maximum power curve, and track this curve through its control mechanisms. The maximum power curves need to be obtained via simulations or off-line experiment on individual wind turbines or from the datasheet of WT which makes it difficult to implement with accuracy in practical applications. In this method, reference power is generated using a maximum power data curve or using the mechanical power equation of the wind turbine where wind speed or the rotational speed is used as the input. Figure 6 shows the block diagram of a WECS with PSF controller for maximum power extraction. The PSF control block generates the optimal power command *P*opt which is then applied to the grid side converter control system for maximum power extraction as follow [15]:

$$P\_{opt} = K\_{opt} \, ^\ast \, \alpha\_r \, ^3 \, \tag{6}$$

and the control objective is to keep the turbine on this curve as the wind speed varies. For any wind speed, the MPPT device imposes a torque reference able to extract the maximum power.

3

Generator Torque

2 w*g*

12 m/s

**Generator speed**

10 m/s

8 m/s

The load angle control can be explained by analyzing the transfer of active and reactive power between two sources connected by an inductive reactance as shown in Figure 9. The active

14 m/s **Maximum torque** 

6 m/s

**curve (***Topt***)**

Controller Wind Energy

system

w*g*

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

max 0.5 \* \* \* *<sup>m</sup> opt P*

l-

*<sup>r</sup> K AC* r

æ ö <sup>=</sup> ç ÷ ç ÷ è ø

*opt*

(7)

Maximum Power Extraction from Utility-Interfaced Wind Turbines

(8)

167

<sup>2</sup> \* *opt opt opt T K*<sup>=</sup> w

The curve *T*opt is defined by [26]:

*Kopt*

*3.1.4. Load angle control*

×

Reference Torque

**Figure 7.** The block diagram of optimal torque control MPPT method.

**Rated torque**

**Figure 8.** Wind turbine characteristic for maximum power extraction [26].

**Generator torque**

Where

The actual power output, *P*<sup>t</sup> is compared to the optimal power, *P*opt and any mismatch is used by the fuzzy logic controller to change the modulation index of the grid side converter, PWM-VSC as shown in Figure 6. The PWM-VSC is used to interface the WT with the electrical utility and will be controlled through the power angle, *δ* and modulation index, *m*a to control the active and reactive power output from the WTG [15].

**Figure 6.** The block diagram of power signal feedback control [15].

#### *3.1.3. Optimal torque control*

The aim of the torque controller is to optimize the efficiency of wind energy capture in a wide range of wind velocities, keeping the power generated by the machine equal to the optimal defined value. It can be observed from the block diagram represented in Figure 7, that the idea of this method is to adjust the PMSG torque according to the optimal reference torque of the wind turbine at a given wind speed. A typical wind turbine characteristic with the optimal torque-speed curve plotted to intersect the *C*P-max points for each wind speed is illustrated in Figure 8. The curve *T*opt defines the optimal torque of the device (i.e. maximum energy capture), and the control objective is to keep the turbine on this curve as the wind speed varies. For any wind speed, the MPPT device imposes a torque reference able to extract the maximum power. The curve *T*opt is defined by [26]:

$$T\_{\rm opt} = K\_{\rm opt} \, ^\ast \, \phi \, ^2\_{\rm opt} \tag{7}$$

Where

*3.1.2. Power Signal Feedback (PSF) control*

166 New Developments in Renewable Energy

active and reactive power output from the WTG [15].

*Popt*

**Figure 6.** The block diagram of power signal feedback control [15].

w*r*

Lookup Table

*Popt*

*3.1.3. Optimal torque control*

as follow [15]:

In PSF control [14], it is required to have the knowledge of the wind turbine's maximum power curve, and track this curve through its control mechanisms. The maximum power curves need to be obtained via simulations or off-line experiment on individual wind turbines or from the datasheet of WT which makes it difficult to implement with accuracy in practical applications. In this method, reference power is generated using a maximum power data curve or using the mechanical power equation of the wind turbine where wind speed or the rotational speed is used as the input. Figure 6 shows the block diagram of a WECS with PSF controller for maximum power extraction. The PSF control block generates the optimal power command *P*opt which is then applied to the grid side converter control system for maximum power extraction

<sup>3</sup> \* *opt opt r P K*<sup>=</sup>

w

The actual power output, *P*<sup>t</sup> is compared to the optimal power, *P*opt and any mismatch is used by the fuzzy logic controller to change the modulation index of the grid side converter, PWM-VSC as shown in Figure 6. The PWM-VSC is used to interface the WT with the electrical utility and will be controlled through the power angle, *δ* and modulation index, *m*a to control the

Turbine power,

*<sup>r</sup>* Rotational Speed ,

The aim of the torque controller is to optimize the efficiency of wind energy capture in a wide range of wind velocities, keeping the power generated by the machine equal to the optimal defined value. It can be observed from the block diagram represented in Figure 7, that the idea of this method is to adjust the PMSG torque according to the optimal reference torque of the wind turbine at a given wind speed. A typical wind turbine characteristic with the optimal torque-speed curve plotted to intersect the *C*P-max points for each wind speed is illustrated in Figure 8. The curve *T*opt defines the optimal torque of the device (i.e. maximum energy capture),

w

Controller Wind Energy

*Pt*

system

w*r*

(6)

$$K\_{opt} = 0.5 \,\, ^\ast \rho \, A \, ^\ast \left(\frac{r\_m}{\lambda\_{opt}}\right)^3 \, ^\ast \mathbb{C}\_{P-\max} \tag{8}$$

**Figure 7.** The block diagram of optimal torque control MPPT method.

**Figure 8.** Wind turbine characteristic for maximum power extraction [26].

#### *3.1.4. Load angle control*

The load angle control can be explained by analyzing the transfer of active and reactive power between two sources connected by an inductive reactance as shown in Figure 9. The active power, *P*S, and reactive power, *Q*S, transferred from the sending-end to the receiving-end can be calculated from the following equation [26]:

$$P\_s = \frac{V\_s \ V\_R}{X\_{gen}} \sin \delta \tag{9}$$

Where *PSgen*

can be set to zero, *QSgen*

*3.1.4.2. Load angle control for the grid-side converter*

*ref* is the reference value of the active power that needs to be transferred from the

*ref* = 0 (i.e. *V*S and *V*<sup>R</sup> are equal in magnitude). The implementation of this

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169

generator to the dc-link, and *QSgen ref* is the reference value for the reactive power. The reference value *PSgen ref* is obtained from the characteristic curve of the machine for maximum power extraction for a given generator speed, *ω*r. As the generator has permanent magnets, it does not require magnetizing current through the stator, thus the reactive power reference value

load angle control scheme is illustrated in Figure 9. The major advantage of the load angle control is its simplicity. However, as the dynamics of the generator are not considered it may

The objective of the grid-side converter controller is to maintain the dc-link voltage at the reference value by exporting active power to the grid. In addition, the controller is designed to enable the exchange of reactive power between the converter and the grid as required by the application specifications. Also, the load angle control is a widely used grid side converter control method, where the grid-side converter is the sending source *(V*S∠*δ)*, and the grid is the receiving source *(V*R∠0*)*. As known, the grid voltage is selected as the reference; hence, the phase angle *δ* is positive. The reactance *X*grid is the inductor coupling between these two sources [26]. The reference value for the active power,*PSgrid ref* , that needs to be transmitted to the grid

*gen Ps grid Ps*

This figure illustrates the power balance at the dc-link [26] as shown in the following equation:

where *P*C is the power across the dc-link capacitor, *C*, *P*Sgen is the active power output of the generator (and transmitted to the dc-link), and *P*Sgrid is the active power transmitted from the

The dc-link voltage *V*dc can be expressed in terms of the generator output power, *P*Sgen, and the

power transmitted to the grid, *P*Sgrid, as shown in the following [26]:

*C*

Power transmitted to the grid

C Sgen Sgrid P =P -P (13)

not be very effective in controlling the generator during transient operation [26].

can be determined by examining the dc-link dynamics with the aid of Figure 10.

Generator *Pc*

+ \_ *Vdc*

output power

**Figure 10.** Power flow in the dc-link [26].

dc-link to the grid.

$$\mathcal{Q}\_s = \frac{V\_s^2}{X\_{gen}} - \frac{V\_s \ V\_R}{X\_{gen}} \tag{10}$$

**Figure 9.** Load angle control of the generator-side converter [26].

#### *3.1.4.1. Load angle control of the generator-side converter*

The operation of the generator and the power transferred to the dc-link are controlled by adjusting the magnitude and angle of the voltage at the ac terminals of the generator-side converter. This can be achieved using the load angle control technique where the internal voltage of the generator is the sending source *(V*s∠0*)*, and the generator-side converter is the receiving source *(V*R∠*δ)*. The inductive reactance between these two sources is the synchronous reactance of the generator, *X*gen, as shown in Figure 9 [26].

If it is assumed that the load angle *δ* is small, then sin *δ* ≈ *δ* and cos *δ* ≈ 1, Then the voltage magnitude, *V*R, and angle magnitude, *δ*, required at the terminals of the generator-side converter are calculated using Equations (7) and (8) as shown [26]:

$$\delta = \frac{P\_{\text{Seg}}^{ref} X\_{\text{gen}}}{V\_S V\_R} \tag{11}$$

$$V\_R = V\_S - \frac{Q\_{Sgen}^{ref} \, X\_{gen}}{V\_S} \tag{12}$$

Where *PSgen ref* is the reference value of the active power that needs to be transferred from the generator to the dc-link, and *QSgen ref* is the reference value for the reactive power. The reference value *PSgen ref* is obtained from the characteristic curve of the machine for maximum power extraction for a given generator speed, *ω*r. As the generator has permanent magnets, it does not require magnetizing current through the stator, thus the reactive power reference value can be set to zero, *QSgen ref* = 0 (i.e. *V*S and *V*<sup>R</sup> are equal in magnitude). The implementation of this load angle control scheme is illustrated in Figure 9. The major advantage of the load angle control is its simplicity. However, as the dynamics of the generator are not considered it may not be very effective in controlling the generator during transient operation [26].

#### *3.1.4.2. Load angle control for the grid-side converter*

power, *P*S, and reactive power, *Q*S, transferred from the sending-end to the receiving-end can

sin *s R*

*gen gen*

PWM

The operation of the generator and the power transferred to the dc-link are controlled by adjusting the magnitude and angle of the voltage at the ac terminals of the generator-side converter. This can be achieved using the load angle control technique where the internal voltage of the generator is the sending source *(V*s∠0*)*, and the generator-side converter is the receiving source *(V*R∠*δ)*. The inductive reactance between these two sources is the synchronous

If it is assumed that the load angle *δ* is small, then sin *δ* ≈ *δ* and cos *δ* ≈ 1, Then the voltage magnitude, *V*R, and angle magnitude, *δ*, required at the terminals of the generator-side

> *ref Sgen gen S R*

*Q X V V*

*P X V V*

> *ref Sgen gen*

> > *S*

= *VV sR*

d

(9)

**Grid**

*V VV <sup>Q</sup> X X* = - (10)

= (11)

*<sup>V</sup>* = - (12)

*gen V V*

> 2 *s sR*

d*VR*

*s*

*P <sup>X</sup>* <sup>=</sup>

*s*

0 *Vs*

*Psgen X gen*

*Rs gen ref sgen VV XP* d = *ref Psgen*

*VV* -=

*Vs* <sup>=</sup> <sup>0</sup> *ref Qsgen*

**Figure 9.** Load angle control of the generator-side converter [26].

*3.1.4.1. Load angle control of the generator-side converter*

reactance of the generator, *X*gen, as shown in Figure 9 [26].

converter are calculated using Equations (7) and (8) as shown [26]:

d

*R S*

*s gen ref sgen SR V XQ*

be calculated from the following equation [26]:

168 New Developments in Renewable Energy

The objective of the grid-side converter controller is to maintain the dc-link voltage at the reference value by exporting active power to the grid. In addition, the controller is designed to enable the exchange of reactive power between the converter and the grid as required by the application specifications. Also, the load angle control is a widely used grid side converter control method, where the grid-side converter is the sending source *(V*S∠*δ)*, and the grid is the receiving source *(V*R∠0*)*. As known, the grid voltage is selected as the reference; hence, the phase angle *δ* is positive. The reactance *X*grid is the inductor coupling between these two sources [26]. The reference value for the active power,*PSgrid ref* , that needs to be transmitted to the grid can be determined by examining the dc-link dynamics with the aid of Figure 10.

**Figure 10.** Power flow in the dc-link [26].

This figure illustrates the power balance at the dc-link [26] as shown in the following equation:

$$\mathbf{P\_{C}} = \mathbf{P\_{S\_{S} \text{gen}}} \text{--} \mathbf{P\_{S\_{S} \text{grid}}} \tag{13}$$

where *P*C is the power across the dc-link capacitor, *C*, *P*Sgen is the active power output of the generator (and transmitted to the dc-link), and *P*Sgrid is the active power transmitted from the dc-link to the grid.

The dc-link voltage *V*dc can be expressed in terms of the generator output power, *P*Sgen, and the power transmitted to the grid, *P*Sgrid, as shown in the following [26]:

$$V\_{dc} = \sqrt{\frac{2}{C} \int (P\_{\text{Sgen}} - P\_{\text{Sgrid}}) dt} \tag{14}$$

**3.2. MPPT algorithms for a WT without wind speed sensor**

The HCS [11], control algorithm continuously searches for the peak power of the wind turbine. The maximum power can be extracted from WTG without requiring information about the wind and generator speeds (Hill-Climb Searching, HCS) [1, 11]. It can overcome some of the common problems normally associated with the other two methods, TSR and PSF. The tracking algorithm depends on the location of the operating point. According to the changes in power and speed the desired optimum signal has been computed in order to track the point of maximum power. Figure 13 shows the principle of HCS control where the operating point is moving toward or away from the maximum turbine power according to increasing (down-hill region) or decreasing the dc current, Idm (up-hill region). The down-hill and up-hill regions are named according to the trend of the system output power with respect to the inverter dc-link voltage, *V*dc for a wind energy system. If an increase of *I*dm leads to an increase of the system output power, the HCS method considers the turbine running in the down-hill region, and *I*dm should keep increasing toward the maximum power point; otherwise, the turbine is considered as running in the up-hill region, and *I*dm decreasing will be the choice of the HCS method towrds

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171

Reference [11] introduces an advanced hill climb searching, AHCS which has been proposed to maximize Pm, through detecting the inverter output power and inverter dc-link voltage. The authors use a diode rectifier to convert the three-phase output ac voltage of a generator to *V*dc

*3.2.1. Hill-Climb Searching (HCS)*

the maximum power point [11].

**Figure 13.** HCS control principle [11].

as shown in Figure 14.

*3.2.1.2. Advanced Hill-Climb Searching (HCS) method*

*3.2.1.1. Principle of Hill-Climb Searching (HCS)*

Equation (12) calculates the actual value of *V*dc. The reference value of the active power, *PSgrid ref* , to be transmitted to the grid is calculated by comparing the actual dc-link voltage, *V*dc, with the desired dc-link voltage reference, *V*dc-ref. The error between these two signals is processed by a PI-controller, whose output provides the reference active power*PSgrid ref* , as shown in Figure 11. Figure 12 illustrates the implementation of the load angle control scheme for the grid-side converter with unity power factor [26].

**Figure 11.** Calculation of active power reference,*PSgrid ref* , (suitable for simulation purposes) [26].

**Figure 12.** Load angle control of the grid-side converter [26].

### **3.2. MPPT algorithms for a WT without wind speed sensor**

#### *3.2.1. Hill-Climb Searching (HCS)*

( ) <sup>2</sup> *V P P dt dc Sgen Sgrid <sup>C</sup>* = - <sup>ò</sup> (14)

PI Controller

> d

*Vs VR*0

*Psgrid*

*X grid*

*ref sgrid P*

**Grid**

Equation (12) calculates the actual value of *V*dc. The reference value of the active power, *PSgrid ref* , to be transmitted to the grid is calculated by comparing the actual dc-link voltage, *V*dc, with the desired dc-link voltage reference, *V*dc-ref. The error between these two signals is processed by a PI-controller, whose output provides the reference active power*PSgrid ref* , as shown in Figure 11. Figure 12 illustrates the implementation of the load angle control scheme for the

*VD C*

*DCref V*

PWM

*Vs=VR*

*s R grid*

> *ref sgrid*

*Q X*

*s*

*grid*

*ref sgrid V V P X*

*<sup>s</sup> <sup>R</sup> V*

d=

*ref* <sup>=</sup><sup>0</sup> *V* =*V* + *Qsgrid*

grid-side converter with unity power factor [26].

*C* 2 Integrator

**Figure 11.** Calculation of active power reference,*PSgrid ref* , (suitable for simulation purposes) [26].

*grid Ps*

*ref PSgrid*

*VR*

**Figure 12.** Load angle control of the grid-side converter [26].

*gen Ps*

170 New Developments in Renewable Energy

#### *3.2.1.1. Principle of Hill-Climb Searching (HCS)*

The HCS [11], control algorithm continuously searches for the peak power of the wind turbine. The maximum power can be extracted from WTG without requiring information about the wind and generator speeds (Hill-Climb Searching, HCS) [1, 11]. It can overcome some of the common problems normally associated with the other two methods, TSR and PSF. The tracking algorithm depends on the location of the operating point. According to the changes in power and speed the desired optimum signal has been computed in order to track the point of maximum power. Figure 13 shows the principle of HCS control where the operating point is moving toward or away from the maximum turbine power according to increasing (down-hill region) or decreasing the dc current, Idm (up-hill region). The down-hill and up-hill regions are named according to the trend of the system output power with respect to the inverter dc-link voltage, *V*dc for a wind energy system. If an increase of *I*dm leads to an increase of the system output power, the HCS method considers the turbine running in the down-hill region, and *I*dm should keep increasing toward the maximum power point; otherwise, the turbine is considered as running in the up-hill region, and *I*dm decreasing will be the choice of the HCS method towrds the maximum power point [11].

**Figure 13.** HCS control principle [11].

#### *3.2.1.2. Advanced Hill-Climb Searching (HCS) method*

Reference [11] introduces an advanced hill climb searching, AHCS which has been proposed to maximize Pm, through detecting the inverter output power and inverter dc-link voltage. The authors use a diode rectifier to convert the three-phase output ac voltage of a generator to *V*dc as shown in Figure 14.

**Figure 14.** Typical wind power generation system connected to a utility grid [11].

*Vdc* is related to the generator angular rotational speed (*ωr*) by a function of the generator field current (*If* ) and the load current (*Ig*) as shown [11]:

$$V\_{dc} = k(I\_{f'}I\_{\underline{g}})^\* \ o\_r \tag{15}$$

Mode Swich Rules

*dVdc Vdc*

AHCS & Memory Updating Rules

*dm I*

During its initial mode, before the algorithm has been trained, the magnitude of *Idm* is deter‐ mined by the maximum power error driven (MPED) control. MPED control is the implemen‐ tation of the conventional HCS method in terms of wind energy system characteristics. During its training mode, the algorithm continually records and updates operating parameters into its programmable lookup table for its intelligent memory feature. Since this method is trainable with its intelligent memory, it allows itself to adapt to work with different WT. As a result, it is a solution to the customization problems of many algorithms. Another advantage of this algorithm is that it does not require mechanical sensors (like anemometers) which lowers its cost and eliminates its associated practical problems. However, it can be seen in [11] that the algorithm is relatively slow and complex as it has three different modes of operation. Another drawback is that the algorithm cannot take into account of the changes in air density, which

*3.2.2. MPPT algorithm by directly adjusting the DC/DC converter duty cycle and modulation index*

MPPT Algorithm by Directly Adjusting the dc/dc Converter duty ratio, *D*, and Modulation Index of the PWM-VSC, *ma*, is shown in Figure 16. In this direct drive converter, the mechanical power from the WT model is fed to the PMSG. The three-phase output voltages of the PMSG are fed to the three- phase diode bridge rectifier. There is no control on the output voltage of the diode bridge rectifier so it cannot be connected directly to the PWM because the PWM inverter needs constant dc voltage. So, a dc/dc converter should be used to control the dc-link voltage. Depending on the dc output voltage required from the dc/dc converter, boost or buck converter can be used. In this study, the dc output voltage, *Vd,out* is required to be higher than input dc voltage, *Vd,in,* so the boost converter is used. By controlling the dc voltage to be constant by controlling of D the boost converter and *ma* the maximum available power from the wind can be extracted. The main drawback of this system is the diode bridge and boost converter are unidirectional power flow devices, so the PMSG has to work only in generator mode which may affect the stability of the system at abnormal conditions. A high capacitance of the dc link

Application Mode Training Mode Initial Mode

Max-Power Error Driven Control

affects the power characteristics quite significantly.

capacitor can remedy the effects of this drawback [18].

*of the PWM-VSC*

**Figure 15.** Structure of the intelligent maximum wind power extraction algorithm [11].

Direct current Demon control (Memory access)

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173

*dt*

*dPout Pout dt*

The algorithm uses the relationship between the turbine mechanical power (*Pm*), and the electrical system output power (*Pout*) given by Equation (14). By differentiating Equation (14) to get a relationship for Δ*Pm*, Equation (15) is obtained:

$$P\_m = P\_{load} + T\_f \ \*o\_r + o\_r \ \*J\frac{do\_r}{dt} = \frac{P\_{out}}{\eta} + T\_f \ \*o\_r + o\_r \ \*J\frac{do\_r}{dt} \tag{16}$$

$$
\Delta P\_m = \frac{\Delta P\_{out}}{\eta} + T\_f \stackrel{\*}{\star} \Delta \alpha\_r + \Delta (\alpha\_r \stackrel{\*}{\star} J \frac{d\alpha\_r}{dt}) \tag{17}
$$

Authors noted that if the sampling period of the control system is adequately small then the term *k*(*If* , *Ig* ) can be considered as a constant value *k* during a sampling period. *Tf* \*ω and η can also be considered as constant values in the same sampling period. Based on the above assumptions, Equation (15) leads to Equation (16) for digital control purposes.

$$
\Delta P\_m = \frac{\Delta P\_{out}}{\eta} + J K^2 \, ^\*\Delta (V\_{dc} \, ^\*\frac{dV\_{dc}}{dt}) \tag{18}
$$

In order to establish rules to adjust the system's operating point, this method evaluates the values of Δ*Pout* and Δ(*Vdc*\**dVdc*/*dt*) (which represents Δ(*ωr*\**d*ω*r*/*dt*) ) based on Equation (14). Depending on the values of Δ*Pout* and Δ(*Vdc*\**dVdc*/*dt*) the polarity of the inverter current demand control signal (*Idm*) is decided according to Equation (16). There are three basic modes for this method, i) initial mode, ii) training mode, and iii) application mode as shown in Figure 15.

**Figure 15.** Structure of the intelligent maximum wind power extraction algorithm [11].

**dc–dc converter**

*Vdc* is related to the generator angular rotational speed (*ωr*) by a function of the generator field

The algorithm uses the relationship between the turbine mechanical power (*Pm*), and the electrical system output power (*Pout*) given by Equation (14). By differentiating Equation (14)

w

\*\* \*\* *r out <sup>r</sup>*

h

\* (\* ) *out <sup>r</sup>*

Authors noted that if the sampling period of the control system is adequately small then the

also be considered as constant values in the same sampling period. Based on the above

<sup>2</sup> \*( \* ) *out dc*

*dt*

In order to establish rules to adjust the system's operating point, this method evaluates the values of Δ*Pout* and Δ(*Vdc*\**dVdc*/*dt*) (which represents Δ(*ωr*\**d*ω*r*/*dt*) ) based on Equation (14). Depending on the values of Δ*Pout* and Δ(*Vdc*\**dVdc*/*dt*) the polarity of the inverter current demand control signal (*Idm*) is decided according to Equation (16). There are three basic modes for this method, i) initial mode, ii) training mode, and iii) application mode as shown in Figure 15.

, *Ig* ) can be considered as a constant value *k* during a sampling period. *Tf*

 w

w

w w

w

D = + D +D (17)

D= + D (18)

=+ + =+ + (16)

( , )\* *V kI I dc f g r* =

*m load f r r frr d P <sup>d</sup> PP T J T J dt dt* w

> *m fr r P d PT J dt*

assumptions, Equation (15) leads to Equation (16) for digital control purposes.

*m dc <sup>P</sup> dV P JK V*

h

D

**Power Electronic converter system**

**Utility** 

**Electrical loads**

(15)

 w

\*ω and η can

**Wind Turbine Rectifier Inverter**

**Wind Power Generation System Maximum Power Control System**

**Figure 14.** Typical wind power generation system connected to a utility grid [11].

) and the load current (*Ig*) as shown [11]:

to get a relationship for Δ*Pm*, Equation (15) is obtained:

w w

h

D

**Synchronous generator**

**Variable speed** 

172 New Developments in Renewable Energy

current (*If*

term *k*(*If*

During its initial mode, before the algorithm has been trained, the magnitude of *Idm* is deter‐ mined by the maximum power error driven (MPED) control. MPED control is the implemen‐ tation of the conventional HCS method in terms of wind energy system characteristics. During its training mode, the algorithm continually records and updates operating parameters into its programmable lookup table for its intelligent memory feature. Since this method is trainable with its intelligent memory, it allows itself to adapt to work with different WT. As a result, it is a solution to the customization problems of many algorithms. Another advantage of this algorithm is that it does not require mechanical sensors (like anemometers) which lowers its cost and eliminates its associated practical problems. However, it can be seen in [11] that the algorithm is relatively slow and complex as it has three different modes of operation. Another drawback is that the algorithm cannot take into account of the changes in air density, which affects the power characteristics quite significantly.

### *3.2.2. MPPT algorithm by directly adjusting the DC/DC converter duty cycle and modulation index of the PWM-VSC*

MPPT Algorithm by Directly Adjusting the dc/dc Converter duty ratio, *D*, and Modulation Index of the PWM-VSC, *ma*, is shown in Figure 16. In this direct drive converter, the mechanical power from the WT model is fed to the PMSG. The three-phase output voltages of the PMSG are fed to the three- phase diode bridge rectifier. There is no control on the output voltage of the diode bridge rectifier so it cannot be connected directly to the PWM because the PWM inverter needs constant dc voltage. So, a dc/dc converter should be used to control the dc-link voltage. Depending on the dc output voltage required from the dc/dc converter, boost or buck converter can be used. In this study, the dc output voltage, *Vd,out* is required to be higher than input dc voltage, *Vd,in,* so the boost converter is used. By controlling the dc voltage to be constant by controlling of D the boost converter and *ma* the maximum available power from the wind can be extracted. The main drawback of this system is the diode bridge and boost converter are unidirectional power flow devices, so the PMSG has to work only in generator mode which may affect the stability of the system at abnormal conditions. A high capacitance of the dc link capacitor can remedy the effects of this drawback [18].

**Figure 16.** Modelling of wind turbine driving permanent magnet synchronous generator.

The active and reactive power can be obtained in terms of *ma* and *D* of the boost converter as shown in Equation (17) and Equation (18), respectively [18].

$$P\_{out} = \frac{\sqrt{3} \, m\_a \, V\_{d,in} \, V\_{LLLI} \, \* \sin \delta}{2\sqrt{2} \, (1 - D) X\_s} \tag{19}$$

where *Pout* is the converter output power, *ω<sup>r</sup>* is the generator speed, *J* is the combined turbine

**dc–dc converter**

**Wind Turbine Rectifier Inverter Utility** 

This part shows how a maximum power can be extracted from a WTG without requiring information about the wind and generator speeds. In the system of Figure 17, the converter dc-link voltage is proportional to the generator speed, *Vdc* = *K*ω*r*, since the generator terminal voltage is proportional to the speed. Thus, Equation (19) can be expressed in terms of *Vdc* as [1]:

> 2 *out dc*

*K dt*

<sup>2</sup> ( ) *out dc*

*K dt*

*Vdc* is proportional to the inverter terminal voltage *Vinv* divided by the inverter amplitude modulation index, *ma*. Thus,*ΔVdc* =*Δ*(*Vinv* / *ma*).To extract maximum power from the wind, a small perturbation is applied to the angle of the inverter terminal voltage, *δ*. *ΔPout*and *Δ*(*Vinv* / *ma*) are estimated and their signs determine whether the operating point is moving toward or away from the maximum turbine power, Figure 18. Depending on the operating point direction of movement, the decision is to increase or decrease the angle *δ* or to keep it constant. Table 1 describes the decision that is made based on the sign of the inverter output power variation *ΔPout*and that of the ratio of the inverter terminal voltage to the amplitude modulation index*Δ*(*Vinv* / *ma*). With the proposed algorithm for maximum power extraction, only voltage and current at the inverter terminal need to be measured, and no information

= + (22)

Maximum Power Extraction from Utility-Interfaced Wind Turbines

D= + D (23)

*m dc P dV <sup>J</sup> P V* h

*m dc <sup>P</sup> <sup>J</sup> dV P V*

h

about the wind and generator speeds and the dc-link voltage is required [1].

D

**system**

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175

and generator moment of inertia and *η* is the overall system efficiency.

**Synchronous generator**

**Figure 17.** Grid-connected wind-turbine generation system [1].

Taking the derivative of Equation (20), we deduce

*A. Real power*

$$\mathcal{Q}\_{out} = \frac{\sqrt{3} \, m\_a V\_{d,in}}{2\sqrt{2} \, (1 - D) X\_s} \left( V\_{LLII} \, \* \cos \delta - \frac{\sqrt{3} \, m\_a V\_{d,in}}{2\sqrt{2} \, (1 - D)} \right) \tag{20}$$

Where;

*δ*: torque angle at the electric utility side.

*Xs*: synchronous reactance of the electric utility.

It is clear from Equation (17) and Equation (18) that the active and reactive power can be controlled by controlling modulation index, ma of the PWM inverter and duty ratio of the boost converter.

#### *3.2.3. Maximum power extraction and reactive power technique*

#### *3.2.3.1. Decoupled control of the active and reactive power, dependently*

This method presents an algorithm for maximum power extraction and reactive power control of an inverter based variable-speed wind-turbine generator without wind speed sensor. The algorithm does not require information about the wind and generator speeds or the inverter dclink voltage and thus, is dependent of specifications of the wind turbine generation system [1].

Consider the wind-turbine generation system of Figure 17. The turbine mechanical power *Pm* and the generator output power *Pg* are related by

$$P\_m = Pg + o\_r\* "\int \frac{d\alpha\_r}{dt} = \frac{P\_{out}}{\eta} + o\_r\* "\int \frac{d\alpha\_r}{dt} \tag{21}$$

where *Pout* is the converter output power, *ω<sup>r</sup>* is the generator speed, *J* is the combined turbine and generator moment of inertia and *η* is the overall system efficiency.

**Figure 17.** Grid-connected wind-turbine generation system [1].

#### *A. Real power*

Boost

Wind turbine Common

The active and reactive power can be obtained in terms of *ma* and *D* of the boost converter as

, 3 sin 2 2 (1 ) *a d in LLU*

, , 3 3 cos 2 2 (1 ) 2 2 (1 ) *a d in a d in*

<sup>=</sup> ç ÷ \* - - - è ø

*m V m V*

It is clear from Equation (17) and Equation (18) that the active and reactive power can be controlled by controlling modulation index, ma of the PWM inverter and duty ratio of the boost

This method presents an algorithm for maximum power extraction and reactive power control of an inverter based variable-speed wind-turbine generator without wind speed sensor. The algorithm does not require information about the wind and generator speeds or the inverter dclink voltage and thus, is dependent of specifications of the wind turbine generation system [1].

Consider the wind-turbine generation system of Figure 17. The turbine mechanical power *Pm*

*m r r dP d P Pg J <sup>J</sup> dt dt* w

w

\* \* *r out <sup>r</sup>*

h

 w  w

=+ = + (21)

*mV V*

*s*

æ ö

d

<sup>=</sup> - (19)

(20)

*D X* \*

*D X D* d

Grid-side converter

collecting point Bridge

Inductive reactor

converter PMSG

174 New Developments in Renewable Energy

shown in Equation (17) and Equation (18), respectively [18].

*out*

*out LLU*

*Q V*

*3.2.3. Maximum power extraction and reactive power technique*

*3.2.3.1. Decoupled control of the active and reactive power, dependently*

*δ*: torque angle at the electric utility side.

*Xs*: synchronous reactance of the electric utility.

and the generator output power *Pg* are related by

Where;

converter.

*s*

*P*

rectifier

**Figure 16.** Modelling of wind turbine driving permanent magnet synchronous generator.

This part shows how a maximum power can be extracted from a WTG without requiring information about the wind and generator speeds. In the system of Figure 17, the converter dc-link voltage is proportional to the generator speed, *Vdc* = *K*ω*r*, since the generator terminal voltage is proportional to the speed. Thus, Equation (19) can be expressed in terms of *Vdc* as [1]:

$$P\_m = \frac{P\_{out}}{\eta} + \frac{J}{K^2} V\_{dc} \frac{dV\_{dc}}{dt} \tag{22}$$

Taking the derivative of Equation (20), we deduce

$$
\Delta P\_m = \frac{\Delta P\_{out}}{\eta} + \frac{J}{K^2} \Delta (V\_{dc} \frac{dV\_{dc}}{dt}) \tag{23}
$$

*Vdc* is proportional to the inverter terminal voltage *Vinv* divided by the inverter amplitude modulation index, *ma*. Thus,*ΔVdc* =*Δ*(*Vinv* / *ma*).To extract maximum power from the wind, a small perturbation is applied to the angle of the inverter terminal voltage, *δ*. *ΔPout*and *Δ*(*Vinv* / *ma*) are estimated and their signs determine whether the operating point is moving toward or away from the maximum turbine power, Figure 18. Depending on the operating point direction of movement, the decision is to increase or decrease the angle *δ* or to keep it constant. Table 1 describes the decision that is made based on the sign of the inverter output power variation *ΔPout*and that of the ratio of the inverter terminal voltage to the amplitude modulation index*Δ*(*Vinv* / *ma*). With the proposed algorithm for maximum power extraction, only voltage and current at the inverter terminal need to be measured, and no information about the wind and generator speeds and the dc-link voltage is required [1].

**Figure 18.** Wind turbine output power versus speed [1].


**Table 1.** Maximum power tracking algorithm [1].

#### *B. Reactive power*

The inverter should be able to regulate its output reactive power to provide the reactive power demand of the utility system, Figure 17. The inverter output reactive power must be controlled so as the maximum real power extraction is not violated. The real and reactive power compo‐ nents (*Pout, Qout* ) at the inverter output terminals are [1]:

$$P\_{out} = \frac{V\_{inv}\,V\_{sys}}{X\_T}\sin(\delta)\tag{24}$$

3

*<sup>X</sup>* <sup>=</sup>

*out*

( )

1

*3.2.3.2 Decoupled control of the active and reactive power, independently*

+

d

modulation index and the voltage angle of the inverter.

*P*

*P*

*P*

sampling time *nT* and (*n* +1)*T* is

2 2

( )

*m VV*

2 2

( 1) ( 1) 1

*m VV*

1 ( )

*m m*

2 2

*<sup>X</sup>* <sup>=</sup>

3

3

Equation (23), the inverter voltage angle must satisfy the following condition.

*a dc sys*

*mV V*

*T*

Assuming that *Vdc* does not change over the small sampling period *T*, *Pout* corresponding to the

*a n dc sys out n n T*

*a n dc sys out n n T*

To keep the real power constant, i.e., *Pout (n+1)* = *Pout (n)*, while providing a desired reactive power,

( 1) sin sin( ) *a n n n a n*

+ é ù <sup>=</sup> ê ú

Figure 19 shows a flowchart of the proposed algorithm for maximum power extraction and reactive power control of a wind-turbine generator. The inputs are the three-phase voltages and currents at the inverter output terminals and the outputs are the required amplitude

In this study [17], simple ac-dc-ac power conversion system and proposed modular control strategy for grid-connected wind power generation system have been implemented. Grid-side inverter maintains the dc-link voltage constant and the power factor of line side can be adjusted. Input current reference of dc/dc boost converter is decided for the maximum power point tracking of the turbine without any information of wind or generator speed. As the proposed control algorithm does not require any speed sensor for wind or generator speed, construction and installation are simple, cheap, and reliable. The main circuit and control block diagrams are shown in Figure 20. For wide range of variable speed operation, a dc-dc boost converter is utilized between 3-phase diode rectifier and PWM-VSC. The input dc current is regulated to follow the optimized current reference for maximum power point operation of turbine system. Grid PWM-VSC supply currents into the utility line by regulating the dc-link voltage. The active power is controlled by q-axis current through regulating the dc-link voltage whereas the reactive power can be controlled by d-axis current via adjusting the power factor

ê ú ë û


 d

<sup>+</sup>

*X*

sin( )

d

sin( )

d

sin( )

d

+ + = (28)

(26)

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177

Maximum Power Extraction from Utility-Interfaced Wind Turbines

(27)

(29)

$$Q\_{out} = \frac{V\_{inv} \, V\_{sys}}{X\_T} \cos(\delta) - \frac{\left(V\_{sys}\right)^2}{X\_T} \tag{25}$$

*Vsys* is the utility system voltage and *XT* is the reactance between the inverter and the utility system. It is seen from Equation (22) and Equation (23) that *Vinv* and *δ* can be controlled so as *Qout* is regulated at a desired value while *Pout* is kept constant at its maximum corresponding to the wind speed. Substituting *Vinv* in Equation (22) by *<sup>3</sup> 2 2 ma Vd,* This equation can be

deduced as follow:

Maximum Power Extraction from Utility-Interfaced Wind Turbines http://dx.doi.org/10.5772/54675 177

$$P\_{out} = \frac{\sqrt{3} \ m\_a V\_{dc} V\_{sys}}{2\sqrt{2}X\_T} \sin(\delta) \tag{26}$$

Assuming that *Vdc* does not change over the small sampling period *T*, *Pout* corresponding to the sampling time *nT* and (*n* +1)*T* is

$$P\_{out(n)} = \frac{\sqrt{3} \, m\_{a(n)} \, V\_{dc} \, V\_{sys}}{2\sqrt{2} \, X\_T} \sin(\delta\_n) \tag{27}$$

$$P\_{out(n+1)} = \frac{\sqrt{3} \, m\_{a(n+1)} V\_{dc} \, V\_{sys}}{2\sqrt{2} \, X\_T} \sin(\delta\_{n+1}) \tag{28}$$

To keep the real power constant, i.e., *Pout (n+1)* = *Pout (n)*, while providing a desired reactive power, Equation (23), the inverter voltage angle must satisfy the following condition.

$$\mathcal{S}\_{n+1} = \sin^{-1}\left[\frac{m\_{\mathfrak{a}(n)}}{m\_{\mathfrak{a}(n+1)}}\sin(\mathcal{S}\_n)\right] \tag{29}$$

Figure 19 shows a flowchart of the proposed algorithm for maximum power extraction and reactive power control of a wind-turbine generator. The inputs are the three-phase voltages and currents at the inverter output terminals and the outputs are the required amplitude modulation index and the voltage angle of the inverter.

#### *3.2.3.2 Decoupled control of the active and reactive power, independently*

**Turbine shaft velocity**

**) Decision**

(24)


*ma Vd,* This equation can be

*Vinv ma*

> 0 > 0 Increase δ < 0 < 0 Decrease δ > 0 < 0 No change < 0 > 0 No change

The inverter should be able to regulate its output reactive power to provide the reactive power demand of the utility system, Figure 17. The inverter output reactive power must be controlled so as the maximum real power extraction is not violated. The real and reactive power compo‐

sin( ) *inv sys*

cos( ) *inv sys sys*

*V V V <sup>Q</sup> X X* <sup>=</sup>

*T T*

*Vsys* is the utility system voltage and *XT* is the reactance between the inverter and the utility system. It is seen from Equation (22) and Equation (23) that *Vinv* and *δ* can be controlled so as *Qout* is regulated at a desired value while *Pout* is kept constant at its maximum corresponding

d

d

( ) 2

*2 2*

*T*

*V V*

*<sup>X</sup>* <sup>=</sup>

*Up HILL Down HILL*

**Turbine power**

**Δ***Pout* **Δ(**

nents (*Pout, Qout* ) at the inverter output terminals are [1]:

*out*

*P*

*out*

to the wind speed. Substituting *Vinv* in Equation (22) by *<sup>3</sup>*

**Figure 18.** Wind turbine output power versus speed [1].

176 New Developments in Renewable Energy

**Table 1.** Maximum power tracking algorithm [1].

*B. Reactive power*

deduced as follow:

In this study [17], simple ac-dc-ac power conversion system and proposed modular control strategy for grid-connected wind power generation system have been implemented. Grid-side inverter maintains the dc-link voltage constant and the power factor of line side can be adjusted. Input current reference of dc/dc boost converter is decided for the maximum power point tracking of the turbine without any information of wind or generator speed. As the proposed control algorithm does not require any speed sensor for wind or generator speed, construction and installation are simple, cheap, and reliable. The main circuit and control block diagrams are shown in Figure 20. For wide range of variable speed operation, a dc-dc boost converter is utilized between 3-phase diode rectifier and PWM-VSC. The input dc current is regulated to follow the optimized current reference for maximum power point operation of turbine system. Grid PWM-VSC supply currents into the utility line by regulating the dc-link voltage. The active power is controlled by q-axis current through regulating the dc-link voltage whereas the reactive power can be controlled by d-axis current via adjusting the power factor

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

Maximum Power Extraction from Utility-Interfaced Wind Turbines

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

179

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

> Generator - side controller

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.

Generator-side converter

Grid-side converter

Grid- side controller

Utility grid

**system with electric utility**

for control circuit and FLC.

PMSG

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

**4.1. Wind energy conversion system description**

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

of the grid side converter as shown in Figure 20. The phase angle of utility voltage is detected using Phased Locked Loop, *PLL*, in d-q synchronous reference frame [17].

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