**1.3. Wind power density**

Concerning power density and its relation to wind speed, the report given in [4] pre‐ sented the features of wind power distributions that were analytically obtained from wind distribution functions. Simple equations establishing a relationship between mean power density and wind speed have been obtained for a given location and wind tur‐ bine. Different concepts relating to wind power distribution functions were shown among them the power transported by the wind and the theoretical maximum converti‐ ble power from wind, according to the Betz' law. Maximum convertible power from the wind was explained within more realistic limits, including an approximate limit to the maximum power from a wind turbine, was obtained. In addition, different equations were obtained establishing relationships between mean power density and mean wind speed. These equations are simple and useful when discarding locations for wind tur‐ bine installation [4].

#### **1.4. Wind power applications**

The range of wind power usage is scarce. One of the most important usages is electrici‐ ty. Hubbard and Shepherd [5] considered wind turbine generators, ranging in size from a few kilowatts to several megawatts, for producing electricity both singly and in wind power stations that encompass hundreds of machines. According to the researchers' claims, there are many installations in uninhabited areas far from established residences, and therefore there are no apparent environmental impacts in terms of noise. The re‐ searchers do point out, however, situations in which radiated noise can be heard by res‐ idents of adjacent neighborhoods, particularly those who live in neighborhoods with low ambient noise levels [5].

Wind power is used worldwide, not only in developed countries. Specific studies [6, 7] presented a detailed study of a Manchegan windmill while considering the technologi‐ cal conditions of the original Manchegan windmills. In addition, a wind evaluation of the region was carried out, the power and momentum of the windmills were calculat‐ ed, and the results obtained were discussed, along with a comparison with the type of Southern Spanish windmill. These windmills were important for wheat milling and had been an important factor in the socio-economic development of rural Spain for centu‐ ries [6, 7].

**1.2. Aerodynamics aspects of wind turbines**

wind farms [3].

4 Advances in Wind Power

**1.3. Wind power density**

bine installation [4].

**1.4. Wind power applications**

ambient noise levels [5].

Reviews about many of the most important aerodynamic research topics in the field of wind energy are shown in the report of a different study [3] Wind turbine aerodynamics concerns the modeling and prediction of aerodynamic forces, such as performance predictions of wind farms, as well as the design of specific parts of wind turbines, such as rotor-blade ge‐ ometry. The basics of blade-element momentum theory were presented along with guide‐ lines for the construction of airfoil data. Various theories for aerodynamically optimum rotors were discussed, and recent results on classical models were presented. State-of-the-art advanced numerical simulation tools for wind turbine rotors and wakes were reviewed, in‐ cluding rotor predictions as well as models for simulating wind turbine wakes and flows in

Concerning power density and its relation to wind speed, the report given in [4] pre‐ sented the features of wind power distributions that were analytically obtained from wind distribution functions. Simple equations establishing a relationship between mean power density and wind speed have been obtained for a given location and wind tur‐ bine. Different concepts relating to wind power distribution functions were shown among them the power transported by the wind and the theoretical maximum converti‐ ble power from wind, according to the Betz' law. Maximum convertible power from the wind was explained within more realistic limits, including an approximate limit to the maximum power from a wind turbine, was obtained. In addition, different equations were obtained establishing relationships between mean power density and mean wind speed. These equations are simple and useful when discarding locations for wind tur‐

The range of wind power usage is scarce. One of the most important usages is electrici‐ ty. Hubbard and Shepherd [5] considered wind turbine generators, ranging in size from a few kilowatts to several megawatts, for producing electricity both singly and in wind power stations that encompass hundreds of machines. According to the researchers' claims, there are many installations in uninhabited areas far from established residences, and therefore there are no apparent environmental impacts in terms of noise. The re‐ searchers do point out, however, situations in which radiated noise can be heard by res‐ idents of adjacent neighborhoods, particularly those who live in neighborhoods with low

Wind power is used worldwide, not only in developed countries. Specific studies [6, 7] presented a detailed study of a Manchegan windmill while considering the technologi‐ cal conditions of the original Manchegan windmills. In addition, a wind evaluation of the region was carried out, the power and momentum of the windmills were calculat‐ ed, and the results obtained were discussed, along with a comparison with the type of Another example is considered in [8]. This study, conducted with reference to land in Syria, evaluated both wind energy potential and the electricity that could be generated by the wind. An appropriate computer program was especially prepared and designed to perform the required calculations, using the available meteorological data provided by the Syrian Atlas. The program is capable of processing the wind data for any specific area that is in accordance with the needed requirements in fields of researches and ap‐ plications. Calculations in the study show that a significant energy potential is available for direct exploitation. The study also shows that approximately twice the current elec‐ tricity consumption in Syria can be generated by wind resources [8].

The potential usage of wind power at Kudat and Labuan for small-scale energy demand was given in [9]. According to their statement, the acquisition of detailed knowledge about wind characteristics at a site is a crucial step in planning and estimating perform‐ ance for a wind energy project. From this study, the researchers concluded that sites at Kudat and Labuan that they had considered during the study years were unsuitable for large-scale wind energy generation. However, they did confirm that small-scale wind en‐ ergy could be generated at a turbine height of 100 meters [9]. In light of their findings, James and others [10] reported that the potential impact of the UK's latest policy instru‐ ment, the 2010 micro-generation tariffs, is considered applicable to both micro-wind and photovoltaics.As the researchers observed, building-mounted micro-wind turbines and photovoltaics have the potential to provide widely applicable carbon-free electricity gen‐ eration at the building level. Because photovoltaic systems are well understood it is easy to predict performance using software tools or widely accepted yield estimates. Microwind research, however, is far more complex, and in comparison, it is poorly under‐ stood [10].

Abdeen [11] addresses another example of wind power usage. As the researcher observed, the imminent exhaustion of fossil energy resources and the increasing demand for energy were the motives for Sudanese authorities to put into practice an energy policy based on ra‐ tional use of energy. The authorities also based their conclusions on exploitation of new and renewable energy sources. It was pointed out that after 1980, as the supply of conventional energy has not been able to follow the tremendous increase in production demand in rural areas of Sudan; a renewed interest for the application of wind energy has been shown in many places. Therefore, the Sudanese government began to pay more attention to wind en‐ ergy utilization in rural areas. Because the wind energy resource in many rural areas is suffi‐ cient for attractive application of wind pumps, although as fuel it is insufficient, the wind pumps will be spread on a rather large scale in the near future. Wind is a form of renewable energy that is always in a non-steady state due to the wide temporal and spatial variations of wind velocity. Results suggested that wind power would be more profitably used for lo‐ cal and small-scale applications, especially for remote rural areas. The study finds that Su‐ dan has abundant wind energy [11]. Another recent study [12] considered the wind power in Iran. According to the study's claims, climate change, global warming, and the recent worldwide economic crisis have emphasized the need for low carbon emissions while also ensuring economic feasibility. In their paper, the researchers investigated the status and wind power potential of the city of Shahrbabak in Kerman province in Iran. The technical and economic feasibility of wind turbine installation was presented, and the potential of wind power generation was statistically analyzed [12].

#### **1.5. Types of wind turbines**

There are different types of wind turbines: bare wind turbines, augmented wind turbines, horizontal axis wind turbines, and vertical axis wind turbines, just to mention a few.

## *1.5.1. Bare wind turbines*

According to research findings as given by [13], the derivation of the efficiency of an ideal wind turbine is attributed to the three prominent scientists associated with the three princi‐ pal aerodynamic research schools in Europe during the first decades of the previous centu‐ ry: Lanchester, Betz, and Joukowsky. According to this study, detailed reading of their classical papers had shown that Lanchester did not accept that the velocity through the disc is the average of the velocities far upstream and far downstream, by which his solution is not determined. Betz and Joukowsky used vortex theory to support Froude's result and de‐ rived the ideal efficiency of a wind turbine at the same time. This efficiency has been known as the Joukowsky limit in Russia and as the Betz limit everywhere else. As the researchers suggested, because of the contribution of both scientists, this result should be called the Betz-Joukowsky limit everywhere [13]. The maximal achievable efficiency of a wind turbine is found to be given by the Betz number *B* = 16/27. Derivation of the classical Betz limit could be followed as given by [14] and [15].

The question of the maximum wind kinetic energy that can be utilized by a wind turbine, which is of fundamental importance for employment of wind energy, was reconsidered in [16]. According to their study, the researchers observed that in previous studies, an answer to this question was obtained only for the case of an infinite number of turbine-rotor blades, in the framework of application of the one-dimensional theory of an ideal loaded disk with‐ out loss for friction and turbulence taken into account. This implies that for an ideal wind turbine, the maximum energy that can be extracted from the wind kinetic energy, or the power coefficient, does not exceed the Betz limit. Based on the exact calculation of the Gold‐ stein function, the researchers determined the maximum power coefficient of an ideal wind turbine having a finite number of blades. As was expected, the maximum turned out to be always lower than the absolute Lanchester-Betz-Joukowski limit. According to their find‐ ings, with an increase in the number of blades, the power coefficient rises approaching the estimate of Glauert for a rotor with an infinite number of blades, only if by taking wake flow twisting into account [16].

In a different proposal, Cuerva and Sanz-Andre´s presented an extended formulation of the power coefficient of a wind turbine [17]. Their formulation was a generalization of the BetzLanchester expression for the power coefficient as a function of the axial deceleration of the wind speed provoked by the wind turbine in operation. The extended power coefficient took into account the benefits of the power produced and the cost associated to the produc‐ tion of this energy. By means of the proposed simple model, the researchers evidenced that the purely energetic optimum operation condition giving rise to the Betz-Lanchester limit (maximum energy produced) does not coincide with the global optimum operational condi‐ tion (maximum benefit generated) if cost of energy and degradation of the wind turbine during operation is considered. The new extended power coefficient, according to the re‐ searchers claim, is a general parameter useful to define global optimum operation condi‐ tions for wind turbines, considering not only the energy production but also the maintenance cost and the economic cost associated to the life reduction of the machine [17].

## *1.5.2. Augmented wind turbines*

in Iran. According to the study's claims, climate change, global warming, and the recent worldwide economic crisis have emphasized the need for low carbon emissions while also ensuring economic feasibility. In their paper, the researchers investigated the status and wind power potential of the city of Shahrbabak in Kerman province in Iran. The technical and economic feasibility of wind turbine installation was presented, and the potential of

There are different types of wind turbines: bare wind turbines, augmented wind turbines,

According to research findings as given by [13], the derivation of the efficiency of an ideal wind turbine is attributed to the three prominent scientists associated with the three princi‐ pal aerodynamic research schools in Europe during the first decades of the previous centu‐ ry: Lanchester, Betz, and Joukowsky. According to this study, detailed reading of their classical papers had shown that Lanchester did not accept that the velocity through the disc is the average of the velocities far upstream and far downstream, by which his solution is not determined. Betz and Joukowsky used vortex theory to support Froude's result and de‐ rived the ideal efficiency of a wind turbine at the same time. This efficiency has been known as the Joukowsky limit in Russia and as the Betz limit everywhere else. As the researchers suggested, because of the contribution of both scientists, this result should be called the Betz-Joukowsky limit everywhere [13]. The maximal achievable efficiency of a wind turbine is found to be given by the Betz number *B* = 16/27. Derivation of the classical Betz limit

The question of the maximum wind kinetic energy that can be utilized by a wind turbine, which is of fundamental importance for employment of wind energy, was reconsidered in [16]. According to their study, the researchers observed that in previous studies, an answer to this question was obtained only for the case of an infinite number of turbine-rotor blades, in the framework of application of the one-dimensional theory of an ideal loaded disk with‐ out loss for friction and turbulence taken into account. This implies that for an ideal wind turbine, the maximum energy that can be extracted from the wind kinetic energy, or the power coefficient, does not exceed the Betz limit. Based on the exact calculation of the Gold‐ stein function, the researchers determined the maximum power coefficient of an ideal wind turbine having a finite number of blades. As was expected, the maximum turned out to be always lower than the absolute Lanchester-Betz-Joukowski limit. According to their find‐ ings, with an increase in the number of blades, the power coefficient rises approaching the estimate of Glauert for a rotor with an infinite number of blades, only if by taking wake flow

In a different proposal, Cuerva and Sanz-Andre´s presented an extended formulation of the power coefficient of a wind turbine [17]. Their formulation was a generalization of the Betz-

horizontal axis wind turbines, and vertical axis wind turbines, just to mention a few.

wind power generation was statistically analyzed [12].

could be followed as given by [14] and [15].

twisting into account [16].

**1.5. Types of wind turbines**

6 Advances in Wind Power

*1.5.1. Bare wind turbines*

It was suggested in [18] that one could extract more power from the wind by directing the wind by a diffuser that could be incorporated into the system. The benefit of such a device is to decrease the size of the system and thus decrease its cost [18].

According to [19], the performance of a diffuser-augmented wind turbine has been estab‐ lished by matching the forces acting on the blade element to overall momentum and energy balances. Good agreement with experimental data was obtained [19]. Based on computa‐ tional fluid dynamics (CFD), an actuator disc CFD model of the flow through a wind turbine in a diffuser was developed and validated [20, 21]. Their research presumed a flow increase could be induced by a diffuser. They showed that from a one-dimensional analysis the Betz limit could be exceeded by a factor that is proportional to the relative increase in mass flow through the rotor. This result was verified by theoretical one-dimensional analysis by the CFD model [20, 21]. Supporting the same idea, [22] Sharpe stated that it is theoretically pos‐ sible to exceed the Lanchester-Betz limit. His study presented a general momentum theory for an energy-extracting actuator disc that modeled a rotor with blades having radially uni‐ form circulation. The study included the effects of wake rotation. Although the study re‐ ports that the general momentum theory is well known, the fall in pressure that is caused by the rotation of the wake that the theory predicts, is not usually recognized. Accounting for the wake rotational pressure drop changes some of the established conclusions of the mo‐ mentum theory that appear in the literature. The conclusion from the study is that the theo‐ ry establishes no loss of efficiency associated with the rotating wake [22]. Experimental and numerical investigations for flow fields of a small wind turbine with a flanged diffuser were carried out in [23].

The considered wind-turbine system gave a power coefficient higher than the Betz limit, which they attributed to the effect of the flanged diffuser. The experimental and numerical results gave useful information about the flow mechanism behind a wind turbine with a flanged diffuser. In particular, a considerable difference was seen in the destruction process of the tip vortex between the bare wind turbine and the wind turbine with a flanged diffuser [23]. According to the findings given in [24], suitable techniques to convert a country's wind availability (mostly in the low-speed regimes) as a renewable energy source must be scruti‐ nized in order to achieve effective and efficient conversion. In this study, the researchers de‐ scribed efforts to step up the potential power augmentation offered by the Diffuser Augmented Wind Turbine (DAWT). Modification of the internal profile of the diffuser oc‐ curred by replacing the interior profile of the diffuser with an optimized airfoil shape as the interior profile of the diffuser. Additional velocity augmentation of approximately 66% could be achieved with the optimized profile when compared to a diffuser with an original flat interior [24]. As was pointed out in [25, 26], although there is an increase in maximum performance of a DAWT that is proportional to the mass flow of air, with application of sim‐ ple momentum theory, the amount of energy extracted per unit of volume with a DAWT is the same as for an ordinary bare wind turbine [25, 26].

#### **1.6. Modeling controversy**

Debate is ongoing around the issue of DAWT. In a recent study, a general momentum theo‐ ry to study the behavior of the classical free vortex wake model of Joukowsky was used [27]. This model, as the researchers reported, has attained considerable attention as it shows the possibility of achieving a power performance that greatly exceeds the Lanchester-Betz limit for rotors running at low tip speed ratios. This behavior was confirmed even when includ‐ ing the effect of a center vortex, which, without any simplifying assumptions, allowed azi‐ muthal velocities and the associated radial pressure gradient to be taken into account in the axial momentum balance. In addition, a refined model that remedies the problem of using the axial momentum theorem was proposed. Using this model the power coefficient never exceeds the Lanchester-Betz limit, but rather tends to zero at a zero tip speed ratio [27]. As asserted in [28], for reasons of energy and momentum conservation a conventional diffuser system, as it is commonly used in water turbines cannot augment the power of a wind tur‐ bine beyond the Betz limit. However, if the propeller of the turbine is embedded into an ex‐ ternal flow of air from which by means of its static structure energy can be transferred to the internal flow through the propeller, the propeller can supersede the Betz limit with respect to this internal flow [28]. Features of such practical methods toward achieving such im‐ provements in wind power are discussed in [29].

#### **1.7. Blades design**

According to the report given by [30], the main problem of a wind turbine generator design project is the design of blades capable of satisfying, with optimum performance, the specific energy requirement of an electric system [30]. Simulations are very important to facilitate engineering and design of wind turbines for many reasons, especially those that concentrate upon reducing cost and saving human time. With regard to the designing the rotor blades, a CFD model for the evaluation of energy performance and aerodynamic forces acting on a straight-bladed vertical-axis Darrieus wind turbine was presented [31]. A modified blade el‐ ement momentum theory for the counter-rotating wind turbine was developed [32]. This en‐ abled the investigation of the effects of design parameters such as the combinations of the pitch angles, rotating speeds, and radii of the rotors on the aerodynamic performance of the counter-rotating wind turbine [32].

## **1.8. Wind farms**

nized in order to achieve effective and efficient conversion. In this study, the researchers de‐ scribed efforts to step up the potential power augmentation offered by the Diffuser Augmented Wind Turbine (DAWT). Modification of the internal profile of the diffuser oc‐ curred by replacing the interior profile of the diffuser with an optimized airfoil shape as the interior profile of the diffuser. Additional velocity augmentation of approximately 66% could be achieved with the optimized profile when compared to a diffuser with an original flat interior [24]. As was pointed out in [25, 26], although there is an increase in maximum performance of a DAWT that is proportional to the mass flow of air, with application of sim‐ ple momentum theory, the amount of energy extracted per unit of volume with a DAWT is

Debate is ongoing around the issue of DAWT. In a recent study, a general momentum theo‐ ry to study the behavior of the classical free vortex wake model of Joukowsky was used [27]. This model, as the researchers reported, has attained considerable attention as it shows the possibility of achieving a power performance that greatly exceeds the Lanchester-Betz limit for rotors running at low tip speed ratios. This behavior was confirmed even when includ‐ ing the effect of a center vortex, which, without any simplifying assumptions, allowed azi‐ muthal velocities and the associated radial pressure gradient to be taken into account in the axial momentum balance. In addition, a refined model that remedies the problem of using the axial momentum theorem was proposed. Using this model the power coefficient never exceeds the Lanchester-Betz limit, but rather tends to zero at a zero tip speed ratio [27]. As asserted in [28], for reasons of energy and momentum conservation a conventional diffuser system, as it is commonly used in water turbines cannot augment the power of a wind tur‐ bine beyond the Betz limit. However, if the propeller of the turbine is embedded into an ex‐ ternal flow of air from which by means of its static structure energy can be transferred to the internal flow through the propeller, the propeller can supersede the Betz limit with respect to this internal flow [28]. Features of such practical methods toward achieving such im‐

According to the report given by [30], the main problem of a wind turbine generator design project is the design of blades capable of satisfying, with optimum performance, the specific energy requirement of an electric system [30]. Simulations are very important to facilitate engineering and design of wind turbines for many reasons, especially those that concentrate upon reducing cost and saving human time. With regard to the designing the rotor blades, a CFD model for the evaluation of energy performance and aerodynamic forces acting on a straight-bladed vertical-axis Darrieus wind turbine was presented [31]. A modified blade el‐ ement momentum theory for the counter-rotating wind turbine was developed [32]. This en‐ abled the investigation of the effects of design parameters such as the combinations of the pitch angles, rotating speeds, and radii of the rotors on the aerodynamic performance of the

the same as for an ordinary bare wind turbine [25, 26].

provements in wind power are discussed in [29].

counter-rotating wind turbine [32].

**1.7. Blades design**

**1.6. Modeling controversy**

8 Advances in Wind Power

Vermeer and others surveyed wind farms. The focus of this study was on standalone tur‐ bines and wind farm effects. The survey group suggested that when assembling many wind turbines together, several issues should be considered [33]. Other research studies discussed the issue of optimizing the placement of wind turbines in wind farms [34]. Factors consid‐ ered included multidirectional winds and variable wind speeds, the effect of ambient turbu‐ lence in the wake recovery, the effect of ground, variable hub height of the wind turbines, and different terrains [34]. A review of the state of the art and present status of active aeroe‐ lastic rotor control research for wind turbines was presented in [35]. A wind farm controller was reported in [36]. That controller distributes power references among wind turbines while it reduces their structural loads.

In this study the effect of losses are considered and discussed for bare wind turbines and for shrouded wind turbines.
