stiffness of the gyro platform κ is tuned to the seventh bending modes.

exquisite construction, since the gyro's rotor should be balanced as well as possible.

ðτ 0

Ωð Þς dς

Svetlana Pavlovna Nikitenkova1 \* and Dmitry Anatolyevich Kovriguine2

\*Address all correspondence to<EMAIL_ADDRESS>
1 Radiophysics Faculty, Nizhny Novgorod State University n.a. N.I. Lobachevsky, Nizhny Novgorod, Russia

2 Applied Mathematics Chair, Nizhny Novgorod Technical State University n.a. R.E. Alekseev, Nizhny Novgorod, Russia

#### References

[4] Zhuravlev VF. Global evolution of state of the generalized Foucault pendulum. Mechanics of Solids. 1998;33(6):1-6

**Chapter 4**

**Provisional chapter**

**Wind-Induced Vibrations to Tall Buildings and Wind**

While wind generated noise maybe limited in magnitude and effect, wind-induced structures' vibrations could be a devastation (i.e., Tacoma Bridge Collapse 1940). This occurs with just above moderate wind speed increase, if it can excite a structure with its natural frequencies. When this occur, structures enter a phase of oscillations until collapse. However, with proper understanding of vibrations in structures these vibrations can be eliminated. Studying vibrations can be experimental through wind-tunnel and or by simulations. Wind in buildings can induce two types of motions: static or sustained; as building drift and oscillatory or resonant vibration. Motion is composed of three contributions: sway in two horizontal or perpendicular directions and torsion. This vibration would considerably affect the habitability and stability of building spaces gauged through a life cycle assessment study, habitability perception and determination or acceleration measurements and estimation. The novelty of aerodynamic design and optimization in providing vibration free tall buildings and wind turbines with added savings that otherwise be incurred by adoption of costly structural and/or supplementary damping technologies highlighted. Better habitability, safety and comfort without added costs. State of the art in wind vibrations reviewed, together with factors influenc-

**Wind-Induced Vibrations to Tall Buildings and Wind**

DOI: 10.5772/intechopen.72094

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

**Turbines**

**Turbines**

Abdel Rahman Elbakheit

**Abstract**

Abdel Rahman Elbakheit

Additional information is available at the end of the chapter

ing control vibration in tall buildings and wind turbines.

**Keywords:** wind vibrations in tall buildings, vertex shedding in tall buildings, aerodynamic optimization of tall buildings, habitability and vibration conception in buildings, wind turbine integration in tall buildings, wind vibrations in turbines

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72094

**Provisional chapter**

#### **Wind-Induced Vibrations to Tall Buildings and Wind Turbines Turbines**

**Wind-Induced Vibrations to Tall Buildings and Wind**

DOI: 10.5772/intechopen.72094

Abdel Rahman Elbakheit Abdel Rahman Elbakheit

[4] Zhuravlev VF. Global evolution of state of the generalized Foucault pendulum. Mechan-

[5] Stanovnik A, Jurčič-Zlobec B. Numerical study of the elastic pendulum on the rotating

[6] Lynch DD. HRG Development at Delco, Litton, and Northrop Grumman. Proc. of Anniversary Workshop on Solid-State Gyroscopy (19–21 May 2008. Yalta, Ukraine). Kyiv-

[7] Bryan GH. On the beats in the vibrations of a revolving cylinder or bell. Proceedings of Cambridge Philosophical Society of Mathematics and Physical Sciences. 1890;VII(III):101-111

[8] Zhuravlev VF, Klimov DM. Wave Solid-State Gyro. Moscow: Nauka Publisher; 1985 (in

[9] Bose A, Puri S, Banerjee P. Modern Inertial Sensors and Systems. Prentice-Hall of India:

[10] Osiander R, Ann Garrison Darrin M, Champion JL. MEMS and Microstructures in Aero-

[11] Kovriguine DA. Geometrical nonlinearity stabilizes a wave solid-state gyro. Archive of

[13] Kovriguine DA, Potapov AI. Nonlinear oscillations in a thin ring - I, II. Acta Mechanica.

[14] Kovriguine DA. On non-linear resonant excitation of a wave solid-state gyro. Proc. of Int. Cong. MV2 New advances in modal synthesis of large structures, non-linear, damped

and non-deterministic cases, Jezequel Ed., École Centrale de Lyon. 1995;2:575-586 [15] Kovriguine DA. Geometrical nonlinearity stabilizes a wave solid-state gyro. Archive of

[17] Janke-Emde-Lösch: Tafeln Höherer Funktionen. Sechste auflage. Neubearbeitet von F.

[18] Gledzer EB, Dolzhansky FW, Obukhov AM. Systems of hydrodynamic type and their

[19] Nayfeh A, Balachandran B. Applied Nonlinear Dynamics: Analytical. New-York: Com-

[20] Love AEH. The free and forced vibrations of an elastic spherical shell containing a given mass of liquid. Proceedings of the London Mathematical Society. 1887;1(1):170-207

[16] Whitham GB. Linear and Nonlinear Waves. New-York: Wiley-Interscience; 1995

Lösch, B.G.Teubuer, Verlagsgesellschaft. Stuttgard. 1960

applications. Moscow: Nauka Publisher; 1981 (in Russian)

putational and Experimental Methods. Wiley; 1995

space Applications. Taylor & Francis Publisher. ISBN<PHONE_NUMBER>; 2005

[12] Phillips OM. The dynamics of the upper ocean. Cambridge Univ. Press; 1977

earth. ISRN Mathematical Physics. 2012, Article ID 806231;2012:1-7

60 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

Kharkiv. ATS of Ukraine, ISBN 978–976–0-25248-5; 2009

ics of Solids. 1998;33(6):1-6

Russian)

New Delhi, II; 2008

1998;126:189-212

Applied Mechanics. 2014;84(2):159-172

Applied Mechanics. 2014;84(2):159-172

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72094

#### **Abstract**

While wind generated noise maybe limited in magnitude and effect, wind-induced structures' vibrations could be a devastation (i.e., Tacoma Bridge Collapse 1940). This occurs with just above moderate wind speed increase, if it can excite a structure with its natural frequencies. When this occur, structures enter a phase of oscillations until collapse. However, with proper understanding of vibrations in structures these vibrations can be eliminated. Studying vibrations can be experimental through wind-tunnel and or by simulations. Wind in buildings can induce two types of motions: static or sustained; as building drift and oscillatory or resonant vibration. Motion is composed of three contributions: sway in two horizontal or perpendicular directions and torsion. This vibration would considerably affect the habitability and stability of building spaces gauged through a life cycle assessment study, habitability perception and determination or acceleration measurements and estimation. The novelty of aerodynamic design and optimization in providing vibration free tall buildings and wind turbines with added savings that otherwise be incurred by adoption of costly structural and/or supplementary damping technologies highlighted. Better habitability, safety and comfort without added costs. State of the art in wind vibrations reviewed, together with factors influencing control vibration in tall buildings and wind turbines.

**Keywords:** wind vibrations in tall buildings, vertex shedding in tall buildings, aerodynamic optimization of tall buildings, habitability and vibration conception in buildings, wind turbine integration in tall buildings, wind vibrations in turbines

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

#### **1. Introduction**

#### **1.1. Building's aerodynamic performance to control wind induced vibrations**

Generally speaking Wind affects buildings with two distinct effects, Buffeting and vertex shedding [1, 2] (i.e., Drift and oscillation as mentioned above). The first happens in the along wind direction force producing drag or overturning. If we consider a wind boundary layer acting on a tall square plan buildings with an angle α to the horizontal axis X, **Figure 1**. Wind velocity would be gradient along the Z-axis that is to say the highest wind speed would occur in the upper most position of the boundary layer and the lowest wind speed would be close to the ground. The building would experience a drag along all major axes X, Y, that are measured using local mean force coefficient CfD, and overturning or torsional moments over the X, Y and Z direction measured using overturning moments coefficients over the X-axis CML, over the Y-axis CMD, and over the Z-axis CMT, such as Shown in **Figure 1**. The second wind induced effect (i.e., Oscillations) is rather more complex in its cause, but usually happens perpendicular to the direction of wind flow and can be measured using fluctuating moments coefficient CFL presented in **Figure 1**.

As the expression of Strouhal gives the natural frequency *N* as a function of wind speed and

Having established that, this is generally have little effects on low-rise buildings. But the effect is highly pronounced in tall Buildings. With the new advancement in tall building structures, where high strength material coupled with reduced weight, it is made possible to design even more slender, more taller buildings quite easily and the trend is on the rise. These conditions makes high-rise buildings more prone to be excited by winds in the upper layers of the atmo-

On the other hand, only very specific wind speeds would cause the vertex shedding effect for any given tall structure by virtue of its three dimensional form and/or cross sectional plans. As mentioned above uniform plans of square **Figure 2**, rectangular **Figure 3**, circular **Figure 4** and similar shapes are more susceptible to trigger vertex shedding. This happens as wind approaches a high-rise structure it separated into two streams along the sides of the building by the plan shape creating equal vertices along each side faces of the building that are identical in shape and

However, only at certain wind speeds the vertices would be greater in size and stronger in velocity magnitude to force its way on one side of the tube. Thus forcing the structure to

**Figure 2.** Computational fluid dynamics image for air flow around a square tube under vertex shedding effect, with

*u*

*b* (1)

Wind-Induced Vibrations to Tall Buildings and Wind Turbines

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63

width of the building as follows:

size **Figure 2**.

stages of vertex formation.

*N* = *S* \_\_

where S = Strouhal number, U = wind speed, b = building width.

sphere that are usually with higher wind speed magnitudes.

As an aerodynamic reaction, wind induced vibrations or oscillations always triggered by the shape and form of the object subjected to wind flow [3]. The more uniform and symmetrical the form is, the more likely for it to oscillate in wind flows. Therefore, considering these factors first would lead to permanent passive solutions to vibrations in structures due to wind. There has been growing evidence from research of wind-induced vibration that symmetrical cross sections of structures may produce vibrations to structures at one of their natural frequencies.

**Figure 1.** Aerodynamic forces acting on a basic square tall building.

As the expression of Strouhal gives the natural frequency *N* as a function of wind speed and width of the building as follows:

$$N = S \frac{u}{b} \tag{1}$$

where S = Strouhal number, U = wind speed, b = building width.

**1. Introduction**

coefficient CFL presented in **Figure 1**.

**Figure 1.** Aerodynamic forces acting on a basic square tall building.

**1.1. Building's aerodynamic performance to control wind induced vibrations**

62 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

Generally speaking Wind affects buildings with two distinct effects, Buffeting and vertex shedding [1, 2] (i.e., Drift and oscillation as mentioned above). The first happens in the along wind direction force producing drag or overturning. If we consider a wind boundary layer acting on a tall square plan buildings with an angle α to the horizontal axis X, **Figure 1**. Wind velocity would be gradient along the Z-axis that is to say the highest wind speed would occur in the upper most position of the boundary layer and the lowest wind speed would be close to the ground. The building would experience a drag along all major axes X, Y, that are measured using local mean force coefficient CfD, and overturning or torsional moments over the X, Y and Z direction measured using overturning moments coefficients over the X-axis CML, over the Y-axis CMD, and over the Z-axis CMT, such as Shown in **Figure 1**. The second wind induced effect (i.e., Oscillations) is rather more complex in its cause, but usually happens perpendicular to the direction of wind flow and can be measured using fluctuating moments

As an aerodynamic reaction, wind induced vibrations or oscillations always triggered by the shape and form of the object subjected to wind flow [3]. The more uniform and symmetrical the form is, the more likely for it to oscillate in wind flows. Therefore, considering these factors first would lead to permanent passive solutions to vibrations in structures due to wind. There has been growing evidence from research of wind-induced vibration that symmetrical cross sections of structures may produce vibrations to structures at one of their natural frequencies. Having established that, this is generally have little effects on low-rise buildings. But the effect is highly pronounced in tall Buildings. With the new advancement in tall building structures, where high strength material coupled with reduced weight, it is made possible to design even more slender, more taller buildings quite easily and the trend is on the rise. These conditions makes high-rise buildings more prone to be excited by winds in the upper layers of the atmosphere that are usually with higher wind speed magnitudes.

On the other hand, only very specific wind speeds would cause the vertex shedding effect for any given tall structure by virtue of its three dimensional form and/or cross sectional plans. As mentioned above uniform plans of square **Figure 2**, rectangular **Figure 3**, circular **Figure 4** and similar shapes are more susceptible to trigger vertex shedding. This happens as wind approaches a high-rise structure it separated into two streams along the sides of the building by the plan shape creating equal vertices along each side faces of the building that are identical in shape and size **Figure 2**.

However, only at certain wind speeds the vertices would be greater in size and stronger in velocity magnitude to force its way on one side of the tube. Thus forcing the structure to

**Figure 2.** Computational fluid dynamics image for air flow around a square tube under vertex shedding effect, with stages of vertex formation.

To arrive at a building form or shape that is vertex shedding free can involves computational Simulations and or wind tunnel experimentation trying to break the symmetry of the buildings plans and forms. Mooneghi and Kargarmoakhar [4], proposed minimal intervention to any proposed buildings forms by the additions of small fins and corner modifications that help considerably reduce the shedding effect. Several studies have been conducted on this subject in the past (e.g., Gu and Quan [5], Irwin [6], Irwin et al. [7]) but each case study should be carefully evaluated to avoid unfavorable effects in building behavior. This is identical to what would typically be applied in manufacturing industries exhaust or stack chimneys, undersea cables previously mentioned examples of industries. However, these solutions may not always be practically or technically feasible to integrate into building's facade systems,

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A more efficient approach for dealing with this issue in buildings is to Further modify forms three dimensionally in what is known as aerodynamic design modification of building forms based on combinations of the cross sections and their combinations three dimensionally compared to basic square tall buildings. A good example for this point is Burj Khlifa Tall building in Dubai, where the building have tapering plans being reduced with height, as well as break-

Tamura et al. [8], presented a systematic study of building forms subjected to wind influence ranging from simple forms to more complex combinations under direct wind and cross winds using wind tunnel's scaled models as well as computational fluid dynamics. Among the figures tested are basic forms include Square, rectangle, Circle and ellipse, Tilted and snaked or winded three dimensional tubes. Corner modifications, tapered, bulged, helical, top-openings all in different modifications and finally composite forms of several basic shapes, **Table 1**.

The study compared values of overturning moments co-efficient CMD, CML, fluctuating overturning moments co-efficient CFL, Local mean wind force co-efficient CfD, in the along

ing the uniformity of form plans 2-dimenstionally and 3-dimensionally, **Figure 6**.

**Figure 5**.

Totaling 31 models in 7-categories.

**Figure 5.** Minor aerodynamic modifications [4].

**Figure 3.** Computational fluid dynamics image for air flow around a rectangular tube under vertex shedding effect.

sway to the other side. The structure would sway back to position and beyond by virtue of its elasticity. Then comes the succeeding vertex to push the structure further to the opposite side. This is where the Oscillation process would typically starts. The oscillations would be sustained by the differences in wind pressures along the opposite sides of the building swept across that eventually cause the tall structure to continue to sway in the direction perpendicular to the wind's main stream. This phenomena has been experienced widely in some industries such as factory's Chimney stacks, undersea cables, bridges, tall buildings and so forth and whenever a main stream fluid passes across a uniform geometrical object.

These oscillations of structures/objects caused by vertex shedding because of wind speed produce air pressures similar in behavior to the sinusoidal waves of sound. However, opposite in its process to the normal process of sound generation. Sound is generated whenever an object moves in air causing a succession of higher and lower pressure regions, which can be presented (i.e., heard) as a sound wave. Therefore, we can expect noise produced accompanying vertex shedding of structures or objects.

Nevertheless, with the right building three-dimensional design configuration and cross sections of it plan, it would be possible to totally control any possible wind induced vibrations in tall buildings. Thus providing great savings that otherwise needed to increase the mass (concrete), stiffness (reinforcement) and damping (restraint) needed to stabilizing structures against excessive wind vibrations.

**Figure 4.** Computational fluid dynamics image for air flow around a circular tube under vertex shedding effect.

To arrive at a building form or shape that is vertex shedding free can involves computational Simulations and or wind tunnel experimentation trying to break the symmetry of the buildings plans and forms. Mooneghi and Kargarmoakhar [4], proposed minimal intervention to any proposed buildings forms by the additions of small fins and corner modifications that help considerably reduce the shedding effect. Several studies have been conducted on this subject in the past (e.g., Gu and Quan [5], Irwin [6], Irwin et al. [7]) but each case study should be carefully evaluated to avoid unfavorable effects in building behavior. This is identical to what would typically be applied in manufacturing industries exhaust or stack chimneys, undersea cables previously mentioned examples of industries. However, these solutions may not always be practically or technically feasible to integrate into building's facade systems, **Figure 5**.

A more efficient approach for dealing with this issue in buildings is to Further modify forms three dimensionally in what is known as aerodynamic design modification of building forms based on combinations of the cross sections and their combinations three dimensionally compared to basic square tall buildings. A good example for this point is Burj Khlifa Tall building in Dubai, where the building have tapering plans being reduced with height, as well as breaking the uniformity of form plans 2-dimenstionally and 3-dimensionally, **Figure 6**.

Tamura et al. [8], presented a systematic study of building forms subjected to wind influence ranging from simple forms to more complex combinations under direct wind and cross winds using wind tunnel's scaled models as well as computational fluid dynamics. Among the figures tested are basic forms include Square, rectangle, Circle and ellipse, Tilted and snaked or winded three dimensional tubes. Corner modifications, tapered, bulged, helical, top-openings all in different modifications and finally composite forms of several basic shapes, **Table 1**. Totaling 31 models in 7-categories.

The study compared values of overturning moments co-efficient CMD, CML, fluctuating overturning moments co-efficient CFL, Local mean wind force co-efficient CfD, in the along

**Figure 5.** Minor aerodynamic modifications [4].

sway to the other side. The structure would sway back to position and beyond by virtue of its elasticity. Then comes the succeeding vertex to push the structure further to the opposite side. This is where the Oscillation process would typically starts. The oscillations would be sustained by the differences in wind pressures along the opposite sides of the building swept across that eventually cause the tall structure to continue to sway in the direction perpendicular to the wind's main stream. This phenomena has been experienced widely in some industries such as factory's Chimney stacks, undersea cables, bridges, tall buildings and so forth

**Figure 3.** Computational fluid dynamics image for air flow around a rectangular tube under vertex shedding effect.

These oscillations of structures/objects caused by vertex shedding because of wind speed produce air pressures similar in behavior to the sinusoidal waves of sound. However, opposite in its process to the normal process of sound generation. Sound is generated whenever an object moves in air causing a succession of higher and lower pressure regions, which can be presented (i.e., heard) as a sound wave. Therefore, we can expect noise produced accompany-

Nevertheless, with the right building three-dimensional design configuration and cross sections of it plan, it would be possible to totally control any possible wind induced vibrations in tall buildings. Thus providing great savings that otherwise needed to increase the mass (concrete), stiffness (reinforcement) and damping (restraint) needed to stabilizing structures

**Figure 4.** Computational fluid dynamics image for air flow around a circular tube under vertex shedding effect.

and whenever a main stream fluid passes across a uniform geometrical object.

64 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

ing vertex shedding of structures or objects.

against excessive wind vibrations.

Meaning that they are the safest in terms of habitability and design safety. This was echoed with even better results for the models with extra-helical angles. Setbacks produced the minimal wind pressures because of reduced surface area with height; however, they experienced larger excitations of spectral wind speed than the original basic square form. Rendering it with worst expected habitability. This means that aerodynamic modifications can generally

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Undoubtedly that vibrations to structures would produce uncomfortable sensations to occupants especially in the highest floor due to more excessive vibrations. However, people perceive motion quiet comfortably, but it is the rate of motion (i.e., accelerations) that causes uneasy or discomfort. Therefore, vibrations are normally expressed as fractions of acceleration due to gravity in the form of (milli-g). Human perception to vibration is a complex sensation that encompass subjective and objective factors. The former is dealing with issues that may be subject to individual's age, culture, experience and so forth, while the latter is well-established physical phenomena that is measured, determined and occur with consensus among humans. To give some indication what certain levels of "milli-g" actually mean for a human being (i.e., Objectively), the following extract from a monograph on wind-induced motion of tall build-

5 milli-g: perceptible to some occupants but, provided that such building motion does not occur frequently or continuously for an extended period of time, unlikely to cause significant

35–40 milli-g: a fear and safety threshold, sufficiently severe enough to cause some occupants

Occupant's response (i.e., subjectively) to wind vibrations come in different symptoms grading according to the severity of the motion – from concern, anxiety, fear, vertigo, dizziness, headaches and nausea. Some of these symptoms are often enhanced by the presence of audio stimulus, such as, wind noises, creaking noises due to building sway and/or visual stimulus, which is particularly relevant in the case of a tall building exhibiting highly three-dimensional modes of vibration. It should also be noted that perceptibility of wind-induced motion is inversely proportional to the square root of the product of mass, stiffness and damping; this means that, in order to halve the perceptibility, the "mass × stiffness × damping" quantity needs to be increased by a factor of 4.

In 2004 the Architectural Institute of Japan (AIJ), produced a guideline to the levels of windinduced accelerations that is relating to the natural frequencies of buildings. Focusing on 1 year

 \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ √ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

(*mass*) × (*stiffness*) × (*dampness*) (2)

*perceptibility* = 1

ings, published by the American Society of Civil Engineers [9], is provided:

improve or eliminate vertex-shedding excitations.

adverse occupant response or alarm;

to lose balance;

10 milli-g: perceptible to the vast majority of occupants;

**1.3. Habitability in some international building codes**

**1.2. Occupant's perception to wind induced vibrations**

**Figure 6.** Burj Khalifa tower in Dubai. Modifications in plans shape and sizes with height.

wind, cross wind and torsional directions CMT, **Figure 1**. Distribution of wind pressure coefficient Cp and response analysis is also evaluated for these models. In order to determine the habitability of the studied models eigenvalue analysis and response analysis were conducted.

Corner cut and helical square models were the lowest in design values for spectral wind speed for one-year return period, which is far better than the response of the basic square model.

**Table 1.** Possible modifications in three-dimensional tubes to reduce vertex shedding effect.

Meaning that they are the safest in terms of habitability and design safety. This was echoed with even better results for the models with extra-helical angles. Setbacks produced the minimal wind pressures because of reduced surface area with height; however, they experienced larger excitations of spectral wind speed than the original basic square form. Rendering it with worst expected habitability. This means that aerodynamic modifications can generally improve or eliminate vertex-shedding excitations.

#### **1.2. Occupant's perception to wind induced vibrations**

Undoubtedly that vibrations to structures would produce uncomfortable sensations to occupants especially in the highest floor due to more excessive vibrations. However, people perceive motion quiet comfortably, but it is the rate of motion (i.e., accelerations) that causes uneasy or discomfort. Therefore, vibrations are normally expressed as fractions of acceleration due to gravity in the form of (milli-g). Human perception to vibration is a complex sensation that encompass subjective and objective factors. The former is dealing with issues that may be subject to individual's age, culture, experience and so forth, while the latter is well-established physical phenomena that is measured, determined and occur with consensus among humans.

To give some indication what certain levels of "milli-g" actually mean for a human being (i.e., Objectively), the following extract from a monograph on wind-induced motion of tall buildings, published by the American Society of Civil Engineers [9], is provided:

5 milli-g: perceptible to some occupants but, provided that such building motion does not occur frequently or continuously for an extended period of time, unlikely to cause significant adverse occupant response or alarm;

10 milli-g: perceptible to the vast majority of occupants;

wind, cross wind and torsional directions CMT, **Figure 1**. Distribution of wind pressure coefficient Cp and response analysis is also evaluated for these models. In order to determine the habitability of the studied models eigenvalue analysis and response analysis were conducted. Corner cut and helical square models were the lowest in design values for spectral wind speed for one-year return period, which is far better than the response of the basic square model.

**Figure 6.** Burj Khalifa tower in Dubai. Modifications in plans shape and sizes with height.

66 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

**Table 1.** Possible modifications in three-dimensional tubes to reduce vertex shedding effect.

35–40 milli-g: a fear and safety threshold, sufficiently severe enough to cause some occupants to lose balance;

Occupant's response (i.e., subjectively) to wind vibrations come in different symptoms grading according to the severity of the motion – from concern, anxiety, fear, vertigo, dizziness, headaches and nausea. Some of these symptoms are often enhanced by the presence of audio stimulus, such as, wind noises, creaking noises due to building sway and/or visual stimulus, which is particularly relevant in the case of a tall building exhibiting highly three-dimensional modes of vibration.

It should also be noted that perceptibility of wind-induced motion is inversely proportional to the square root of the product of mass, stiffness and damping; this means that, in order to halve the perceptibility, the "mass × stiffness × damping" quantity needs to be increased by a factor of 4.

$$\text{ss} \times \text{stiffness} \times \text{damping}'' \text{ quantity needs to be increased by a factor of 4.}$$

$$\text{perceptibility} = \frac{1}{\sqrt{(\text{mass}) \times (\text{stiffness}) \times (\text{damques})}} \tag{2}$$

#### **1.3. Habitability in some international building codes**

In 2004 the Architectural Institute of Japan (AIJ), produced a guideline to the levels of windinduced accelerations that is relating to the natural frequencies of buildings. Focusing on 1 year return period (i.e., the maximum acceleration for a structure that can happen in a single year). The process involves determining buildings spectral response for a year and plotting it into a graph of a relationship between building's natural frequencies and acceleration. The position of the building's plotted response will determine the percentage of people who would be affected by the ensued acceleration. **Figure 7**, depicts the graph from the AIJ.

The graph lines in **Figure 7** denotes 5-levels of percentages of people perceiving the acceleration effect. (i.e., AIJ H-10, H-30, H-50, H-70, H-90) were the number denotes the percentage of people perceived the effect. The higher the plotted position of a building's response on **Figure 7**, the worse is peoples experience inside it.

Following the AIJ recommendations, back in 2007, the International Organization for Standardization (ISO) published a set of guidelines, which have now become the most widely adopted criteria for habitability design internationally [ISO 10137, 2007] also in **Figure 7**. The acceleration limits (again set against a 1-year return period) vary with the natural period of the structure and they are more stringent for residential developments than for office buildings, **Figure 7**.

#### **1.4. Intrinsic damping**

Intrinsic damping is the natural properties of building materials and construction processes of withstanding wind effects without extra-means or supplementary damping. It is normally required for a yearly return period (the highest wind occurring within a year), however, longer periods would be favorable but very rear. The exact estimation of intrinsic damping can only be determined through actual measurements due to the many factors contributing to it. According to [8] main sources of intrinsic damping are:

of building's structures and the wind forces applied to it. With outrigger systems, diagrid, bundle tubes having the most stable and least deflection while, framed systems having the highest deflections due to wind.(details of these systems is outside the scope of this

**Figure 7.** Comparison of average perception thresholds (where not indicated the return period is not specified by the

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We can generally measure two types of deflections due to wind in buildings. Overall deflection over the whole height of the building, which recommended being in the region of H/500 to H/300, Smith [9]. This normally perceived in the acceleration and habitability of buildings. The second is in plane or story deflection to individual units like doors, windows, cladding and similar systems from normal vertical and often affects the services, operations as well as soundness within buildings. With greater deflection of this type, building components like

For example, if we consider a 200 m residential tall building with a natural frequency of 0.25 Hz exhibiting a total building drift of 0.35 m under 50-year return period winds, this would meet the widely used H / 500 limit. If the corresponding total drift under 10-year return period winds is, say, 0.25 m and assuming that 50% of this is governed by dynamic behavior (i.e., vertex shedding) - which, in the across-wind direction, is not untypical – then the resulting wind-induced peak acceleration would move toward a rather undesirable

).

Wind turbines come in different shapes and sizes, but they all convert wind power into electricity by converting wind motion into a mechanical movement and eventually into electricity. The conversion into mechanical movement can be partly converted into vibrations that

doors windows, etc. may lose operation and stick in frames.

**2. Wind induced vibrations in wind turbines**

30 milli-g (50% × 0.25 m × [2 × π × 0.25 Hz]2

publication).

relative code.

Many completed buildings are been monitored globally trying to establish intrinsic damping magnitudes under wind service periods (yearly, 10-year, 50-year…).

#### *1.4.1. Wind deflection criteria*

Wind deflection in buildings is due to both the drag and oscillations wind forces. Is it very limited to negligible in low-buildings. However, in tall buildings, it is dependent on the type

return period (i.e., the maximum acceleration for a structure that can happen in a single year). The process involves determining buildings spectral response for a year and plotting it into a graph of a relationship between building's natural frequencies and acceleration. The position of the building's plotted response will determine the percentage of people who would be

The graph lines in **Figure 7** denotes 5-levels of percentages of people perceiving the acceleration effect. (i.e., AIJ H-10, H-30, H-50, H-70, H-90) were the number denotes the percentage of people perceived the effect. The higher the plotted position of a building's response on **Figure 7**, the

Following the AIJ recommendations, back in 2007, the International Organization for Standardization (ISO) published a set of guidelines, which have now become the most widely adopted criteria for habitability design internationally [ISO 10137, 2007] also in **Figure 7**. The acceleration limits (again set against a 1-year return period) vary with the natural period of the structure and they are more stringent for residential developments than for office build-

Intrinsic damping is the natural properties of building materials and construction processes of withstanding wind effects without extra-means or supplementary damping. It is normally required for a yearly return period (the highest wind occurring within a year), however, longer periods would be favorable but very rear. The exact estimation of intrinsic damping can only be determined through actual measurements due to the many factors contributing to it.

Many completed buildings are been monitored globally trying to establish intrinsic damping

Wind deflection in buildings is due to both the drag and oscillations wind forces. Is it very limited to negligible in low-buildings. However, in tall buildings, it is dependent on the type

affected by the ensued acceleration. **Figure 7**, depicts the graph from the AIJ.

68 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

worse is peoples experience inside it.

According to [8] main sources of intrinsic damping are:

• Foundation and soil types (soil-structure interaction);

magnitudes under wind service periods (yearly, 10-year, 50-year…).

• Friction between members and connections;

• Structural system and joint types;

• Other nonstructural members;

ings, **Figure 7**.

**1.4. Intrinsic damping**

• Material damping;

• Interior partitions; • Exterior cladding;

• Vibration amplitude.

*1.4.1. Wind deflection criteria*

**Figure 7.** Comparison of average perception thresholds (where not indicated the return period is not specified by the relative code.

of building's structures and the wind forces applied to it. With outrigger systems, diagrid, bundle tubes having the most stable and least deflection while, framed systems having the highest deflections due to wind.(details of these systems is outside the scope of this publication).

We can generally measure two types of deflections due to wind in buildings. Overall deflection over the whole height of the building, which recommended being in the region of H/500 to H/300, Smith [9]. This normally perceived in the acceleration and habitability of buildings. The second is in plane or story deflection to individual units like doors, windows, cladding and similar systems from normal vertical and often affects the services, operations as well as soundness within buildings. With greater deflection of this type, building components like doors windows, etc. may lose operation and stick in frames.

For example, if we consider a 200 m residential tall building with a natural frequency of 0.25 Hz exhibiting a total building drift of 0.35 m under 50-year return period winds, this would meet the widely used H / 500 limit. If the corresponding total drift under 10-year return period winds is, say, 0.25 m and assuming that 50% of this is governed by dynamic behavior (i.e., vertex shedding) - which, in the across-wind direction, is not untypical – then the resulting wind-induced peak acceleration would move toward a rather undesirable 30 milli-g (50% × 0.25 m × [2 × π × 0.25 Hz]2 ).

#### **2. Wind induced vibrations in wind turbines**

Wind turbines come in different shapes and sizes, but they all convert wind power into electricity by converting wind motion into a mechanical movement and eventually into electricity. The conversion into mechanical movement can be partly converted into vibrations that reduces the efficiency of conversion to electricity. Besides, generating noise as well as faults due to vibrations.

With modeling of vibrations the failure of key components such as tower post, drive train, gear and blades can be greatly reduced if not eliminated. The main causes to vibrations can be varied according to each particular part of the turbine, however, almost all causes are due to aerodynamic behavior. Yet till different components have different types of vibrations and vibration causes. Tower's vibration, for instance, has a low frequency magnitude from 0 to 200 Hz, while the gear and drive train have high frequency (3–20 kHz). We can distinguish between these cases for the different components as follows:

Tower Post: the main support of the turbine, which is normally towering high to capture more wind speed. Its geometrical uniform cross section can cause considerable aerodynamic vibrations in the same manner discussed in point 1.1 and subsection above. It worth mentioning here that tall buildings can function as supports to wind turbines in the same manner.

Turbine blade: Turbine blades can cause vibrations in the turbine, associated gear and tower post if they or anyone of them has different pitch angles. This will cause unsteady rotational angular speed. Vibrations may be sever in above rated wind speeds (normally 12 m/s and above). According to Peng Guo and David Infield [10], "increasing the blade pitch angle beyond stall point may lead to aerodynamic lift coefficient decreases and the drag coefficient increases leading to increased thrust causing tower to deflect and vibrations to increase."

along the sides of buildings. Buildings can in fact provide the structural support as well as the continuous and sustained flow of wind needed to generate the required power, Elbakheit [11]. The acceptable process involves further optimization to tall buildings aerodynamic form as well as buildings structural loadings. Adding wind turbines to buildings (especially tall buildings) or existing buildings after construction may render the structure under vertex shedding effect, as it will change totally the aerodynamic response of the building as well as

Wind-Induced Vibrations to Tall Buildings and Wind Turbines

http://dx.doi.org/10.5772/intechopen.72094

71

Nevertheless, there are many models of wind turbines that are more quiet with less vibration such as Vertical axis wind turbines that can be integrated with tall buildings with little draw backs. In addition, using a number of small capacity wind turbines of less than 100 kW would break wind aerodynamic forces into small manageable portions compared with the option of using large turbines of over 100 kW. This also reduce the burden of maintenance and provide

A high level of vibration control is achievable with the right aerodynamic design solutions in

Vertex shedding is an aerodynamic phenomenon that triggers oscillations and vibrations in various fields of construction as well as industries. Symmetrical plans' cross-sectional con-

Introducing transformations in plans, horizontally and vertically is the key to control windinduced vibrations in both buildings and various industry establishments. Corner modification, fins, torsional or spiral additions are among the favorable solutions in chimneystacks,

the resulting wind speeds around buildings.

**Figure 8.** Wind turbines integration in tall buildings.

backup should any single turbine fails. **Figure 8**.

undersea cables and similar structures.

buildings, wind turbines and any industry establishments.

figurations are the most susceptible to wind induced vibrations.

**4. Conclusions**

Because of the strong connectivity of the different parts together it may be difficult from start to distinguish the source of vibration in wind turbines. Not even with close monitoring, therefore, Peng Guo and David Infield [10] proposed a simulation depending on nonlinear state estimation technique NSET whereby it would be easily to compare turbine vibrations, wind speed, angle of blade, power generated and torque at normal and specific time steps. This will relate the positions of the blade pitch of the turbine, the conditions of the wind speed with the ensued aerodynamic response of power generation, stalling or vibrations. Therefore, potentially identifying the cause of vibration. NSET would also predict the magnitude of these vectors in a given timeframe, when comparing the prediction to the normally monitored data, any discrepancies may indicate a possible cause of failure including vibrations. However, NEST involves a mathematical modeling of the parameters simulated (i.e., turbine vibrations, wind speed, angle of blade, power generated and torque) and establish its validity to the actually recorded values from active monitoring beforehand. Only when the validity of the simulation is established the comparison process my take place. This process has not been used on many cases so its validity at large is not that solid. In addition to having, to distinguish between different operational modes (i.e., below rated wind speeds or above rated wind speeds); would mean making a simulation for each mode separately to be able to compare the results.

#### **3. Wind turbines integration in tall buildings**

The integration of wind turbine technologies in tall buildings poses great potential to harness the resources, which is abundant around tall buildings. This can be either on the top or

**Figure 8.** Wind turbines integration in tall buildings.

along the sides of buildings. Buildings can in fact provide the structural support as well as the continuous and sustained flow of wind needed to generate the required power, Elbakheit [11]. The acceptable process involves further optimization to tall buildings aerodynamic form as well as buildings structural loadings. Adding wind turbines to buildings (especially tall buildings) or existing buildings after construction may render the structure under vertex shedding effect, as it will change totally the aerodynamic response of the building as well as the resulting wind speeds around buildings.

Nevertheless, there are many models of wind turbines that are more quiet with less vibration such as Vertical axis wind turbines that can be integrated with tall buildings with little draw backs. In addition, using a number of small capacity wind turbines of less than 100 kW would break wind aerodynamic forces into small manageable portions compared with the option of using large turbines of over 100 kW. This also reduce the burden of maintenance and provide backup should any single turbine fails. **Figure 8**.

#### **4. Conclusions**

reduces the efficiency of conversion to electricity. Besides, generating noise as well as faults

With modeling of vibrations the failure of key components such as tower post, drive train, gear and blades can be greatly reduced if not eliminated. The main causes to vibrations can be varied according to each particular part of the turbine, however, almost all causes are due to aerodynamic behavior. Yet till different components have different types of vibrations and vibration causes. Tower's vibration, for instance, has a low frequency magnitude from 0 to 200 Hz, while the gear and drive train have high frequency (3–20 kHz). We can distinguish

Tower Post: the main support of the turbine, which is normally towering high to capture more wind speed. Its geometrical uniform cross section can cause considerable aerodynamic vibrations in the same manner discussed in point 1.1 and subsection above. It worth mentioning

Turbine blade: Turbine blades can cause vibrations in the turbine, associated gear and tower post if they or anyone of them has different pitch angles. This will cause unsteady rotational angular speed. Vibrations may be sever in above rated wind speeds (normally 12 m/s and above). According to Peng Guo and David Infield [10], "increasing the blade pitch angle beyond stall point may lead to aerodynamic lift coefficient decreases and the drag coefficient increases leading to increased thrust causing tower to deflect and vibrations to increase."

Because of the strong connectivity of the different parts together it may be difficult from start to distinguish the source of vibration in wind turbines. Not even with close monitoring, therefore, Peng Guo and David Infield [10] proposed a simulation depending on nonlinear state estimation technique NSET whereby it would be easily to compare turbine vibrations, wind speed, angle of blade, power generated and torque at normal and specific time steps. This will relate the positions of the blade pitch of the turbine, the conditions of the wind speed with the ensued aerodynamic response of power generation, stalling or vibrations. Therefore, potentially identifying the cause of vibration. NSET would also predict the magnitude of these vectors in a given timeframe, when comparing the prediction to the normally monitored data, any discrepancies may indicate a possible cause of failure including vibrations. However, NEST involves a mathematical modeling of the parameters simulated (i.e., turbine vibrations, wind speed, angle of blade, power generated and torque) and establish its validity to the actually recorded values from active monitoring beforehand. Only when the validity of the simulation is established the comparison process my take place. This process has not been used on many cases so its validity at large is not that solid. In addition to having, to distinguish between different operational modes (i.e., below rated wind speeds or above rated wind speeds); would

mean making a simulation for each mode separately to be able to compare the results.

The integration of wind turbine technologies in tall buildings poses great potential to harness the resources, which is abundant around tall buildings. This can be either on the top or

**3. Wind turbines integration in tall buildings**

here that tall buildings can function as supports to wind turbines in the same manner.

between these cases for the different components as follows:

70 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

due to vibrations.

A high level of vibration control is achievable with the right aerodynamic design solutions in buildings, wind turbines and any industry establishments.

Vertex shedding is an aerodynamic phenomenon that triggers oscillations and vibrations in various fields of construction as well as industries. Symmetrical plans' cross-sectional configurations are the most susceptible to wind induced vibrations.

Introducing transformations in plans, horizontally and vertically is the key to control windinduced vibrations in both buildings and various industry establishments. Corner modification, fins, torsional or spiral additions are among the favorable solutions in chimneystacks, undersea cables and similar structures.

Three-dimensional form modifications are the more efficient solutions for tall building structures.

**References**

2004

410-420

between Economy and Stiffness. 2010

ing. Probabilist Eng Mech. 1997;**12**(1):9-31

buildings: Review. J Build Eng. 2016;**6**:225-235

and Industrial Aerodynamics. 2008;**96**(6-7):701-712

[1] Kawada T, Scott R. History of the Modern Suspension Bridge : Solving the Dilemma

Wind-Induced Vibrations to Tall Buildings and Wind Turbines

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73

[2] Gurley KR, Tognarelli MA, Kareem A. Analysis and simulation tools for wind engineer-

[3] Li T, Zhang JY, Zhang WH, Zhu MH. Vortex-induced vibration characteristics of an elastic circular cylinder. World Academy of Science, Engineering and Technology. 2009

[4] Mooneghi MA, Kargarmoakhar R. Aerodynamic mitigation and shape optimization of

[5] Quan Ga. Study on wind loads and responses of tall buildings and structures. The Seventh Asia-Pacific Conference on Wind Engineering; November 8-12, 2009; Taipei, Taiwan;

[6] Irwin PA. Bluff body aerodynamics in wind engineering. Journal of Wind Engineering

[7] Irwin P, Kilpatrick J, Robinson J, Frisque A. Wind and tall buildings: Negatives and posi-

[8] Aerodynamic and flow characteristics of tall buildings with various unconventional

[9] Smith MA, Caracoglia L. A Monte Carlo based method for the dynamic "fragility analysis" of tall buildings under turbulent wind loading. Engineering Structures. 2011;**33**(2):

[10] Infield PGD. Wind turbine tower vibration modelling and monitoring by the nonlinear

[11] Elbakheit AR. Factors enhancing aerofoil wings for wind energy harnessing in buildings. Building Services Engineering Research & Technology. 2014;**35**(4):417-437

tives. Structural Design of Tall and Special Buildings. 2008;**17**(5):915-928

configurations. International High-Rise Building Journal. 2013;**2**(3)

state estimation technique (NSET). Energies. 2012:5279-5293

Corner cut and helical and spiral plan modifications in various angles and configurations can considerably reduce or eliminate the vertex shedding effect in tall buildings. Setbacks, although it is a form of three-dimensional plan modification, yet due to the reduced mass at the top of tall buildings might trigger vibrations more severe than the standard uniform plans.

The recommended limit for wind vibrations or oscillations for a structure is in the range of H/300 to H/500 were, H is the height of the buildings.

Human perception to vibration varies and depends on acceleration (rate of motion) related to gravity acceleration g. Alarming vibrations occurs above 30 milli-g.

Tall buildings provide a promising building type for wind energy integration. Furthermore, the addition of wind turbines into building either new or retrofitting can render the building under vertex shedding. Exercise extreme caution to optimize wind flows around buildings to enhance power generation as well as to avoid vertex shedding.

Wind Vibrations in wind turbine caused either by turbine tower cross-sectional symmetry and/or by, the unbalanced pitch angles of turbine blades. Therefore, checking turbine blade angles first would assures of turbine's stability, if vibration still exists, then it will be the symmetrical cross section of the supporting post.

Further aerodynamic optimizations research in tall buildings' 3-dimensional configuration and/or aerofoils for integration of sizable small-scale wind-harnessing technologies can add to the safety, habitability of tall buildings with renewable energy at hand.

#### **Acknowledgements**

The author would like to express his appreciation to the Deanship of Scientific Research at King Saud University for the provision of funding through the College of Architecture and Planning Research Center.

#### **Author details**

Abdel Rahman Elbakheit

Address all correspondence to<EMAIL_ADDRESS>
Department of Architecture and Building Science, King Saud University, Riyadh, Saudi Arabia

#### **References**

Three-dimensional form modifications are the more efficient solutions for tall building

Corner cut and helical and spiral plan modifications in various angles and configurations can considerably reduce or eliminate the vertex shedding effect in tall buildings. Setbacks, although it is a form of three-dimensional plan modification, yet due to the reduced mass at the top of tall buildings might trigger vibrations more severe than the standard uniform

The recommended limit for wind vibrations or oscillations for a structure is in the range of

Human perception to vibration varies and depends on acceleration (rate of motion) related to

Tall buildings provide a promising building type for wind energy integration. Furthermore, the addition of wind turbines into building either new or retrofitting can render the building under vertex shedding. Exercise extreme caution to optimize wind flows around buildings to

Wind Vibrations in wind turbine caused either by turbine tower cross-sectional symmetry and/or by, the unbalanced pitch angles of turbine blades. Therefore, checking turbine blade angles first would assures of turbine's stability, if vibration still exists, then it will be the sym-

Further aerodynamic optimizations research in tall buildings' 3-dimensional configuration and/or aerofoils for integration of sizable small-scale wind-harnessing technologies can add

The author would like to express his appreciation to the Deanship of Scientific Research at King Saud University for the provision of funding through the College of Architecture and

Department of Architecture and Building Science, King Saud University, Riyadh, Saudi

H/300 to H/500 were, H is the height of the buildings.

metrical cross section of the supporting post.

**Acknowledgements**

Planning Research Center.

Abdel Rahman Elbakheit

**Author details**

Arabia

gravity acceleration g. Alarming vibrations occurs above 30 milli-g.

72 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

enhance power generation as well as to avoid vertex shedding.

Address all correspondence to<EMAIL_ADDRESS>
to the safety, habitability of tall buildings with renewable energy at hand.

structures.

plans.

**Chapter 5**

Provisional chapter

**State Feedback Nonlinear Control Strategy for Wind**

Synchronous Generator for Maximum Power Extraction

DOI: 10.5772/intechopen.72366

This chapter addresses the problem of controlling the Complete chain of the wind turbine system using the permanent magnet synchronous generator (PMSG) connected with the Distribution network via an AC/DC/AC converters through LCL filter, the control to be applied in different parts of the system, whose objectives are three: (1) adjust the generator speed to track a varying reference signal; (2) the control of the network-side converter must be maintained the current injected into the network in a unit power factor correction (PFC); (3) regulating the DC Link voltage at a constant value. Firstly, the mathematical modeling for all system components studied in d-q frame and its state space equation are established to simplify the proposed control, thereafter a nonlinear backstepping approach is used in this work to achieve the objectives indicated above. The performance of the proposed approach is evaluated based on the various simulations results carried out

Keywords: wind energy, PMSG, AC/DC/AC converter, LCL filter, nonlinear control,

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

State Feedback Nonlinear Control Strategy for Wind

**Turbine System Driven by Permanent Magnet**

Turbine System Driven by Permanent Magnet

**Synchronous Generator for Maximum Power**

**Extraction and Power Factor Correction**

Yasser Boussairi, Abdelmajid Abouloifa, Ibtissam Lachkar, Chaouqi Aouadi and

Yasser Boussairi, Abdelmajid Abouloifa, Ibtissam Lachkar, Chaouqi Aouadi and

and Power Factor Correction

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

under Matlab/Simulink/Simpower software.

backstepping approach, PFC

http://dx.doi.org/10.5772/intechopen.72366

Abdelatif Hamdoun

Abdelatif Hamdoun

Abstract

#### **State Feedback Nonlinear Control Strategy for Wind Turbine System Driven by Permanent Magnet Synchronous Generator for Maximum Power Extraction and Power Factor Correction** State Feedback Nonlinear Control Strategy for Wind Turbine System Driven by Permanent Magnet Synchronous Generator for Maximum Power Extraction and Power Factor Correction

DOI: 10.5772/intechopen.72366

Yasser Boussairi, Abdelmajid Abouloifa, Ibtissam Lachkar, Chaouqi Aouadi and Abdelatif Hamdoun Yasser Boussairi, Abdelmajid Abouloifa, Ibtissam Lachkar, Chaouqi Aouadi and Abdelatif Hamdoun

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72366

#### Abstract

This chapter addresses the problem of controlling the Complete chain of the wind turbine system using the permanent magnet synchronous generator (PMSG) connected with the Distribution network via an AC/DC/AC converters through LCL filter, the control to be applied in different parts of the system, whose objectives are three: (1) adjust the generator speed to track a varying reference signal; (2) the control of the network-side converter must be maintained the current injected into the network in a unit power factor correction (PFC); (3) regulating the DC Link voltage at a constant value. Firstly, the mathematical modeling for all system components studied in d-q frame and its state space equation are established to simplify the proposed control, thereafter a nonlinear backstepping approach is used in this work to achieve the objectives indicated above. The performance of the proposed approach is evaluated based on the various simulations results carried out under Matlab/Simulink/Simpower software.

Keywords: wind energy, PMSG, AC/DC/AC converter, LCL filter, nonlinear control, backstepping approach, PFC

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 1. General introduction

Nowadays, the demand for electrical energy continues to increase, as the intense industrialization of the last decades and the multiplication of electric household appliances has led to considerable electrical energy needs. The various traditional power stations use fossil fuels (coal, oil, natural gas, etc.) and, consequently, development, fissile sources (nuclear energy) such as uranium, hydrocarbons and Water, thermal power plants are responsible for releases of atmospheric gases. Nuclear energy has an undeniable advantage of not causing pollution, but the risk of a nuclear accident remains, and which increases over the years like the storage of non-repeatable nuclear waste. The treatment and burial of waste are real problems that make this energy unattractive for future generations [1].

In this chapter, we present a technique to control two power converters which is based on the backstepping approach, it Draws the attention of many researchers in the field of control of electrical machines [10–13]. The importance of backstepping controllers lies in: the high accuracy, fast dynamic response, stability, simplicity of design and implementation, and vis-à-vis robustness changes in internal or external parameters [14]. The rest of this paper is organized as follows. In Section 2 the mathematical model detailed and the state space of the system studies are presented, and the control proposed based on the technical backstepping for the whole system are presented in Section 3. Section 4 present the simulation example in the

State Feedback Nonlinear Control Strategy for Wind Turbine System Driven by Permanent Magnet Synchronous…

http://dx.doi.org/10.5772/intechopen.72366

77

platform MATLAB/Simulink/Simpowers, we end this chapter with a conclusion.

2. Modeling of the wind system based on a synchronous generator

nomena)

associated with the rectifier

2.1. AC/DC rectifier-generator modeling

its dynamic model.

In the second part of this chapter we have proposed the concept of a complete wind chain. In this part, we establish a mathematical model of the whole wind chain by insisting in particular on the Multiphysics character (taking into account the mechanical, magnetic, electrical phe-

The modeling of the wind turbine requires the modeling of the electric generator, the power

• The first part is devoted to the modeling of the permanent magnet synchronous machine

• In the second part, we present the modeling of the converter on the network side

The control of an electric motor is a difficult task and requires, above all, a good knowledge of

This part will consist in describing the machine mathematically with its nonlinear model by putting some working hypotheses in evidence [16, 17], which allowed the study of behavior of

> pϕf j

ω id � p

j ω � 1 J

ϕf ω þ

1 Ld

1 Lq

1 Lq Tl (1)

vq (2)

vd (3)

j id þ

iq � f

converter and the filter of the control system [15]. This section divided into two parts:

(inverter); connected to the grid via an LCL filter show by Figure 1.

the latter. The model adopted is based on the transformation of PARK.

dt ¼ Ld � Lq

> did dt ¼ � Rs Ld id þ p Ld Lq ω iq þ

dω

diq dt ¼ � Rs Lq iq � p Ld Lq

Expressed in the d-q coordinates, are given the following state space form:

All these disadvantages have prompted researchers to reduce their exploitation to solve their problems, using the so-called "renewable" energies (wind and solar). The latter are perfectly in line with the overall effort to reduce CO2 emissions. Wind power is clearly in the forefront. This energy is transformed into mechanical energy by wind turbines and then converted to electrical energy by generators [2]. Therefore, there are different wind turbine configurations installed in large scale; The major distinction among them is made between generator synchronous or asynchronous [3].

After having transformed wind energy into electrical energy, it is necessary to adapt it to the load it is feeding or the network to which our production system is connected, since the wind turbines considered as generator of variable power. Where the voltage supplied by the generator undergoes variations due to fluctuations in the speed of rotation thereof as a function of the wind speed. This results in a variation in the electrical power supplied to the load supplied. Moreover, the shape and frequency of the supplied voltage are not necessarily adapted to the load. To solve these problems, it is necessary to use power electronics via a generator-side rectifier and a network-side inverter, new control approaches are learned to optimize this generation of energy.

In this chapter, we use the permanent magnet synchronous generator (PMSG) a variable speed, which found a particular interest in applications of wind energy, because have many advantages such are considered stable, their small size and high energy efficiency, ability of operation at slow speed and they do not need a gearbox [4, 5]. The last years have seen rapid progress in the control of nonlinear systems related to renewable energies. This system has been treated using several control strategies ranging from simple techniques, for example so-called oriented flow control (FOC) [6], to more sophisticated nonlinear approaches, which poses a major problem which is the need to use a mechanical sensor (speed, load torque). This imposes an additional cost and increases the complexity of the assemblies, for example, feedback linearization [7], hybrid mode/slip/neuro fuzzy control [8], the direct control of the couple (DTC) [9].

In nonlinear control or having non-constant parameters systems, conventional control laws may be inadequate because they are not strong especially when the demands on accuracy and other dynamic characteristics of systems. We must appeal to non-sensitive control laws to changes in parameters, to disturbance and nonlinearities, On the other hand.

In this chapter, we present a technique to control two power converters which is based on the backstepping approach, it Draws the attention of many researchers in the field of control of electrical machines [10–13]. The importance of backstepping controllers lies in: the high accuracy, fast dynamic response, stability, simplicity of design and implementation, and vis-à-vis robustness changes in internal or external parameters [14]. The rest of this paper is organized as follows. In Section 2 the mathematical model detailed and the state space of the system studies are presented, and the control proposed based on the technical backstepping for the whole system are presented in Section 3. Section 4 present the simulation example in the platform MATLAB/Simulink/Simpowers, we end this chapter with a conclusion.

#### 2. Modeling of the wind system based on a synchronous generator

In the second part of this chapter we have proposed the concept of a complete wind chain. In this part, we establish a mathematical model of the whole wind chain by insisting in particular on the Multiphysics character (taking into account the mechanical, magnetic, electrical phenomena)

The modeling of the wind turbine requires the modeling of the electric generator, the power converter and the filter of the control system [15]. This section divided into two parts:

#### 2.1. AC/DC rectifier-generator modeling

1. General introduction

nous or asynchronous [3].

generation of energy.

make this energy unattractive for future generations [1].

Nowadays, the demand for electrical energy continues to increase, as the intense industrialization of the last decades and the multiplication of electric household appliances has led to considerable electrical energy needs. The various traditional power stations use fossil fuels (coal, oil, natural gas, etc.) and, consequently, development, fissile sources (nuclear energy) such as uranium, hydrocarbons and Water, thermal power plants are responsible for releases of atmospheric gases. Nuclear energy has an undeniable advantage of not causing pollution, but the risk of a nuclear accident remains, and which increases over the years like the storage of non-repeatable nuclear waste. The treatment and burial of waste are real problems that

76 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

All these disadvantages have prompted researchers to reduce their exploitation to solve their problems, using the so-called "renewable" energies (wind and solar). The latter are perfectly in line with the overall effort to reduce CO2 emissions. Wind power is clearly in the forefront. This energy is transformed into mechanical energy by wind turbines and then converted to electrical energy by generators [2]. Therefore, there are different wind turbine configurations installed in large scale; The major distinction among them is made between generator synchro-

After having transformed wind energy into electrical energy, it is necessary to adapt it to the load it is feeding or the network to which our production system is connected, since the wind turbines considered as generator of variable power. Where the voltage supplied by the generator undergoes variations due to fluctuations in the speed of rotation thereof as a function of the wind speed. This results in a variation in the electrical power supplied to the load supplied. Moreover, the shape and frequency of the supplied voltage are not necessarily adapted to the load. To solve these problems, it is necessary to use power electronics via a generator-side rectifier and a network-side inverter, new control approaches are learned to optimize this

In this chapter, we use the permanent magnet synchronous generator (PMSG) a variable speed, which found a particular interest in applications of wind energy, because have many advantages such are considered stable, their small size and high energy efficiency, ability of operation at slow speed and they do not need a gearbox [4, 5]. The last years have seen rapid progress in the control of nonlinear systems related to renewable energies. This system has been treated using several control strategies ranging from simple techniques, for example so-called oriented flow control (FOC) [6], to more sophisticated nonlinear approaches, which poses a major problem which is the need to use a mechanical sensor (speed, load torque). This imposes an additional cost and increases the complexity of the assemblies, for example, feedback linearization [7],

In nonlinear control or having non-constant parameters systems, conventional control laws may be inadequate because they are not strong especially when the demands on accuracy and other dynamic characteristics of systems. We must appeal to non-sensitive control laws to

hybrid mode/slip/neuro fuzzy control [8], the direct control of the couple (DTC) [9].

changes in parameters, to disturbance and nonlinearities, On the other hand.

The control of an electric motor is a difficult task and requires, above all, a good knowledge of its dynamic model.

This part will consist in describing the machine mathematically with its nonlinear model by putting some working hypotheses in evidence [16, 17], which allowed the study of behavior of the latter. The model adopted is based on the transformation of PARK.

Expressed in the d-q coordinates, are given the following state space form:

$$\frac{d\boldsymbol{\omega}}{dt} = \left(\frac{\left(\mathcal{L}\_d - \mathcal{L}\_q\right)}{\dot{\jmath}}\dot{\mathbf{i}}\_d + \frac{p\phi\_f}{\dot{\jmath}}\right)\dot{\mathbf{i}}\_q - \frac{\mathcal{f}}{\dot{\jmath}}\boldsymbol{\omega} - \frac{\mathbf{1}}{\dot{\jmath}}\boldsymbol{T}\_l \tag{1}$$

$$\frac{d\dot{i}\_q}{dt} = -\frac{R\_s}{L\_q}\dot{i}\_q - p\frac{L\_d}{L\_q}\omega\ \dot{i}\_d - p\frac{1}{L\_q}\phi\_f\omega + \frac{1}{L\_q}v\_q\tag{2}$$

$$\frac{d\mathbf{i}\_d}{dt} = -\frac{R\_s}{L\_d}\mathbf{i}\_d + p\frac{L\_d}{L\_q}\omega \mathbf{i}\_q + \frac{1}{L\_d}\mathbf{v}\_d \tag{3}$$

Figure 1. Architecture of AC/DC/AC power converter in wind power system.

where Rs is the resistance of the stator windings, (Ld, Lq) are d and q axis inductances, (id, iq) are the dq components of the stator current, φf amplitude of the flux induced by the permanent magnets of the rotor in the stator phases, p number of pole pairs, j combined inertia of rotor and load, Tl shaft mechanical torque, f combined viscous friction of rotor and load, ω angular velocity of the rotor (vd, vq) denote the averaged stator voltage in dq- coordinate (Parks transformation of the triphase stator voltages) these voltages are expressed in function of the corresponding control action:

$$
\upsilon\_q = \upsilon\_{dc}\mu\_1; \quad \upsilon\_d = \upsilon\_{dc}\mu\_2 \tag{4}
$$

voltages across the capacitor, in the grid side and in the output of inverter respectively. The

State Feedback Nonlinear Control Strategy for Wind Turbine System Driven by Permanent Magnet Synchronous…

Elaborate partial model uses binary control signals, to develop the control laws, and it will be based on the average model in which each variable is replaced by its average value over a

The state space equations obtained up to now are put together to get a state space model of the whole system including the AC/DC/AC converters combined with the synchronous generator.

> pϕf j

> > 1 Lq

x1 x2 þ

x1 x3 � p

j x1 � 1 J

ϕf x1 þ

1 Ld

1 Lq

ð Þ �r2x4 þ x5 � vr (12)

C ð Þ x6 � x4 (13)

ð Þ �r2x6 þ vdcu � x6 (14)

j x3 þ

x2 � f

where x represents an averaging value over a cutting period of a real signal.

x\_ 1 ¼ Ld � Lq

> x\_ 3 ¼ � Rs Ld x3 þ p Ld Lq

> > x\_ 4 ¼ 1 L2

x\_ 6 ¼ 1 L1

computation time, while maintaining the nonlinear aspect [20].

x\_ 5 ¼ 1

The main challenge of our research work is to design a control law for the permanent magnet synchronous generator, which is more powerful for monitoring control, disturbance rejection, stability, parametric uncertainties of robustness, compliance with constraints Physics and

Since a few years, many evolutions have been made within the framework of the control of the nonlinear systems whose backstepping technique forms part. The backstepping approach is a systematic and recursive methodology for the synthesis of nonlinear control laws, the basic idea of backstepping control is to make the system looped, equivalent to cascaded order one subsystems Stable in the Lyapunov sense, which gives it robust qualities and an asymptotic

x\_ 2 ¼ � Rs Lq x2 � p Ld Lq

vo ¼ vdcu (8)

http://dx.doi.org/10.5772/intechopen.72366

79

Tl (9)

vdcu1 (10)

vdcu2 (11)

inverter undergoes the equations:

Now, let us introduce the following notation:

ω ¼ x1; iq ¼ x2; id ¼ x3; i2 ¼ x4; vc ¼ x5; i1 ¼ x6

The whole model is rewritten here by:

3. Nonlinear controller design

switching period.

#### 2.2. DC/AC inverter-grid modeling

The supply network is connected to a single-phase inverter consisting of four semiconductors (IGBT with antiparallel diodes for bidirectional current mode) displayed in two branches. A single switch on the same leg can be conductive at the same time, this converter connecting with the network through an LCL filter, the latter they minimize the amount of current distortion injected into the utility grid [18, 19]. Applying Kirchhoff's laws, this subsystem is described by the following set of differential equations:

$$\frac{d\dot{\mathbf{i}}\_2}{dt} = \frac{1}{L\_2}(-r\_2\dot{\mathbf{i}}\_2 + \mathbf{v}\_c - \mathbf{v}\_r) \tag{5}$$

$$\frac{dv\_c}{dt} = \frac{1}{C}(i\_1 - i\_2) \tag{6}$$

$$\frac{di\_1}{dt} = \frac{1}{L\_1}(-r\_2\mathbf{i}\_1 + \mathbf{v}\_{dc} - \mathbf{v}\_c) \tag{7}$$

where L1and L2 are the self-inductances, r1 and r2 are its parasitic resistances, (i1, i2) are the components of the current flowing the inductors L1 and L2 respectively. (vc, vr, vo) are the voltages across the capacitor, in the grid side and in the output of inverter respectively. The inverter undergoes the equations:

$$
\upsilon\_o = \upsilon\_{dc}\mu\tag{8}
$$

Elaborate partial model uses binary control signals, to develop the control laws, and it will be based on the average model in which each variable is replaced by its average value over a switching period.

Now, let us introduce the following notation:

$$\omega = \mathbf{x}\_1; i\_q = \mathbf{x}\_2; i\_d = \mathbf{x}\_3; i\_2 = \mathbf{x}\_4; v\_c = \mathbf{x}\_5; i\_1 = \mathbf{x}\_6$$

where Rs is the resistance of the stator windings, (Ld, Lq) are d and q axis inductances, (id, iq) are the dq components of the stator current, φf amplitude of the flux induced by the permanent magnets of the rotor in the stator phases, p number of pole pairs, j combined inertia of rotor and load, Tl shaft mechanical torque, f combined viscous friction of rotor and load, ω angular velocity of the rotor (vd, vq) denote the averaged stator voltage in dq- coordinate (Parks transformation of the triphase stator voltages) these voltages are expressed in function of the

The supply network is connected to a single-phase inverter consisting of four semiconductors (IGBT with antiparallel diodes for bidirectional current mode) displayed in two branches. A single switch on the same leg can be conductive at the same time, this converter connecting with the network through an LCL filter, the latter they minimize the amount of current distortion injected into the utility grid [18, 19]. Applying Kirchhoff's laws, this subsystem is

where L1and L2 are the self-inductances, r1 and r2 are its parasitic resistances, (i1, i2) are the components of the current flowing the inductors L1 and L2 respectively. (vc, vr, vo) are the

vq ¼ vdcu1; vd ¼ vdcu2 (4)

ð Þ �r2i2 þ vc � vr (5)

C ð Þ i1 � i2 (6)

ð Þ �r2i1 þ vdc � vc (7)

corresponding control action:

2.2. DC/AC inverter-grid modeling

described by the following set of differential equations:

Figure 1. Architecture of AC/DC/AC power converter in wind power system.

78 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

di2 dt ¼ 1 L2

di1 dt ¼ 1 L1

dvc dt ¼ 1 where x represents an averaging value over a cutting period of a real signal.

The state space equations obtained up to now are put together to get a state space model of the whole system including the AC/DC/AC converters combined with the synchronous generator. The whole model is rewritten here by:

$$\dot{\mathbf{x}}\_1 = \left(\frac{(\mathbf{L}\_d - \mathbf{L}\_q)}{\dot{\mathbf{j}}} \mathbf{x}\_3 + \frac{p\phi\_f}{\dot{\mathbf{j}}}\right) \mathbf{x}\_2 - \frac{f}{\dot{\mathbf{j}}} \mathbf{x}\_1 - \frac{1}{\dot{\mathbf{J}}} T\_l \tag{9}$$

$$\dot{\mathbf{x}}\_{2} = -\frac{R\_{s}}{L\_{q}}\mathbf{x}\_{2} - p\frac{L\_{d}}{L\_{q}}\mathbf{x}\_{1}\,\mathbf{x}\_{3} - p\frac{1}{L\_{q}}\phi\_{f}\mathbf{x}\_{1} + \frac{1}{L\_{q}}v\_{d\epsilon}u\_{1} \tag{10}$$

$$\dot{\mathbf{x}}\_3 = -\frac{R\_s}{L\_d}\mathbf{x}\_3 + p\frac{L\_d}{L\_q}\mathbf{x}\_1\,\mathbf{x}\_2 + \frac{1}{L\_d}\mathbf{v}\_{dc}\boldsymbol{\mu}\_2\tag{11}$$

$$
\dot{\mathbf{x}}\_4 = \frac{1}{L\_2}(-r\_2\mathbf{x}\_4 + \mathbf{x}\_5 - v\_r) \tag{12}
$$

$$
\dot{\mathbf{x}}\_5 = \frac{1}{\mathbf{C}} (\mathbf{x}\_6 - \mathbf{x}\_4) \tag{13}
$$

$$\dot{\mathbf{x}}\_{\delta} = \frac{1}{L\_1} (-r\_2 \mathbf{x}\_{\delta} + \mathbf{v}\_{d\varepsilon} \mathbf{u} - \mathbf{x}\_{\delta}) \tag{14}$$

#### 3. Nonlinear controller design

The main challenge of our research work is to design a control law for the permanent magnet synchronous generator, which is more powerful for monitoring control, disturbance rejection, stability, parametric uncertainties of robustness, compliance with constraints Physics and computation time, while maintaining the nonlinear aspect [20].

Since a few years, many evolutions have been made within the framework of the control of the nonlinear systems whose backstepping technique forms part. The backstepping approach is a systematic and recursive methodology for the synthesis of nonlinear control laws, the basic idea of backstepping control is to make the system looped, equivalent to cascaded order one subsystems Stable in the Lyapunov sense, which gives it robust qualities and an asymptotic global stability of the tracking error. For each subsystem, a so-called virtual control law is calculated, in order to ensure the convergence of the first-order subsystems characterizing the continuation of trajectories toward their equilibrium states (tracking errors are zero). The determination of the control laws that flows from this approach is based on the use of Lyapunov functions [14]

Usually the current of the d-axis must be set to zero in order to keep the flow constant in the air gap of the machine [22]. The current of the q-axis must follow a reference signal of the external

State Feedback Nonlinear Control Strategy for Wind Turbine System Driven by Permanent Magnet Synchronous…

In order, the PMSG speed is used as a reference value for a controller to capture the maximum

To solve the speed monitoring problem, the velocity control error and its path designated by

e1 ¼ x1 � x

Let a virtual input x used to ensure the stability of the speed loop, the dynamics of the speed

pϕf j

j Ω � 1 j Tl � x\_ ref

j x3 þ

x2 � f

The asymptotic stability of the resulting closed loop system is guaranteed according to Lyapunov stability theorem. To the speed of tracking error goes to zero, the Lyapunov func-

> V1 ¼ 1 2 e 2

If this function is always positive (it is the case now) and its derivative is always negative, the

For the derivative of the test to be still negative, it must take the derivative of the form:

Where k1 > 0 is a positive control parameter introduced by the backstepping method, which must always be positive and non-zero in order to satisfy the stability criteria of the Lyapunov function. In addition, this parameter influences the dynamics of the control. By following the backstepping method, a virtual command x2 used to ensure the stability of the velocity loop is

> þ f j x1 þ 1 J Tl þ x ref 1 � k1e1 (20)

ref

1 (15)

http://dx.doi.org/10.5772/intechopen.72366

81

1 (17)

V\_ 1 ¼ e1e\_1 (18)

V\_ 1 ¼ �k1e1 (19)

1 (16)

speed loop [23].

power of the incident energy of the wind turbine.

3.1.1. Step 1: calculation of the virtual control law iqref

1 e\_1 ¼ Ld � Lq

tion is constructed for the subsystem is given by:

The derivative of the function is written as follows:

x2 ¼ j p Ld � Lq

x3 þ pϕf

error will be stable and tends to zero.

given by the following equation:

the reference value are defined:

control error is given by:

e\_1 ¼ x\_ � x\_ ref

From the point of view of control, this is expressed in the following three objectives:

The control to be applied in different parts of the system. The generator-side converter is mainly used to control the speed of the generator to extract the maximum output power at different wind speeds [16, 18], the mains-side converter is mainly used to control reactive power on the one hand and Maintain the voltage In the DC bus capacitor of the constant value and make the current output of the inverter in phase with the gate voltage.

A nonlinear recoil control design scheme is developed for PMSG speed tracking control.

#### 3.1. Generator speed control

The system includes a fast mode (electrical currents) and a slow (mechanical) mode. The adopted control strategy uses cascaded loops, two internal loops to control the currents of the d and q axes, and an external loop to control the speed of the generator, in order to guarantee satisfactory speed reference tracking quality despite [21]. The uncertainties of the generator parameters. In this sense, we go through three steps, as shown in Figure 2. In each step, we calculate the associated error and we ensure the stability of the system by choosing the good function of Lyapunov in order to find the commands.

Figure 2. Rotor-side converter control system.

Usually the current of the d-axis must be set to zero in order to keep the flow constant in the air gap of the machine [22]. The current of the q-axis must follow a reference signal of the external speed loop [23].

In order, the PMSG speed is used as a reference value for a controller to capture the maximum power of the incident energy of the wind turbine.

#### 3.1.1. Step 1: calculation of the virtual control law iqref

global stability of the tracking error. For each subsystem, a so-called virtual control law is calculated, in order to ensure the convergence of the first-order subsystems characterizing the continuation of trajectories toward their equilibrium states (tracking errors are zero). The determination of the control laws that flows from this approach is based on the use of

From the point of view of control, this is expressed in the following three objectives:

80 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

value equal to the nominal input voltage of the drive.

function of Lyapunov in order to find the commands.

and make the current output of the inverter in phase with the gate voltage.

i. Speed control: forces the speed of the generator to follow a reference signal varies.

ii. PFC: the current injected into the network must be sinusoidal and in phase with the AC

iii. Check the voltage of the DC bus at a given reference. This is usually set to a constant

The control to be applied in different parts of the system. The generator-side converter is mainly used to control the speed of the generator to extract the maximum output power at different wind speeds [16, 18], the mains-side converter is mainly used to control reactive power on the one hand and Maintain the voltage In the DC bus capacitor of the constant value

A nonlinear recoil control design scheme is developed for PMSG speed tracking control.

The system includes a fast mode (electrical currents) and a slow (mechanical) mode. The adopted control strategy uses cascaded loops, two internal loops to control the currents of the d and q axes, and an external loop to control the speed of the generator, in order to guarantee satisfactory speed reference tracking quality despite [21]. The uncertainties of the generator parameters. In this sense, we go through three steps, as shown in Figure 2. In each step, we calculate the associated error and we ensure the stability of the system by choosing the good

Lyapunov functions [14]

supply voltage.

3.1. Generator speed control

Figure 2. Rotor-side converter control system.

To solve the speed monitoring problem, the velocity control error and its path designated by the reference value are defined:

$$e\_1 = \mathbf{x}\_1 - \mathbf{x}\_1^{r\circ} \tag{15}$$

Let a virtual input x used to ensure the stability of the speed loop, the dynamics of the speed control error is given by:

$$\dot{\mathbf{e}}\_{1} = \dot{\mathbf{x}} - \dot{\mathbf{x}}\_{1}^{\eta\dagger} \qquad \qquad \dot{\mathbf{e}}\_{1} = \left(\frac{(\mathbf{L}\_{d} - \mathbf{L}\_{\eta})}{\dot{\mathbf{j}}} \mathbf{x}\_{3} + \frac{p\phi\_{f}}{\dot{\mathbf{j}}}\right) \mathbf{x}\_{2} - \frac{f}{\dot{\mathbf{j}}} \boldsymbol{\Omega} - \frac{1}{\dot{\mathbf{j}}} \mathbf{T}\_{l} - \dot{\mathbf{x}}\_{1}^{\eta\dagger} \tag{16}$$

The asymptotic stability of the resulting closed loop system is guaranteed according to Lyapunov stability theorem. To the speed of tracking error goes to zero, the Lyapunov function is constructed for the subsystem is given by:

$$V\_1 = \frac{1}{2}c\_1^2\tag{17}$$

If this function is always positive (it is the case now) and its derivative is always negative, the error will be stable and tends to zero.

The derivative of the function is written as follows:

$$
\dot{V}\_1 = \varepsilon\_1 \dot{e}\_1 \tag{18}
$$

For the derivative of the test to be still negative, it must take the derivative of the form:

$$
\dot{V}\_1 = -k\_1 e\_1 \tag{19}
$$

Where k1 > 0 is a positive control parameter introduced by the backstepping method, which must always be positive and non-zero in order to satisfy the stability criteria of the Lyapunov function. In addition, this parameter influences the dynamics of the control. By following the backstepping method, a virtual command x2 used to ensure the stability of the velocity loop is given by the following equation:

$$\mathbf{x}\_{2} = \frac{j}{p\left(\mathbf{L}\_{d} - \mathbf{L}\_{q}\right)\mathbf{x}\_{3} + p\phi\_{f}} \left( + \frac{f}{j}\mathbf{x}\_{1} + \frac{1}{J}T\_{l} + \mathbf{x}\_{1}^{ref} - k\_{1}\mathbf{e}\_{1} \right) \tag{20}$$

Once the virtual input x1 defined in the first loop to stabilize the dynamics of (13), we define the second error on the current as follows:

$$e\_2 = \mathbf{x}\_2 - \mathbf{x}\_2^{r\notin} \tag{21}$$

e\_3 ¼ � Rs Ld x3 þ p Ld Lq

3 introduced by the backstepping method,

Rs Ld x3 � p Ld Lq

Ld x3 þ p Ld Lq

u2 ¼ Ld vdc

The third function of Lyapunov is selected so that:

V\_ 3 ¼ e3 � Rs

Using (28)–(30), the control law is given by:

3.2. DC/AC inverter-grid control design

3.2.1. Step 4: stabilization of subsystem (12)

Let us introduce the following error on the current:

4 ¼ i2ref the reference of the signal

the current loop, taking Lyapunov's candidate function as:

form V\_ 3 ¼ �k3e2

the current.

With x ref x1x2 þ

State Feedback Nonlinear Control Strategy for Wind Turbine System Driven by Permanent Magnet Synchronous…

V3 ¼ 1 2 e 2

So that the derivative of the criterion is always negative, the derivative of V1 must take the

x1x2 þ

Our goal is to inject active energy into the network while maintaining a very good power factor (PFC). This means that the three-phase system absorbed by the converter should be sinusoidal and in phase with the supply mains voltage [18]. We are therefore looking for a regulator that forces the current to follow a reference signal of the form. For the moment, the quantity is any real positive. The controller will now be designed by applying the backstepping control technique to the system of Eqs. (12)–(14); The synthesis ends in three stages since the relative degree of the system is equal to three when the output considered is

e4 ¼ L2 x4 � x

Given the Eq. (12) of the whole model, the dynamics of the error can be written as follows:

e\_4 ¼ �r2x4 þ x5 � vr � L2x\_

Suppose that x5 is the virtual control input used to ensure the overall asymptotic stability of

ref 4

ref

1 Ld

x1x2 þ x\_

vdcu2 � x\_

ref 3 � k3e3 (31)

ref 3

1 Ld

vdcu2 � x\_

ref

3 (28)

83

http://dx.doi.org/10.5772/intechopen.72366

3 (30)

3 (29)

¼ �k3e 2

(32)

4 (33)

#### 3.1.2. Step 2: calculation of the final control law u1

This step makes it possible to determine the control law u1 of the global system

Using Eq. (21), the temporal derivatives given by:

$$\dot{e}\_2 = \dot{\mathbf{x}}\_2 - \dot{\mathbf{x}}\_2^{\text{ref}} \qquad \qquad \dot{e}\_2 = -\frac{R\_s}{L\_q}\mathbf{x}\_2 - p\frac{L\_d}{L\_q}\mathbf{x}\_1\,\mathbf{x}\_3 - p\frac{1}{L\_q}\phi\_f\mathbf{x}\_1 + \frac{1}{L\_q}v\_{dt}\mu\_1 - \dot{\mathbf{x}}\_2^{\text{ref}} \tag{22}$$

In order to ensure the convergence of the tracking error to zero, also requires that the current be regulated and limited, we use the extension of the following Lyapunov function:

$$V\_2 = V\_1 + \frac{1}{2}e\_2^2\tag{23}$$

Its temporal derivative is given by the following equation:

$$
\dot{V}\_2 = \dot{V}\_1 + e\_2 \dot{e}\_2 \tag{24}
$$

Finally, in order to make V\_ 2 negative, the voltage control input of the q-axis can be found by choosing V\_ 2 by the following equation:

$$
\dot{V}\_2 = -k\_2 e\_2^2 \tag{25}
$$

Where k2 0 is a design constant.

We deduce the law of final control:

$$u\_1 = \frac{L\_q}{\upsilon\_{dc}} \begin{bmatrix} -k\_2 c\_2 - \frac{p}{j} \left( (L\_d - L\_q) \mathbf{x}\_3 + \phi\_f \right) e\_1 + \\\ R\_s \\ \frac{R\_s}{L\_q} \mathbf{x}\_2 + p \frac{L\_d}{L\_q} \mathbf{x}\_1 \ x\_3 - p \frac{1}{L\_q} \phi\_f \mathbf{x}\_1 + \dot{\mathbf{x}}\_2^{ref} \end{bmatrix} \tag{26}$$

#### 3.1.3. Step 3: calculating the control law u2

This stage interests us to stabilize the subsystem (11) which aims to force the current id is equal to 0.

The current tracking error:

$$e\_3 = x\_3 - x\_3^{r\circ} \tag{27}$$

Its temporal derivative is given by the following equation:

State Feedback Nonlinear Control Strategy for Wind Turbine System Driven by Permanent Magnet Synchronous… http://dx.doi.org/10.5772/intechopen.72366 83

$$\dot{e}\_3 = -\frac{R\_s}{L\_d} \mathbf{x}\_3 + p \frac{L\_d}{L\_q} \mathbf{x}\_1 \mathbf{x}\_2 + \frac{1}{L\_d} \mathbf{v}\_{dc} u\_2 - \dot{\mathbf{x}}\_3^{ref} \tag{28}$$

The third function of Lyapunov is selected so that:

Once the virtual input x1 defined in the first loop to stabilize the dynamics of (13), we define

e2 ¼ x2 � x

x1 x3 � p

In order to ensure the convergence of the tracking error to zero, also requires that the current

V2 ¼ V1 þ

Finally, in order to make V\_ 2 negative, the voltage control input of the q-axis can be found by

V\_ 2 ¼ �k2e

j Ld � Lq

This stage interests us to stabilize the subsystem (11) which aims to force the current id is equal

e3 ¼ x3 � x

ref

x1 x3 � p

�k2e2 � p

Rs Lq x2 þ p Ld Lq

2

� �x3 þ ϕf � �

> 1 Lq

be regulated and limited, we use the extension of the following Lyapunov function:

1 Lq

ϕf x1 þ

1 Lq

V\_ 2 ¼ V\_ 1 þ e2e\_2 (24)

e1þ

ref 2

ϕf x1 þ x\_

vdcu1 � x\_

ref

2 (23)

2 (25)

3 (27)

2 (22)

(26)

This step makes it possible to determine the control law u1 of the global system

Lq x2 � p Ld Lq

82 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

Its temporal derivative is given by the following equation:

u1 ¼ Lq vdc

Its temporal derivative is given by the following equation:

ref

2 (21)

the second error on the current as follows:

3.1.2. Step 2: calculation of the final control law u1

Using Eq. (21), the temporal derivatives given by:

2 e\_2 ¼ � Rs

choosing V\_ 2 by the following equation:

Where k2 0 is a design constant.

We deduce the law of final control:

3.1.3. Step 3: calculating the control law u2

The current tracking error:

to 0.

e\_2 ¼ x\_ 2 � x\_ ref

$$V\_3 = \frac{1}{2}e\_3^2\tag{29}$$

So that the derivative of the criterion is always negative, the derivative of V1 must take the form V\_ 3 ¼ �k3e2 3 introduced by the backstepping method,

$$\dot{V}\_3 = e\_3 \left( -\frac{R\_s}{L\_d} \mathbf{x}\_3 + p \frac{L\_d}{L\_q} \mathbf{x}\_1 \mathbf{x}\_2 + \frac{1}{L\_d} \mathbf{v}\_{d\ell} \mathbf{u}\_2 - \dot{\mathbf{x}}\_3^{ref} \right) = -k\_3 e\_3^2 \tag{30}$$

Using (28)–(30), the control law is given by:

$$\mu\_2 = \frac{L\_d}{\upsilon\_{dc}} \left[ \frac{R\_s}{L\_d} \mathbf{x}\_3 - p \frac{L\_d}{L\_q} \mathbf{x}\_1 \mathbf{x}\_2 + \dot{\mathbf{x}}\_3^{ref} - k\_3 e\_3 \right] \tag{31}$$

#### 3.2. DC/AC inverter-grid control design

Our goal is to inject active energy into the network while maintaining a very good power factor (PFC). This means that the three-phase system absorbed by the converter should be sinusoidal and in phase with the supply mains voltage [18]. We are therefore looking for a regulator that forces the current to follow a reference signal of the form. For the moment, the quantity is any real positive. The controller will now be designed by applying the backstepping control technique to the system of Eqs. (12)–(14); The synthesis ends in three stages since the relative degree of the system is equal to three when the output considered is the current.

#### 3.2.1. Step 4: stabilization of subsystem (12)

Let us introduce the following error on the current:

$$\mathbf{e}\_4 = \mathbf{L}\_2 \left( \mathbf{x}\_4 - \mathbf{x}\_4^{ref} \right) \tag{32}$$

With x ref 4 ¼ i2ref the reference of the signal

Given the Eq. (12) of the whole model, the dynamics of the error can be written as follows:

$$\dot{\varepsilon}\_4 = -r\_2 \mathbf{x}\_4 + \mathbf{x}\_5 - \upsilon\_r - L\_2 \dot{\mathbf{x}}\_4^{\mathrm{ref}} \tag{33}$$

Suppose that x5 is the virtual control input used to ensure the overall asymptotic stability of the current loop, taking Lyapunov's candidate function as:

$$V\_4 = \frac{1}{2}e\_4^2\tag{34}$$

Since x6is not the actual control inputs, we define a third tracking error between the stabiliza-

State Feedback Nonlinear Control Strategy for Wind Turbine System Driven by Permanent Magnet Synchronous…

ref 6

(43)

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85

6 (44)

6 (45)

(46)

e6 ¼ L1 x6 � x

The third design step consists in choosing the actual control signal u, so that all errors (e4, e5, e6) converge to zero. To this end, we should ensure that these errors depend on the actual control

To analyze the error system, composed of Eqs. (43), (44), consider the candidate of the aug-

V6 ¼ V5 þ

2 5 þ e5

r1x1 þ x5 þ L1x\_

PMSG: Rs ¼ O:425 Ω, Ld ¼ Lq ¼ O:0084 H, φf ¼ O:433 Wb, j ¼ O:02 Kg:m:m, p¼ 4

Network and filter: vg ¼ 220V, 50 Hz, L1 ¼ L2 ¼ 5e�3H, r1 ¼ r2 ¼ 50e�3Ω

Speed and id regulator: k1 ¼ 2e�2, k2 ¼ 7:2e�3, k3 ¼ 2e�2

PFC regulator: k4 ¼ 3e�4, k5 ¼ 8e�3, k6 ¼ 3e�2

Vdc regulator: kp ¼ 18e�4, ki ¼ 9e�5

Simulation of the wind energy conversion (WEC) system the global control system described by Figure 3 is simulated using the Matlab/Simulink (V. R2015a), operating under Windows 8. The controlled part is a wind system including the synchronous generator and the associated AC DC/AC power converters via LCL filter with the numerical values (Figures 4 and 5):

1 vdc

> > e5 C þ e\_6

ref 6 � 1 L1

u � L1x\_

ref

e5 � k6e6 (47)

e\_6 ¼ �r1x6 � x5 þ

V\_ 5 ¼ �k5e

tion functions and the virtual control input the x6.

signal. We begin to focus on; It follows from (43) that:

Using (44)–(46), the control law of the system is given by:

u ¼ 1 vdc

4. Simulation results and discussion

3.2.3. Step 6: stabilization of subsystem (14)

mented Lyapunov function:

The derivative is given by:

Controller parameters:

The derivative of this equation gives:

$$
\dot{V}\_4 = \varepsilon\_4 \dot{e}\_4 \tag{35}
$$

A judicious choice of x5 and rendering V4 negative definitive and providing stability for the dynamics of e4 is x5 = x ref 5 such that:

$$V\_4 = -k\_4 e\_4^2\tag{36}$$

By following the backstepping method and to ensure a continuous stability voltage, the virtual control x5is given by the following equation:

$$\mathbf{x}\_5 = r\_2 \mathbf{x}\_4 + \mathbf{v}\_r + L\_2 \dot{\mathbf{x}}\_4^{ref} - k\_4 \mathbf{e}\_4 \tag{37}$$

Since x5is not the actual control input, we define a second tracking error between the stabilization function x ref 5 and the virtual control input x5.

$$\mathbf{e}\_5 = \mathbb{C}\left(\mathbf{x}\_5 - \mathbf{x}\_5^{r\circ}\right) \tag{38}$$

3.2.2. Step 5: stabilization of subsystem (13)

The temporal derivative of e5 is given by:

$$
\dot{\mathbf{e}}\_5 = \mathbf{x}\_6 - \mathbf{x}\_4 - \mathbf{C} \dot{\mathbf{x}}\_5^{\text{ref}} \tag{39}
$$

The virtual input x ref 5 is used to ensure the stability of the voltage loop. Then, considering the candidate for the Lyapunov function:

$$V\_5 = V\_4 + \frac{1}{2}e\_5^2\tag{40}$$

We obtain the derivative of (40)

$$
\dot{V}\_5 = -k\_4 e\_4^2 + e\_4 \left(\frac{\mathcal{e}\_4}{\mathcal{C}} + \dot{\mathcal{e}}\_5\right) \tag{41}
$$

It can easily be verified that the time derivativeV\_ 5 is a negative defined function if the control input is chosen such that:

$$\mathbf{x}\_6 = \mathbf{x}\_4 + k\_4 \mathbf{e}\_4 + \mathbf{e}\_5 \left(k\_5 \mathbf{e}\_5 + \frac{1}{\mathbf{C}} \mathbf{e}\_4\right) \tag{42}$$

where k5 > 0 is a positive synthetic constant. Indeed, this choice would imply that e5 ¼ �k5e5 what clearly establishes the exponential stability of the system (13)

Since x6is not the actual control inputs, we define a third tracking error between the stabilization functions and the virtual control input the x6.

$$\mathbf{e}\_6 = L\_1 \left( \mathbf{x}\_6 - \mathbf{x}\_6^{\text{ref}} \right) \tag{43}$$

#### 3.2.3. Step 6: stabilization of subsystem (14)

V4 ¼ 1 2 e 2

A judicious choice of x5 and rendering V4 negative definitive and providing stability for the

V4 ¼ �k4e

By following the backstepping method and to ensure a continuous stability voltage, the virtual

Since x5is not the actual control input, we define a second tracking error between the stabiliza-

e5 ¼ C x5 � x

e\_5 ¼ x6 � x4 � Cx\_

V5 ¼ V4 þ

2 4 þ e4

x6 ¼ x4 þ k4e4 þ e5 k5e5 þ

where k5 > 0 is a positive synthetic constant. Indeed, this choice would imply that e5 ¼ �k5e5

V\_ 5 ¼ �k4e

what clearly establishes the exponential stability of the system (13)

x5 ¼ r2x4 þ vr þ L2x\_

2

ref

ref 5

ref

5 is used to ensure the stability of the voltage loop. Then, considering the

e4 C þ e\_5

1 C e4

The derivative of this equation gives:

ref

control x5is given by the following equation:

5 such that:

84 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

5 and the virtual control input x5.

dynamics of e4 is x5 = x

tion function x

The virtual input x

ref

3.2.2. Step 5: stabilization of subsystem (13) The temporal derivative of e5 is given by:

ref

It can easily be verified that the time derivativeV\_

candidate for the Lyapunov function:

We obtain the derivative of (40)

input is chosen such that:

4 (34)

4 (36)

4 � k4e4 (37)

5 (39)

5 (40)

5 is a negative defined function if the control

(38)

(41)

(42)

V\_ 4 ¼ e4e\_4 (35)

The third design step consists in choosing the actual control signal u, so that all errors (e4, e5, e6) converge to zero. To this end, we should ensure that these errors depend on the actual control signal. We begin to focus on; It follows from (43) that:

$$\dot{\varepsilon}\_{6} = -r\_{1}\mathbf{x}\_{6} - \mathbf{x}\_{5} + \frac{1}{\upsilon\_{dc}}\boldsymbol{\mu} - L\_{1}\dot{\mathbf{x}}\_{6}^{\mathrm{ref}} \tag{44}$$

To analyze the error system, composed of Eqs. (43), (44), consider the candidate of the augmented Lyapunov function:

$$V\_6 = V\_5 + \frac{1}{2}e\_6^2\tag{45}$$

The derivative is given by:

$$
\dot{V}\_5 = -k\_5 c\_5^2 + e\_5 \left(\frac{\mathcal{C}\_5}{\mathcal{C}} + \dot{e}\_6\right) \tag{46}
$$

Using (44)–(46), the control law of the system is given by:

$$\mu = \frac{1}{\upsilon\_{dc}} \left( r\_1 \mathbf{x}\_1 + \mathbf{x}\_5 + L\_1 \dot{\mathbf{x}}\_6^{\prime \prime \prime} - \frac{1}{L\_1} e\_5 - k\_6 e\_6 \right) \tag{47}$$

#### 4. Simulation results and discussion

Simulation of the wind energy conversion (WEC) system the global control system described by Figure 3 is simulated using the Matlab/Simulink (V. R2015a), operating under Windows 8. The controlled part is a wind system including the synchronous generator and the associated AC DC/AC power converters via LCL filter with the numerical values (Figures 4 and 5):

$$\text{PMSG:} \ R\_s = \text{O.425 } \Omega \text{, } \mathcal{L}\_d = \mathcal{L}\_q = \text{O.0084 } \mathcal{H}, \,\varphi\_f = \text{O.433 } \text{Wb}, \,\mathrm{j} = \text{O.02 } \text{Kg.m.m.} \text{, } \mathbf{p} = 4$$

Network and filter: vg ¼ 220V, 50 Hz, L1 ¼ L2 ¼ 5e�3H, r1 ¼ r2 ¼ 50e�3Ω

Controller parameters:

Speed and id regulator: k1 ¼ 2e�2, k2 ¼ 7:2e�3, k3 ¼ 2e�2

PFC regulator: k4 ¼ 3e�4, k5 ¼ 8e�3, k6 ¼ 3e�2

Vdc regulator: kp ¼ 18e�4, ki ¼ 9e�5

Figure 3. Block diagram of control system including the synchronous generator associated AC/DC/AC power converters.

The rate of the current isq tends to a constant value and has the same shape as that of the torque; We deduce that the electromagnetic torque is directly proportional to the current isq

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Figures 8 and 9 respectively show the current i2 injected in the network and its reference

Figures 10 and 11, respectively, show the shape of the DC bus voltage vdc for a reference vdcref

For this second simulation part, a random wind profile was applied in order to test the degree

The above figures show the results of the command by Backstepping applied to the GSAP. The objective is to control the operation of the closed loop system by varying the first reference rotational speed of 0 rad/s at 80 rad/s and then at a final value equal to the nominal speed: 157 rad/s. Figures 12–15, show the simulation results obtained using the nominal parameters

obtained from the DC bus controller and the error between these two signals

(400 V) and the current i2 inject into the network with the supply voltage.

of continuity and efficiency of the control used in this chapter.

shown in Figures 6 and 7 respectively.

Figure 6. The current along the axis q.

Figure 5. Figure of current isd for a reference 0.

Figure 4. Figure of the rotor speed for a reference 100 (rad/s).

The speed rotation ω of the generator does not change much value, it remains practically equal to the reference value Ωref was shown by the appearance of the error between these two signals which is zero, the current path isd takes the value 0 set at the start, and also notice clearly in the transitional regime the speed of the system with the regulator

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Figure 5. Figure of current isd for a reference 0.

Figure 6. The current along the axis q.

The speed rotation ω of the generator does not change much value, it remains practically equal to the reference value Ωref was shown by the appearance of the error between these two signals which is zero, the current path isd takes the value 0 set at the start, and also notice clearly in the

Figure 3. Block diagram of control system including the synchronous generator associated AC/DC/AC power converters.

86 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

transitional regime the speed of the system with the regulator

Figure 4. Figure of the rotor speed for a reference 100 (rad/s).

The rate of the current isq tends to a constant value and has the same shape as that of the torque; We deduce that the electromagnetic torque is directly proportional to the current isq shown in Figures 6 and 7 respectively.

Figures 8 and 9 respectively show the current i2 injected in the network and its reference obtained from the DC bus controller and the error between these two signals

Figures 10 and 11, respectively, show the shape of the DC bus voltage vdc for a reference vdcref (400 V) and the current i2 inject into the network with the supply voltage.

For this second simulation part, a random wind profile was applied in order to test the degree of continuity and efficiency of the control used in this chapter.

The above figures show the results of the command by Backstepping applied to the GSAP. The objective is to control the operation of the closed loop system by varying the first reference rotational speed of 0 rad/s at 80 rad/s and then at a final value equal to the nominal speed: 157 rad/s. Figures 12–15, show the simulation results obtained using the nominal parameters

Figure 7. The electromagnetic force Te.

Figure 10. DC bus voltage regulation.

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Figure 11. Current i2 and vg:.

Figure 12. Figure of the rotor speed for a various reference.

Figure 8. Flow of i2 injected into the grid.

Figure 9. Error behavior between current i2 and its reference.

of the generator. These figures describe the good system performance in a closed loop in terms of trajectory tracking and disturbance rejection on multiple speeds: low and high speed. In addition, the current d-axis of good follows its reference. Figures 16, 17, show that the output current in phase with the power supply voltage and the DC link is stable at a constant value which is check the control objectives.

State Feedback Nonlinear Control Strategy for Wind Turbine System Driven by Permanent Magnet Synchronous… http://dx.doi.org/10.5772/intechopen.72366 89

Figure 10. DC bus voltage regulation.

Figure 11. Current i2 and vg:.

of the generator. These figures describe the good system performance in a closed loop in terms of trajectory tracking and disturbance rejection on multiple speeds: low and high speed. In addition, the current d-axis of good follows its reference. Figures 16, 17, show that the output current in phase with the power supply voltage and the DC link is stable at a constant value

which is check the control objectives.

Figure 9. Error behavior between current i2 and its reference.

Figure 8. Flow of i2 injected into the grid.

Figure 7. The electromagnetic force Te.

88 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

Figure 12. Figure of the rotor speed for a various reference.

Figure 13. Error behavior between rotor speed and its reference.

Figure 16. Current i2 injected into the grid.

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Figure 17. Current i2 and vg .

Figure 18. Active and reactive power.

Figure 14. Current id and its reference.

Figure 15. Error behavior between current id and its reference.

State Feedback Nonlinear Control Strategy for Wind Turbine System Driven by Permanent Magnet Synchronous… http://dx.doi.org/10.5772/intechopen.72366 91

Figure 16. Current i2 injected into the grid.

Figure 13. Error behavior between rotor speed and its reference.

90 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

Figure 14. Current id and its reference.

Figure 15. Error behavior between current id and its reference.

Figure 17. Current i2 and vg .

Figure 18. Active and reactive power.

The active and inverted power injected into the grid are presented at the Figure 18, the reactive power tends toward its reference value Qref ¼ 0, for the active power it is observed that the variation in the speed of the machine influences the variation in power, When the speed of the generator very large the value of the active power becomes greater

References

2007. pp. 7-28

2007. IEEE; 2007. pp. 1-6

gies and Power Quality (ICREPQ14); 2014

Industry Applications. 2010;46(1):331-339

Access Journal. 2014;2(1):161-167

Electrique 2014; 2014

[1] Bianchi FD, Mantz RJ, De Battista H. The Wind and Wind Turbines. London: Springer;

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[2] Rolan A, Luna A, Vazquez G, Aguilar D, and Azevedo G. Modeling of a variable speed wind turbine with a permanent magnet synchronous generator. In 2009 IEEE Interna-

[3] Yin M, Li G, Zhou M, Zhao C. Modeling of the wind turbine with a permanent magnet synchronous generator for integration. In Power Engineering Society General Meeting,

[4] Belloni F, Chiumeo R, Gandolfi C, Villa A. Simulation model of a permanent magnet synchronous generator for grid studies. In International Conference on Renewable Ener-

[5] Haque ME, Negnevitsky M, Muttaqi KM. A novel control strategy for a variable-speed wind turbine with a permanent-magnet synchronous generator. IEEE Transactions on

[6] Saleh KI, Mohammed OA, Badr MA. Field oriented vector control of synchronous motors with additional field winding. IEEE Transactions on Energy Conversion. 2004;19:95-101

[7] Yang ZP, Wang MH, Liu CL, Hou, Cai YB. Variable structure control with sliding mode for self-controlled synchronous motor drive speed regulation. IEEE International Sympo-

[8] Elmas C, Ustun O. A hybrid controller for the speed control of a permanent magnet

[9] Pyrhonen O, Niemela M, Pyrhonen J, and Kaukonen J. Excitation control of DTC controlled salient pole synchronous motor in field weakening range. International Workshop

[10] Camara MMS, Camara MB, et al. Modélisation et commande d'une génératrice synchrone à aimant permanant pour la production et l'injection des énergies offshores

[11] Kechich A, Mazari B. La commande par mode glissant: Application à la machine synchrone `a aimants permanents (approche linéaire). Afrique. Science. 2008;4(1):21-37

[12] Ding Z, Wei G, Ding X. Speed identification and control for permanent magnet synchronous motor via sliding mode approach. Systems Science & Control Engineering: An Open

[13] Aimene M, Payman A, Dakyo B. Commande par platitude d'un système de conversion d'energie éolienne à vitesse variable connectée au réseau. In Symposium de G'enie

synchronous motor drive. Control Engineering Practice. 2008;16(3):260-270

on Advanced Motion Control, AMC '98, Coimbra; 1998. pp. 294-298

dans un réseau. In Symposium de Génie Electrique 2014; 2014

sium on Industrial Electronics (ISIE), Vol. 2; 1992. pp. 620-624

tional Symposium on Industrial Electronics. IEEE; 2009. pp. 734-739

#### 4.1. Interpretation of results

From the simulation results obtained, it can be noted from the first view that the regulator based on the backstepping approach has practically slightly better performances than those of the conventional regulator, especially in dynamic conditions, Where it can be observed in all the figures presented in the simulations that the response time for is very short for the signals to restore to the maximum values, so this fast correction either of the velocity or the currents or voltages translates the continuation of our system And assured the performance of our regulator

In the injection part, the power to the network it is observed that our regulator respects the characteristics of our grid that it is the frequency or the phase on the one hand, and on the other hand the power injected to the network one notes that the power Reactive voltage tends to zero and the active power reacted with the variation of the speed of the generator when the speed reaches the maximum power is totally transmitted to the network.

#### 5. Conclusion

In this chapter, the nonlinear control of the wind conversion chain based on a synchronous generator with permanent magnet controlled by the electronic converters with MLI control was presented. This electrical combination enabled us to execute the control strategy designed to this wind system studied which was the extraction of the maximum power called "MPPT", also the injection of the current to the network with a good power factor at the "Using a speed control controlled by a backstepping approach. The simulation results obtained in this chapter clearly show an acceptable degree of efficiency of the chosen regulation which causes the system to return to its optimum point after a variation of the wind speed.

#### Author details

Yasser Boussairi1 \*, Abdelmajid Abouloifa1 , Ibtissam Lachkar2 , Chaouqi Aouadi1 and Abdelatif Hamdoun1

\*Address all correspondence to<EMAIL_ADDRESS>
1 LTI Lab, Faculty des Sciences Ben M'sik, University Hasan II of Casablanca, Casablanca, Morocco

2 LISER Lab, ENSEM of Casablanca, University Hasan II of Casablanca, Casablanca, Morocco

#### References

The active and inverted power injected into the grid are presented at the Figure 18, the reactive power tends toward its reference value Qref ¼ 0, for the active power it is observed that the variation in the speed of the machine influences the variation in power, When the speed of the

From the simulation results obtained, it can be noted from the first view that the regulator based on the backstepping approach has practically slightly better performances than those of the conventional regulator, especially in dynamic conditions, Where it can be observed in all the figures presented in the simulations that the response time for is very short for the signals to restore to the maximum values, so this fast correction either of the velocity or the currents or voltages translates the continuation of our system And assured the performance

In the injection part, the power to the network it is observed that our regulator respects the characteristics of our grid that it is the frequency or the phase on the one hand, and on the other hand the power injected to the network one notes that the power Reactive voltage tends to zero and the active power reacted with the variation of the speed of the generator when the

In this chapter, the nonlinear control of the wind conversion chain based on a synchronous generator with permanent magnet controlled by the electronic converters with MLI control was presented. This electrical combination enabled us to execute the control strategy designed to this wind system studied which was the extraction of the maximum power called "MPPT", also the injection of the current to the network with a good power factor at the "Using a speed control controlled by a backstepping approach. The simulation results obtained in this chapter clearly show an acceptable degree of efficiency of the chosen regulation which causes the

, Ibtissam Lachkar2

1 LTI Lab, Faculty des Sciences Ben M'sik, University Hasan II of Casablanca, Casablanca,

2 LISER Lab, ENSEM of Casablanca, University Hasan II of Casablanca, Casablanca, Morocco

, Chaouqi Aouadi1 and

generator very large the value of the active power becomes greater

92 Vibration Analysis and Control in Mechanical Structures and Wind Energy Conversion Systems

speed reaches the maximum power is totally transmitted to the network.

system to return to its optimum point after a variation of the wind speed.

\*, Abdelmajid Abouloifa1

\*Address all correspondence to<EMAIL_ADDRESS>
4.1. Interpretation of results

of our regulator

5. Conclusion

Author details

Yasser Boussairi1

Morocco

Abdelatif Hamdoun1

[14] Krstic M, Kanellakopoulos I, Kokotovic PV. Adaptive nonlinear control without overparametrization. Systems & Control Letters. 1992;19(3):177-185

**Chapter 6**

Provisional chapter

**DC-Link Control Schemes in Multilevel Converters for**

DOI: 10.5772/intechopen.72360

DC-Link Control Schemes in Multilevel Converters for