An Overview of Wind Energy Technology and Control
Hamid Allamehzadeh, Member IEEE
Eastern New Mexico University
Department of Mathematical Sciences/Electronics Engineering
Station 18, Portales, NM, USA
Abstract
In this paper the horizontal axis wind turbine structure, major components, and fundamental of operation of each block was briefly discussed. The tools and techniques used in design and control of large-scale wind turbine were also reviewed. Some overview of the various stages of turbine operation and control strategies used to maximize energy capture in below rated wind speeds was presented; however, the emphasis was on control to alleviate loads when the turbine was operating at maximum power. The nonlinear model of wind turbines and their linear version for design of controllers were explained and developed. Finally, the available linear control techniques for capturing maximum power from the wind were conferred.
Keywords: Nonlinear Model, Linear Model, Pitch Control, Control Methods, Generator torque
Introduction
Wind energy is one of the fastest growing sectors in renewable energy that encompasses several branches of engineering and sciences. It is recognized to be cost effective, 5C per KWh, and environmental friendly. According to the World Wind Energy Association, the global capacity wind turbines grew from 7 GW in 1997 to 282 GW by 2012at an average rate of 22% per year [1]. Figure 1 indicates the evolution of the cumulative installed capacity worldwide form 1997-2012. The market for new wind turbines reached a new record: 44.6 GW were installed in 2012, an increase of 12% compared with 2011 when 39.8 GW was erected, [1]. The contribution of wind power to the energy supply has reached a substantial share even on the global level: Wind energy alone around the globe by the end of 2011 contribute 580 Terawatts hours to the worldwide electric supply, more than 3% of the global electricity demand. In the year 2012, 100 countries were identified where wind energy was used for electricity generation; Iceland the only country that has 100% of its energy supply coming from renewable energy. Latin America and Eastern Europe continue to represent the world regions with highest growth rate. Denmark is the leader in terms of installed wind power capacity per person: Per inhabitant, the country has installed wind capacity of 752 Watt. Among the major countries, also Spain, Portugal, Sweden, Germany, and Ireland rank among the top ten, Figure 2. The USA rank 12th with close to 200 Watts per person, and China ranks 36th with 56 Watts per person, both far behind their global strategicposition, however, still above world average. Historically, wind energy has been used for hundreds of years for milling grains, pumping water, and sailing the seas. The use of this energy for electricity can be traced back to late nineteen century with development of 12 KWDC wind generator [2]. However, since 1980s that technology matured enough to produce electricityreliably and efficiently. Over the past two decades, variable speed wind turbines with modern sophisticated controller improved the overall efficiency of wind turbines in such a way that can compete with oil and coal energy. The size of wind turbines has increased from a few kilowatts for residential use to several megawatts in large wind farms. In addition to on-land installations, large wind turbines have been pushed to off-shore location to harvest more energy and reduce their impacts on landscapes. In 2012, the growth in offshore wind was well above the average grow rate of the onshore wind sector. The share of offshore wind in the total wind capacity worldwide went up from 15% to 19 in 2012. The UK represented 74% of the offshore market (46% in 2011) and Denmark kept in the second position in total offshore installations, however, with a very modest growth of only 7% [1]. Major drivers such as climate change, depletion of fossil fuels as well nuclear resources, further improvements in wind energy and related technology will have a decisive impact on the mid-term and long-term prospects of wind power. In order to make use of the full potential of wind and other renewable energies, it will be of curtail importance to strengthen the related frameworks, institutions, and policies. Special consideration has to be given to the development of renewable energy in the so-called developing countries. In spite of the need to reinforce national and international policies and to acceleratethe deployment of wind power, it can be observed that appetite for investment in wind power is strong and many projects are in the pipeline.Further substantial growth can especially be expected in China, Europe and North America. In 2016, the global capacity is expected to reach 500 GW. As figure 3 indicates, by the end of year 2020, at least 1000 GW can be expected installed globally.Wind turbines can be classified in two categories based on their axis of rotation: Horizontal- Axis Wind Turbines (HAWT) and Vertical- Axis Wind Turbines (VAWT), [12], as shown in Figure 4. In this paper we mainly focus on HAWTs because of their dominance in the utility wind turbine market. HAWTs have aerodynamic and practical advantages over VAWTs at utility scale [2],[3]. The generating capacity of commercially available HWAT ranges from about 1 KW to several megawatts, Figure 5. The larger HWATs are more cost effective and as a result, the wind turbine companies are working on designing immense turbines that can deliver up to 15 MW or higher.The main objective of this paper is to provide tutorials on major aspects of wind turbines including modeling and control. This paper is outlined as follow: Fundamentals of wind turbine, wind energy conversion systems, nonlinear and linear modeling, and design of controllers for improving their efficiency.
Fundamentals of Wind Turbine
The major components of wind turbine are tower, nacelle, and rotor, as indicated in Figure 6. The airfoil-shaped blades capture the kinetic energy of the wind and transform it into the rotational kinetic energy of the wind turbine’s rotor. The rotor drives the low-speed shaft, which in turn drives the gearbox. The gearbox increases the rotational speed and drives the generator by means of the high-speed shaft. The gearbox, high speedshaft, and generator are contained in the nacelle, along with part of the low-speed shaft. Direct drive configurations without gearboxes are being developed to eliminate costly gearbox failures. Wind turbines may be variable or fixed speed. Variable speed turbines operate at their maximum aerodynamic efficiency for a higher fraction of the time but require electrical power processing so that the generated electricity can be fed into the electrical grid at the properfrequency. Variable-speed turbines are more cost effective and thus more popular than constant-speed turbines at the utility scale level because of advances in generator and power electronics technologies. Variable-speed operation can also reduce turbine loads, since sudden increases inwind energy due to gusts can be absorbed by an increase in rotor speed rather than by component bending. The goals and strategies of wind turbine control are affected by the turbine configuration. A HAWT can be upwind, with the rotor on the upwind side of the tower, or downwind, with the rotor on the downwind side of the tower. This choice affects the turbine dynamics and thus thestructural design. A wind turbine can also be variable pitch or fixed pitch, meaning that the blades may or may not beable to rotate about their longitudinal axes. Variable-pitch turbines might allow all or part of their blades to rotate alongthe pitch axis. Fixed-pitch machines are less expensive to build, however, the ability of variable-pitch turbines to relieveloads and affect the aerodynamic torque has driven their supremacy in modern utility-scale turbine markets.
The power characteristics of a wind turbine are defined by the power curve that relates the mechanical power of the turbine to the wind speed. The information on power curve provided by the manufacturer certifies the performance of the wind turbine within the specified data. Typically, a power curve is characterized by three regions: cut-in wind speed, rated wind speed, and cut-out wind speed as described in Figure 7, where is the mechanical power and is the wind speed. The cut-in speed is the speed at which wind turbine hardly start to operate and deliver power. The system produces nominal power at rated speed which is also the rated output power of the generator. The cut-out speed is the highest speed at which the turbine is allowed to operate; beyond that speed the turbine will be locked to prevent excessive damage. The captured power is proportional to the cubic of the wind speed until the wind speed reaches its rated value. To deliver captured power to the grid at different wind speeds, the wind generator should be properly controlled with variable speed operation. As the wind speed increases beyond the rated speed, aerodynamic power control of blades must be used to keep the power at the rated value. This task is performed through the linear and nonlinear controllers with various techniques. Therefore, modeling and control of wind turbine play a significant role in overall efficiency of the wind turbine system.
Momentum theory using an actuator disc model of awind turbine rotor shows that the maximum aerodynamicefficiency, called the Betz limit [2], [6], is approximately59% of the wind power. The aerodynamic efficiency, whichis the ratio of the captured turbine power to the available wind power, is given
(1)
Where is the instantaneous extracted turbine power and is the available power in the wind. The available wind power can be calculated by
(2)
In (2), is the air density, and A is the swept area by the rotor, R is the radios of the rotor, and v is the instantaneous velocity of the wind.
Modeling of Wind Energy Conversion System (WECS)
A complete model of WECS consists of five interconnected blocks: Pitch Actuator System, Rotor Aerodynamics, Drive Train Model, Generator Control systems, and Generator Model. Details of individual blocks are given in [7], [8] and [9].Mathematical equations that govern these blocks are:
- Pitch Subsystem model
The pitch subsystem model is divided into two blocks: the pitch controller and the pitch angleactuator. The pitch controller determines the pitch angle from the difference between the measured and the desired rotor speed. Thepitch angle actuator consists of an actuator that rotates all the blades to a certain pitch angle, β that is equal to the desired one,.The pitch actuator is a nonlinear servo that can be modeledin closed loop as a first-order dynamic system with saturation in the amplitude and derivative of the output signal [10]. The dynamic behavior of the pitch actuator operating in its linear region is described by the following differential equation
(3)
Whereare the actual and desired pitch angle and is the time constant of the pitch system. Typically, β ranges form and varies at a maximum rate of [10].
- Rotor Aerodynamic System
The power generated by a wind turbine comes from the kinetic energy of the wind and depends on the power coefficient,, according to the expression below where is the air stream kinetic power, ρ is the air density, is the surface covered by the wind wheel of radius R and v is the average wind speed at the hub height.This power coefficient is unique for each turbine and usually provided by the manufacturer [9], [10], and [30].
(4)
Similarly, are the turbine torque and turbine power respectively, R is the length of the blade; is the power coefficient,
is the tip speed ratio and is the angular speed of the rotor
- Drive Train Model (Gearbox)
The drive train of a WECS transfers the aerodynamic torqueon the blades to the generator shaft. It encompasses the rotor,the low- and high-speed shafts and the gearbox. A two-mass representation of the drive train is described by the following equations [9]:
(5)
Where are the inertia of the turbine and the generator, respectively; is the drive train torsional torque; n is the gear ratio; are the shaft stiffness and damping coefficients, respectively.
- Generator Model
(6)
Where are the generator torque, torque set point and time constant, respectively, [29].
Using the Taylor Series expansion, the nonlinear turbine torque equation can be linearized around operating points (as
(7)
Where (8)
The linearized rotor-speed perturbation equation is then given by
(9)
A pitch controller can be designed based on the pitch-angle perturbation to regulate rotor speed, where the perturbedwind speed dv is the disturbance. Unfortunately, neither the reduction to a single degree of freedom nor the linearization to a single operating point is reasonable for large, flexible structures operating under diverse conditions, and thus controllers designed
Solely using (9) are unlikely to work. Some of the engineering design tools used by wind turbine manufacturers, developers, and control engineers include [11]–[19], [33].
Control Methods
The primary objective of controlling variable speed wind turbine is to maximize the power coefficient at specific speed and pitch angle. Using electromechanical or hydraulic actuators, pitch angle can be maintained atthe optimally efficient pitch angle. However, tip-speed ratio depends on the incoming wind speed v and is thereforecontinually changing. Thus, Generator control region is primarily concerned with varying the rotor speed to trackthe wind speed while the blades are aligned at optimal power pitch angle. On large wind turbines, the pitch angle is used to regulate the power around the turbine nominal power in stall or pitch control region. Since the turbine power is related to rotor torque and speed, the rotor torque must be kept constant if are required to be constant [22].
(10)
In stall or pitch control region, the pitch control loop regulates the rotor speed ω to the turbine’s rated speed so that the turbine operates at its rated power.Bianchi provide a detailed description of wind turbine control including the four combinations variable and fixed pitch together with variable and fixed speed [20]. There have been two main approaches in control of wind turbines: generator torque control and pitch control using linear and advanced control techniques.
Generator Torque Control
In this approach a torque controller sets the generator torque which is also the load torque given by
(11)
Where k is given by
(12)
and is the optimal tip-speed-ratio at maximum power coefficient .When a first order model of the wind turbine is given by[22]
(13)
Where are the turbine torque and electrical load respectively.
It is not difficult to conclude that the combined closed loop system is
(14)
A controller uses control law in (14) to adjust the rotor angular velocity for optimum result.As (14) indicates, whenand .Therefore, the control law (14) causes the turbine to either accelerate or decelerate to track . For further detail refer to [21], [22].
Rotor Pitch Angle Control
Classical control design such as Proportional-Integral-Derivative (PID) was used for several wind turbines pitch angle control [23]. The PID control pitch law
(15)
Where is the rotor speed error and the desired rotor speed is . Since the PID derivative term is sensitive to measurement noise, the derivative term is combined with a low pass filter so that at highfrequency this term would not be dominant term in (15). The transfer function of (15) including a low pass filter can be obtained as [31]
(16)
PI gains on many utility-scale wind turbines are gain scheduledbecause the pitch authority is nonlinear in generator control region.The output signal can be either blade pitch angle or rate of
change. A summary of generator control region pitch control for speed regulationis provided in [23]. A systematic method for selectingthe PID pitch control gains is presented in [25].
The desired blade pitch anglechanges from its nominal value only in stall or pitch Region, when it isused to limit rotor speed and power. While collective blade pitch requires only a single-input,single-output (SISO) controller, many utility-scale turbinesallow the blades to be pitched independently. As a result, multi-input, multi-output (MIMO) individualblade pitch controllers can be designed for improved performance[27]–[29] and [32].
Summary
In this paper data from World Wind Energy Association were used to discuss the past, present, and future of wind energy. Then, major components of a wind turbine and their function werediscussed briefly. The paper was mainlyfocused on exploring methods for finding proper nonlinear mathematical modelof wind turbines. Various methods for linearizing the nonlinear model around some operating points which are usually rotor angular speed, pitch angle, and wind speed were conferred. Finally, feedback control techniques for maximizing the turbine power form the available wind power were discussed in the last section.
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