Notes Topic 3 - 1 2 3 1 2 3 3.1 Wind turbine classification...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 2 3 1 2 3 3.1 Wind turbine classification INTRODUCTION WIND RESOURCES WIND TURBINE COMPONENTS AND CONCEPTS INTRODUCTION ........................................................................................................................................1 WIND RESOURCES....................................................................................................................................1 WIND TURBINE COMPONENTS AND CONCEPTS ..............................................................................1 3.1 Wind turbine classification.....................................................................................................................2 3.2 Components of a typical wind turbine ...................................................................................................5 3.2.1 The rotor assembly ..........................................................................................................................8 3.2.2 The power train................................................................................................................................8 3.2.3 The nacelle.....................................................................................................................................10 3.2.4 The tower and foundations ............................................................................................................10 3.2.5 The power conditioning and control unit.......................................................................................10 3.3 Variations on the common HAWT design ...........................................................................................10 3.4 Wind Turbine Concepts........................................................................................................................15 3.4.1 Extraction of power from the wind................................................................................................15 3.4.2 Energy conversion and efficiency .................................................................................................18 3.4.3 Power Curves.................................................................................................................................18 3.4.4 Energy Output................................................................................................................................20 Figure 3-1 Horizontal-Axis Wind Turbines and Vertical-Axis Wind Turbines..................................................2 Figure 3-2 Western Power engineer with one of the nine 225kW Vestas machines at Ten Mile Lagoon Wind Farm ..............................................................................................................................................................3 Figure 3-3 Installing one of the twelve 1.8MW Enercon machines at the Albany Wind Farm ..........................3 Figure 3-4 Atlantic Orient Corporation, AOC 15/50 machine ............................................................................4 Figure 3-5 Borsig Energy’s Nordex N80 2MW machine....................................................................................5 Figure 3-6 NEG Micon NM900/52 – a 900W machine with rotor diameter 52.2m ...........................................6 Figure 3-7 FloWind VAWTs in Altamont Pass, California ................................................................................6 Figure 3-8 Schematic diagram showing the components of a typical HAWT ....................................................7 Figure 3-9 Sketch of the power train assembly of a wind turbine.......................................................................8 Figure 3-10 Mechanical analogues of synchronous and induction generators...................................................9 Figure 3-11 Schematic diagram of a pitch-controlled HAWT ..........................................................................11 Figure 3-12 Enercon produce direct-drive, variable speed wind turbines.........................................................13 Figure 3-13 The Nordic 1000 – a 1MW, two-bladed wind turbine...................................................................14 Figure 3-14 Three 20kW Westwind wind turbines at Exmouth........................................................................15 Figure 3-15 Streamtube analysis of a wind turbine rotor ..................................................................................16 Figure 3-16 The Betz Limit - The theoretical maximum amount of power that can be extracted from the air by a wind turbine.........................................................................................................................................17 Figure 3-17 Schematic diagram showing the form of a wind turbine power curve ..........................................19 Figure 3-18 Power curve for an NEG Micon NM900/52 wind turbine ............................................................19 Figure 3-19 Wind frequency distribution for a site in Hamilton Hill................................................................20 Figure 3-20 Breakdown of Annual Energy Output for each wind speed for NEG Micon NM900/52 machine at Hamilton Hill ..........................................................................................................................................21 Table 3-1 Data of multi-megawatt wind turbines under production in 1999 ....................................................11 Many designs have been proposed for harnessing the power of the wind (see p 279, Boyle, G. Renewable Energy – Power for a Sustainable Future). There are three types of wind energy devices – those that operate using aerodynamic lift forces (e.g. fan-type), those that use aerodynamic drag forces (e.g. Savonius) and those that use a combination of both (e.g. Savonius Darrieus). For the same swept area, the speed (rpm) and power extracted by a lift-driven turbine are many times greater than the speed (rpm) and power extracted by a turbine that uses drag forces. Thus drag-driven turbines are used as mechanical devices e.g. for pumping water, than for electricity production. The aerodynamics of wind turbines will be investigated further in Topic 4. Wind turbines can be further described in terms of the orientation of the axis about which the blades of the machine rotate. A wind turbine with blades rotating around a horizontal-axis (e.g. fan type) is known as a horizontal-axis wind turbine (HAWT) whereas a machine with blades rotating around a vertical-axis (e.g. Savonius type) is known as a vertical-axis wind turbine (VAWT). Figure 3-1 Horizontal-Axis Wind Turbines and Vertical-Axis Wind Turbines © 1998 by the American Wind Energy Association. (Source: http://www.awea.org/faq/basiccf.html) When describing the type of machine, wind turbines are commonly classified in terms of the following parameters: HAWT or VAWT The number of blades e.g. 1-bladed, 2-bladed, 3-bladed etc. The type of power configuration (e.g. grid-connected or stand-alone) For example the type of wind turbines installed at Ten Mile Lagoon wind farm (see Figure 3-2) in Esperance are 3-bladed, grid-connected, HAWT’s made by the Danish company Vestas. 3-1 3-2 Figure 3-4 Atlantic Orient Corporation, AOC 15/50 machine Figure 3-2 Western Power engineer with one of the nine 225kW Vestas machines at Ten Mile Lagoon Wind Farm (Source: http://www.westernpower.com.au/our_environment/renewable_energy/innovation/new_challenge.html) In addition, the description of the turbine may also give an indication of: The position of the rotor with respect to the tower e.g. upwind or downwind. The type of transmission system e.g. gearbox or direct-drive The type of rotor speed control e.g. fixed speed, 2-speed, variable speed The type of yaw control e.g., active or passive The type of power control e.g. stall regulation, pitch regulation The type of power conditioning e.g. direct-coupled, inverter-coupled The type of tower e.g. tubular, lattice, guyed (Source: http://library.thinkquest.org/20331/history/timeline1600.html) Classification with respect to size of machine can vary from source to source and have changed as the size of wind turbines have increased over the years. For this course we shall define: The terms in the list above are simply presented for familiarity here and will be explored in greater depth later in the course. As an example, the wind turbines installed in the Albany wind farm are 3-bladed, upwind, variable-speed, inverter-coupled HAWT’s manufactured by the German company Enercon. Small turbines: 0.1-100 kW Medium turbines: 100-600 kW Large turbines: 600-2000 kW X-Large (Multi-megawatt) turbines: 2000-5000kW (see Figure 3-5) Figure 3-3 Installing one of the twelve 1.8MW Enercon machines at the Albany Wind Farm (Source: http://www.westernpower.com.au/html/home/environment/renewable_energy/renewable_wind.html - albanygallery.) The turbine make or model number usually gives an indication of the size of the machine either in terms of the rotor diameter, the rated power of the generator or both. For example, an AOC 15/50 machine is a 50kW machine with a rotor diameter of 15m made by the Atlantic Orient Corporation. The AOC 15/50 is classified as a `small’ wind turbine. 3-3 3-4 Figure 3-5 Borsig Energy’s Nordex N80 2MW machine Figure 3-6 NEG Micon NM900/52 – a 900W machine with rotor diameter 52.2m (Source: http://www.jxj.com/magsandj/rew/2001_03/great_expectations.html) (Source: http://www.waverlyia.com/WLP/Wind/skeets4.html) 3.2 Components of a typical wind turbine In this course we shall focus on the most common configuration for a modern wind turbine – a large sized HAWT that is directly connected to the electricity grid. Figure 3-6 shows an example of such a turbine – an NEG Micon 900/52 wind turbine. Figure 3-7 FloWind VAWTs in Altamont Pass, California This course does not cover VAWT’s. Although VAWT’s provide easy access to the generator and avoid the need for mechanisms for orienting the machine into the wind, the Darrieus machine is the only VAWT to have been produced in significant numbers (and the main manufacturer of Darrieus turbines, FloWind of the USA went bankrupt in 1997). VAWT’s have the disadvantages of low incoming wind speeds, low efficiency and starting difficulties. In addition, it is difficult to replace the main rotor bearing without disassembling the whole machine. Figure 3-7 shows some FloWind wind turbines at a wind farm in Altamont Pass in California. (Source: http://www.res-us.com/altamont.html) 3-5 3-6 3.2.1 The rotor assembly The blades of most modern turbines are made of fibreglass and are manufactured by hand ‘lay-up’ in a procedure similar to the building of boat hulls. Layer upon layer of fibreglass cloth (like that used in car kits) is placed in half-shell moulds of the blades. As each layer is added, the cloth is coated with a polyester or epoxy resin. When two half-shells are complete they are glued together to produce the complete blade. The blades have a circular root and each blade root is bolted to a central rotor hub that transmits the motion of the blades as a torque. The most common configuration for HAWT rotors is 3 blades attached to a rigid hub i.e. a hub that is rigidly attached to the turbine shaft. The main components of a HAWT can be divided into 5 sections, namely: 1. Rotor assembly 2. Power train assembly 3. Nacelle 4. Tower and foundations 5. Power conditioning and control unit. Figure 3-8 shows a schematic diagram for a typical, 3-bladed, stall-regulated, grid-connected HAWT. The circular root of the blade gradually changes to a thick aerofoil at around 25% of the blade length. Outboard of this location, the aerofoil profile thins, the chord tapers and the blade twists with increasing radius along the blade. The twist and thickness of the rotor blade vary along its length in such a way that turbulence occurs behind the blade whenever the wind speed becomes too high. This turbulence causes some of the wind’s energy to be shed, minimising power output at higher speeds. This phenomenon is known as aerodynamic stall and is used as a passive control to limit the peak power and prevent damage to the machine. This type of power control is known as stall regulation and the machine is described as a stallregulated or stall-controlled HAWT. Stall-controlled machines also have brakes on the blade tips to bring the rotor to a standstill, if the turbine needs to be stopped in an emergency. The tip brakes consist of short outboard sections of each blade that are turned perpendicular to the direction of motion, using aerodynamic drag to stop the rotor or at least limit its speed. Figure 3-8 Schematic diagram showing the components of a typical HAWT 3.2.2 The power train The power train of a wind turbine is a series of mechanical and electrical components that convert the torque on the rotor hub to electrical power. For a typical HAWT, the power train is made up of a transmission system (a turbine shaft, gearbox and generator drive shaft), a rotor brake and an electrical generator. In addition there is equipment for control, cooling and lubrication of the power train. Due to the fluctuating power output from the rotor, the transmission system must be designed for high dynamic torque loads. Figure 3-9 Sketch of the power train assembly of a wind turbine (Source: http://cedrl.mets.nrcan.gc.ca/e/412/retscreen/retscreen_windenergy_project_e.html) The following section aims to give a brief overview of the components of a typical wind turbine and these concepts will be explored in more depth in later sections in the course. (Source: AN Bonus Wind Turbines) 3-7 3-8 The turbine shaft is a low-speed or primary shaft along which the torque of the rotor is transmitted. The turbine shaft must be designed to meet structural requirements since the weight of the rotor and rotor torque oscillations cause fatigue loading on the shaft. A speed-increasing gearbox is used to convert from the low-speed, high torque power received from the wind turbine rotor to high speed, low torque power, which is required for the generator. The step-up ratio is determined by blade tip speed, rotor diameter and the design of the generator. For a typical HAWT, the gearbox transforms the 20 to 50 revolutions per minute (rpm) of the rotor, to the 1000 or 1500 rpm required to drive the generator. The generator drive shaft transmits the torque from the gearbox to the generator. The rotor brake disk is mounted on the generator drive shaft, rather than the turbine shaft, for greater braking power (equal to the square of the step-up ratio). For a stall-regulated machine in an emergency situation (e.g. high winds, loss of connection to the network etc.), the rotor brakes and the tip brakes provide two independent systems, each capable of bringing the wind turbine under control. Large grid-connected HAWT’s use a three-phase alternating current (AC) generator to convert mechanical power to electrical power. The key factors involved in the design of HAWT power trains are those of cost, power quality, and torsional damping (to attenuate cyclic torques). In an electrical power system, almost all the large generators are Synchronous AC generators, operating at exactly the same frequency as the network to which they are connected. A HAWT produces cyclic torque oscillations at the frequency at which the blades pass the tower (blade passing frequency). If these torque pulsations are at the natural frequency of the wind turbine system, large oscillations of the power train occur. Asynchronous (Induction) AC generators are often chosen for wind turbines since they operate at a slightly higher speed than synchronous generators (referred to as slip speed) and are not ‘locked in’ to the frequency of the network. In this manner, the cyclic torque fluctuations at the wind turbine rotor can be absorbed by very small changes in the slip speed and the induction generator provides a significant softness or damping to the power train (see Figure 3-10). Induction generators produce lower power quality and lower efficiency than synchronous generators but they are less expensive and require no external voltage regulators. Figure 3-10 Mechanical analogues of synchronous and induction generators 3.2.3 The nacelle The power train is enclosed within a combination of trusses or box beams constructed from welded and bolted steel sections and referred to as the nacelle. For the nacelle to turn and keep the rotor shaft properly aligned with the wind, HAWT’s require a yaw drive mechanism. Large wind turbines have an automatic yaw control system with a wind vane mounted on top of the nacelle. The wind vane senses the relative wind direction and the control system operates the active yaw drives to rotate the nacelle to a specified azimuthal angle. Yaw slip rings or cable-wrap devices are used to transfer electrical power, control signals, and operational data from the moving nacelle to stationary cables in the tower. The nacelle may contain other auxiliary equipment including a control computer, hydraulic and lubrication pumps and reservoirs, safety equipment and service power for lights and maintenance tools. 3.2.4 The tower and foundations A wind turbine tower must be designed to withstand loads due to wind and gravity. In addition, the resonant frequencies of the tower must avoid coincidence with induced frequencies from the rotor or be damped out. Most modern wind turbines have tubular towers, usually made of steel or reinforced concrete shell, that allow access to the nacelle during bad weather conditions. A typical HAWT tower also includes a ladder and/or a lift for maintenance as well as cables for carrying power, control signals, and data from the nacelle to the ground (see Section – The nacelle). Wind turbine towers are usually supported on massive spread foundations of reinforced concrete. The tower is secured to the foundation using anchor bolts that extend down to the bottom of the concrete. The key parameters for foundation design are resistance to overturning and the pressure tolerance of the soil. 3.2.5 The power conditioning and control unit The voltage tension generated by medium and large wind turbines is usually 690V 3-phase AC. Depending on the standards of the local electrical grid, power conditioning and control equipment (e.g. transformers, circuit breakers etc) is used to raise the voltage to around 10,000 – 30,000 volts. The interfacing of the HAWT with the electric utility (or other distribution system) is carried out in a ground equipment station containing the power conditioning and control equipment as well as a control unit, and data loggers. Some or all of these components may be located within the base section of the tower. The fully automatic control unit is required for the operation and protection of the wind turbine and must be capable of controlling the automatic start-up, and shutdown of the machine in varying wind conditions. The data loggers are used to monitor the performance of the wind turbine and provide information on wind speed and direction, operational status and power production etc. 3.3 Variations on the common HAWT design A number of factors influence HAWT design including site practicalities such as the degree of extreme winds and/or turbulence at the site or the degree of accessibility of the site and the difficulty of transporting the turbine. There are a number of variations on the typical stall-regulated, fixed speed, direct grid-connected HAWT and they are presented here, roughly in order of most common to least common. Where possible, reference has been given to the design trends of the latest product range of large wind turbines and to the multi-megawatt wind turbines under production in recent times (see Table 3-1). In addition a short section is presented on small wind turbines. (Source: Walker, J.F. and Jenkins, N., Wind Energy Technology, p48) 3-9 3-10 Table 3-1 Data of multi-megawatt wind turbines under production in 1999 Type Control Rotor No. of Rated Capacity System Diameter (m) Blades (kW) Enercon E-70 Germany P 70 3 1800 Zond Z1800 USA P 80 3 1800 NEG Micon 2000/72 Denmark AS 72 3 2000 NEG Micon 2000/78 Denmark AS 78 3 2000 Wincon 2000 Denmark AS 70 3 2000 DeWind 90 Germany P 90 3 2500 Kvarner 3MW Sweden P 86 3 3000 Kvarner Sweden P 86 3 3500 Enercon E-112 Germany P 112 3 4000 Multibrid Germany S 100 3 5000 Legend - (P) pitch, (S) stall, (AS) active stall, (FS) fixed speed, (VS) variable speed Country Rotor Speed Control VS VS FS FS FS VS VS VS VS VS (Source: Ackermann, T. and Söder, L., Renewable and Sustainable Energy Reviews 4 (2000), p346) Pitch Regulated Machines Traditionally, HAWT have used stall-regulation as a method of power control and subsequently around 70% of turbines installed in the world today are stall-regulated machines. For the current range of large machines available on the market, the choice of stall regulation or pitch regulation of power is evenly split. In a pitch controlled wind turbine, the hub contains a blade pitch mechanism that uses hydraulic actuators to rotate the blades about their (longitudinal) axis controlling the amount of torque and power produced by the rotor (see Figure 3-11). This control mechanism is particularly employed to control the peak power produced by the machine but is also employed during starting and stopping of the machine. Pitch control is more efficient than stall control but blade pitch mechanisms are associated with high costs and high maintenance. For a pitch-regulated machine, the pitch regulation can be used to gradually bring the rotor to a standstill and thus the rotor brake is usually applied only when the turbine is ‘parked’ (i.e. not in operation) or when the machine is receiving attention for maintenance. In a 1999 survey of multi-megawatt machines under development, 90% of turbines were to employ some form of pitch regulated control (see Table 1). This includes active stall control, which is a combination of pitch control and stall control. For more detail on active stall control see Topic 9. Variable Speed (Indirect Grid-Connected) Machines Most wind turbines run at almost constant speed and are directly connected to the grid. With indirect grid connection, however, the wind turbine generator can run on its own, separate mini AC-grid that is controlled electronically using power electronics. The frequency of the alternating current in the stator of the generator has the freedom to vary and the generator accelerates or decelerates depending on the fluctuations in the rotor output. The main advantage of this variable speed operation is that it reduces the peak torque on the power train and subsequently reduces wear on the gearbox and generator (in addition the fatigue loads on the tower and rotor blades may also be reduced). In some cases indirect grid-connected machines operate at a range of rotational speeds that make the use of a gearbox unnecessary e.g. the Enercon E40 500kW machine that operates with a variable rotational speed of 18-41 rpm (see Figure 3-12). A wind turbine operating without a gearbox is referred to as a direct-drive machine and has the advantage of significantly lower maintenance costs over turbines with gearboxes. Another advantage of variable speed systems is that the power electronics of the system can be used to improve the power quality in the electrical grid, which is particularly useful if the turbine is operating on a weak electrical grid. Finally, by accelerating and decelerating the rotor speed according to the variation in the wind speed, the machine can operate at the optimal tip speed ratio i.e. the tip speed ratio associated with the maximum power coefficient. Figure 3-11 Schematic diagram of a pitch-controlled HAWT The disadvantages of indirect grid-connection revolve around the power electronics - their cost and the associated energy losses. Most manufacturers of large wind turbine have chosen constant speed over a variable speed configuration but it is interesting to note that in a 1999 survey around 70% of the multimegawatt machines currently under development are variable speed machines. This is an indication of the decreasing cost of power electronics and the economic viability of indirect grid-connection. (Source: Walker, J.F. and Jenkins, N., Wind Energy Technology, p37) 3-11 3-12 Figure 3-12 Enercon produce direct-drive, variable speed wind turbines Figure 3-13 The Nordic 1000 – a 1MW, two-bladed wind turbine (Source: To be confirmed) (Source: http://www.empowerglos.com/thetechnology.htm) Two-Bladed Machines Currently three-bladed wind turbines dominate the market for grid-connected HAWT’s and only two manufacturers out of the ten producing multi-megawatt machines have opted for a two-bladed design. Twobladed wind turbines have the advantage of lower blade costs and, since the weight on the top of the tower is lighter, lower tower costs. In order to compete with the energy capture of a three-bladed rotor, however, a two-bladed machine must operate at higher rpm leading to problems with aerodynamic noise and blade erosion. In addition, three-blade HAWT’s are viewed as more ‘aesthetically pleasing’ than two-blade HAWT’s. The forces on a two-bladed machine are less evenly balanced than the forces on a three-bladed machine and the fluctuating forces on the blades as they sweep through a varying velocity field (due to e.g. gusts and wind shear) cause greater cyclic loading on the turbine shaft of a two-blade machine. In order to counter this, a two-bladed HAWT rotor usually has a teetered hub where the rotor is hinged at the hub in such a way as to allow the plane of rotation of the rotor to tilt backwards and forwards a few degrees. This rocking motion occurs cyclically, increasing the lift force on one blade while decreasing it on another in order that the loading on the two blades can be balanced. 3-13 Downwind Machines Most wind turbines have an "upwind" design where they face into the wind with the nacelle and tower downstream. Downwind turbines are also available on the market and are designed so that the wind passes the tower before reaching the blades. The advantage of a downwind machine is that the rotor naturally aligns itself with the wind direction, removing the need for a yaw system. Downwind rotors, however, suffer increased noise and cyclic loads due to the interference of the tower wake, referred to as tower shadow. Small Wind Turbines Small wind turbine systems (< 100kW) for electricity production are used for off-grid applications, such as houses in remote areas, sailing boats, or recreational vehicles. They are often are used in combination with batteries and/or small diesel generation systems. In March 2002, a demonstration project was established in Exmouth, WA to incorporate three 20kW Westwind turbines into a diesel mini-grid in order to offset the reliance of remote areas on diesel-powered electricity generation (see Figure 3-14). The design of small wind turbine systems differs significantly from that of large, grid-connected wind turbines. Since small wind turbines have shorter blades they must operate at higher rotor speeds to increase their energy capture. Small wind turbines thus operate at different tip speed ratios than larger machines and the blades of small wind turbines are designed for different aerodynamic profiles. Another difference between large and small wind turbines is the design of the transmission-generation system. Most small wind turbines systems are direct-driven, variable speed systems with synchronous generators using permanent magnets. Also the power and overspeed regulation of small wind turbines vary significantly, e.g. mechanically controlled pitch systems or yaw systems instead of electronically controlled systems. Vertical or horizontal furling is also used for the overspeed protection of small wind systems. High reliability and low maintenance are even more important for small wind turbines than large wind turbines, as maintenance and repair of single wind turbines in remote locations has an important impact on the overall economics of small wind turbines. 3-14 Figure 3-14 Three 20kW Westwind wind turbines at Exmouth Figure 3-15 Streamtube analysis of a wind turbine rotor (Source: Walker, J.F. and Jenkins, N. Wind Energy Technology (1997), p12) The relationship between the velocities is given by: Equation 3-1 (Source: Courtesy of Western Power Corporation) v0 > v1 > v 2 3.4 Wind Turbine Concepts In Topic 2, the characteristics of the wind, including the energy content of the wind were discussed. The following section derives equations for the efficiency of a wind turbine at extracting the energy content of the wind. 3.4.1 Extraction of power from the wind Only a proportion of available energy in the wind can be converted to useful energy by the wind turbine. The available power for a wind turbine is equal to the change in kinetic energy of the air as it passes through the rotor. The simplest model for the aerodynamics of this process is referred to as the Rankine-Froude actuator disk model. The rotor is approximated by an actuator disk i.e. an infinite number of thin blades rotating at a tip speed greater than the wind speed. The wind stream is approximated by a column or stream tube of air flowing through the disk. In order to satisfy Bernoulli’s Law and conserve the mass flow rate of air, the stream tube expands as it passes the rotor. Changes in the density of the air can be treated as negligible since the airflow velocities are relatively low. Figure 3-15 shows the actuator disk with the expanding stream tube due to the changing velocity of the wind as it passes through the rotor. where v0 is the velocity of the air upstream of the rotor, v1 is the velocity at the rotor and v2 is the velocity downstream of the rotor. The power P extracted by the rotor is given by the rate of change in kinetic energy across the disk: Equation 3-2 P= 1 1 2 2 Mv0 − Mv2 2 2 where M is the mass flow rate and is conserved along the length of the streamtube i.e. Equation 3-3 M = ρA0 v0 = ρA1v1 = ρA2 v 2 The coefficient of power extracted gives the efficiency of the conversion process from wind power to turbine power. It is defined as the ratio of the energy extracted by the turbine to the energy that would have flowed through the swept area of the rotor if the turbine had not been present. Thus, Equation 3-4 Cp = 3-15 P 0.5ρA1v 0 3 3-16 NB. For the time being we are concerned only with the aerodynamic power extracted by the rotor and transmitted to the shaft of the rotor. The complete wind turbine system would also have further mechanical and electrical conversions (with associated losses) to give a coefficient of power output. This will be addressed in more detail in Section 3.4.2. The aerodynamicist Albert Betz showed theoretically that there is an upper limit to the amount of energy that can be extracted from the wind. Applying the laws of conservation of mass, momentum and pressure over the rotor disk, it can be shown that: Equation 3-5 Exercise 3-1 Show that Cp has a maximum value of 16/27 when a = 1/3. Solution: Differentiate Cp with respect to a and find the local optima. Use the sign of the second derivative to determine the form of the local optima. Exercise 3-2 Show that the velocity of the air stream at the disk is the average of the velocities upstream and downstream of the disk. Solution: Use Equation 3-2 together with the fact that the power extracted by the disk is the product of the force on the disk and the velocity of the air stream at the disk. C p = 4a (1 − a ) 2 for Exercise 3-3 Derive Equation 3-5. Equation 3-6 a = 1− Solution: Use Equation 3-4 and Equation 3-6 together with the fact that the power extracted by the disk is the product of the force on the disk and the velocity of the air stream at the disk. v1 v0 where a is a measure of the slow-down of the air stream due to the rotor and is referred to as the axial interference factor. Hence the theoretical limit of the amount of power that can be extracted (i.e. if the rotor could extract power from the wind without any losses) is only 16/27 = 59% of the available power in the wind. This is referred to as the Betz Limit. Figure 3-16 shows the difference between available energy in the wind, the limit of power extraction and the actual turbine output for an NEG Micon 900/52 at a wind site with mean wind speed 7m/s. For each wind speed, the power is multiplied by the probability of that wind speed dependent on the wind frequency distribution of the site. The result is a power density distribution as shown in Figure 3-16. Section 3.44 explains more about wind frequency distributions. Figure 3-16 The Betz Limit - The theoretical maximum amount of power that can be extracted from the air by a wind turbine The above analysis is a simplified model of the way that a wind turbine extracts energy from the wind and we will enlarge on this subject in Topic 4, which is specifically devoted to wind turbine aerodynamics. 3.4.2 Energy conversion and efficiency In the previous section the Cp of the rotor was defined as the coefficient of power extracted by the rotor from the wind. Incorporating power losses in transmission and electrical output leads to a coefficient of power output Cpout given by the ratio of electrical power output to available power in the wind. The coefficient of power output indicates how efficiently the wind turbine system converts the energy in the wind to electricity. This will incorporate terms related to e.g. the gearbox/bearings efficiency (95% if good) and the generator efficiency (80% or more for a permanent magnet generator or grid-connected induction generator). If the machine has indirect-grid connection, the efficiency of the inverter needs to be taken into account (95% if good). Figure 3-16 shows that the NEG Micon 900/52 has a peak Cpout of around 42%. This is a typical value for the “Cpmax” of a wind turbine. 3.4.3 Power Curves Manufacturers of wind turbines usually present data indicating the performance of their wind turbines in a more straightforward way than power density or Cpout curves and they are known simply as power curves. The power curve indicates the net electrical energy output from a wind turbine as a function of wind speed. And is determined either by theoretical predictions or field tests carried out according to international power performance standards such as those prescribed by e.g. The International Electrotechnical Committee (IEC) (see http://www.nrel.gov/wind/certification/Certification/standards/iec_stds.html) or Germanischer Lloyd (http://www.germanlloyd.org/mba/wind/). For the field tests, wind speeds are measured on a meteorological mast located within 2-4 rotor diameters from the turbine. This placement is far enough to avoid interference effects of the turbine on the wind measurement but not too far to lose the correlation between the wind speed and the turbine power. The wind speed readings are measured by an anemometer placed at a height on the mast that is within a few percent of hub-height. The power curves are plotted using 10-minute averaged data to remove transient effects from the power trend. 3-17 3-18 The general form of a power curve for a wind turbine is shown below in Figure 3-17. The cut-in wind speed is the wind speed at which the turbine starts to produce net power. Due to mechanical and electrical losses in the system, the cut-in wind speed is higher than the wind speed required to start the blades rotating. The cutout wind speed is the speed above which the turbine is stopped in order to protect the turbine from overloading and/or overspeeding. The rated power is the maximum power output of the wind turbine at the output terminals of the generator (including losses) and the rated wind speed is the wind speed at which this rated power is produced. Figure 3-18 shows the power curve for an NEG Micon NM900/52 machine. The availability of a turbine is defined as that percentage of time when the turbine is actually available to produce power. Typically the availability for a modern wind turbine is in the range 95-99%. Note that although the turbine is available, the turbine only produces useful power for wind speeds between cut-in and cut-out. The ratio of the actual energy generated in a given time period to the energy produced if the wind turbine had run at its rated power over that period is known as the capacity factor. A typical value for the capacity factor of a wind turbine is around 25-30%. Exercise 3-4 If a 1.8MW Enercon machine has a mean power output of 540kW over a week and is available for 95% of the time, what is the capacity factor of the machine? (Solution: 28.5%) Figure 3-17 Schematic diagram showing the form of a wind turbine power curve 3.4.4 Energy Output The energy output of a wind turbine is calculated with knowledge of the power curve of the wind turbine together with the wind statistics at the site at which the turbine is situated. The first step is to sort the wind speeds and associated power data into wind speed bins. Undertaking this sorting using 1m/s wind speed bins gives acceptable accuracy for energy output calculations. For instance all wind speeds between 0.5m/s and 1.5m/s will be sorted into a bin with midpoint equal to 1m/s, all wind speeds between 1.5m/s and 2.5m/s will be sorted into a bin with midpoint equal to 2m/s etc. Once the sorting into wind speed bins is complete, a number of statistics can be produced such as the average wind speed in each bin and the average power reading in each bin. The number of readings in each bin gives an indication of the probability of a particular wind speed occurring at the site. If the wind data is recorded for a sufficiently long period then a wind probability curve can be plotted. The probability of wind speeds greater than say, 15m/s will be very low and the wind probability curve will be skewed to the left and drop off quickly at high wind speeds. Another way of representing the wind probability curve is to multiply the probabilities by the number of hours in a given period of time e.g. the number of hours in a year. This yields a wind frequency distribution Φ that, for each wind speed bin, represents the number of hours in the time period that the wind would be expected to blow with speed given by the range of the wind speed bin. Thus, Φi is the no. of hours in the ith wind speed bin. Figure 3-19 shows the wind frequency distribution for a site with mean wind speed of 7m/s in Hamilton Hill. (Source: http://www.awea.org/faq/basicpp.html) Figure 3-18 Power curve for an NEG Micon NM900/52 wind turbine Figure 3-19 Wind frequency distribution for a site in Hamilton Hill 3-19 3-20 If Pi is the power corresponding to the midpoint of the ith wind speed bin (as given by the power curve of the wind turbine) then the energy output of the turbine over the given time interval is: mean wind speed and (iii) multiply the power in kW by the number of hours in a year to get kWh produced over the year. Equation 3-7 Solution: Power and wind speed have a cubic i.e. non-linear relationship. The mean power output will be the mean of the cube of the wind speeds. The approach above computed the cube of the mean wind speed, which is not the same thing. Thus the power computed in part (ii) of the approach above is NOT the mean power output and the annual energy output computed in (iii) will be incorrect. n E = ∑ Pi Φi i =1 where n is the number of wind speed bins. Thus the Annual Energy Output (AEO) of an NEG Micon NM900/52 wind turbine at the site in Hamilton Hill can be estimated by performing, for each wind speed bin, the multiplication of power in kW with number of hours per year to yield the number of kWh (see Error! Reference source not found.). The AEO can then be calculated by summing up the columns of the graph. In this case the AEO of the NEG Micon machine comes to 2.23GWh. Figure 3-20 Breakdown of Annual Energy Output for each wind speed for NEG Micon NM900/52 machine at Hamilton Hill References: [1] Ackermann, T. and Söder, L. (2000), Wind Energy Technology and Current Status: A Review, Renewable & Sustainable Energy Reviews, 4, pp 318-321. [2] Boyle, G., (ed.) (1996) Renewable Energy – Power for a Sustainable Future, Oxford University Press, USA, pp 279-283. [3] IEC Wind Turbine Standard 61400-12, Performance Measurement Techniques (1998) [4] International Energy Agency, Expert Group Study on Recommended Practices for Wind Turbine Testing and Evaluation, Power Performance Testing, 2nd ed., IEA, (1990). [5] Spera, D. (1998) Wind Turbine Technology, ASME Press, USA. [6] Walker, J.F. and Jenkins, N. (1997) Wind Energy Technology, John Wiley and Sons, UK., p1116;52-56 Useful websites: http://www.windpower.dk/tour/wtrb/comp/ http://www.windpower.org/tour/wres/betz.htm http://www.windpower.org/tour/wres/pow/index.htm If data is not available from the site for binning purposes but values for the Weibull parameters (as defined in Topic 2) have calculated using software prediction tools (e.g. http://www.wasp.dk/), then an estimate of the energy output can be obtained by using the Weibull distribution curve together with the power curve for the turbine. Exercise 3-5 Discuss why the annual energy output CANNOT be computed by the following steps: (i) find the mean wind speed at the site, (ii) using the power curve, find the power corresponding to the 3-21 3-22 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online