Power and Energy Analysis of Commercial Small Wind Turbine Systems

Nikola Milivojevic, Student Member, IEEE, Igor Stamenkovic, Student Member, IEEE, Nigel Schofield, Member, IEEE, e-mail: nikola@magdrive-technologies.com Abstract Small wind turbines harvest wind energy to provide carbon free energy for residential and small commercial applications. Current technology consists of a diode-bridge rectifier and an off-the-shelf generator. Such a simplified system does not utilize the full capacity of the turbine because the generator drive system is not designed specifically for wind turbine applications. This paper presents the technology that is commonly used in small wind turbines today. The relationship of the wind turbines mechanical characteristics and the generator power characteristics are explained and some basic design considerations for small wind systems are discussed. The tests utilize a permanent magnet (PM) generator which is connected to the grid via an industrial inverter, and run for different speeds to examine the output power characteristics. Standard operation as well as the control of such a system is covered in detail. I. INTRODUCTION Wind generation of electrical energy is a promising energy resource for its sustainable nature and its very low net carbon impact. Large wind power systems, with outputs in megawatts, have clear advantages over small wind power systems because of the economy of scale. However, large wind turbines are typically used in very specific and usually remote areas that satisfy permitting criteria, and usually rely on the availability and capacity of existing transmission lines. On the other hand, small wind power systems are very attractive to support the energy demand for either local residential and small businesses or for developing countries where the electrical grid infrastructure is limited [1]. Harvesting small amounts of wind energy, on a large volume of scale provides a significant contribution toward global renewable energy. To-date, the return on the investment in small wind power systems relatively low in terms of kWh/$ (return on investment), mainly due to low manufacturing volumes and the moderate efficiency of the existing energy conversion process. The energy conversion process through commercially available small wind turbines includes blades that convert the wind energy into rotational mechanical energy on the shaft and an electric generator that is both simple in design and manufactured in small quantities by the wind turbine developer or retrofitted off-the-shelf general purpose machine [24]. This paper discusses the power and energy of commercial small wind systems based on the small wind systems and related components that are currently available in the market. Section II presents the basic theory of wind turbines, showing the mechanical characteristics of wind turbines. It also explains important industry terms such as the wind turbine capacity factor, wind speed probability, etc. Section III outlines commonly used methods of improving small wind systems power output by changing the blade length. Design considerations for a direct-drive PM generator, as well as its efficiency, are presented in Section IV. Finally, Section V presents testing results of a currently available wind generator connected to the grid via standard industrial inverter. II. POWER CHARACTERISTICS OF THE SMALL WIND TURBINE A wind turbine converts the kinetic energy of the wind stream into electric energy. Torque is generated by the aerodynamic lift force of turbines blades, and transferred to the rotor shaft. In this way, the linear kinetic energy of the wind (Pw) is converted into rotational energy of the turbine shaft (Pt). Connected to the same shaft, the electric generator converts mechanical rotational energy into electrical (Pel). A rectifier, then, is used to convert electrical alternating current (AC) into electrical direct current (DC), while inverter converts it from DC to AC, providing power Pgrid to grid.

Fig. 1. Power flow of direct-drive wind turbine system

Fig. 1 shows the power flow of a wind turbine system. Wind power Pw can be expressed using equation 1:

1 1 (1) R 2 v3 = S v3 2 2 where is the air density at the turbine site (typically 1.225kg/m), R is the blade length, v is the wind linear velocity at the turbine height for a given location, and S is swept area of the blades (R), . Mechanical power that the wind turbine extracts from the wind is actually the power on the shaft of the turbine - Pt, and represents the input power for electrical machine (generator): 1 (2) Pt = R 2 v 3 C p ( ) 2 where Cp () is the turbine power coefficient. This power depends on the aerodynamics of the turbine. The maximum theoretical power that can be extracted from the wind is determined by the Betz Law and is equal to 59.3% of total wind power [5-6]. Pw =

R (3) v where is the shaft speed. Hence, combining equations 2 and 3, the wind turbine power is directly proportional and controlled to the shaft speed. Fig. 2 shows that the turbine power coefficient (Cp) as a function of the tip speed ratio for different turbine blades.

Hence, the wind power harvested by the wind turbine is a function of wind speed and wind turbines aerodynamic blade design. Note that this design, or blade airfoil, is defined by a function called tip speed ratio (), presented by Eq. 2:

Of vital importance for each small wind system is the energy output throughout of the year. This annual energy production depends on the wind speed probability distribution, the mean wind speed and the power curve of a specific turbine. The first two parameters are highly dependent on the turbine location. Wind speed probability is the wind distribution for a given location based on a mean wind speed. It is known as Weibull distribution [11-12], and is defined in Eq. 4.
c v W (v ) = e A v A c v
c

(4)

where c is the shape parameter of the Weibull function, v is wind speed and A the mean wind speed. The shape parameter is equal to 2 for the land installations. Mean, or average, wind speeds are average wind speeds throughout a given period of time for a particular location. The National Renewable Energy Laboratory (NREL) defines seven different wind classes according to their mean wind speeds [13]. These wind classes are given in Table I.
TABLE I: WIND CLASS DEFINITION

Fig. 2. Wind turbine power coefficient curve Cp in respect to tip speed ratio for one type of blades [8]

Fig. 2 shows the aerodynamic characteristic of the turbine as a parabolic function; therefore there is a maximum possible output power for variable wind speeds which is in the knee of the curve. Hence, the operating point of the turbine must be kept in the knee of the Cp curve (highest value of Cp). Maximum Power Point Tracking (MPPT) algorithms are used to keep the operating point at its highest value, by controlling the rotational speed of the turbine [7-8].

Wind class 1 2 3 4 5 6 7

Mean wind speed [m/s] 5.6 6.4 7.0 7.5 8.0 8.9 12

Fig.4 shows the wind speed probability function for three different wind speeds of classes 2, 4 and 6. For example, wind speed class of 2 is common for Illinois, class 4 for the north-western parts of Texas, while class 6 is common for the very windy regions of Wyoming.

Fig. 3: Wind turbine power in respect to shaft speed, for different wind speeds

Fig. 4. Wind speed probability function for different wind speed classes

Fig. 3 presents the wind turbine output power (Pt) with respect to the shaft speed (w), for different wind speeds (dashed lines). The solid line is the desired power curve which indicates the maximum power output at various wind speeds using the MPPT technique.. An important point is that appropriate control of the shaft speed enables maximum turbine power output. Therefore, a variable speed electric drive is very important in achieving the maximum power output over a wide wind speed range [9-10].

In order to design an electric generator that matches the wind turbines expected duty cycle, or turbine power density characteristic depends on the turbine specification [14]. The power density of the turbine (r(v)) can be express by Eq. 5:

r (v ) = W (v )

Pt (v) Pt rated

(5)

where W(v) is the value of the Weibull function for different wind speeds, Pt(v) is the turbines power and Ptrated is the turbines rated power.

increases by 78% over that of the 6m diameter blade and the rated power is reached at a wind speed of 9.9m/s. Therefore, rated conditions are met at a lower wind speed when blade length is increased. Further discussion in Section IV explains how this impacts the design requirements of the electric generator. Using Eq. 1, the new wind speed at which the rated parameters of the small wind systems are met is given with Eq. 8.

v 3 new =
Fig. 5. Wind turbine power density curve r(v) for different wind speed classes

R2 v 3 rated => vnew = 10.82m / s R 2 new

(8)

Wind turbine power density curves shown in Fig. 5 provide the basis for design requirements for an electric generator. Cost effective generator designs take into consideration the available wind power, directly linked to the wind speed, and its probability distribution. For example, the available wind power at 15m/s is substantially more probable for the locations defined with wind class 6, than for the locations defined with class 2, according to Fig. 4b. Therefore, smaller and a less expensive electric generator is more a economical solution for a location with a wind class of 6. The total annual generated energy in terms of kWh is calculated as a sum of the multiplication of the turbine power and the power density for a certain wind speed, expressed by Eq. 6:

Fig. 5 shows the turbine power curves that relate to three different blade lengths. The solid line is the wind generator power/speed characteristic for commercial small wind system whose blade length is equal to 6m and rated parameters designed for the wind speed equal to 12m/s.

Etotal = 8760hrs Pt rated r (v)

vmax

(6)

Fig. 6. Wind turbine power curves for different blade lengths

where Ptrated is the turbine rated power, and rt(v) is the turbines power density value for wind speed v. A parameter frequently used to describe the performance of a wind turbine at certain location is called the capacity factor. It is defined as turbine's actual production over a given period of time with the amount of power the turbine would have produced if it had run at full capacity for the same amount of time, as shown by equation (7):

Fig. 6 illustrates the approach of blade length variation that current systems use in order to improve energy output of small wind system for locations with different wind classes. The major gain is in increasing overall energy output of the turbine when installed on the sites with low wind speeds. The actual gain can be calculated if the new generated power/speed characteristics and the wind speed distribution functions are known. Table II shows the capacity factor for different mean wind speeds (wind classes 2, 4 and 6) for three different rated wind speeds of the wind turbine. The conclusion is that for lower wind speeds (wind class 2), the turbine with a rated wind speed of 9.9m/s is giving the most energy output, which is obtained by just increasing the blade length.
TABLE III: CAPACITY FACTOR VARIATION FOR
DIFFERENT MEAN AND RATED WIND SPEEDS

C[%] =

E total Pt rated Time

(7)

The typical capacity factor of large wind turbines is 3545%, while a small wind turbine has a capacity factor of 2035% [15]. The reasons for the smaller capacity factor of small wind systems are mainly due to the wind turbines power characteristic and its simplified power control, which will be detailed later. III. CURRENT SOLUTIONS TO IMPROVE THE WIND TURBINES POWER CURVE As it can be observed from Eq. 1, the wind turbines power input is a function of the swept area. The first example is a commercial small wind system with a blade diameter of 6m and designed for a wind speed of 12m/s. By increasing the blade diameter to 7m, the swept area will increase by 36%, increasing the turbine power by 36% as well. Furthermore, if the blade diameter is 8m, the turbine power

rated wind speed [m/s] 9.9 10.8 12

capacity factor for wind class 2 29.52% 26.52% 22.64%

capacity factor for wind class 4 36.15% 32.82% 29.97%

capacity factor for wind class 6 41.48% 39.32% 36.94%

The gain in energy output for smaller mean wind speeds (wind class 2) is more obvious than for higher wind speeds (wind class 6). The gain in energy is 30% for lower mean

wind speeds, while for higher mean wind speed is only 12%. Although it looks like small wind turbines should have a much lower rated wind speed, because that results in a higher capacity factor, and this may be one of the main reasons the rated speed is usually kept at 12m/s. IV. ANALYSIS OF THE ELECTRICAL GENERATOR OF A SMALL WIND TURBINE SYSTEM The generated wind turbine power in at various wind speeds is shown in Fig. 7 for both large (pitch controlled) and small (blade-stall/furling controlled) wind turbines. The four characteristic regions indicate specific operating principles of wind generators.

The overall efficiency of the small wind turbine is highly dependent on the generator design and the power converter efficiency. Permanent magnet direct-drive generators have high torque and a power density that is favorable for the wind industry. In addition, a direct drive generator, because of its flexibility to implement a number of pole pairs, is very adaptable to low-speed applications [22]. Knowing that the usual frequency of wind generators is in the range 35-60Hz the effective way to keep low speeds is to increase the generators pole pairs - see Eq. 7:

p=

60 f n

(9)

Increasing of pole pairs usually results in the increase of the diameter of electric generator [23]. Total power losses in PM generators come from mechanical, copper and stator core losses. Copper losses depend on phase resistance of the generator and the rms value of the armature (loading) current. Such losses are produced in the generators stator and cause the machines temperature to increase. If the phase current has harmonics, then total copper power losses can be calculated as shown in the Eq. 10.

Pcu = 3 Ra (I ai )
i =0

(10)

Fig. 7. Power curve of variable-speed pitch controlled (solid line) and market available small wind turbine for different wind speeds

Stator core losses consist of hysteresis (Ph) and eddy current losses (Pe). If ke and kh are constants, and Bmax is peak flux density, then such losses can be determined by Eq. 11 [24]:

In the first region, there is no power generation for wind speeds smaller than the cut-in wind speed. Once the wind speed exceeds cut-in speed, MPPT control strategy is applied and the generator is controlled to reach maximum rotor efficiency (keeping Cp at a maximum value). After reaching the rated wind speed, the system operates in a reduced power mode. At this point large turbines employ pitch control, while turbines without pitch control use the furling principle or aerodynamic characteristic of the blades in order to reduce rotor efficiency and keep the power at its nominal value. At higher the wind speeds the pitch angle of the blades is higher which reduces the value of power coefficient Cp () [16-18]. Pitch control is not used for small wind turbines because of its cost. However, two other mechanisms are used to limit the captured wind power. Furling (passive pitch) is the method of putting the nacelle of the turbine out of the wind (for high winds) which limits the captured wind power, but increases the stress of the turbine. Some manufacturers attach a spring to the blade, so during high winds the blade leans back, limiting the captured wind power. Another technique, blade stalling, employs the stall effect, in which case for high wind speeds the air does not flow along the blade, but creates turbulence which results in a great reduction of the Cp value. The blades are designed in a way to initiate the stalling effect for wind speeds above rated [19-20]. The majority of commercial small wind systems are directdrives, designs without a gearbox, providing a more efficient and cost effective solution [21].

Pcore = Pe + Ph Pcore = (k e f B 2 max + k h f 2 B 2 max ) weight

(11)

Mechanical losses depend only on the shaft speed of the generator and are defined with Eq. 12. (12) Pmeh = c The generators efficiency is defined by the ratio of generator output power to turbine power. An alternative way is to measure the DC power output Pdc, which is the power at the rectifier end. Then, generator efficiency is given by Eq. 13.

Pdc Pdc + Pcu + Pcore + Pmeh

(13)

Overall efficiency of the small wind turbine system depends on the turbines efficiency and the generators efficiency. Two efficiencies are independent, but both depend on the shaft speed . Fig. 8 shows turbine power vs. shaft speed for different wind speeds. Two generator characteristics are also presented in Fig. 8 the line OAC represents the power-speed characteristic of the generator designed to reach rated conditions at 0.75 p.u. of the shaft speed, while the line OBC is the characteristic of the generator that reaches the rated conditions at 1 p.u. of the shaft speed. The first generator design (OAC curve) is capable of utilizing the entire power from the turbine. However, the same design reaches maximum power point at speeds that exceed the generator rated speed (shown in Fig. 8 for the wind speeds equal to 8, 10, and 12m/s). This increases the

mechanical and stator core losses. The second generator design (OBC curve) can track the maximum power point

Fig. 10. Usual topology of small wind system with PM generator

Fig. 8. Power vs. shaft speed of a generator for different wind speeds

Because of the machine being three phase the voltage ripple after the diode rectifier will be repeated 6 times in the period. Therefore, the relationship between the DC link voltage and peak-to-peak line voltage can be derived by formulae:

below rated speed, but is not capable processing all available turbine power (shown in Fig. 8 for the wind speed equal to 12m/s). Lastly, generator OAC has a smaller rated speed and, thus, needs higher torque and more active material volume to provide the same rated power as the second generator. Therefore, the choice of rated power/speed of the generator is the trade-off between cost invested to increase power rating and the cost of non-captured energy. V. RESULTS OF TESTING A WIND GENERATOR CONNECTED TO THE GRID VIA A TYPICAL INVERTER The typical configuration is the wind generator connected to a diode bridge and then an inverter that is connected to the grid as shown in fig. 9. The system consists of a PM machine, diode bridge rectifier, protection circuit, DC link circuit and grid-tied inverter.

Vdc =

1 3 3 6 /Vdc ( ) d = VLL peak = Vg T 6

/6

(15)

where Vg is the RMS value of the generators phase voltage. Using the power balance equation, the relationship between AC and DC currents is found by formulae [25]:

Ig =

I dc

(16)

Because commercial inverter has a power to input voltage (Vdc) characteristic as a linear function, the dc current (input current for the inverter) can be controlled, and thus indirectly control the generators phase current as well. Fig. 11 shows the linear function between the input DC voltage and the power of the inverter.

Fig. 11. Power vs. dc link voltage transfer function of inverter

Fig. 9. Testing rig schematic

Additional resistors (so called dumb load) are used as part of a protection circuit. When voltage passes a certain value the excessive output is dissipated in phase resistors, therefore protecting the generator from high speeds, which would otherwise cause a high DC link voltage that can damage the equipment in the system. The output of the generator is three phase sine wave voltage Vg and quasi sine wave current Ig. After the diode bridge, the voltage and current has the dc values Vdc and Idc (Fig. 10). The power balance equation looks like: (14) 3 I g V g = Vdc I dc

Parameters of the inverter, Vdcmin and Vdcmax, can be adjusted for different types of turbines, so this market available inverter can be applied to wide range of market available turbines. Fig. 12 shows the waveforms of the grids voltage and current that is the output of the inverter. The overall efficiency of the inverter is between 93% and 96% for the speed range.

[6]

[7] [8]

[9]

Fig. 12. The waveform of DC link current (Idc), voltage (Vdc), grid voltage (Vac) and grid current (Iac), for lower (figure a) and higher (figure b) speeds when wind generator is connected to the grid via inverter

[10]

VI. CONCLUSIONS The paper presents the current state of small wind turbine technology. A direct drive PM wind generator, which is used in small wind system, is tested in lab conditions; connected to the grid via a typical inverter that mapped to the generators speed-power characteristic, and controls the power output as a function of the DC link voltage. A solution for increasing the power/energy output of the turbine for various locations is changing blade from its standard length. Such mechanical adjustment creates a different power/speed curve, resulting in turbines with more input power for smaller wind speeds. It is shown that for lower wind speed locations, increasing the length by 10-15% results in 30% energy increase. Such mechanical alternations do not increase the small wind systems efficiency, but rather increase the harvested amount of wind power for smaller wind speeds. Existing technical solutions do not achieve the full capacity of the turbine. ACKNOWLEDGMENT This work was supported by WE Energies, as a part of research under the grant number: 11-083. The partners on the project are: Lakeshore Technical College, Focus on Energy and MagDrive. Special thanks to Mr. Anthony Baroud for true support and understanding. REFERENCES
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