Volume 2 wind energy 2 06 – energy yield of contemporary wind turbines

Volume 2 wind energy 2 06 – energy yield of contemporary wind turbines Volume 2 wind energy 2 06 – energy yield of contemporary wind turbines Volume 2 wind energy 2 06 – energy yield of contemporary wind turbines Volume 2 wind energy 2 06 – energy yield of contemporary wind turbines Volume 2 wind energy 2 06 – energy yield of contemporary wind turbines Volume 2 wind energy 2 06 – energy yield of contemporary wind turbines Volume 2 wind energy 2 06 – energy yield of contemporary wind turbines

DP Zafirakis, AG Paliatsos, and JK Kaldellis, Technological Education Institute of Piraeus, Athens, Greece

© 2012 Elsevier Ltd All rights reserved

2.06.1 From Wind Power to Useful Wind Energy

2.06.1.1 Assessment of Wind Energy Losses

2.06.2 Wind Potential Evaluation for Energy Generation Purposes

2.06.2.1 Wind Speed Distributions

2.06.2.2.2 Standard deviation – Empirical method

2.06.2.2.3 Maximum likelihood method

2.06.2.2.4 Moment method

2.06.2.2.5 Energy pattern factor method

2.06.2.3 The Impact of the Scale and Shape Factor Variation

2.06.2.4 Performance Assessment for the Weibull Distribution

2.06.2.5 Long-Term Study of Wind Energy Potential

2.06.2.6 Calm Spell Period Determination

2.06.2.7 Wind Gust Determination

2.06.3 Power Curves of Contemporary Wind Turbines

2.06.3.1 Description of a Typical Wind Turbine Power Curve

2.06.3.2 Producing a Wind Turbine Power Curve

2.06.3.3 Power Curve Modeling

2.06.3.3.1 Linear model

2.06.3.3.3 Quadratic model

2.06.3.4 Power Curve Estimation

2.06.4 Estimating the Energy Production of a Wind Turbine

2.06.4.1 From the Instantaneous Power Output to Energy Production

2.06.4.2 Estimating the Annual Wind Energy Production

2.06.4.3 Estimating the Mean Power Coefficient

2.06.4.4 The Impact of the Scale Factor Variation on the Mean Power Coefficient

2.06.4.5 The Impact of the Shape Factor Variation on the Mean Power Coefficient

2.06.4.6 The Impact of the Shape and Scale Factor Variation on the Annual Energy Production

2.06.4.7 Energy Contribution of the Ascending and Rated Power Curve Segments

2.06.4.8 Energy Yield Variation due to the Use of Theoretical Distributions

2.06.5 Parameters Affecting the Power Output of a Wind Turbine

2.06.5.1 The Wind Shear Variation

2.06.5.2 Extrapolation of the Shape and Scale Parameters of Weibull at Hub Height

2.06.5.3 Estimation of Wind Speed at Hub Height, Upstream of the Machine

2.06.5.4 The Impact of Air Density Variation

2.06.5.5 The Impact of the Wake Effect

2.06.6 The Impact of Technical Availability on Wind Turbine Energy Output

2.06.6.1 Causes of Technical Unavailability

2.06.6.2 Estimating Technical Availability

2.06.6.3 Experience Gained from the Monitoring of Technical Availability

2.06.7 Selecting the Most Appropriate Wind Turbine

2.06.7.1 The Role of Wind Turbine Databases

2.06.7.2 Selecting the Most Appropriate Wind Turbine

2.06.7.3 Determination of General Trends

Glossary Rated power speed The minimum wind speed at which a Aerodynamic coefficient A measure of the wind turbine given wind turbine operates at its rated power

Betz limit The maximum theoretical value that the distribution, which is analogous to the average wind aerodynamic coefficient may get Its value is equal to 16/27 speed of the area under investigation

Capacity factor The ratio of actual energy production of Shape factor The second critical parameter of Weibull the machine for a given time period to the respective distribution, which is reversibly analogous to the potential energy production of the same machine if it had standard deviation of wind speeds in the area of operated at its rated power for the entire time period investigation

Cut-in speed The wind speed at which a given wind Technical availability Configured by the hours of

Mean power coefficient Provides a measure of how poor scheduled maintenance and unforeseen faults of the

given site Typical values range between 0.2 and 0.6

2.06.1 From Wind Power to Useful Wind Energy

Wind turbines are man-made machines developed to exploit wind energy potential in order to produce electricity More specifically, wind turbines are used to convert the kinetic energy of wind first into mechanical energy and accordingly into electricity, with each

of the energy conversion stages existing introducing – as expected – energy losses that need to be considered Mechanisms of energy losses are described in order to assess the ability of contemporary wind turbines to exploit the kinetic energy of wind and thus provide useful wind energy for covering electricity needs

2.06.1.1 Assessment of Wind Energy Losses

Power PA carried by a wind stream of constant speed V and given air density ρ crossing through a surface of area A that is vertical to the wind speed vector is provided by eqn [1]:

The wind power of a wind stream is found to be analogous to the third order of wind speed, thus suggesting remarkable variation of the former with only minor variation of wind speed (e.g., 10% variation in wind speed implies 33% variation in wind power) Nevertheless, even in the ideal case that both electromechanical and turbulence losses [1] are considered to be negligible, it is impossible to entirely capture the available wind power flux Reasons for that include the following:

1 Based on the mass continuity theory, the air mass crossing the rotor of a wind turbine should maintain sufficient wind speed in order to escape fast enough downstream of the rotor This results in a loss of appreciable power carried by the wind stream leaving the wind turbine rotor

2 A small percentage of the air mass that should cross through the rotor area is actually crossing it by, due to the deflection of streamlines imposed by the rotor on the incident wind stream

3 Finally, a small percentage of the wind kinetic energy is also not exploited due to inability of the rotor to immediately turn itself toward the wind direction (thus, there is a time lag), although with the introduction of new electronic systems, response of the wind rotor to changes of wind direction has considerably improved [2] On the other hand, in the case of successive sudden changes of wind speed direction, partial loss of available wind energy amounts is inevitable

Except for the above-mentioned reasons explaining the reduced exploitation of available wind power, mechanical and aerodynamic losses upon the rotor blades along with additional restrictions further reduce the actually exploited wind energy More specifically, as also reflected in Figure 1, potentially and actually exploited wind power is found to be considerably lower than the respective theoretical wind power flux and is thus not actually analogous to the third power of wind speed, as may be easily misinterpreted, due to the following:

1 A part of the wind stream kinetic energy remains unexploited due to the fact that for low wind speeds encountered, the wind turbine

is unable to rotate since friction losses in the shafts and the gearbox are higher than the power produced by the machine As a result, production of exploitable power begins when power production by the wind turbine Pwt exceeds these losses of zero load Pc, that is, Pwt ≥ Pc, which coincides with the point that available wind speed exceeds the cut-in wind speed Vc of the wind turbine (i.e., the wind speed at which the wind turbine starts to operate) Thus, it becomes clear that for wind speeds that are lower than

Theoretical vs exploitable wind power flux

12 000

Theoretical power flux

Maximum exploitable power flux (Betz limit)

10 000

Power flux exploited by the machine

8000 Theoretical vs exploitable wind power flux

the respective cut-in speed of the machine, wind power available is not captured by the wind turbine At this point, it should be underlined that although such wind speeds are not appreciable in terms of magnitude, they are of primary importance when it comes to probability [3], meaning that since it is quite possible for such low wind speeds to appear, considerable amounts of wind energy are eventually lost Note that even in areas of high-quality wind potential, the possibility of encountering wind speeds below

4 m s−1 (which is a normal cut-in wind speed) on an annual basis may reach 40% On the other hand, cut-in wind speeds usually range from 2.5 to 5 m s−1, with the large-scale machines normally presenting (at least during the past) higher cut-in wind speeds due

to the considerably heavier structure Nevertheless, acknowledging the importance of low wind speed exploitation, considerable efforts have been encountered during recent years for the transition of cut-in speeds to lower values [4]

2 Power output of a wind turbine being lower than the respective available wind power is also due to energy losses upon the rotor blades Such losses include friction losses between the wind stream and the blades, off-design losses, and turbulence losses, all together known as aerodynamic losses of the rotor Note that the respective losses correspond to a rather considerable part of the available kinetic energy of wind and are quantified through the introduction of the aerodynamic coefficient Cp of the rotor, usually ranging from 0.35 to 0.45 Also keep in mind that Cp generally depends on the type of the machine and the tip speed ratio

λ, while it cannot exceed the respective theoretical upper limit Cpmax of 16/27 (known as the Betz limit) [5], see also Figure 2 [6], based on the actuator disk theory, that is, application of a simple linear momentum theory model λ is given by eqn [2], where D

is the rotor diameter and nr is the rotor rotational speed in rpm:

of the machine is achieved is called rated speed and is symbolized with VR Thus, for wind speeds that exceed the rated speed of the machine, considerable amounts of wind energy cannot be captured by the machine due to power regulation (Figure 3) In practice, the rated power speed of wind turbines usually ranges between 10 and 14 m s−1

4 Safety reasons impose interruption of the machine’s operation at very high wind speeds [8] (e.g., above Beaufort 9), with the respective cut-out or furling speed VF of the machine usually found in the range of 20 m s−1 (for smaller scale wind turbines) to

30 m s−1 (for quite solid machines) In that case, the entire wind energy carried by wind speeds that are higher than the cut-out

Single blade rotor Darrieus rotor

Tip speed ratio (λ)

The impact of power regulation on the exploitation of

available wind energy 120%

With power regulation

Figure 2 Cp –λ curves of different wind turbine rotors [6]

wind speed remains unexploited On the other hand, however, unlike the possibility of low wind speeds appearing, such wind speeds are quite rare (normally below 5% on an annual basis)

5 On top of aerodynamic losses, mechanical losses of the shafts and the gearbox as well as electrical losses of the electrical generator should also be considered It is estimated that electromechanical losses are relatively limited and correspond to

3–10%, usually considered equivalent to the respective zero load losses Thus, by introducing an electromechanical efficiency factor ηe/m, the output power of the machine Pex is given by eqn [4]:

2

6 Finally, for the precise estimation of energy output in relation to the available kinetic energy of wind, the technical availability Δ

of the installation should also be taken into account Note that the term of technical availability is actually configured by the hours of operation of a given wind turbine or a given wind farm by considering the time period that the machine is kept out of operation due to, for example, scheduled maintenance, unforeseen faults of the machine, and so on [9]

High wind speed losses

Power regulation losses

Aerodynamic losses

Exploited energy

C p

Aerodynamic zero load losses

Hours of the year

Acknowledging the above, in Figure 4, one may obtain the distribution of available wind power into exploited power output by the wind turbine and into the various losses during an entire year period [10]

2.06.2 Wind Potential Evaluation for Energy Generation Purposes

As already realized from Section 2.06.1, characteristics of the local wind resource are critical for the energy production of a wind turbine For the proper evaluation of the available wind energy potential of a given site, knowledge solely of the mean wind speed is not adequate On the contrary, detailed information concerning the probability distribution of different wind speeds during the entire year period along with the determination of the duration of calm spells and the probability–intensity of wind gusts appearing are all necessary to obtain a clear picture

For this purpose, prior to the installation of a wind turbine at a given site, it is very important to first collect all available wind resource data and then proceed to statistical processing for the estimation of the probability density of the wind speed In addition, due to the fact that wind turbines are unable to either operate or produce much below their nominal output, of primary importance

is also the determination of probability and duration for both calm spells and low wind speeds, which is directly relevant to the consideration and specifications of back-up systems On the other hand, determination of wind gusts and extreme wind speeds is related to both loading of the machine and the fact that operation of wind turbines for such high wind speeds is avoided due to safety reasons

Thus, for safe conclusions to be deduced concerning the wind energy potential of a certain location, long-term detailed wind speed measurements are required On the other hand, cost issues and the inevitable time delay induced by the need for long-term measurements often lead to either use of generalized functions [11], which have the ability to sufficiently evaluate the wind potential of a site based on a small number of parameters required, or application of more requiring CFD codes At this point, however, it should be noted that generalized functions do, as expected, imply accuracy issues, while in certain cases may even prove

to be unreliable A short description of the most commonly used wind speed distributions is given in the following paragraphs, aiming to emphasize the role of the main parameters involved in the estimation of energy produced by a wind turbine operating at a given area of specific wind resource characteristics

2.06.2.1 Wind Speed Distributions

2.06.2.1.1 Weibull distribution

The most commonly used distribution for the description of wind regimes is Weibull [12] The Weibull distribution is considered appropriate for the evaluation of temperate zone areas and for an altitude of up to 100 m, and uses two main parameters, namely, the scale c and the shape k factors, so as to determine the probability density f(V) of a specific wind speed to appear (that is actually the probability of a wind speed to be found in the range from V – (dV/2) to V + (dV/2)) under the function of eqn [5] (Figure 5):

� � � �

0.00 0.03 0.06 0.09 0.12 0.15

Experimental Weibull

Application of Weibull function for the estimation of wind

speed probability density

Furthermore, based on the cumulative probability function of the Weibull distribution (eqn [9]), one may also determine the cumulative probability F(V ≤ Vo) of wind speeds being lower than a given upper limit Vo Note also that the cumulative probability function is also complementary to the duration function G(V ≥ Vo), that is, G(V) = 1 – F(V), which, as it may result (see also eqn [10]), determines the probability of wind speeds being higher than a given lower limit Vo (Figure 6):

Weibull-derived cumulative probability and duration curve

c = 6.6 m s−1

k = 1.4

Wind speed (m s−1)

n V� ¼ X

i ¼ 1 with n being the number of bins used and Vi being the average value of each bin

2.06.2.1.3 Other distributions

Although Weibull is the most commonly used probability distribution and Rayleigh comprises an established alternative, the inability

of the former to represent all types of wind regimes satisfactorily (especially those where null speeds are critical or where a bimodal distribution appears) introduces the need to also consider additional distributions that may produce better results in the case of more unusual wind regimes Some examples of such distributions examined by various authors [18–24] include the two- and three-parameter Gamma distribution, the two-parameter lognormal distribution, the two-parameter inverse Gaussian distribution, the two-parameter normal truncated distribution, the two-parameter square-root normal distribution, the three-parameter beta distribution, the Pearson type V distribution, the maximum entropy principle distribution, the Kappa distribution, and the Burr distribution, as well as distribution mixtures such as the singly truncated normal Weibull mixture and the Gamma Weibull mixture distribution

Comparison between Weibull and Rayleigh wind speed distributions for a random wind regime

0.000.030.060.090.120.15

Wind speed (m s−1)

ExperimentalWeibullRayleigh

Thus, in cases of relatively abnormal wind speed regimes, evaluation of additional probability distributions, other than Weibull,

is thought to be essential in order to adequately assess the local wind potential However, since analysis of the above-mentioned probability distributions is out of the scope of this chapter, indication on the performance of each probability distribution for various wind regimes may be obtained from some excellent reviews [13, 25, 26] On the other hand, emphasis is given here to the methods used for the estimation of the main parameters of the most established probability distribution, that is, Weibull, provided

in the following paragraphs [27, 28]

2.06.2.2 Determination of Weibull Main Parameters

with n being the number of wind speed bins considered

2.06.2.2.2 Standard deviation – Empirical method

Using the expressions of average and standard deviation given in eqns [7] and [8], it is possible to calculate the shape factor first, through the numerical solution of the following equation:

− 1:086

σ

V V� ⋅k2 :6674

0:184 þ 0:816 ⋅k2 :73855

Wind speed frequency of a representative windy Aegean Island based on a year's measurements

Wind speed (m s−1Determination of the Weibull scale and shape factors

through linear regression

X

0.00 0.03 0.06 0.09 0.12 0.15

2.06.2.2.3 Maximum likelihood method

In the method of maximum likelihood [15, 31], through the application of the iteration method, one first determines the shape factor and accordingly the scale factor, based on eqns [24] and [25]:

1

n i ¼ 1 Instead, if the data available are given in a frequency distribution format, modification of the above two equations is performed in accordance with the following two expressions, with Vi being, as already mentioned, the average value of the bin n used; f(V) being the respective frequency; and P(V ≥ 0) being the probability for wind speed equal to or exceeding zero:

2.06.2.2.5 Energy pattern factor method

In the specific method, one uses the energy pattern factor Epf, defined as the ratio of the average cube wind speeds to the cube of the average wind speed [32], that is,

n X

1 ⋅ Vi3

n i ¼ 1

n X

1 ⋅ Vi

n i ¼ 1 After estimating the energy pattern factor, the shape factor may be approximated using eqn [32] or [33]:

3:69

Epf

while the scale factor may be given by the use of eqn [7]

The application for some of the above-described calculation methods is given in Figure 9, where two random wind regimes are examined in order to emphasize the potential variation between results obtained Thus, as it may be concluded, for the selection of the most appropriate method of calculation for the Weibull parameters, one should use accuracy judgment criteria on the basis of indices such as the root mean square error (RMSE) and the Chi-square error or the results

of the Kolmogorov–Smirnov test

2.06.2.3 The Impact of the Scale and Shape Factor Variation

In Figures 10 and 11, one may obtain the impact of the scale and shape factor variation on both the wind speed frequency f(V) and the cumulative probability F(V ≤ Vo) estimation on the basis of applying eqns [5] and [9] Based on the results of Figure 10, the lower the value of the scale factor c, the greater is the maximum wind speed frequency appearing, with the exact opposite being concluded from Figure 11 concerning the impact of the shape factor k In the same figures, one may also note that for the lower values of the c factor, the asymptotic of the cumulative probability curve is achieved for lower wind speed values, while again the opposite appears in the case of the k factor variation

Comparison between different methods for the determination of Weibull parameters (wind regime-1)

Wind speed (m s−1)

Comparison between different methods for the determination of Weibull parameters (wind regime-2) 0.24

Experimental Graphical Maximum likelihood Energy pattern factor Standard deviation

Weibull distribution: Cumulative probability vs probability

density in relation to the scale factor c variation

Weibull distribution: Cumulative probability vs probability

density in relation to the shape factor k variation

2.06.2.4 Performance Assessment for the Weibull Distribution

By applying Weibull for some given sites, performance of the distribution in relation to experimental measurements is reflected in Figure 12, where, as one may see, Weibull performance is site-dependent, with strong variations appearing in wind regimes 1 and 2 However, according to the up-to-now gained experience, the Weibull distribution produces rather satisfactory results while, in general, overestimation of the low wind speed frequency (apart from zero values not captured by the Weibull function) and underestimation of the high wind speed frequency should be expected On the other hand, by subtracting wind speed values lower than 1 m s−1 (i.e., the area where the Weibull function imposes zero frequency of wind speed), considerable improvement of the Weibull curve fit may be achieved (Figure 13)

2.06.2.5 Long-Term Study of Wind Energy Potential

One of the most important issues regarding the evaluation of wind potential is the determination of the minimum time period required for the conduction of detailed measurements that will enable solid evaluation of the site under investigation Costs and delays induced by the need to obtain a satisfactory data sample and variability of the wind potential characteristics during the useful lifetime of a wind power project need to be balanced

Weibull performance for three different wind regimes

15

Experimental 1 Experimental 2 Experimental 3 Weibull 1 Weibull 2 Weibull 3

Weibull performance: Original vs readjusted curve 7.5

Readjusted Weibull

Wind speed V (m s−1)

Long-term evolution of the local wind potential

Wind speed (m s−1)

Special attention should be given to the possibility of also obtaining the data of a nontypical wind year that will lead to inaccurate estimation of the machine’s energy yield In general, it is expected that the characteristics of wind potential for a given site shall remain relatively stable from one year to another (Figure 14), although over longer periods one may even encounter variation

in the order of  20% [33] Thus, to minimize uncertainty, measurements of at least 1 year’s time are thought to be necessary, with the extension of the monitoring period further increasing reliability

2.06.2.6 Calm Spell Period Determination

Of major importance for the evaluation of a given site wind potential for the purpose of energy production is the determination of calm spell periods More specifically, by determining different classes of calm spell periods (i.e., from the minimum, e.g., 1 h calm spell to the respective maximum, e.g., 50 consecutive hours of calm spells), one may proceed to the estimation of frequency for each

of the bins selected As a result, one may accordingly produce calm spell period curves, such as those appearing in Figure 15, for different upper limits of wind speed that correspond to the cut-in wind speed Vc of the wind machine under consideration each time Besides, determination of such non-energy production curves is critical in the case of stand-alone wind energy-based systems [34, 35], where detailed sizing of the storage system requires good knowledge of the characteristics of calm spells

Determination of the effect of calm spell periods

Duration of consecutive calm spells (h)

2.06.2.7 Wind Gust Determination

The frequency and intensity of wind gusts, that is, wind speeds exceeding Beaufort 9 for time durations of a few seconds, is also of major concern for the evaluation of a site, with determination of gust probability being achievable on the basis of processing the available wind speed data [36] In this way, the structure of the wind turbine to be installed in a given area of interest may be configured, with more solid and heavier structures used to ensure operation under extreme wind speed conditions Such wind turbines are determined by both higher cut-out wind speeds and survival speeds that even reach 80 m s−1, entailing, of course, a higher purchase cost as well

The probability of extreme wind speeds Vext appearing may be determined through the use of the Fisher–Tippett distribution I, using the following expression:

10 15 20 25 30 35 40 45

2.06.3 Power Curves of Contemporary Wind Turbines

After providing the main directions for the evaluation of wind potential characteristics for energy generation purposes, determination

of the most critical parameters related to the energy performance of a given wind turbine is presented, with emphasis given to the presentation of contemporary wind turbine power curves Through detailed examination of typical wind power curves, interaction between the local wind potential and the wind turbine investigated may afterward lead to the estimation of energy production 2.06.3.1 Description of a Typical Wind Turbine Power Curve

A simplified, though representative, wind turbine power curve, that is, the curve of the machine’s power output Pex as a function of wind speed at hub height, is given in Figure 17(a) As already made clear, no power production is encountered up until sufficient wind speed is exploited, that is, wind speed that exceeds the minimum speed of operation for the wind turbine and ensures coverage

of zero load losses Pc, also known as the cut-in wind speed Vc of the wind turbine As the wind speed increases above the respective cut-in speed of the machine, a constant increase of the output power is noted up to the point of rated speed VR, that is, the minimum wind speed corresponding to the nominal power of the machine PR Note that the increase rate noted in this ascending segment of the wind power curve varies and does not necessarily follow a linear pattern such as the one illustrated in Figure 17(a), with exponential or parabolic patterns also encountered (Figure 17(b)) Finally, in the nominal power segment, where the power curve flattens, an attempt is carried out in order for the power output to remain constant and wind speed-independent through power regulation Power regulation is used so as to avoid extreme loading of the machine and may be achieved with the application of several techniques [7] such as implementation of appropriate aerodynamic designs, pitch control, change of rotor direction, or even variable-speed operation Constant power output is maintained up to the point of the cut-out wind speed VF, where power production of the machine is eliminated so as to protect the machine from heavy loading On the other hand, storm control features [37] recently adopted by certain wind turbine manufactures allow for the gradual reduction of power production in the event of extremely high wind speeds, preventing instant shutdown of the machine and thus allowing for greater wind energy exploitation (the red curve in Figure 17(a)) The respective survival speed Vs is normally found in the area of 50–80 m s−1 (i.e., from

180 km h−1 to almost 290 km h−1), depending on the class of the machine To synopsize, mathematical expression of the typical power curve (without storm control) illustrated in Figure 17(a) may be summarized as

As expected, reduction of both cut-in and rated power speeds implies considerable increase of energy yield (even 25%), explained by the high probability density values of lower wind speeds (in the case of the cut-in speed reduction) as well as from the extension of the nominal power segment (in the case of the rated power speed reduction)

On the other hand, increase of these two characteristic speeds leads to an analogous reduction of energy yield, opposite to the behavior exhibited by the cut-out wind speed, which if increased leads to a minimum increase in wind energy exploitation Similarly, reduction of the cut-out speed leads to reduction of energy yield, which is, however, not as influencing as in the case of the cut-in and rated power speeds, reflecting the relatively lower importance of very high wind speeds Results obtained are directly dependent on the wind potential examined each time; nevertheless, only in extreme cases would increase of the cut-out wind speed allow greater wind energy exploitation than the one accruing from an analogous reduction of the cut-in speed

2.06.3.2 Producing a Wind Turbine Power Curve

Configuration of a wind turbine power curve is directly dependent on the selected power regulation strategy and the operational features of the machine More precisely, depending on the characteristics of the electrical generator selected, rotational speed of the rotor may be either constant or variable, with the second option, although inducing a more expensive solution, also allowing for optimization of the power output over a large range of wind speeds [38] On the other hand, in the case that a constant speed machine is used, operation of the rotor is restricted to a standard rotational speed that is wind speed-independent and thus cannot

Ascending segment

Wind speed (V) (m s−1) (b) 1.2

Wind speed (V) (m s−1)

Influence of the wind turbine operational range on the

energy yield of the machine

(a) Presentation of constant vs variable speed operation

Constant speed B

Variable speed operation

power curve (constant vs variable speed)

Wind speed (m s−1)

obtain maximum power output Furthermore, depending on whether rotor blades are pitchable or fixed, either regulation of power (normally in the nominal power segment of the power curve) is achievable through variation of the pitch angle (pitch regulation or active stall regulation) or a standard angle is selected that takes advantage of the aerodynamic stall phenomenon

As a result, there are three common options used in power regulation, that is, constant speed of the rotor and fixed blades using stall regulation (e.g., NM 1000/60), constant speed of the rotor and pitchable blades using pitch/active stall regulation (e.g., WindMaster 750/48 and Vestas V82) and, finally, variable speed of the rotor and pitchable blades using pitch regulation (e.g., Enercon E126), with activation of power regulation not necessarily restricted in the nominal power segment area of the power curve The influence of the rotor speed regulation is demonstrated in Figure 19, where comparison of constant and variable-speed strategies designates different wind power curve configurations and clearly reflects energy exploitation benefits accruing from the selection of a variable-speed generator

The adoption of fixed or pitchable rotor blades normally influences the nominal power segment of the power curve (Figure 20), where in an effort to both maintain constant power output and limit extreme loading of the machine, either stall (passive control)

or pitch regulation (active control) is performed Up until the mid-1990s, the majority of in-operation wind generators used the stall-control concept; nevertheless, since the introduction of large-scale machines and the imposition of power quality require­ments, pitch regulation dominated in the years to come [39], with the pitch-regulated variable-speed concept being gradually established during the time being (Figure 21)

2.06.3.3 Power Curve Modeling

Description of a wind turbine power curve may be approached by some generic models that are common in the literature [40–44] and are used to describe the ascending segment of a wind turbine power curve, using only the cut-in and the rated power speed of

Time evolution of rotor diameter and pitch-to-stall ratio

Rotor diameter Pitch-to-stall ratio

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

Year

Wind power curves of pitch- and stall-control machines

0 0.2 0.4 0.6 0.8

1 1.2

Stall control Pitch control

Pitch or stall control Constant or variable-speed operation (no pitch)

Wind speed V (m s−1)

the machine These include linear, quadratic, and cubic models, with adjustment of each one clearly depending on the form of the original power curve configured by the manufacturer data

Comparison of generic power curve models for the ascending segment of a typical wind power curve

VR, power output follows the cubic model of eqn [42] Alternatively, eqn [44] may also be used for the application of the quadratic model on the basis of a second expression, that is,

V2−V2

PR VR 2−V2

C while polynomial functions of higher order may also be used to describe the ascending segment of a wind turbine power curve In order to demonstrate the application of the above-mentioned models, a typical example is given in Figure 22, with results obtained reflecting the difference between the outcome of the various models Hence, selection of the most appropriate model for the wind turbine power curve investigated should also take into account evaluation of adjustment to the manufacturer data through the use

of common best-fit criteria

2.06.3.4 Power Curve Estimation

For the estimation of a wind turbine power curve, detailed measured data of wind speed and wind turbine electrical output are required for an appreciable time period in order to assess actual performance of the machine Wind speed measurements may be obtained either from a meteorological mast in the area of the wind turbine or wind park installation, or from the nacelle anemometer downstream of the rotor For any given case, what should be considered is that in order to obtain the actual wind speed at hub height, upstream of the rotor, correction of the original measurements is required Power output measurements, however, may be obtained from the SCADA monitoring system of the machine (Figure 23(a))

Acknowledging the above, the current standard method for the determination of a wind turbine power curve corresponds to the use of IEC 61400-12-1, introduced by the International Electrotechnical Commission [45] According to the standard procedure, collected data of wind speed and power output are transformed into 10-min averages and are accordingly averaged into 0.5 m s−1 wind speed bins Although the method is considered as applicable, especially in the case that sufficient data are available, the inability of capturing short-term wind speed fluctuations designates important limitations that need to be considered, with alternative approaches existing suggesting dynamical and maximum principle methods of power curve determination To proceed

to further analysis, division of available wind speed data into direction sectors per wind speed bin is also desirable (Figure 23(b)), while depending on the terrain and exact point of wind speed measurements, determination of the power curve may also require the use of numerical simulation methods that will also capture any terrain effects [46]

It is common for power curves of all commercial wind turbines to be measured and certified (Figure 24) by independent institutions such as the Deutsches Windenergie-Institut in Germany, included among others in the International Network for Harmonised and Recognised Measurements in Wind Energy (MEASNET), which is responsible for the development of standardiza­tion methods [47] (Table 1)

15.50 (1.6%)

10.80 (6.1%)

8.23 (27.6%) 2%

4%

6%

5.14 (35.0%) 8%

2.06.4 Estimating the Energy Production of a Wind Turbine

After the investigation of typical wind turbine power curves and the assessment of wind resource main characteristics, synthesis of the respective data may lead to estimation of the energy production output of a given wind turbine We provide here an analysis of energy production calculations, with emphasis accordingly given to the impact of wind potential characteristics on the wind energy output of a given wind machine

2.06.4.1 From the Instantaneous Power Output to Energy Production

As already seen, the purpose of a wind turbine is the exploitation of the kinetic energy of wind and the production of useful energy at the outlet of the machine For the estimation of the instantaneous useful power output at a given moment t, knowledge of wind speed at hub height upstream of the rotor turbine V, technical availability of the machine δ, and wind turbine standard power curve Pex(V) are all necessary, with the resulting power production given by eqn [45]:

Figure 24 Example of wind turbine certification

Svend Ole Hansen ApS, wind engineering

Ingenieurbüro Dr.-Ing Dieter Frey

Energy to quality S L

Deutsche WindGuard Consulting GmbH

WINDTEST Ibérica S L

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Figure 25 Instantaneous power output of a wind turbine on the basis of available wind speed measurements, manufacturer’s power curve, and technical availability time series

In order to facilitate any techno-economic calculations required for the evaluation of a wind energy project, it is also convenient

to equate the operation of a wind turbine with that of a hypothetical constant power machine that produces – during a certain time period Δt of mean technical availability Δ – the exact energy amount that the respective wind turbine does

For that reason, one introduces the parameter of the mean power coefficient ω [48], estimated on the basis of eqn [47]:

EðΔtÞ

Using the mean power coefficient, it is assumed that the variable power output wind turbine of rated power PR operates as a constant power machine with rated power equal to PR·ω for a time period of Δ·Δt

2.06.4.2 Estimating the Annual Wind Energy Production

The process for determining the annual energy production of a certain wind turbine may be applied either to ex post, for example, at the end of the year under investigation (so as to evaluate its operation), or in advance, in order to obtain an indication of the energy production to be expected on an annual basis

In the first case, by using the recorded time series of wind speed, meteorological conditions and technical availability of the machine, along with the characteristics of the wind turbine manufacturer power curve, estimation of the expected wind energy production for a time period (to, to + Δt, e.g., 1 year) is possible on the basis of the following equation, modifying eqn [46] in order

to also consider for any variation in standard day conditions:

In the case that estimation of energy production is attempted in advance, the probability density f(V) curve of the local wind potential is used, in combination with the manufacturer power curve, while estimation of a realistic value for the technical availability during the entire year is also required In that case, the energy production of a wind turbine during this certain time period Δt of 1 year (i.e., 8760 h) is estimated on the basis of eqn [47], where the mean power coefficient ω of the wind turbine may

be calculated using eqn [49], considering also that the energy production of a wind turbine is limited within the range of wind speeds from the cut-in to the cut-out wind speed

Power output of a 500kW rated power wind turbine

Typical wind turbine power curve

0.0 0.2 0.4 0.6 0.8 1.0 1.2

ω 2: rated power segment

In conclusion, as one may obtain from eqn [49], the value of the mean power coefficient depends on both the local wind energy resource characteristics and the operational curve of the wind turbine examined In addition, by using eqn [49], it is possible to estimate the contribution of wind speeds up to a certain level, for example, V ≤ Vo, to the respective energy production of a wind machine:

2.06.4.3 Estimating the Mean Power Coefficient

The precise value of the mean power coefficient derives from the detailed knowledge of the available wind energy potential and the operational features of the wind turbine under examination If one wishes to estimate the energy contribution of the transitional (ascending) segment of a typical power curve (i.e., from Vc to VR), eqn [52] may be used:

Figure 27 Calculation of the power coefficient distribution based on the numerical method of Simpson

as considerable because the probability for such high wind speeds to appear is rather low (Figure 18)

For a more detailed estimation of ω and the production of the respective distribution, numerical methods are required [50] Some of the most common numerical integration methods include Simpson’s rule, the trapezoidal rule, and Lagrange interpola­tion The results obtained from the application of Simpson’s rule are given in Figure 27, expressed on the basis of eqn [57], applying for equally distant points, that is, equally distant bins of wind speed:

2.06.4.4 The Impact of the Scale Factor Variation on the Mean Power Coefficient

As already mentioned, the scale factor c of the Weibull distribution is directly related to the mean annual wind speed V� of the area under examination More precisely, when c takes high values, the area of examination is determined by high wind speeds, while the opposite is valid in the case that c takes low values Using five different realistic values for the scale parameter of Weibull (e.g., from

c = 4.0 m s−1 to c = 8.0 m s−1) and a constant shape parameter value k = 1.7, the influence of the scale factor variation on the mean power coefficient distribution for a typical pitch-control wind turbine is obtained from Figure 28

As one may see, differences accruing due to the variation of the scale factor are rather significant, with the ω value obtained for

c = 7.0 m s−1 being almost double the ω value for c = 5.0 m s−1, which practically implies that the specific wind turbine shall produce double the energy amount if installed in an area of c = 7.0 m s−1, in comparison with its operation at an area of c = 5.0 m s−1 As one may easily understand, this also influences the economic performance of the machine, thus designating the importance of the local

Distribution of the mean power coefficient

ω-distribution ω-cumulative distribution

0 0.0

The impact of the scale parameter c variation on the

mean power coefficient ω distribution

0.00 0.08 0.16 0.24 0.32 0.40

The impact of the shape parameter k variation on the

mean power coefficient ω distribution

wind potential scale factor, especially in the case of such great variation entailed in the respective power coefficient The magnitude

of discrepancy between results obtained is even more characteristic for the extreme scale factors currently studied, with the respective power coefficients differing by a factor of almost 4.5 (i.e., ωc = 8.0 = 0.376 and ωc = 4.0 = 0.085), directly related to the ability of annual energy production of the specific wind generator

2.06.4.5 The Impact of the Shape Factor Variation on the Mean Power Coefficient

The shape factor of the Weibull distribution is, as previously mentioned, inversely analogous to the standard deviation of wind speed As a result, low values of the k parameter lead to the production of more ‘flat’ and dispersed probability distributions, while,

on the contrary, high values of the shape factor suggest relatively sharper distributions, with the probability distribution being rather concentrated around the average wind speed value Besides, as already seen, variation of the k parameter also has a slight impact on the average wind speed

In Figure 29, we investigate the effect of the shape parameter variation on the resulting power coefficient, with values selected ranging from k = 1.3 to k = 2.2 and with the scale parameter held constant at c = 6.0 m s−1 As one may see, the impact of the shape parameter may be thought as inconsiderable, especially if taking into account the effect that is induced by the variation of the scale

The impact of the scale and shape parameters on the annual energy yield of a typical 600 kW wind turbine

In order to better demonstrate the influence of the Weibull parameter variation on the actual energy production of a wind generator,

in Figure 30 one may obtain the results concerning the annual energy production of a 600 kW pitch-control machine, assumed to be determined by a mean annual technical availability value of Δ = 0.95 (see also eqn [47]), a rated wind speed VR = 10 m s−1, a cut-in wind speed Vc = 4.0 m s−1, and, finally, a cut-out speed VF = 25 m s−1 As expected, there is a strong influence of the scale parameter

on the annual energy production achieved by the machine, which is almost linear, whereas on the other hand, the shape parameter variation effect is only considerable for either very high or very low values of c Furthermore, as one may obtain from the figure, although for low values of c, it is the lower values of k that seem to achieve a greater energy production, the opposite is valid in the case of a high average wind speed (for c ∼8 m s−1), where the higher k values imply strict concentration of wind speed values around the relatively high mean wind speed of the area

This may be easily justified if considering the fact that the scale parameter is actually a reflection of the average wind speed of the area, whereas the shape parameter is inversely analogous to the standard deviation of wind speeds around the respective average wind speed Thus, in the case of a low average wind speed, that is, low values of the c parameter, low values of k introduce wide dispersion of values around the average wind speed, which is in the specific case desirable, exactly due to the fact that wider dispersion also increases the possibility of higher wind speeds appearing Lower values of wind speed appearing are, of course, of analogous probability; nevertheless, their effect minimizes as the c factor approaches the cut-in wind speed Vc On the contrary, when the scale parameter takes high values, a decrease in the value of the shape parameter implies that it is quite possible for lower wind speeds to appear, that is, something that implies reduction of the energy production, especially in cases that the average wind speed (or c) is close to the machine’s rated wind speed VR (since higher values in that case would produce the same energy production, especially in the case of a pitch-control machine)

2.06.4.7 Energy Contribution of the Ascending and Rated Power Curve Segments

Investigation of energy contribution by each of the two main segments of the wind turbine power curve (Figure 31) is of great interest For this purpose, in Figure 31, one may obtain the energy contribution of both segments, expressed on the basis of the ω1/ω and ω2/ω ratios (see also eqns [51]–[53]) in relation to the random increase of both the k and c parameters, for a wind turbine of

Vc = 5 m s−1, VR = 10 m s−1, and VF = 25 m s−1 As one may see, increase of the Weibull parameters is, as expected, inducing an increase

of ω2, which for the highest of the values studied allows for a contribution of the rated power segment that even approaches 80% The opposite is encountered in the case of the low value scenario, where the contribution of the rated power segment minimizes and the greatest share of energy production derives from the exploitation of wind speeds much below the rated wind speed VR The effect of the Weibull parameters on the energy contribution of ω1 and ω2 is further investigated in Figures 32 and 33 More precisely, in Figure 32, the influence of the k variation for three different values of the scale parameter is studied, for the same wind turbine producing the results of Figure 33 As one may see, the impact of k variation depends on the exact value of the scale parameter In fact, for c values found below the area of rated power wind speed (i.e., c = 6.5 and c = 8.0), an increase of the k value suggests an increase of the ω1 contribution, justified on the basis of a narrower dispersion around the average wind speed, which in these two cases is inferior to the rated power wind speed of the machine (VR = 10 m s−1) In the case that the scale parameter becomes

The impact of the scale and shape factor variation on the contribution of the ω1 power coefficient

Figure 31 The effect of parallel increase of Weibull parameters on the energy production contribution of the ω1 and ω2 power coefficients

Energy production contribution of the ascending and therated power segments of the wind turbine power curve

equal to the rated power wind speed of the machine, an increase of the k factor yields the opposite results, since wind speeds are now gathered in the area of the rated power segment, that is, where ω2 starts to contribute

The above conclusion is further validated by the results of Figure 33, where the ratio of c/VR is plotted against ω2 Based on the results obtained, as the scale parameter approximates the rated wind power speed VR, narrow dispersion of wind speeds achieved for higher values of k brings about an increase in the contribution of the rated power curve segment On the contrary, low values of k for the cases that the c/VR ratio reduces considerably allow for the exploitation of higher wind speeds (due to the wider dispersion of wind speed values) that also fall into the rated power segment of the wind turbine power curve

2.06.4.8 Energy Yield Variation due to the Use of Theoretical Distributions

Estimation of the energy production of a certain wind turbine depends on the set of data used, meaning that this could comprise either a set of actual wind speed measurements or a set of results produced with the application of a certain wind speed distribution

In the second case, as expected, the estimated energy output is directly related to the accuracy of the distribution used; thus selection

of the appropriate distribution is, as already seen, of major importance for a reliable estimation of the energy yield In Figures 34 and 35, a good and a poor adjustment scenario of the Weibull distribution on the given wind regimes is studied, in order to demonstrate the importance of either using the appropriate wind speed distribution or acknowledging the difficult task of describing some more complex wind regimes

More precisely, in Figure 34, results of good Weibull adjustment at a wind regime that appears to be relatively mild are also reflected in the calculation of the ω-distribution, with minor variations noted in the area of low and medium wind speeds, that is, the area where Weibull fails to describe the given wind regime satisfactorily In the case that Weibull presents poor adjustment over the given wind regime, such as in the case of Figure 35, where the given wind regime is rather abrupt, the coincidence of the two ω-distributions, with the difference noted between the two final ω values exceeding 30% (ωexperimental = 0.318 and ωweibull = 0.238)

is also analogous As a result, there is a rather considerable underestimation of the energy output of the wind turbine under examination, due to the fact that Weibull fails to capture the increased probability density of high wind speeds

2.06.5 Parameters Affecting the Power Output of a Wind Turbine

Because the power output of a wind generator is dependent on constantly varying parameters such as wind speed and air density, this variation needs to be considered when attempting a reliable estimation of the actual energy yield In the following paragraphs, some insight

is provided regarding the variation of wind shear, the impact of air density fluctuations, and, finally, the influence of the wake effect 2.06.5.1 The Wind Shear Variation

Acknowledging the lack of existing measurements at the required height, in order to properly predict the energy production output

of contemporary wind turbines, extrapolation is necessary in order to assess wind speeds at hub heights that may well exceed 50 m and even reach 100 m, starting from available wind speed measurements, usually at a height of 10 m above ground level The flow of

performance

Theoretical (Weibull) and experimental cumulative distribution

of power coefficient (scenario of good adjustment)

0.000.050.100.150.200.250.300.35