3.2 Wind turbine

The expected wind energy that can be harvested at a location is highly related to the WT characteristics, e.g., power curve and the available wind resources. Herein a Goldwind 1.5 MW permanent magnet direct-drive (PMDD) WT (GW85/1500) is assumed to be deployed at Ithaca area and used for evaluating the WT's energy and exergy efficiencies. Table 1 provides a summary of technical specifications of the WT. Since this study investigates the WT efficiency performance before real deployment, measured output power data are not available. It is assumed that the WT is performing perfectly according to its power curve, which consists of four operational stages (Figure 2). The WT starts to produce electricity at its cut-in wind speed of 3 ms�<sup>1</sup> , and the produced power is increased to the rated one of 1.5 MW at the rated wind speed of 10.3 ms�<sup>1</sup> . In order to mitigate the fatigue and structural loadings under sustained high wind, WT control systems (e.g., the active blade pitch control) are operated to maintain the aerodynamic loads applied on blades and control the output power to be constant at the rated power. The WT is stopped, when wind speed is larger than the cut-out wind speed of 22 ms�<sup>1</sup> , to keep the whole turbine safe under extreme wind conditions. In this study, the power curve is represented by a six-order polynomial equation of wind speed during the cut-in and rated speeds, which is expressed as

Thermodynamic Analysis of Wind Energy Systems DOI: http://dx.doi.org/10.5772/intechopen.85067


#### Table 1.

MERRA-2 including 10-m eastward wind U10M (in ms�<sup>1</sup>

10-m specific humidity QV10M (in kg kg�<sup>1</sup>

Wind Solar Hybrid Renewable Energy System

<sup>U</sup>10M<sup>2</sup> <sup>þ</sup> <sup>V</sup>10M<sup>2</sup>

is assumed to be deployed in Ithaca, New York.

lated as <sup>U</sup> <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

at its cut-in wind speed of 3 ms�<sup>1</sup>

one of 1.5 MW at the rated wind speed of 10.3 ms�<sup>1</sup>

during the cut-in and rated speeds, which is expressed as

), surface pressure PS (in Pa), 10-m air temperature T10M (in K),

, <sup>p</sup> and the humidity ratio <sup>ω</sup> is calculated from the

from January 2000 to December 2017. The 10-m horizontal wind speed U is calcu-

The expected wind energy that can be harvested at a location is highly related to the WT characteristics, e.g., power curve and the available wind resources. Herein a Goldwind 1.5 MW permanent magnet direct-drive (PMDD) WT

(GW85/1500) is assumed to be deployed at Ithaca area and used for evaluating the WT's energy and exergy efficiencies. Table 1 provides a summary of technical specifications of the WT. Since this study investigates the WT efficiency performance before real deployment, measured output power data are not available. It is assumed that the WT is performing perfectly according to its power curve, which consists of four operational stages (Figure 2). The WT starts to produce electricity

and structural loadings under sustained high wind, WT control systems (e.g., the active blade pitch control) are operated to maintain the aerodynamic loads applied on blades and control the output power to be constant at the rated power. The WT is stopped, when wind speed is larger than the cut-out wind speed of 22 ms�<sup>1</sup>

keep the whole turbine safe under extreme wind conditions. In this study, the power curve is represented by a six-order polynomial equation of wind speed

specific humidity as ω ¼ QV10M=ð Þ 1 � QV10M . In total, there are 18 years of hourly meteorological data used for the thermodynamic analysis of the WT, which

Location of Ithaca, New York, where thermodynamic analysis of a 1.5 WM WT is investigated.

V10M (in ms�<sup>1</sup>

Figure 3.

3.2 Wind turbine

10

), 10-m northward wind

), as well as their hourly time stamps

, and the produced power is increased to the rated

. In order to mitigate the fatigue

, to

Technical specifications of the Goldwind 1.5 MW PMDD WT [17].

$$P\_{out} = \begin{cases} 0, & V\_1 < 3 \text{ ms}^{-1} \text{ or } V\_1 > 22 \text{ ms}^{-1} \\ 0.0184V\_1^6 - 1.3507V\_1^5 + 30.8477V\_1^4 - 320.8737V\_1^3 + 1699.2172V\_1^2 \\ & - 4366.5508V\_1 + 4287.3549 \text{ kW}, \quad 3 \text{ ms}^{-1} \le V\_1 \le 10.3 \text{ ms}^{-1} \\ 1500 \text{ kW}, & 10.3 \text{ ms}^{-1} < V\_1 \le 22 \text{ ms}^{-1} \end{cases} \tag{20}$$

## 4. Results and discussion

With the available meteorological data and the selected WT properties, assumptions are made for calculating the energy and exergy efficiencies: (1) the air pressure, temperature, and humidity are not significantly changed in the swept area of the WT. Thus, the surface pressure data, 10-m air temperature, and 10-m specific humidity obtained from the MERRA-2 data are directly used for the thermodynamic analyses. (2) Due to the wind shear effect in the atmospheric boundary layer, the normal wind profile model with a power law exponent of 0.2 is used to convert the 10-m horizontal wind speed to the hub-height (90 m) wind speed according to the IEC standard [20]. It takes about 0.5 hour to convert six channels (five meteorological channels and one channel for time stamps) from the MERRA-2 netCDF4 data to Matlab data and then to calculate 18 years' hourly energy and exergy efficiencies using the developed Matlab scripts. Results and discussion are elaborated in three aspects: (1) WT efficiency variation in time domain, (2) meteorological variables impact on the efficiencies, and (3) uncertainty of meteorological variables represented by the best-fit distributions.

#### 4.1 Variation of energy and exergy efficiencies in time domain

The energy and exergy efficiencies of the Goldwind WT are calculated by Eqs. (18) and (19), respectively, using the Ithaca meteorological data (wind speed, pressure, temperature, and humidity) retrieved from the MERRA-2 data set. As demonstrated in Figure 4, the variation of energy and exergy efficiencies is more closely following the variation of wind speed comparing with the other three meteorological variables, as wind power is proportional to the cubic of wind speed. Both efficiencies become 0 when the wind speed is less than the cut-in wind speed due to the WT being in idling status at the very low wind speed. As the WT is stopped when wind speed is larger than the cutout wind speed, the efficiencies are also equal to 0. In addition, the energy efficiency present a higher magnitude than that of exergy efficiency, which is consistent with the theoretical derivations (Eqs. (18) and (19)) and previous findings (e.g., [6, 7]). The difference between the two efficiencies is due to exergy destruction caused by irreversibility [7]. The concurrent low temperature and humidity ratio also demonstrate the cold and dry weather in winter of Ithaca.

Figure 5 shows the mean and standard deviation of energy and exergy efficiencies in different years and months. Annual means of energy and exergy efficiencies are smaller than the corresponding standard deviations, which indicates a significant variation of WT efficiency performance in 1 year as also demonstrated in Figure 4(e). Neither energy efficiency nor exergy efficiency exhibits clear trend from 2000 to 2017, even though relatively small and large means are observed in 2005 and 2014, respectively (Figure 5(a)). However, both mean and standard deviation of energy and exergy efficiencies present smaller values in summer than those in winter (Figure 5(b)). This seasonal change of efficiencies is likely related to the fact that high sustained wind speeds with strong variation more frequently occur in winter than in summer at the Ithaca area.

4.2 Impact of meteorological variables on energy and exergy efficiencies

Mean and standard deviation of energy and exergy efficiencies in different (a) years and (b) months.

Relationships between the WT efficiencies and meteorological variables offer the trends of WT efficiency performance as meteorological variables change. Figure 6 shows the scatter diagrams of energy and exergy efficiencies versus the four meteorological variables (wind speed, pressure, temperature, and humidity ratio), as well as their relationships represented by different metrics. A bimodal relationship between the efficiencies and wind speed is observed due to the nonlinearity of the efficiency function with respect to wind speed (Figure 6(a)). The mean curves in Figure 6(a) show that the maximum means of energy and exergy efficiencies are 46.2% and 45.2%, respectively, at the high peaks when the

the efficiencies are linearly proportional to temperature and to the inverse of pressure (Figure 6(b and c)). Figure 6(d) shows that both the energy and exergy

, while the counterparts at the low peaks are 42.7%

. Despite the large variation,

wind speed is equal to 9.2 ms<sup>1</sup>

Thermodynamic Analysis of Wind Energy Systems DOI: http://dx.doi.org/10.5772/intechopen.85067

Figure 5.

13

and 38.1% when the wind speed is equal to 5 ms<sup>1</sup>

#### Figure 4.

Time series of hourly concurrent (a) wind speed U, (b) pressure P, (c) temperature T, (d) humidity ratio ω, and (e) energy efficiency η and exergy efficiency ψ during January 1–7, 2017.

pressure, temperature, and humidity) retrieved from the MERRA-2 data set. As demonstrated in Figure 4, the variation of energy and exergy efficiencies is more closely following the variation of wind speed comparing with the other three meteorological variables, as wind power is proportional to the cubic of wind speed. Both efficiencies become 0 when the wind speed is less than the cut-in wind speed due to the WT being in idling status at the very low wind speed. As the WT is stopped when wind speed is larger than the cutout wind speed, the efficiencies are also equal to 0. In addition, the energy efficiency present a higher magnitude than that of exergy efficiency, which is consistent with the theoretical derivations (Eqs. (18) and (19)) and previous findings (e.g., [6, 7]). The difference between the two efficiencies is due to exergy destruction caused by irreversibility [7]. The concurrent low temperature and humidity ratio also demonstrate the cold and dry weather

Figure 5 shows the mean and standard deviation of energy and exergy efficiencies in different years and months. Annual means of energy and exergy efficiencies are smaller than the corresponding standard deviations, which indicates a significant variation of WT efficiency performance in 1 year as also demonstrated in Figure 4(e). Neither energy efficiency nor exergy efficiency exhibits clear trend from 2000 to 2017, even though relatively small and large means are observed in 2005 and 2014, respectively (Figure 5(a)). However, both mean and standard deviation of energy and exergy efficiencies present smaller values in summer than those in winter (Figure 5(b)). This seasonal change of efficiencies is likely related to the fact that high sustained wind speeds with strong variation more frequently

Time series of hourly concurrent (a) wind speed U, (b) pressure P, (c) temperature T, (d) humidity ratio ω,

and (e) energy efficiency η and exergy efficiency ψ during January 1–7, 2017.

in winter of Ithaca.

Wind Solar Hybrid Renewable Energy System

Figure 4.

12

occur in winter than in summer at the Ithaca area.

Figure 5. Mean and standard deviation of energy and exergy efficiencies in different (a) years and (b) months.

#### 4.2 Impact of meteorological variables on energy and exergy efficiencies

Relationships between the WT efficiencies and meteorological variables offer the trends of WT efficiency performance as meteorological variables change. Figure 6 shows the scatter diagrams of energy and exergy efficiencies versus the four meteorological variables (wind speed, pressure, temperature, and humidity ratio), as well as their relationships represented by different metrics. A bimodal relationship between the efficiencies and wind speed is observed due to the nonlinearity of the efficiency function with respect to wind speed (Figure 6(a)). The mean curves in Figure 6(a) show that the maximum means of energy and exergy efficiencies are 46.2% and 45.2%, respectively, at the high peaks when the wind speed is equal to 9.2 ms<sup>1</sup> , while the counterparts at the low peaks are 42.7% and 38.1% when the wind speed is equal to 5 ms<sup>1</sup> . Despite the large variation, the efficiencies are linearly proportional to temperature and to the inverse of pressure (Figure 6(b and c)). Figure 6(d) shows that both the energy and exergy

#### Figure 6.

Relationships between the WT efficiency (energy efficiency η and exergy efficiency ψ) and meteorological variables including (a) wind speed, (b) pressure, (c) temperature, and (d) humidity ratio. All 18-year samples of hourly η and ψ versus wind speed are used in (a). For demonstration, samples in (b), (c), and (d) are conditionally sampled under a wind speed bin of 9 ms<sup>1</sup> (bin width 1 ms<sup>1</sup> ).

efficiencies are increased by 8% as the humidity ratio is increased from 0.001 to 0.015 kg kg<sup>1</sup> , which indicates humidity plays an important role in affecting the WT efficiency performance.

#### 4.3 Uncertainties of meteorological variables and WT efficiencies

Variation of meteorological variables could have significant impact on not only energy and exergy efficiencies as explained in Section 4.2 but also many other aspects, e.g., fatigue and structural reliability. Although Weibull distribution is often used to represent the uncertainty of mean wind speed in long term [21, 22], few previous studies have sought to address which parent distribution best represents other meteorological variables, e.g., pressure, temperature, and humidity for WT analyses. This is an important omission since these meteorological variables could have critical roles, but maybe indirectly, to WT performance. For example, high air humidity, low wind speed, and temperature above 10°C are preferred by insects that will increasingly foul the leading edges of WT blades and contaminate the blade surface eventually decreasing the aerodynamic performance [23]. Since both the wind speed and pressure considered herein are zero bounded, four positive-valued distribution types (Weibull, lognormal, gamma, and log-logistic; see Figure 7(a and b)) are fitted to wind speed and pressure using maximum likelihood estimation (MLE). Due to the clear two-peak histograms observed for

temperature and humidity ratio, four positive-valued bimodal distributions (bi-Weibull, bi-lognormal, bi-gamma, and bi-log-logistic) are fitted to temperature and humidity ratio (Figure 7(c and d)). The probability density function (PDF) of a bimodal distribution consists of two PDFs with the same distributional type, which

data, and the calculated WT energy and exergy efficiencies are used in Figure 7.

Thermodynamic Analysis of Wind Energy Systems DOI: http://dx.doi.org/10.5772/intechopen.85067

Histograms and distribution fits for (a) wind speed, (b) pressure, (c) temperature, and (d) humidity ratio; and (e) empirical cumulative distribution function of energy and exergy efficiencies. In the legends, the loglikelihood values are in parentheses. The bolded distribution with the largest log-likelihood value is selected as the best-fit distribution and is summarized in Table 2. Recall all 18-year samples of hourly meteorological

where x represents a meteorological variable; (a1, b1) and (a2, b2) are the parameters of the first and the second constituent PDFs, respectively; and w is the weight for the constituent distributions f(x|a1, b1) in the bimodal distribution form. The candidate distribution with the largest log-likelihood value is selected as the

Figure 7 and Table 2 summarize the distributional fits for the four meteorological variables. It is found that the log-logistic distribution is best fit for wind speed

f xð jw; a1; b1; a2; b2Þ ¼ wf xð Þþ ja1; b<sup>1</sup> ð Þ 1 � w f xð Þ ja2; b<sup>2</sup> (21)

is expressed as

15

Figure 7.

best-fit distribution [24].

Thermodynamic Analysis of Wind Energy Systems DOI: http://dx.doi.org/10.5772/intechopen.85067

Figure 7.

efficiencies are increased by 8% as the humidity ratio is increased from 0.001 to

Relationships between the WT efficiency (energy efficiency η and exergy efficiency ψ) and meteorological variables including (a) wind speed, (b) pressure, (c) temperature, and (d) humidity ratio. All 18-year samples of hourly η and ψ versus wind speed are used in (a). For demonstration, samples in (b), (c), and (d)

Variation of meteorological variables could have significant impact on not only

energy and exergy efficiencies as explained in Section 4.2 but also many other aspects, e.g., fatigue and structural reliability. Although Weibull distribution is often used to represent the uncertainty of mean wind speed in long term [21, 22], few previous studies have sought to address which parent distribution best represents other meteorological variables, e.g., pressure, temperature, and humidity for WT analyses. This is an important omission since these meteorological variables could have critical roles, but maybe indirectly, to WT performance. For example, high air humidity, low wind speed, and temperature above 10°C are preferred by insects that will increasingly foul the leading edges of WT blades and contaminate the blade surface eventually decreasing the aerodynamic performance [23]. Since both the wind speed and pressure considered herein are zero bounded, four positive-valued distribution types (Weibull, lognormal, gamma, and log-logistic; see Figure 7(a and b)) are fitted to wind speed and pressure using maximum likelihood estimation (MLE). Due to the clear two-peak histograms observed for

4.3 Uncertainties of meteorological variables and WT efficiencies

are conditionally sampled under a wind speed bin of 9 ms<sup>1</sup> (bin width 1 ms<sup>1</sup>

, which indicates humidity plays an important role in affecting the

).

0.015 kg kg<sup>1</sup>

14

Figure 6.

WT efficiency performance.

Wind Solar Hybrid Renewable Energy System

Histograms and distribution fits for (a) wind speed, (b) pressure, (c) temperature, and (d) humidity ratio; and (e) empirical cumulative distribution function of energy and exergy efficiencies. In the legends, the loglikelihood values are in parentheses. The bolded distribution with the largest log-likelihood value is selected as the best-fit distribution and is summarized in Table 2. Recall all 18-year samples of hourly meteorological data, and the calculated WT energy and exergy efficiencies are used in Figure 7.

temperature and humidity ratio, four positive-valued bimodal distributions (bi-Weibull, bi-lognormal, bi-gamma, and bi-log-logistic) are fitted to temperature and humidity ratio (Figure 7(c and d)). The probability density function (PDF) of a bimodal distribution consists of two PDFs with the same distributional type, which is expressed as

$$f(\mathbf{x}|w, a\_1, b\_1, a\_2, b\_2) = wf(\mathbf{x}|a\_1, b\_1) + (1 - w)f(\mathbf{x}|a\_2, b\_2) \tag{21}$$

where x represents a meteorological variable; (a1, b1) and (a2, b2) are the parameters of the first and the second constituent PDFs, respectively; and w is the weight for the constituent distributions f(x|a1, b1) in the bimodal distribution form. The candidate distribution with the largest log-likelihood value is selected as the best-fit distribution [24].

Figure 7 and Table 2 summarize the distributional fits for the four meteorological variables. It is found that the log-logistic distribution is best fit for wind speed


1.5 MW WT (Goldwind GW82/1500) potentially deployed at Ithaca, New York, is beneficial to WT design, siting, and operation in moderately complex terrain in the

• The WT energy efficiency presents higher magnitude than exergy efficiency based on the theoretical derivation and the calculated time series of

• Although wind speed has a dominating influence, other meteorological variables (i.e., pressure, temperature, and humidity) do have a considerable impact on the WT efficiency performance. The WT efficiencies are linearly associated with pressure and temperature, while it has highly nonlinear

efficiencies. There is no clear trend of annual variations of mean and standard deviation of both energy and exergy efficiencies. However, a clear seasonal change is found that energy and exergy efficiencies studied herein have smaller

• Log-logistic distributions are most appropriate for the wind speed and pressure data retrieved from the MERRA-2 data set at Ithaca, New York. A bi-lognormal

meteorological variables and CDFs of energy and exergy efficiencies could be beneficial for evaluating the reliability of wind power performance considering

Naturally the specific findings are based on reanalysis meteorological data and

Support from the National Natural Science Foundation of China (grant numbers 51475417, U1608256, and 51521064) is gratefully acknowledged. Weifei Hu would like to appreciate Dr. Qinjian Jin and Dr. Frederick Letson at Department of Earth and Atmospheric Sciences, Cornell University, for the introduction and discussion

The authors certify that this work has no conflict of interest with any organiza-

tion or entity in the subject matter or materials discussed in this chapter.

distribution and a bi-gamma distribution are most appropriate for the temperature and humidity ratio, respectively. The obtained PDFs of

realistic meteorological uncertainty in the northeastern United States.

the assumed WT deployment; the methodologies of thermodynamic analysis presented here are applicable for real measured meteorological data and recorded WT performance somewhere else if available. In addition, although the thermodynamic analysis of wind energy systems in this chapter focuses on energy and exergy efficiencies, other variables, e.g., dynamic response, fatigue damage, structural deformation, etc., of the PMDD WT are also potentially affected by the meteoro-

northeastern United States. The key concluding remarks are the following:

energy systems.

Acknowledgements

of the MERRA-2 data.

Conflict of interest

17

values in summer than those in winter.

Thermodynamic Analysis of Wind Energy Systems DOI: http://dx.doi.org/10.5772/intechopen.85067

relationships with wind speed and humidity ratio.

logical variables, which could be investigated in the future.

• The chapter offers the fundamental derivations of energy and exergy efficiencies of WTs considering wind speed, pressure, temperature, and humidity, which lay a foundation for the thermodynamic analysis of wind

#### Table 2.

The best-fit distribution form and distribution parameters for the four meteorological variables.

and pressure (Figure 7(a and b)), despite the commonly used Weibull distribution for mean wind speed. The bi-lognormal and bi-gamma distributions are best fit for temperature and humidity ratio, respectively. The existence of bimodal shape of the distributions of temperature is likely related to the very distinguished high and low temperature corresponding to the summer and winter seasons, respectively, in Ithaca. The same reason explains the bimodal shape for humidity. The obtained specific distributions for the meteorological parameters, provided in Table 2, are readily applicable for WT performance analyses, i.e., fatigue, structure, aerodynamics, and thermodynamics, in moderately complex terrain of the northeastern United States. Figure 7(e) presents the empirical cumulative distribution function (CDF) of energy and exergy efficiencies calculated herein. Due to the large amount of 0 energy and exergy efficiencies when wind speed is below the cut-in wind speed, the CDF curves show that there is a probability of �43% that the efficiencies are equal to 0. The largest discrepancy between CDF of energy and exergy efficiencies occurs at efficiencies equal to 0.4. The presented CDF could be used to evaluate the reliability of wind power performance considering realistic meteorological uncertainty.

## 5. Conclusions

This chapter presents methods and results for thermodynamic analysis of wind energy systems considering four types of meteorological variables, i.e., wind speed, pressure, temperature, and humidity. An improved understanding of WT efficiencies is critically important and necessary before launching any wind projects. The evaluation of WT efficiencies considering thermodynamics, conducted here for an

1.5 MW WT (Goldwind GW82/1500) potentially deployed at Ithaca, New York, is beneficial to WT design, siting, and operation in moderately complex terrain in the northeastern United States. The key concluding remarks are the following:


Naturally the specific findings are based on reanalysis meteorological data and the assumed WT deployment; the methodologies of thermodynamic analysis presented here are applicable for real measured meteorological data and recorded WT performance somewhere else if available. In addition, although the thermodynamic analysis of wind energy systems in this chapter focuses on energy and exergy efficiencies, other variables, e.g., dynamic response, fatigue damage, structural deformation, etc., of the PMDD WT are also potentially affected by the meteorological variables, which could be investigated in the future.
