2.2 Exergy analysis

In thermodynamics, the exergy of a system is defined as the maximum amount of useful work during a process that can bring the system into equilibrium with a reference environment [13]. Based on the second law of thermodynamics, exergy analysis is an alternative useful tool for analysis, evaluation, and design of many power and energy systems, e.g., renewable and traditional energy systems. The significant difference between energy and exergy analyses may be characterized as [6]:


The total exergy Ex of a flow with unit mass generally consists of four parts, which can be expressed as

$$E\infty = E\infty\_{ki} + E\infty\_{po} + E\infty\_{ph} + E\infty\_{ch} \tag{12}$$

where Exki, Expo, Exph, and Exch represent the kinetic, potential, physical, and chemical exergies, respectively. For thermodynamic analysis of WT systems, the potential exergy and chemical exergy are negligible in the total exergy. Thus, the total exergy for a WT can be reduced as

$$E\mathfrak{x} = E\mathfrak{x}\_{ki} + E\mathfrak{x}\_{ph} \tag{13}$$

where the kinetic exergy is defined herein as the maximum possible available kinetic energy that the air flow can produce from a wind speed to a complete stop and the physical exergy includes the enthalpy and entropy changes related to the turbine operation. The physical exergy can be calculated as [6, 7].

$$E\mathbf{x}\_{ph} = c\_p(T\_2 - T\_1) + T\_0 \left( c\_p \ln \left( \frac{T\_2}{T\_1} \right) - R \ln \left( \frac{P\_2}{P\_1} \right) - \frac{c\_p(T\_0 - T\_{ave})}{T\_0} \right) \tag{14}$$

meteorological variables and referring Eqs. (9)–(11), the energy efficiency can be

where Pout is the output power defined by the power curve (see Figure 2). By

TPout pAV<sup>3</sup> 1

� ð Þ Ra <sup>þ</sup> <sup>ω</sup>Rv ln <sup>p</sup>

P0

<sup>þ</sup> <sup>1</sup>:6078ωRaln <sup>ω</sup>

ω0

9 >>>>>>>=

>>>>>>>;

(18)

(19)

<sup>η</sup> <sup>¼</sup> <sup>2</sup>ð Þ Ra <sup>þ</sup> <sup>ω</sup>Rv 1 þ ω

� �ð Þ <sup>T</sup> � <sup>T</sup><sup>0</sup>

� � � �

1 þ 1:6078ω � �

Eqs. (18) and (19) derive the energy and exergy efficiencies given various meteorological variables, which can offer a straightforward evaluation of WT efficiency performance in a perspective of energy and exergy before deploying WTs. Hence, it will be beneficial in wind resource evaluation, wind farm site selection,

� � � �

Using the presented thermodynamic analysis methods for wind energy systems,

the wind energy potential is evaluated by investigating the energy and exergy efficiencies of a Goldwind 1.5 MW WT (model GW82/1500) [17], which is assumed to be deployed at Ithaca, New York, where 18-year reanalysis meteorological data are obtained from the Modern-Era Retrospective analysis for Research and Application, version 2 (MERRA-2), the latest atmospheric reanalysis of the modern satellite era produced by NASA's Global Modeling and Assimilation Office [18]. This section explains the site; the meteorological data including wind speed, pressure, temperature, and humidity; and the characteristics of the WT used for ther-

The wind energy potential is evaluated at Ithaca, which has moderately complex terrain in a landscape dominated by patches of forest, crop fields, hills, waterfalls, and lakes in the Upstate New York (at approximately 42.44° N, 76.50° W, Figure 3). Experiencing a moderate continental climate, Ithaca has long, cold, and snowy winters and warm and humid summers with a dominance of westerly wind flows. The meteorological data are obtained from the MERRA-2 (a meteorological reanalysis data set created by NASA), which has a resolution of 0.5° latitude � 0.625° longitude [19]. Although it does not provide measured data in fields, the meteorological reanalysis is thought as a valuable tool to estimate the long-term variables, such as wind speed and temperature, for subsequent meteorological, climatological, energy, and environmental studies. By specifying the latitude and longitude of Ithaca, five types of meteorological data are retrieved from the

T<sup>0</sup> � �

Eqs. (13), (15), and (17), the exergy efficiency can be reorganized as

<sup>ψ</sup> <sup>¼</sup> Pout

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

> 1 <sup>2</sup>ð Þ Ra <sup>þ</sup> <sup>ω</sup>Rv <sup>T</sup> <sup>þ</sup> cp,a <sup>þ</sup> <sup>ω</sup>cp, <sup>v</sup>

> > � �ln <sup>T</sup>

<sup>þ</sup>T<sup>0</sup> ð Þ Ra <sup>þ</sup> <sup>ω</sup>Rv ln <sup>1</sup> <sup>þ</sup> <sup>1</sup>:6078ω<sup>0</sup>

ð Þ <sup>1</sup> <sup>þ</sup> <sup>ω</sup> pAV<sup>3</sup>

8 >>>>>>><

>>>>>>>:

and new WT design.

modynamic analysis.

3.1 Site and data

9

3. Case study

�T<sup>0</sup> cp,a þ ωcp, <sup>v</sup>

expressed as

where the first term and the second term on the right side of Eq. (14) are the enthalpy and entropy contributions, respectively. cp is the specific heat of the flow; T0,T1,T2,Tave are the reference temperature, inlet temperature, outlet temperate, and average temperature, respectively; P<sup>1</sup> and P<sup>2</sup> are the inlet pressure and outlet pressure, respectively (see Figure 1); and R is a constant related to the gas and water vapor constants. Ideally, temperature and pressure at both inlet and outlet are needed to calculate the physical exergy. However, it is cumbersome to measure the temperatures and pressures at both inlet and outlet for the WT stream tube in real applications, not to mention the situation when evaluating the wind energy resource and/or WT efficiency performance before deploying WTs. In addition, the meteorological variable humidity is not considered in Eq. (14). To handle this difficulty, other studies have provided another formula to calculate the physical exergy for wind energy [3, 5, 14, 15]:

$$\begin{split} \mathbf{Ex}\_{ph} &= \left( c\_{p,a} + \alpha c\_{p,v} \right) (T - T\_0) \\ &- T\_0 \left[ \left( c\_{p,a} + \alpha c\_{p,v} \right) \ln \left( \frac{T}{T\_0} \right) - (R\_a + \alpha R\_v) \ln \left( \frac{p}{P\_0} \right) \right] \\ &+ T\_0 \left[ (R\_a + \alpha R\_v) \ln \left( \frac{\mathbf{1} + \mathbf{1.6078} \alpha \mu\_0}{\mathbf{1} + \mathbf{1.6078} \alpha \nu} \right) + \mathbf{1.6078} \alpha R\_d \ln \left( \frac{\alpha}{\alpha\_0} \right) \right] \end{split} \tag{15}$$

where cp,<sup>a</sup> and cp,<sup>v</sup> are specific heat of air and water vapor, respectively; ω<sup>0</sup> and ω are the humidity ratio of air at the reference state and at the current state, respectively; Ra and Rv are the gas constant and the water vapor constant, respectively; T<sup>0</sup> and P<sup>0</sup> are the reference temperature and atmospheric pressure, respectively; and T and p are measured temperature and pressure in this study.

#### 2.3 Energy and exergy efficiencies

The efficiency for wind energy systems is explained by using energy efficiency η and exergy efficiency ψ. The former is obtained as the ratio of useful energy produced by a WT to the total input wind energy, while the latter is defined as the useful exergy created by a WT to the total exergy of the air flow. These general definitions of energy and exergy efficiencies have been introduced in several literature (e.g., [3, 5–7, 16]). However, the specific definitions of useful energy/exergy for wind energy systems are often not very clearly explained in the literature. In order to avoid confusion, here we define that both the useful energy and useful exergy are equal to the rate of electricity output Eout that a WT can produce under a wind speed (i.e., Eout equals to actual output power Pout). Thus, the energy efficiency and exergy efficiency are calculated as, respectively,

$$\eta = \frac{E\_{out}}{\mathcal{W}\_{wind}}\tag{16}$$

$$
\mu = \frac{E\_{\text{out}}}{E \text{x}} \tag{17}
$$

where Wwind is the total input wind energy equal to the total kinetic energy given in Eq. (1) and Ex is the total exergy given in Eq. (13). By incorporating the Thermodynamic Analysis of Wind Energy Systems DOI: http://dx.doi.org/10.5772/intechopen.85067

meteorological variables and referring Eqs. (9)–(11), the energy efficiency can be expressed as

$$\eta = \frac{2(R\_a + oR\_v)}{1 + o} \frac{TP\_{out}}{pAV\_1^3} \tag{18}$$

where Pout is the output power defined by the power curve (see Figure 2). By Eqs. (13), (15), and (17), the exergy efficiency can be reorganized as

$$\begin{aligned} \boldsymbol{\Psi} &= \frac{P\_{\text{out}}}{\begin{bmatrix} \frac{(1+\alpha)pA}{2(R\_d+\alpha R\_v)T} + (c\_{p,d}+\alpha c\_{p,v})(T-T\_0) \\ -T\_0 \left[ (c\_{p,d}+\alpha c\_{p,v}) \ln \left( \frac{T}{T\_0} \right) - (R\_d+\alpha R\_v) \ln \left( \frac{p}{P\_0} \right) \right]} \\ + T\_0 \left[ (R\_d+\alpha R\_v) \ln \left( \frac{1+1.6078\alpha\_0}{1+1.6078\alpha} \right) + 1.6078\alpha R\_d \ln \left( \frac{\alpha}{\alpha\_0} \right) \right] \end{bmatrix} \end{aligned} \tag{19}$$

Eqs. (18) and (19) derive the energy and exergy efficiencies given various meteorological variables, which can offer a straightforward evaluation of WT efficiency performance in a perspective of energy and exergy before deploying WTs. Hence, it will be beneficial in wind resource evaluation, wind farm site selection, and new WT design.
