2.1 Energy analysis

could cause inaccurate evaluation of WT performance. For example, a dry air assumption (i.e., constant air density) does not really consider the moisture changeability. Baskut et al. discussed the effects of several meteorological variables including air density, pressure difference, humidity, and ambient temperature on exergy efficiency and suggested that neglecting these meteorological variables while planning wind farms could cause important errors in energy calculations [3].

Wind Solar Hybrid Renewable Energy System

2. Theory

performance of WTs.

4

The efficiency performance of a WT can be studied in two aspects, energy and exergy efficiencies. The former is calculated as the ratio of produced electricity to the total wind potential within the swept area of the rotor. Thus, only the kinetic energy of the air flow is considered in the energy efficiency calculation, while other meteorological variables such as pressure and temperature are often neglected. The latter considers the maximum useful work that can be obtained by a system interacting with an environment in thermodynamic equilibrium state [4]. The exergy efficiency along with availability and capacity factor of a small WT (rated power 1.5 kW) has been studied in Izmir, Turkey, to assess the WT system performance [5]. Sahin et al. developed an improved approach for the thermodynamic analysis of wind energy using energy and exergy, which provided a physical basis for understanding, refining, and predicting the wind energy variations [6]. According to [7], exergies are suggested as the most appropriate link between the second law of thermodynamics and the environmental impact, in part because it measures the deviation between the states of the system and the environment. This brief précis thus illustrates the importance of energy and exergy analyses for wind energy systems considering meteorological variables and provides a motivation for the thermodynamic analysis conducted herein. The chapter presents the methods and results of thermodynamic analysis of a 1.5 MW WT, which is assumed to be deployed in the northeastern United States, experiencing meteorological reanalysis data retrieved from the NASA's MERRA-2 data set. Matlab scripts are developed to calculate the energy and exergy efficiencies using the MERRA-2 data set. Section 2 provides the fundamental theory of thermodynamic analysis, particularly in derivations of energy and exergy efficiencies. The studied site, meteorological data, and the selected WT are explained in Section 3, which is followed by results and discussion in Section 4. Concluding remarks are provided in Section 5.

A WT converts kinetic energy from air flow to electrical energy through subassemblies including rotor blades, drivetrain, generator, and electronic control systems, as well as other auxiliary components. As the kinetic energy is extracted, the air flow that passes through the turbine rotor must slow down. Assuming there is a boundary surface that contains the affected air flow inside, a long stream tube extended far from the upstream and to the downstream with varied cross sections is often used to study the thermodynamics of horizontal-axis WTs [6, 7] (Figure 1). The wind speed, pressure, and temperature at the inlet of the stream tube are represented by V1, P1, and T1, respectively. Their counterparts at the outlet are V2, P2, and T<sup>2</sup> and at the rotor are Vave, Pave, and Tave. Here a constant specific humidity ratio is assumed in the stream tube for a short-period time (e.g., 10 minutes or 1 hour). The following sections explain the theory of WT thermodynamics in two aspects, energy analysis and exergy analysis, which both apply the meteorological variables such as wind speed, air density, atmospheric pressure, temperature, and humidity. The use of energy and exergy efficiencies considering a comprehensive set of meteorological variables can enable us to accurately evaluate the efficiency

The energy analysis of WT systems stems from the air flow's kinetic energy Ek that is calculated as

$$E\_k = \frac{1}{2}mV^2\tag{1}$$

where m and V are the mass and speed of the air flow, respectively. The mass m can be further expressed as

$$m = \rho A \mathbf{V} \mathbf{t} \tag{2}$$

where ρ is the air density, A is the rotor swept area perpendicular to the flow, and t is the time that the flow passing through the swept area with speed V. By applying the simple momentum theory, the rate of momentum change is equal to the overall change of velocity times the mass flow rate m\_ , i.e.,

$$
\dot{M} = \dot{m} \left( V\_1 - V\_2 \right) \tag{3}
$$

where V<sup>1</sup> and V<sup>2</sup> are the wind speeds at the inlet and outlet, respectively, of the stream tube (Figure 1). The rate of momentum change is also equal to the resulting thrust force. Thus, the power absorbed by the WT is calculated as

$$P = \dot{m}(V\_1 - V\_2)V\_{\text{ave}} \tag{4}$$

where Vave is the average flow speed at rotor. On the other hand, the rate of kinetic energy change of the flow can be calculated as

$$
\dot{E}\_k = \frac{1}{2}\dot{m}\left(V\_1^2 - V\_2^2\right) \tag{5}
$$

Based on the conservation of energy, Eqs. (4) and (5) should be equal which results in

$$V\_{ave} = \frac{1}{2}(V\_1 + V\_2) \tag{6}$$

Hence, the retardation of the wind before the rotor ð Þ V<sup>1</sup> � Vave is equal to the retardation of the wind after the rotor ð Þ Vave � V<sup>2</sup> . By Eqs. (2), (4), and (6), the rotor power can be calculated as

$$P = \frac{1}{4}\rho A (V\_1 + V\_2)^2 (V\_1 - V\_2) \tag{7}$$

Let <sup>a</sup> <sup>¼</sup> <sup>V</sup><sup>2</sup> V<sup>1</sup> ; Eq. (7) can be reformulated as

$$P = \frac{1}{4}\rho A V\_1^3 (1+a)^2 (1-a) \tag{8}$$

In order to obtain the maximum power, equate 0 to the differentiation of Eq. (8) with respect to <sup>a</sup> resulting in <sup>a</sup> <sup>¼</sup> <sup>1</sup> 3 . Thus, the maximum power Pmax <sup>¼</sup> <sup>8</sup> <sup>27</sup> <sup>ρ</sup>AV<sup>3</sup> <sup>1</sup> is achieved, when the outlet wind speed is equal to one-third of the inlet wind speed. Defining the power coefficient as

$$C\_p = \frac{P}{\frac{1}{2}\rho A V\_1^3} \tag{9}$$

speed and a cutout wind speed, and (4) zero power when the inflow wind speed is

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

1. In real irreversible process, exergy is always consumed; thus it is not subjected to a conservation law. In contrast, energy is neither created nor destroyed, but changing from one form to another, during a process. Thus, it is subjected to

2. Although from a theoretical point of view exergy may be defined without a reference environment, it is often defined as a quantity relative to a

The total exergy Ex of a flow with unit mass generally consists of four parts,

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

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

specified reference environment and is equal to zero when it is in equilibrium

Ex ¼ Exki þ Expo þ Exph þ Exch (12)

Ex ¼ Exki þ Exph (13)

larger than the cutout wind speed (Figure 2).

A typical power curve of WTs with four operational stages I–IV.

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

the conservation of energy law.

with the reference environment.

total exergy for a WT can be reduced as

which can be expressed as

as [6, 7].

7

2.2 Exergy analysis

Figure 2.

characterized as [6]:

the maximum power coefficient is calculated CPmax <sup>¼</sup> <sup>16</sup> <sup>27</sup> ≈0:593. This maximum power coefficient, known as the Lanchester-Betz limit (or Betz limit) [8, 9], explains the maximum power that can be extracted from the air flow and can also be easily derived by other theories (e.g., the rotor disc theory and blade element momentum theory [10]).

Despite the simplicity of Eq. (9) when calculating power coefficient, the total input power in the denominator does not take account of the impacts from pressure, temperature, and humidity. Actually the air density changes as the ambient pressure, temperature, and humidity change, which can be expressed as

$$\rho = \frac{\mathbf{1} + w}{R\_d + aR\_v} \frac{p}{T} \tag{10}$$

where ω (�) is the humidity ratio of air, gas constant Ra = 287.1 J/kg K, water vapor constant Rv = 461.5 J/kg K, and T is the absolute temperature (unit: K). In order to distinguish wind power P, the small letter p is used to represent the pressure (unit: Pa) in the humid air hereafter. Combining Eqs. (9) and (10), the power coefficient of a WT considering a comprehensive set of meteorological variables can be expressed as

$$C\_p = \frac{2(R\_a + aR\_v)}{1 + o} \frac{TP}{pAV\_1^3} \tag{11}$$

The above derivations provide the fundamentals of the theoretically available energy/power that a WT can extract from the air flow. However, various effects could have influence on the real power output, e.g., vortices shed from the blade tip and hub could significantly affect the rotor lift force and power output [11]. Power losses also occur during the energy transformation through rotor to mechanical shaft and to generator that converts angular kinetic energy to electrical energy. In addition, sustained high wind speeds could cause strong fatigue and extreme loads on WT systems without proper turbine control or safety protection. Thus, wind power is intended to be constrained, when the inflow wind speed is beyond a rated value (i.e., rated wind speed), through different strategies commonly including stall regulation, pitch regulation, and yaw control [12]. As a result, the output power Pout of a WT is corresponding to four operating stages: (1) zero power when the inflow wind speed is smaller than a cut-in wind speed, (2) exponentially increased power as the wind speed increases between the cut-in wind speed and the rated wind speed, (3) rated output power when the wind speed is between the rated wind Thermodynamic Analysis of Wind Energy Systems DOI: http://dx.doi.org/10.5772/intechopen.85067

Figure 2.

<sup>P</sup> <sup>¼</sup> <sup>1</sup>

; Eq. (7) can be reformulated as

<sup>P</sup> <sup>¼</sup> <sup>1</sup>

the maximum power coefficient is calculated CPmax <sup>¼</sup> <sup>16</sup>

Let <sup>a</sup> <sup>¼</sup> <sup>V</sup><sup>2</sup> V<sup>1</sup>

with respect to <sup>a</sup> resulting in <sup>a</sup> <sup>¼</sup> <sup>1</sup>

Wind Solar Hybrid Renewable Energy System

Defining the power coefficient as

momentum theory [10]).

ables can be expressed as

6

<sup>4</sup> <sup>ρ</sup>A Vð Þ <sup>1</sup> <sup>þ</sup> <sup>V</sup><sup>2</sup>

<sup>4</sup> <sup>ρ</sup>AV<sup>3</sup>

3

2

<sup>1</sup>ð Þ 1 þ a 2

In order to obtain the maximum power, equate 0 to the differentiation of Eq. (8)

achieved, when the outlet wind speed is equal to one-third of the inlet wind speed.

Cp <sup>¼</sup> <sup>P</sup> 1 <sup>2</sup> <sup>ρ</sup>AV<sup>3</sup> 1

Despite the simplicity of Eq. (9) when calculating power coefficient, the total input power in the denominator does not take account of the impacts from pressure, temperature, and humidity. Actually the air density changes as the ambient

power coefficient, known as the Lanchester-Betz limit (or Betz limit) [8, 9], explains the maximum power that can be extracted from the air flow and can also be easily derived by other theories (e.g., the rotor disc theory and blade element

pressure, temperature, and humidity change, which can be expressed as

<sup>ρ</sup> <sup>¼</sup> <sup>1</sup> <sup>þ</sup> <sup>ω</sup> Ra þ ωRv

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

The above derivations provide the fundamentals of the theoretically available energy/power that a WT can extract from the air flow. However, various effects could have influence on the real power output, e.g., vortices shed from the blade tip and hub could significantly affect the rotor lift force and power output [11]. Power losses also occur during the energy transformation through rotor to mechanical shaft and to generator that converts angular kinetic energy to electrical energy. In addition, sustained high wind speeds could cause strong fatigue and extreme loads on WT systems without proper turbine control or safety protection. Thus, wind power is intended to be constrained, when the inflow wind speed is beyond a rated value (i.e., rated wind speed), through different strategies commonly including stall regulation, pitch regulation, and yaw control [12]. As a result, the output power Pout of a WT is corresponding to four operating stages: (1) zero power when the inflow wind speed is smaller than a cut-in wind speed, (2) exponentially increased power as the wind speed increases between the cut-in wind speed and the rated wind speed, (3) rated output power when the wind speed is between the rated wind

where ω (�) is the humidity ratio of air, gas constant Ra = 287.1 J/kg K, water vapor constant Rv = 461.5 J/kg K, and T is the absolute temperature (unit: K). In order to distinguish wind power P, the small letter p is used to represent the pressure (unit: Pa) in the humid air hereafter. Combining Eqs. (9) and (10), the power coefficient of a WT considering a comprehensive set of meteorological vari-

p

TP pAV<sup>3</sup> 1

. Thus, the maximum power Pmax <sup>¼</sup> <sup>8</sup>

ð Þ V<sup>1</sup> � V<sup>2</sup> (7)

ð Þ 1 � a (8)

<sup>27</sup> <sup>ρ</sup>AV<sup>3</sup> <sup>1</sup> is

<sup>27</sup> ≈0:593. This maximum

<sup>T</sup> (10)

(9)

(11)

A typical power curve of WTs with four operational stages I–IV.

speed and a cutout wind speed, and (4) zero power when the inflow wind speed is larger than the cutout wind speed (Figure 2).
