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Renewable Energy 28 (2003) 295310
www.elsevier.com/locate/renene
Exergy analysis of renewable energy sources
Christopher Koroneos *, Thomas Spachos,Nikolaos Moussiopoulos
Laboratory of Heat Transfer and Environmental Engineering, Aristotle University Thessaloniki, 54006
Thessaloniki, Greece
Received 13 March 2001; accepted 22 May 2001
Abstract
Oil crises in the past years made more obvious the dependency of economies on fossil fuels.As a consequence, the need for new energy sources became more urgent. Renewable energysources could provide a solution to the problem, as they are inexhaustible and have less adverse
impacts on the environment than fossil fuels. Yet, renewable energy sources technology hasnot reached a high standard at which it can be considered competitive to fossil fuels. Thepresent study deals with the exergy analysis of solar energy, wind power and geothermalenergy. That is, the actual use of energy from the existing available energy is discussed. Inaddition, renewable energy sources are compared with the non-renewable energy sources onthe basis of efficiency. 2002 Published by Elsevier Science Ltd.
Keywords: Exergy; Renewable energy sources; Environment
1. Introduction
As fossil fuels such as oil and coal are being depleted, the need for using renewableenergy sources (RES) is becoming more and more urgent. Support for this viewbecomes greater as RES technologies, besides being beneficial for the environment,become economically sustainable.
The present study makes use of the concept of exergy for the analysis of RES,in addition to the energy analysis, which is based on the first law of thermodynamicsand which provides a qualitative evaluation of the losses in the different components
* Corresponding author. Tel.: +30-31-995968; fax: +30-31-996012.
E-mail address: [email protected] (C. Koroneos).
0960-1481/03/$ - see front matter 2002 Published by Elsevier Science Ltd.
PII: S 0 9 6 0 - 1 4 8 1 ( 0 1 ) 0 0 1 2 5 - 2
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of the system. The exergy analysis, based on the second law of thermodynamics,
provides a clearer view of the energy losses in the system, as it presents quantitative
and qualitative evaluation of the different losses.
2. The exergy concept
Exergy is defined as:
Exergy is the property of the system, which gives the maximum power that
can be distracted from the system, when it is brought to a thermodynamic equilib-
rium state from a reference state [1].
The exergy transfer can be associated with mass flow, with work interaction andwith heat interaction [2]. Dynamic and kinetic exergy are two more forms of exergy
that exist in RES technology.
The exergy associated with heat interaction is given by the equation [3]:
EA
TT0T Qi dA, (1)
where A is the heat exchange surface, T0 is the ambient temperature, Tis the tempera-
ture at which the heat transfer takes place and Qi is the heat transfer rate.
The exergy associated with mass flow is divided to chemical, physical and mixingexergy. Chemical exergy is given by [4]:
Ex0chem,in
j1
vjExchem,refjrG0i , (2)
where vj is the specific volume of the jth component and rG0i is the reaction exergy
so as to bring the component to the reference state, and is equal to the standard
Gibbs energy change. n is the number of components and 0 is the reference condition.
Physical exergy, which is defined as the work obtained when the working fluidis brought from the reference condition to the ambient condition, is given by:
Exphysactual0 F n
i1
xiHFiT0
n
i1
xiSFi G
n
i1
xiHGi T0
n
i1
xiSGi , (3)
where H is the enthalpy, S is the entropy and x the molar ratio of the ith component.
F refers to the liquid phase whereas G refers to the vapor phase, as changes in
composition may occur.
Finally, mixing exergy, which has always a negative value, may be calculated
using algorithms for the mixing enthalpy and entropy:
ExmixmixHT0mixS. (4)
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Fig.
1.
Sketchof
asolarpowersystem.
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nbWnet/Exlu, (9)
where Wnet is the net work produced by the heat exchanger and Exlu is the available
exergy of the working fluid of the heat engine cycle. It is given by the equation:ExluQu[1T0/TR0], (10)
where Qu is the useful transferred heat and TR0 is the ambient temperature of the
Rankine cycle.
The total efficiency of the system is the product of the two separate efficienciesof the subsystems:
ntotWnet/Exi. (11)
Table 1 presents numerical data from the exergetic analysis of the system. Thefirst column gives the input exergy of each component, while the second columngives the output exergy. The difference between the input exergy and the output
exergy is the exergy loss, which is presented in the third column. The fourth column
gives the % exergy loss:
ExlossExinExout
Exin100%.
Finally, the fifth column gives the efficiency of each component based on the secondlaw of thermodynamics:
nExout
Exin100%.
Fig. 2 presents the exergy losses occurring in the different components of the sys-
tem.
As can be seen from the results, the exergy losses in the collectorreceiver subsys-
Table 1
Exergetic analysis of a solar thermal power system [5]
Subsystem Exergy received Exergy Exergy loss Exergy loss Second law
(kW) delivered (kW) (kW) (%) ef ficiency
(1) (2) (3) (4) (5)
Collector Exi=270.82 Exc=78.82 I1=192.19 70.96 29.03
Receiver Exc=78.82 Exu=53.768 I2=24.862 31.618 68.38
Collector Exi=270.82 Exu=53.768 I1,2=217.05 80.146 19.854
receiver
Boiler heat Exu=53.77 Exu=51.845 Ihx=1.92 3.577 96.424
exchanger
Heat engine Exlu=51.845 W=34.511 I3=17.334 33.434 66.566
Total system Exi=270.82 W=34.511 I=236.30 87.254 12.743
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Fig. 2. Losses in the different components of the solar power plant.
tem have the greatest value. An energetic analysis would show that the percentageenergy lost in the heat engine subsystem (72.37%) is greater than that lost in thecollectorreceiver subsystem (56.30%) [5]. The high exergy losses in the collectorreceiver subsystem are due to the fact that the lost energy is of great quality in this
subsystem, while in the heat engine subsystem the lost energy is of low quality.
2.2. Exergetic analysis of wind power systems
The efficiency of a wind turbine depends on its type (i.e., if it is of horizontal orvertical axis), on the rotor diameter and on the wind speed.
Wind turbines are classified according to their nominal power. Table 2 represents
Table 2
Power produced (kW) from three wind turbines for different wind speeds [6]
Wind speed (m/s) Turbine type
600 kW/48 m 750 kW/48 m 1 MW/60 m
5 52 48 86
6 93 95 150
7 153 168 248
8 235 259 385
9 329 362 535
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Fig. 4. Change of the produced power per rotor surface for three different wind turbines, in relation to
the wind speed change.
Fig. 5. Utilization of the winds potential in relation to the wind speed.
is given by the product 1/2rv3, where r is the density of the wind, which is takenequal to 1.225 kg/m3, and v is the wind speed.
It is understandable that wind turbines cannot take advantage of the total power
of the wind (Figs. 5 and 6). According to Betzs law, wind turbine can take advantageof up to 60% of the power of the wind. Nevertheless, in practice, their efficiency isabout 40% for quite high wind speeds. The rest of the energy density of the wind
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Fig. 6. Exergy losses in the different components of a wind turbine.
not obtainable is exergy loss. This exergy loss appears mainly as heat. It is attributed
to the friction between the rotor shaft and the bearings, the heat that the cooling
fluid abducts from the gearbox, the heat that the cooling fluid of the generator abductsfrom it and the thyristors, which assist in smooth starting of the turbine and which
lose 12% of the energy that passes through them.
2.3. Exergy analysis of geothermal power systems
Geothermal steam can be used for electricity production (Fig. 7).
The geothermal fluid (point 1) expands directly in the turbine T, producing workthat is partially needed for the movement of the two compressors of non-condensed
steam. Point 2 is the end of the expansion and is determined by the conditions
imposed in the first mixing condenser M1. Its working pressure is much lower thanatmospheric in order to maximize the produced work. A saturated mixture of CO2steam exits from the top of the condenser (point 3), while the condensed steam exits
from the bottom (point 2w) at the same pressure. The CO2steam mixture is com-pressed and then it is sent to another mixing condenser M2 (point 4) which worksat a higher pressure. The uncondensed substances exit from the top of the second
compressor (point 5) and are disposed to the environment (point 6). The water leav-
ing the second condenser (point 3w) is mixed with the water coming from the firstcondenser and the mixture is pumped to the cooling tower (point 5w). The cooling
water is then re-entered in the mixing condensers and the redundant water is disposed
in the reservoir [7].
The specific exergy (ex) of a fluid is [8]:
ex
i yi(hi
h0i)
T0i yi(si
s0i)
i yiex
ch
i
RT0i y
i ln(giyi), (12)
where y is the molar ratio, h is the enthalpy, T0 is the ambient temperature, s is the
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Fig. 7. Sketch of a geothermal power plant. T: turbine, A: alternator, C1: first compressor, C2: second
compressor, M1: first mixing condenser, M2: second mixing condenser, P: pump, CT: cooling tower.
entropy, R is the gas constant and g is the chemical reactivity coefficient. Thesubscript i refers to the component, the subscript 0 refers to the ambient conditions
and exchi is the chemical exergy of the ith component.
In order to calculate the exergy, the reference condition of each chemical substance
is considered to be at the temperature of 25C and pressure of 1 atm. The evaluation
of exergy losses can be compared with the indirect evaluation of losses, which is
the output exergy minus the input exergy. The exergy loss in our system is:
exergy lossm1{ex1exair(P0, T0)}W, (13)
where m1 is the mass flow rate at point 1, ex1 is the exergy of the geothermal fluidat point 1, exair(P0, T0) is the exergy of the air at ambient conditions and W is the
produced work.
Finally, the efficiency of the geothermal plant is defined as the ratio of the pro-duced power to the exergy of the input geothermal fluid. That is:
nxW
m1{ex1exair(P0, T0)}. (14)
Table 3 presents the results of the exergy analysis for the geothermal power plantunder consideration.
Exergy losses in different components of the system are depicted in Fig. 8.
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Table 3
Power and losses of a typical geothermal plant in Larderello area [7]
Power
a
(kW) Losses
a
(kW) Losses
b
%
Turbine 55,805 12,011 21.52
First compressor 1367 286 2.96
Second compressor 873 171 1.87
Mixing and feed pump 773 312 1.94
Cooling tower 960 7593 20.36
First condenser 7800 13.98
Second condenser 457 1.76
Second condenser disposal stage 526
Cooling tower disposal stage 2809
Total 51,832 31,965
a Produced power is positive while consumed power is negative.b Power losses plus other losses divided by the turbine power.
Fig. 8. Losses in the different components of a geothermal power plant.
3. Comparison between renewable and non-renewable energy sources
An important difference between RES and fossil fuels lies in the fact that renew-
able energy sources are inexhaustible and of low or zero economic value before
being converted to a useful form. Only their cost restricts the device that is necessaryfor the collection of energy, e.g., construction of the network for the collection of
solar radiation [9].
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Fig. 10. Net energy produced by renewable and non-renewable energy systems as a function of time
from the start of the plant construction.
Table 4
Net energy converted in relation to the energy invested on main energy systems [9 11]
Efficiency 1a (%) Ef ficiency 2b (%)
Solar thermal 25 52
Natural gas and oil 20 48
Lignite 34
Nuclear cracking 10
Solar electric 3 12.75
Wind electric 39
Geothermal 35.6
Sources: Slesser M, Hounam I. Solar energy breeders. Nature 1976;244:262 and Koening H. Personal
communication, 1980.a Efficiency 1=(Net produced energy/Energy invested)100%.b Efficiency 2=(Output energy/Input energy)100%.
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tioned is that the plants shown in Table 4 have the same life period. In fact, the
lifetime of systems using RES is greater than that of systems using fossil fuels.
The results are presented in graphical form in Figs. 11 and 12.
The basics used for comparison of these systems is the price per produced energyunit in useful form. With this calculation system, the future value of non-renewable
energy sources is reduced.
4. Conclusion
This work deals with three different kinds of system that use renewable energy
sources as input. Specifically, it deals with systems that use solar energy, wind powerand geothermal energy.
From the results it can be seen that some of the systems appear to have high
efficiencies, and in some cases they are greater than the efficiency of systems usingnon-renewable energy sources. In other cases, like the conversion of solar energy to
electricity, the efficiencies are lower, in order to meet the electricity needs of cities.A significant advantage from the usage of renewable energy systems is that they
are environmentally friendly, since they emit very few dangerous pollutants. On the
other hand, their main disadvantage lies in their incapability to take advantage of a
big part of the available energy. This is balanced by the fact that RES are inexhaust-
ible.
Greece is a country that has sunny weather for most of the year. Moreover, its
Fig. 11. Energy converted by a system in relation to the energy invested in it for different kinds of
energy sources.
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Fig. 12. Energy output in relation to the energy input for different kinds of systems and energy sources.
islands, as well as its coasts, sustain the installation of wind turbines for exploitation
of the high wind capacity existing in these areas. Finally, there are some geothermal
fields, which unfortunately remain unexploited. By using these energy sources,Greece could meet a great part of its energy needs, making its dependence on fossil
fuels significantly smaller.
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