Download pdf - Exergetic analysis and performance evaluation of parabolic trough concentrating solar thermal power plant (PTCSTPP)

at SciVerse ScienceDirect

Energy 39 (2012) 258e273

Contents lists available

Energy

journal homepage: www.elsevier .com/locate/energy

Exergetic analysis and performance evaluation of parabolic trough concentratingsolar thermal power plant (PTCSTPP)

V. Siva Reddy a,*, S.C. Kaushik a, S.K. Tyagi b

aCentre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, Indiab Sardar Swaran Singh National Institute of Renewable Energy, Jalandhar-Kapurthala Road, Wadala Kalan, Kapurthala 144601 (Punjab), India

a r t i c l e i n f o

Article history:Received 9 July 2011Received in revised form16 December 2011Accepted 14 January 2012Available online 17 February 2012

Keywords:Parabolic troughThermal powerExegetic analysisEnergetic analysisPTCSTPPSTPP

* Corresponding author. Tel.: þ91 9891742963.E-mail address: [email protected] (V.S. Reddy

0360-5442/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.energy.2012.01.023

a b s t r a c t

Energetic and exergetic analysis has been carried out for the components of the solar thermal powerplant system (parabolic trough collector/receiver and Rankine heat engine). The energetic and exergeticlosses as well as efficiencies for typical parabolic trough concentrating solar thermal power plant(PTCSTPP) under the specific operating conditions have been evaluated. Operating pressures fora Rankine heat engine have been optimized for maximum efficiency. It has been found that, the energeticand exergetic efficiencies of PTCSTPP increased by 1.49% and 1.51% with increasing pressure from 90 to105 bar respectively. Progression of the STPP from the variable load to full load conditions, the year roundaverage energetic efficiency can be increased from 22.01% to 22.62% for the location of Jodhpur, and incase of Delhi, it can be increased from 20.98% to 21.50%. Year round average exergetic efficiency can beincreased, from 23.66% to 24.32% for the location of Jodhpur and in case of Delhi, it can be increased from22.56% to 23.11%. Land areas required for the 50 MWe thermal power plants are 79.2 ha and 118.8 harespectively for the locations of Jodhpur and Delhi.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

India is the major consumers of electricity due to the rapideconomic growth and large population. A massive increase in baseload electric power generation by conventional coal fired plantswould lead to greenhouse gas emissions. Development of solarenergy power generation technologies on a large scale is requiredfor controlling environmental problems. Then coal can also playa comparablymajor and long-term role for future. So far, 921MWofconcentrated Solar Power (CSP) plants has been installed world-wide and Parabolic Trough Concentrators contributing 93% of totalinstalled capacity. It required direct normal solar radiation and it isthe major drawback of it. A heat storage reservoir must be inte-grated into the oil circuit as suggested by Vogel and Henry [1] toaccess its power around the clock.

Numbers of design and performance evaluation methods ofPTCSTPP are available in literature. Few of them are discussed here.Wittmann et al. [2] proposed a methodology to set up aneconomically optimized bidding strategy at the energy exchange.Quaschning et al. [3] proposed a new method for estimating theoptimized solar field size as a function of the solar irradiance.

).

All rights reserved.

Birnbaum et al. [4] suggested an additional thermal inertia tostabilize the steam temperature for a safe turbine operation. Gauland Rabl [5] investigated the incidence-angle modifier for parabolictroughs to clarify the connection between collector tests andprediction of long-term energy delivery by a collector array.

The exergetic performance analysis not only determines themagnitudes, location and causes of irreversibilities in the plants,but also provides more significant assessment of the individualcomponents efficiency of plant [6]. Siva Reddy et al. [7] presentedcomponent wise energy and exergy analysis review of differentthermal power plants. Kaushik et al. [8] has presented second lawanalysis based on the exergy concept for a solar thermal powersystem. Relevant energy flow and exergy flow diagrams are drawnto show the various thermodynamic and thermal losses. It wasreported that the main energy loss takes place at the condenser ofthe heat engine part whereas the maximum exergy loss takes placein the collector-receiver assembly.

Gupta and Kaushik [9] carried out the energy and exergy anal-ysis for the different components of a proposed conceptual directsteam generation solar trough power plant. It was found that themaximum energy loss takes place in the condenser followed by thesolar collector field (including the trough concentrators andabsorbers), while the maximum exergy loss occurs in the solarcollector field. Palenzuela et al. [10] presented a thermodynamicevaluation of different configurations for coupling parabolic-trough

mailto:[email protected]

www.sciencedirect.com/science/journal/03605442

http://www.elsevier.com/locate/energy

http://dx.doi.org/10.1016/j.energy.2012.01.023



Fig. 1. Direct normal irradiation (DNI). Variation for length of day throughout the yearfor the location Jodhpur.

Fig. 3. Direct normal irradiation (DNI). Variation for length of day throughout the yearfor the location Delhi.

V.S. Reddy et al. / Energy 39 (2012) 258e273 259

solar power plants and desalination facilities in a dry location.Blanco-Marigorta [11] performed exergetic analysis and evaluationof two different cooling technologies for the power cycle ofa 50 MWe solar thermal power plant. Kopac and Hilalci [12] studiedthe effect of ambient temperature on the exergy efficiency of Cat-alagzi power plant in Turkey. The highest exergy losses were re-ported in the boiler, whereas highest energy losses take place in thecondenser. It was also found that an increase in ambient temper-ature decrease the exergy efficiency of all the components ofa power plant except the condenser. In this analysis, they assumeda constant condenser pressure at different ambient temperatureswhich are not consistent with the actual situation. Aljundi [13]studied energy and exergy analysis of Al-Hossien power plant inJordan and showed that maximum exergy destruction occurs in theboiler (77%) followed by the turbine (13%). He also discussed theeffect of varying the reference environment state on the exergyanalysis and found that for moderate change in the reference state,no significant changes in the performance of themajor componentsare realized.

In the present analysis, the tropical locations of Jodhpur andDelhi are selected. The DNI, ambient temperature and windvelocities are collected from EERE website [14]. Direct NormalIrradiation (DNI) variation for length of the day throughout the year

Fig. 2. Dry bulb temperature. Variation for length of day throughout the year for thelocation Jodhpur.

for the location of Jodhpur is illustrated in Fig.1. The DNI of the solarradiation for the location Jodhpur is highest in the month ofFebruary and lowest in August. Highest DNI length of the day is 11 hin June and lowest is 8 h for December. Dry bulb temperaturevariation for length of the day throughout the year for the locationof Jodhpur has been shown in Fig. 2. The DNI variations for thelocation of Delhi have been shown in Fig. 3. The DNI of the solarradiation for the locations Delhi is highest in November and lowestin August. Highest DNI length of the day is 11 h in June and lowest is6 h for December. Dry bulb temperature variation for length of theday throughout the year for the location Delhi has been shown inFig. 4. Monthly average wind speed (m/s) variation for length of theday throughout the year for the locations of Jodhpur and Delhi areshown in Fig. 5. In Jodhpur, wind velocity is high therefore theconvective heat loss of the receiver is higher in Jodhpur comparedto Delhi. The designed DNI for the location of Jodhpur and Delhi aretaken as 870W/m2 and 620W/m2 respectively for parabolic troughthermal power plant model analysis. (This is considered based onthe available average peak solar irradiation throughout the year).

An attempt has been made to develop a model for solar fieldusing the Matlab simulation program for present study. TheRankine power cycle is separately modeled with an engineering

Fig. 4. Dry bulb temperature. Variation for length of day throughout the year for thelocation Delhi.

Fig. 5. Monthly average wind speed (m/s). Variation for length of day throughout theyear for the locations Jodhpur and Delhi.

V.S. Reddy et al. / Energy 39 (2012) 258e273260

equation solver [15]. Detailed exergetic analysis procedure forparabolic trough thermal power plant has been explained. Most ofthe researchers [12,13] assumed a constant pressure in thecondenser even though the ambient temperature varied consider-ably, which is not consistent with the actual situation. The noveltyof present study is that, the exergetic and energetic optimization ofthe operating pressures of the Rankine cycle for the maximumpossible efficiency has been done with an allowable dryness frac-tion in the last stage of the low pressure turbine outlet by consid-ering a variation of condenser pressure with respect to ambienttemperature. Exergetic and energetic performance analysis of thePTCSTPP are compared here for two different cases (variation ofload of STPP and full load operation of STPP).

2. System description of 50 MWe PTCSTPP

The solar thermal power system consisting of two subsystems,the collector - receiver subsystem and Rankine heat enginesubsystem is shown in Fig. 6. The collector receiver subsystem

HPH1

20

17

Boiler

EXP1

HPH2

H

Parabolic Trough Collector Array

CP

CP

ColdTank

a

b

21

HotTank

A A

A

A Collector

Module12

Module1

Fig. 6. Simplified schematic view of the 50 M

consists of parabolic - trough mirror. The solar radiations areconcentrated on the focal line and impinge on an absorber tube.Heat is transferred by heat transfer fluid Therminol VP-1 oil asshown in Fig. 7. Parabolic Trough Collector Array consists of 80loops; each loop contains 4 collectors for Jodhpur and 6 collectorsfor Delhi location on the basis of the DNI availability to obtaindesign operating temperature of Therminol VP-1. Each collector ismade up of twelve modules of 12.27 m long. Parabolic trough hasbeen placed NeS collector axis orientation, because the total annualenergy is greater than the one collected for E-W orientation.Therminol VP-1 oil at 566 K is pumped from a ‘cold’ storage tankthrough the receiver where it is heated to 643 K and then on toa ‘hot’ tank for storage. When power is needed from the plant, hotTherminol VP-1 oil is pumped to a boiler that produces super-heated steam for a conventional Rankine cycle system. From theboiler, Therminol VP-1 oil returned to the cold tank where it isstored and eventually reheated in the receiver. In over analysis thepower plant working in the daytime (6e10 h based on theavailability of solar radiation) only. In a direct two-tank thermalenergy storage system with 3 h of full-load storage capacity can beuse to produce constant power output. In the analysis, PTCSTPP iscompared here for two cases (variation of load of STPP and full loadoperation of STPP).

The Rankine heat engine subsystem consists of high and lowpressure turbine (HPT and LPT), Boiler (B), condensate extractpump (CEP), boiler feed water pumps (BFP), a dearetor, a generator(G), a condenser, three low pressure feed water heaters (LPH), twohigh pressure feed water heaters (HPH) and circulating pumps (CP).The feed water is preheated in three low pressure closed feedwaterheaters, a deaerator, and two high pressure closed feedwaterheaters. It enters the boiler at the maximum steam temperature ofthe power cycle at nearly 643 K. In order to avoid a large humidityfraction in steam at the turbine exhaust, steam reheating is alsoconsidered for modeling. T-S cycle diagram is presented in Fig. 8.

3. Thermodynamic analysis for 50 MWe PTCSTPP

The analysis of the individual components of PTCSTPP (Fig. 6)has been carried out by ignoring the kinetic and potential energychanges and assuming steady state operation.

Deaerator

7

C

LPH1LPH2LPH3

1213

16

18

8

5

2

11

1

4

19 3

22

6

15

BFP

G

109

LPT

14

EXP2CEP

P-Drum

1

HPT

23

25 2924 26 2827

EXP3 EXP4 EXP5

We parabolic trough solar power plant.

Fig. 7. Parabolic trough collector.


3.1. Thermal power plant (TPP) subsystem

In an open flow system there are three types of energy transferacross the control surface namely working transfer, heat transfer,and energy associated with mass transfer and/or flow. The first lawof thermodynamics or energy balance for the steady flow process ofan open system is given by:

X_Qk þ _m

�hi þ

C2i2

þ gZi

�¼ _m

�ho þ C2o

2þ gZo

�þ _W (1)

Where Qk heat transfer to system from source at temperature Tk,and W is the net work developed by the system. The other nota-tions C is the bulk velocity of the working fluid, Z, is the altitude ofthe stream above the sea level, g is the specific gravitational force.

The energetic or first law efficiency hI of a system and/or systemcomponent is defined as the ratio of energy output to the energyinput to system/component i.e.

hI ¼ Desired output PowerInput Power supplied

(2)

Second law analysis is a method that uses the conservation ofmass and degradation of the quality of energy along with theentropy generation in the thermodynamic point of view andimprovement of energy systems. Exergetic analysis is a usefulmethod; to complement but not to replace energy analysis.

Fig. 8. T-S diagram of 50 MWe parabolic trough solar power plant.

The exergy flow for steady flow process of an open system isgiven by

X�1� Ta

Tk

�_Qk þ

Xin

_mJi ¼ JW þXout

_mJo þ _Idestroyed (3)

J ¼ _mh�

h0 � h0o

�� Taðs� s0Þ

i(4)

h0 ¼ hþ C2

2þ gZ (5)

_Idestroyed ¼ Ta _Sgen (6)

where Ji and Jo are exergy associated with mass inflow andoutflows are respectively, JW is useful work done on/by system,_Idestroyed is irreversibility of process and h0 is the methalpy assummation of enthalpy(h). The irreversibility may be due to heattransfer through finite temperature difference, mixing of fluids atdifferent temperature and mechanical friction. Exergetic analysis isan effective means, to pinpoint losses due to irreversibility in a realsituation.

The exergetic or second law efficiency is defined as

hII ¼Actual thermal efficiency

maximum possible ðreversibleÞ thermal efficiency

¼ Exergy outputExergy input

(7)

To analyze the possible realistic performance, a detailed exergyanalysis of the Rankine heat engine has been carried out byignoring the kinetic and potential energy change. For steady stateflow the exergy balance for a thermal system is given as below:

JW ¼Xnk¼1

�1� Ta

Tk

�_Qk þ

Xrk¼1

��_mJ

�i �

�_mJ

�o

k � Ta _Sgen

(8)

The key component of exergetic analysis of thermal power planthas been explained in Appendix A.

Owing to fluctuation in availability of solar radiation, solarthermal power plant to be performs at part load conditions. Themain equations characterizing part-load model for components inthe power cycle based on the mass flow rate of steam are givenbelow.

According to Bartlett [16], the percent reduction in turbine (HPTand LPT) efficiency, as a function of the flow ratio:

% Reduction ¼ 0:191� 0:409��

_m_mref

�þ 0:218�

�_m

_mref

�2

(9)

The change in pump (CEP&BFP) efficiency is expressed asa function of the mass flow ratio [17], for constant speed pumps,

hpump

hpump ref¼ em0 þ 2ð1� em0Þ

�_m

_mref

�� ð1� em0Þ

�_m

_mref

�2

(10)

em0 is a parameter defining the shape of the efficiency curve. Itsvalue is zero for constant speed pumps; in this study it has beenassumed that all the pumps are at constant speed.


Generator efficiency variation form 92.5%e98% approximately.According to Patnode [18], SEGS VI generator efficiency variationhas been given

hgenerator ¼ 0:908þ 0:258� Load� 0:3� Load2 þ 0:12

� Load3 (11)

3.2. Parabolic trough concentrator (PTC) sub system

The total solar power input to parabolic trough is QI receivedby the collector system. It is equivalent to falling on the apertureplane of the collector. The QI is calculated from the beam compo-nent of solar radiation with incident angle effect relations by thefollowing

QI ¼ Ib$Aa$Nc$Nr $Nm$cos q (12)

Aa ¼ ðW� DcoÞL (13)

Where Ib is direct normal irradiation (DNI) and is measured in theplane normal to the sun, The angle of incidence (q) represents theangle between the beam radiation on a surface and the planenormal to that surface, L is mirror length in module.

The total exergetic solar power input to parabolic trough [19]

ExI ¼ QIJs ¼ QI

1� 4

3

�TaTs

�þ 13

�TaTs

�4�(14)

The ratio Js is dimensionless because energy and exergy areexpressed in the same units; however, for some interpretations Jscan be recognized as the amount of kJ of exergy per amount of kJ ofenergy for any radiation at given temperatures Ts and Ta. It can berecognized in the same way as the efficiency of the maximumtheoretical conversion of radiation energy to radiation exergy.Where Tsy5600 K is apparent black body temperature of sun, andTa is atmospheric temperature.

The angle of incidence varies the course of the day (as well asthroughout the year) and heavily influences the performance of thecollectors. The determination method has been explained inAppendix B.

The solar power absorbed Qa by receiver/absorber of solarparabolic trough collector field can be estimated by

Qa ¼ Ib$KðqÞ$Aa$Nc$Nr $Nm$gr$sg$aa$IF$ hd$End Loss (15)

The total exergetic solar power absorbed by the receiver/absorber of solar parabolic trough collector field

Exa ¼ QaJa ¼ Qa

1� Ta

Tr

�(16)

The end losses are function of the focal length of the collector,the length of the collector, and the incident angle [17]:

End Loss ¼ 1� f$tan qLsc

(17)

Incident Angle Modifier (K(q)):The incident angle affects to the direct normal irradiation on the

mirror aperture. This effect is accounted for the incident anglemodifier for Euro trough collector [20] ([20] sited in [21])

KðqÞ ¼ cos q� 2:859621� 10�05$q2 � 5:25097� 10�04$q

(18)

The useful thermal power gain Qu by thermic fluid can bedetermined by

Qu ¼ mfCpðTe � TiÞ (19)

Qu ¼ Fr½Qa � UlArðTi � TaÞ� (20)

Ar ¼ pDi L (21)

The collector heat removal factor Fr for considered segment isgiven by

Fr ¼ mfCpUlAr

2641� e

��

UlArF0mf Cp

�375 (22)

The collector efficiency factor F0 is given by

F0 ¼ 1=Ul

"1Ul

þ Do

Dihfþ Do

2krln�Do

Di

�#(23)

The useful exergetic gain Exu by thermic fluid through segment

Exu ¼ mf ½Je �Ji� ¼ _mf ½ðhe � hiÞ � Taðse � siÞ� (24)

The heat loss from the PTC collector is basically due to heat lossfrom the absorber tube. Absorber tube is enveloped with vacuumby glass tube to reduce heat loss. The heat loss for a given Tr of anabsorber tube depends on the thermal resistances between theabsorber tube surface and the surroundings. The one dimensionaltheoretical heat loss model gives slightly lower Ul value, whichmaybe accounted for by the conduction losses through the receiversupport brackets. Accordingly, a reliable analytical calculation ofheat losses is impossible. However, the value of Ul which are10e12% higher [22] than Ul calculated by one dimensional modelmay be taken. The heat loss coefficient Ul for various values of Trranging from 350 to 800 K calculated iteratively [23] by solving thefollowing equations (25)e(28):

Ql ¼ UlpD0ðTr � TaÞL (25)

q0loss ¼ q0c�s ¼ pDcohwðTco � TaÞ þ εcpDcos�T4co � T4s

�(26)

q0loss ¼ q0c�c ¼ 2pkcðTci � TcoÞ=lnðDco=DciÞ (27)

q0loss ¼ q0r�c ¼ pDos�T4r � T4ci

�.1εr

þ Do

Dci

�1εc

� 1��

(28)

To access for finding outside/inside convective heat transfercoefficient of the absorber/receiver tube are given in Appendix C:

4. Exergetic and energetic analysis of 50 MWe PTCSTPP

The solar thermal power system considered in the present studyhas 80 loops of the parabolic trough collector array oriented NeSaxis and E-W operating in a tracking mode. The analysis wascarried out for locations of Jodhpur and Delhi. In the present model,Euro-Trough Collector (receiver tubes, reflector and optical)parameters are considered. The various design parameters of theparabolic collector loop are given in Table 1. Heat transfer fluid inthe solar field is taken as Therminol VP-1, because it is the only heattransfer fluid working between temperatures 285 Ke673 K andthermally stable. Inlet temperature of Therminol VP-1 oil in PTChas taken as 566 K. Electric power consumed by circulating pumpsfor flow of heat transfer fluid in the absorber tubes has also beenconsidered.

Table 2Nominal values for the 50 MWe steam power cycle [21].

High pressure turbine inlet temperature (K) 643High pressure turbine inlet pressure (IP) (bar) 90High pressure turbine efficiency (%) 85.5Low pressure turbine efficiency (%) 89.5Electro-mechanical efficiency (%) 98Extraction point pressuresExtraction no. 2 (bar) 0.5044 � IPExtraction no. 3 (bar) 0.2289 � IPExtraction no. 6 (bar) 0.0972 � IPExtraction no. 7 (bar) 0.0403 � IPExtraction no. 8 (bar) 0.0136 � IPExtraction no. 9 (bar) 0.003846 � IPPressure drop in extraction and reheating lineExtraction line no. 2 (%) 2.5Extraction line no. 3 (%) 3Reheating line (%) 11.75Extraction line no. 6 (deaerator) (%) 4.5Extraction line no. 7 (%) 3Extraction line no.8 (%) 3Extraction line no. 9 (%) 3.5Condenser extract pump (CEP)Isentropic efficiency 75Electro-mechanical efficiency 98Boiler Feedwater pump (BFP)Isentropic efficiency 78Electro-mechanical efficiency 98Low/high pressure closed feedwater heatersTerminal temperature difference (�C) 1.5Drain cooling approach (�C) 5.0Condenser Condensing pressure (bar) 0.08Steam generator Thermal efficiency (%) 98Nominal Steam mass flow rate (kg/s) 63.42Power consumption for cooling tower system 0.03 � output PowerPower consumption for circulating pumps(CP) 0.01 � output Power

Table 1Geometrical and optical parameters for the collector loop considered [21,25,26].

Absorber tube outer diameter (m) 0.07Absorber tube inner diameter (m) 0.065Glass envelope outer diameter (m) 0.115Glass envelope inner diameter (m) 0.109Design point parameters

JodhpurNumber of collectors 4Solar beamradiation (W/m2)

870

Longitude (�) 73.017ELatitude (�) 26.28NIncidence angle(NeS axisorientation) (�)

12.03

Design point parametersDelhi

Number of collectors 6Solar beamradiation (W/m2)

620

Longitude (�) 77.18ELatitude (�) 28.57NIncidence angle(NeS axisorientation) (�)

9.48

Number of modules per collector 12Width of the module (m) 5.76Length of every module (m) 12.27Mirror length in every module (m) 11.9Ambient temperature (�C) 31Incidence angle (NeS axis orientation) (�) 12.03Focal length (m) 1.71Drive HydraulicOptical parameters for the collectorIntercept factor 0.92Mirror reflectivity (gr) 0.92Glass transmissivity (sg) 0.945Solar absorptivity (aa) 0.94Peak optical efficiency (ho) 0.75Thermal emissivity (εr)[21] 0.04795 þ 0.0002331

� Tr (�C)Losses due to shading of heat collector element

(HCE) by dust on the envelope hd

0.98


The heat engine Rankine cycle model is considered for singlereheating for avoiding dryness fraction in the last stages of lowpressure turbine. According to the size of the cycle, the feed waterwill be preheated through three low pressure closed feedwaterheaters, a deaerator, and two high pressure closed feedwaterheaters. Design parameters like operating pressures, temperaturesand isentropic efficiency of turbine and pumps are considered asshown in Table 2, from the Montes et al. [21].

The maximum steam temperature in the power cycle is nearly643 K. Turbine inlet pressure is 90 bar and condensing pressure of0.08 bar is referred to water cooled condenser. Electric powerconsumed by the cooling tower pump has been taken into accountas it is one of the main auxiliary power consumptions of the solarthermal power plant. Heat exchangers are defined by temperaturedifferences between streams. Nominal values adopted for TTD(terminal temperature difference), and DCA (drain cooling approach)are assumed to be respectively 1.5 K and 5 K. These values maychange when heat exchangers are working at part-load conditions.

Table 3 shows the results of energetic and exergetic analysis of50MWe PTCSTPP at HPT inlet pressure of 90 bar and temperature of643 K. Electric power consumption for circulating pump (CP) of336 kW, cooling tower pumps of 1.2 MWhave been considered. It isfound from the results that the main energetic power loss takesplace at the heat engine circuit through the condenser which is82.13MW, followed by the collector-receiver system, i.e. 72.75MW,although the power losses loss at other sections of the system isalso not so small. The energetic efficiency of PTC circuit is 66.89%,and overall energetic efficiency of PTCSTPP is 24.01%. However, theresults of the exergetic analysis of PTCSTPP show a differentbehavior. Apparently, the collector-receiver assembly is the main

part where the exergetic power losses are maximum (124.47 MW)followed by the condenser having low exergetic power losses of4.48MW. The percentage exergetic efficiency of PTC circuit is 39.09%,and overall exergetic efficiency of PTCSTPP is 25.81%. Apart fromthe above analysis, the energetic power loss in feedwater heatersand deaerator are negligible, but exergetic power loss is not sosmall. These results show similar trend as reported by Xu et al. [27].

4.1. Model validation

Present model was validated with the model developed byMontes et al. [21] for 50 MWe thermal power plant and results ofparticular design for that location are presented in Table 4. It is clearthat the results obtain by model developed for Jodhpur and Delhilocations (power block efficiency and solar file efficiency) are veryclose to the Montes et al. [21] model. More discussion onimprovement in the power cycle efficiency by raising the turbinepressure is analyzed in next section.

4.2. Improvement potential for 50 MWe PTCSTPP

It is evident to the results of exergetic analysis that large exer-getic losses take place in the solar collector and receiver. Theexergetic loss in the collector can be reduced by increasing theconcentration ratio of collector which is limited due to material anddesign considerations like heat transfer fluid availability. The effi-ciency of the heat engine can be increased by the optimization ofoperating pressures of the cycle. The analysis has been carried outfor different condenser temperatures with optimum pressurevalue, determined at outlet steam having a dryness fraction morethan 0.88 at LPT outlet.

Fig. 9 shows the variation of exergetic efficiency with highpressure turbine (HPT) at inlet pressure for different condenser

Table 3Results of 50 MWe PTCSTPP (at turbine inlet pressure 90 bar and 643 K).

S.No Components Energetic powerinput (kW)

Energetic poweroutput (kW)

Energetic powerloss (kW)

Exergetic powerinput (kW)

Exergetic poweroutput (kW)

Exergetic powerloss (kW)

Energeticefficiency(hI)%

Exergeticefficiency(hII) %

1 Collector 219,736 159,776 59,960 204,365 114,845 89,520.5 72.71 56.202 Receiver 159,776 146,981 12,795 114,845 79,890.6 34,953.93 91.99 69.563 Collector-Receiver 219,736 146,981 72,755 204,365 79,890.6 124,474.4 66.89 39.094 Boiler 146,981 143,934 3047 79,890.6 67,787 12,103.57 97.93 84.855 High pressure

turbine(HPT)18,964 16,214 2750 17,892 16,214 1678 85.50 90.62

6 Low pressureturbine(LPT)

44,995 40,271 4724 44,660 40,271 4389 89.50 90.17

7 Condensate feedwater pump(CFP)

57.33 42.99 14.34 57.33 43.72 13.61 74.99 76.26

8 Boiler feed waterpump(BFP)

992 773.7 218.3 992 846 146 77.99 85.28

9 High presure feedwater heater (HPH1)

12,942 12,942 0 5631 5291 340 100.00 93.96


10,173 10,173 0 3886 3638 248 100.00 93.62

11 Low presure feedwater heater (LPH1)

7226 7226 0 1995 1728 267 100.00 86.62


6798 6798 0 1401 1140 261 100.00 81.37


5761 5761 0 745.5 523.1 222.4 100.00 70.17

14 Deaerator 46,237 46,237 0 7672 7397 275 100.00 96.4215 Condenser e e 82,128 e e 4477 e e

17 Over all power plant 219,736 52,749 166,987 204,365 52,749 151,616 24.01 25.81

Fig. 9. Variation of exergetic efficiency with high pressure turbine inlet pressure forvarious condenser temperatures.


temperatures varied from 309 K to 321 K at HPT inlet temperature643 K. With all condenser temperatures, exergetic efficiency isincreasing with respect to HPT inlet pressure. By the increment ofcondenser temperatures, exergetic efficiency decreases with lowercondenser temperatures. Variation of energetic efficiency with HPTinlet pressure for various condenser temperatures from 309 K to321 K at HPT inlet temperature 643 K has been shown in Fig. 10.With all condenser temperatures, energetic efficiency is increasingwith HPT inlet pressure. By the increase of condenser temperatures,energetic efficiency decreases.

Fig. 11 reveals the variation of dryness fractions with HPT inletpressure for various condenser temperatures from 309 K to 321 K atHPT inlet temperature of 643 K. At all condenser temperatures,dryness fraction is decreasing with respect to HPT inlet pressure. Bythe decrease of condenser temperatures, dryness fraction increaseswith lower condenser temperatures. The solar thermal power plantoperating with high DNI condition only, and ambient conditionsmore than 309 K; if the temperature gap between the ambient andcondenser is intolerable than power consumption for cooling towerpumps increases. The operating temperature and pressure of the

Table 4Geometrical parameters for the collector loop considered for model validation.

Given designed atmospheric conditions of Montes et al. [21]:Design point parameters for the 50 MWe solar thermal power plant.Design point parameters (Almeria, Spain)Solar beam radiation (W/m2) 850Longitude (�) 2.35 WLatitude (�) 37.09 NZenith angle (�) 13.85Ambient temperature (�C) 25Incidence angle (NeS axis orientation) (�) 13.65

From the Monteset al. [21]

From presentmodel

Number of loops 80 80Solar thermal power (MWth) 150.3 150.0Power block thermal demand (MWth) 142.6 144.03Power cycle efficiency (%) 38.21 37.84Solar filed efficiency (%) 70.23 70.41

Fig. 10. Variation of energetic efficiency with high pressure turbine inlet pressure forvarious condenser temperatures.

Fig. 11. Variation of dryness fraction with high pressure turbine inlet pressure forvarious condenser temperatures.


condenser are considered for these analyses are 315 K and 0.082 barrespectively. At this condenser condition, HPT inlet pressure canincrease up to 105 barwith an allowable dryness fraction of above 0.88.

Table 5 shows the property data of the stream state points fora 50 MWe steam power plant cycle at the HPT inlet pressure andtemperature 105 bar and 643 K respectively. Table 6 shows theresults of energetic and exergetic analysis of 50 MWe PTCSTPP atHPT pressure of 105 bar and 643 K. The energetic efficiency ofPTCSTPP is increased by 1.49%, and the exergetic efficiency ofPTCSTPP is increased by 1.51% as compared to HPT pressure of90 bar. As far as the exergetic efficiency of feed water heaters andthe boiler of the Rankine heat engine are concerned, it is increasedwith increasing operating pressure whereas exergetic power loss isdecreased.

Table 5Stream data for 50 MWe steam power cycle (at turbine inlet pressure 105 bar and 643 K

S. ID Fluid Mass flow(kg/s)

Temperature(K)

Pressure(bar)

1 Steam 65.52 643 1052 Steam 7.405 556.3 52.963 Steam 4.961 494.9 24.034 Steam 53.16 494.9 24.035 Steam 53.16 643 21.216 Steam 3.254 552.5 10.217 Steam 3.202 460.7 4.2328 Steam 2.845 382.9 1.4289 Steam 2.537 349.08 0.403810 Steam 41.32 315 0.0820511 Water 49.9 315 0.0820512 Water 49.9 315.08 10.2113 Water 49.9 346.72 10.2114 Water 49.9 380.5 10.2115 Water 49.9 416.1 10.2116 Water 65.52 451.8 10.2117 Water 65.52 454.5 137.618 Water 65.52 491.8 137.619 Water 65.52 537.5 137.620 Water 7.405 496.8 51.3721 Water 7.405 494.9 24.0322 Water 12.37 459.5 23.3123 Water 12.37 453.8 10.2124 Water 3.202 385.5 4.10525 water 3.202 382.9 1.42826 Water 6.047 351.72 1.38527 Water 6.047 349.08 0.403828 Water 8.583 320.08 0.391729 Water 8.583 314.97 0.08205

5. Analysis for year round performance of 50 MWe PTCSTPP

The energetic and exergetic efficiencies of design power plantsare about 24.23% and 26.20% respectively, but the power plantperformance at actual DNI condition and given incident angle isvaried throughout the year. Based on the full year use of solarthermal power, heat engine cycle load will also change. So, in thisanalysis year round performance of PTCSTPP two cases of variableload and full load (with thermal storage) operation of STPP havebeen compared, for the locations of Jodhpur and Delhi.

The effect of solar incidence angle in the winter season is clearlyshown while comparing the Fig. 12 and Fig. 13 for the location ofJodhpur and Fig. 14 and Fig. 15 for the location of Delhi. Effect ofincident angle at Delhi is higher than the Jodhpur. With a fixednorth-south orientation and east-west single-axis tracking system,the incidence angle is much larger at noon in December thanmorning or evening hours, its variations results are illustrated byFigs. 13 and 15. Variation of efficiencies with mass flow rate ofsteam for various components in PTCSTPP has been shown inFig. 16. Variation of motor and generator efficiencies is low withmass flow rate of the steam. Isentropic efficiency of turbines (HPT,LPT) varies from 0.76% to 0.89%; isentropic efficiency of pumps (BFP,CEP) varies from 0.21% to 0.78% for the operation STP from thepartial load to full load.

Energetic and exergetic efficiency of the PTC for the locationJodhpur has been shown in Fig. 17 and Fig. 18. Energetic and exer-getic efficiency of PTCSTPP has been shown in Fig. 19 and Fig. 20 forthe Jodhpur location. In the month of April, May and June,maximum energetic and exergetic efficiencies, maximum length ofthe solar day and low fluctuation in efficiency, are obtained,because the incident angle effect is the minimum compared toother months. In the month of December and January, minimumenergetic and exergetic efficiencies due to high incident angle.

The overall energetic efficiency of the PTC varies from 50.23% to67.97%, and exergetic efficiency varies from 30.59% to 39.13%, and

).

Sp. enthalpy(kJ/kg)

Sp. entropy(kJ/kg K)

Energeticpower (kW)

Exergeticpower (kW)

2983 6.021 195,468 77,7772854 6.061 21,131 77432722 6.11 13,505 44612722 6.11 144,708 47,8053179 6.996 168,981 57,9923006 7.033 9780 29512833 7.086 9069 22992659 7.155 7564 14892484 7.23 6301 827.82296 7.326 94,858 4511175.8 0.5996 8771 85.62177.1 0.5995 8839 137.4309.4 0.9995 15,441 769.2451.3 1.39 22,523 2023602.8 1.77 30,081 3903757.9 2.128 49,660 8279772.3 2.137 50,864 9309941.5 2.486 61,691 13,290

1155 2.901 75,700 19,158961.7 2.547 7121 1516961.7 2.554 7121 1501792.5 2.2 9799 1722792.5 2.204 9799 1708472 1.446 1511 142.7472 1.446 1511 141.9329.6 1.06 1933 106.1329.6 1.06 1933 105.4197.2 0.6527 1692 25.69197.2 0.6534 1692 24.04

Table 6Results of 50 MWe PTCSTPP (at turbine inlet pressure 105 bar and 643 K).

S. No Components Energetic powerinput (kW)

Energetic poweroutput (kW)

Energetic powerloss (kW)

Exergetic powerinput (kW)

Exergetic poweroutput (kW)

Exergetic powerloss (kW)

Energeticefficiency(hI)%

Exergeticefficiency(hII) %

1 Collector 219,736 159,776 59,960 204,365 114,845 89,520.5 72.71 56.202 Receiver 159,776 146981 12,795 114,845 79,890.6 34,953.93 91.99 69.563 Collector-Receiver 219,736 146,981 72,755 204,365 79,890.6 124,474.4 66.89 39.094 Boiler 146,981 144,041 2940 79,890.6 68,806 11,084.6 97.99 86.125 High pressure

turbine(HPT)18,860 16,125 2735 17,768 16,125 1643 85.50 90.75

6 Low pressureturbine(LPT)

46,267 41,409 4858 45,916 41,409 4507 89.50 90.18

7 Condensate feedwater pump(CFP)

67.93 50.95 16.98 67.93 51.82 16.11 75.00 76.28

8 Boiler feedwater pump(BFP)

1204 939.3 264.7 1204 1030 174 78.015 85.55


14,009 14,009 0 6227 5868 359 100 94.23


10,827 10,827 0 4240 3981 259 100 93.89


7558 7558 0 2156 1880 276 100 87.20


7082 7082 0 1524 1254 270 100 82.28


6602 6602 0 907.5 631.8 275.7 100 69.62

14 Deaerator 49,660 49,660 0 8562 8279 283 100 96.6915 Condenser e e 81313 e e 4440 e e

17 Over all power plant 219,736 53,550 166186 204,365 53,550 150,815 24.37 26.20


the overall exergetic efficiency of the PTCSTPP varies from 15.32% to26.81%, and energetic efficiency varies from 14.25% to 24.89%.Energetic and exergetic efficiency of the PTC for the Delhi locationhas been shown in Fig. 21 and Fig. 22. Energetic and exergeticefficiency PTCSTPP has been shown in Fig. 23 and Fig. 24. for theDelhi location. In April, May and June, maximum energetic andexergetic efficiencies, maximum lengths of the solar day is ob-tained, because the incident angle effect is minimum as comparedto other months. Owing to high incident angle, energetic andexergetic efficiencies are minimum in the month of December andJanuary. The overall energetic efficiency of the PTC varies from42.27% to 65.59%, and exergetic efficiency varies from 27.42% to38.03%. The overall exergetic efficiency of the PTCSTPP varies from13.85% to 25.84%, and energetic efficiency varies from 12.90% to24.05%.

Fig. 12. Variation of DNI, cos (Ѳ) and DNI cos (Ѳ) at Jodhpur on may 15, 2009.

The performance of the PTCSTPP has yield better efficiency atJodhpur as compared to Delhi, this may due to the high DNIavailability, and less effect of incidence angle as compared to Delhi.Table 7 revealed detailed comparative performance results of50 MWe PTCSTPP for the locations of Jodhpur and Delhi. At a fullload condition of thermal power input to the STPP, it has potentialto increase the electrical energy generation capacity up to3050.4 MWhe at Jodhpur and 2755.42 MWhe at Delhi locations. Forthe Jodhpur location with 79.2 ha land area, has been estimated, toproduce 113.6 � 103 MWhe at a solar radiative energy input of502.2 � 103 MWh per annum. In the similar fashion for the Delhilocation, it has been estimated about 118.8 ha land area, to produce115.7� 103 MWhe at a solar radiative energy input 538 � 103 MWhper annum. Energetic efficiency of the PTCSTPP in the locationJodhpur and Delhi with variation of load 22.01%, 20.98% and with

Fig. 13. Variation of DNI, cos (Ѳ) and DNI cos (Ѳ) at Jodhpur on December 15, 2009.

Fig. 14. Variation of DNI, cos (Ѳ) and DNI cos (Ѳ) at Delhi on may 15, 2009.

Fig. 15. Variation of DNI, cos (Ѳ) and DNI cos (Ѳ) at Delhi on December 15, 2009.

Fig. 16. Variation of efficiencies with mass flow rate of steam for various componentsin PTCSTPP.

Fig. 17. Variation of PTC energetic efficiencies for length of day throughout the year forthe Jodhpur location.

Fig. 18. Variation of PTC exergetic efficiencies for length of day throughout the year forthe Jodhpur location.

Fig. 19. Variation of PTCSTPP energetic efficiencies for length of day throughout theyear for the Jodhpur location.


Fig. 20. Variation of PTCSTPP exergetic efficiencies for length of day throughout theyear for the Jodhpur location.

Fig. 21. Variation of PTC energetic efficiencies for length of day throughout the year forthe Delhi location.

Fig. 22. Variation of PTC exergetic efficiencies for length of day throughout the year forthe Delhi location.

Fig. 23. Variation of PTCSTPP energetic efficiencies for length of day throughout theyear for the Delhi location.

Table 7Year round comparative performance analysis results of a 50 MWe PTCSTPP, for thetropical locations of Jodhpur and Delhi.

S. No Parameters for a year Jodhpur Delhi

Energetic Exergetic Energetic Exergetic

1 Solar radiative energyinput (MWh)

502,221.13 467,163.08 538,175.24 500,747.15

2 Useful thermal energyoutput of PTC (MWhth)

310,898.28 169,016.99 317,638.84 173,197.15

3 Overall year roundefficiency of PTC (%)

61.90 36.18 59.02 34.58

4 Electrical energy output(Variation of load)(MWhe)

110,552.02 110,552.02 112,960.4 112,960.4

5 Overall year roundefficiency of plant(Variation of load) (%)

22.01 23.66 20.98 22.56

6 Electrical energy output(Full load) (MWhe)

113,602.42 113,602.42 115,715.82 115,715.82

7 Overall year roundefficiency of plant(Full load) (%)

22.62 24.32 21.50 23.11

8 Total Collectorfield area

720,000m2 108,0000m2

9 Required Landarea (hectare)

79.2 118.8

Bold represents the efficiency variation with variable load to full load condition.

Fig. 24. Variation of PTCSTPP exergetic efficiencies for length of day throughout theyear for the Delhi location.



fixed load 22.62%, 21.50% respectively. Exergetic efficiency of thePTCSTPP in the location Jodhpur and Delhi with variation of load23.66%, 22.56% and with fixed load 24.32%, 23.11% respectively.

6. Conclusion

The energetic and exergetic analysis has been carried out for theyear round operation of PTCSTPP for the locations of Jodhpur andDelhi in India. It is found from the results that the main energeticpower loss takes place at the heat engine circuit through thecondenser, followed by the collector-receiver system, whereas theresult of the exergetic analysis of PTCSTPP shows a differentbehavior. Apparently, the solar collector-receiver assembly is themain area where the exergetic power losses are greatest. By theincrease of the operating pressures of the STPP from 90 bar to105 bar pressure, the energetic efficiency of PTCSTPP is increased by1.49%, and exergetic efficiency of PTCSTPP is increased by 1.51%.

For the both locations in the month of April, May and June,maximum energetic and exergetic efficiencies, maximum length ofthe solar days are obtained, because the effect of incident angle isrelatively minimum as compared to other months. Owing to highincidence angle, energetic and exergetic efficiencies are minimumin the month of December and January. Progression of the STPPfrom the variable load to full load condition the year round averageenergetic efficiency can be increased, from 22.02% to 22.62%respectively for the location of Jodhpur, and in case of Delhi, it canbe increased from 20.98% to 21.50% respectively. Exergetic effi-ciency can be increased, from 23.66% to 24.32% respectively for thelocation of Jodhpur and in case of Delhi, it can be increased from22.56% to 23.11% respectively. For the over all year round operationof PTCSTPP, Jodhpur location is found to be better as compared toDelhi in performance. Land areas required for the 50 MWe thermalpower plants are 79.2 ha and 118.8 ha respectively for the locationsof Jodhpur and Delhi.

Nomenclature

Aa Absorber Area (m2)Ar Receiver Area (m2)C Concentration ratioCp Specific heat of Therminol VP-1 (kJ/kg.K)Do Receiver outside diameter (m)Di Receiver inside diameter (m)Dci Glass cover inside diameter (m)Dco Glass cover outside diameter (m)ExI Exergetic solar power input to parabolic trough (kW)Exa Exergetic solar power absorbed by the receiver/absorber

(kW)Exu Exergetic thermal power gain by thermic fluid (kW)Fr Collector heat removal factorF0 Collector efficiency factorIF Intercept FactorIb Solar beam radiation (DNI) (W/m2)_Idestroyed Irreversibility (kW)K(q) Incident Angle ModifierKf Thermal conductivity of Therminol VP-1 (W/m.K)Kr Thermal conductivity of Receiver (W/m.K)L Mirror length in module (m)mf Mass flow rate ofTherminol VP-1 (kg/s)_m Mass flow rate of steam in Rankine power cycle(kg/s)_mref Design mass flow rate of steam in Rankine power

cycle(kg/s)Nc Number of collectorsNr Number of rows

Nm Number of modulesQI Solar power input to parabolic trough (kW)Qa Solar power absorbed by receiver/absorber (kW)Qu Useful thermal power gain by thermic fluid (kW)Ts Sun temperature (K)Ti Therminol VP-1 inlet temperature (K)Te Therminol VP-1 outlet temperature (K)Tr Receiver temperature (K)Ta Atmospheric temperature (K)Ul Heat loss coefficient (W/m2.K)W Width of parabolic trough (m)J Exergetic availability (kW)gr Reflectivity of reflectorsg Transmissivity of glassaa Absorptivity of absorberqz Zenith angled Declination angleu Hour angle

Abbreviations

B BoilerBFP Boiler feed water pumpsCP Circulating pumpsCSP Concentrated Solar PowerCEP Condensate extract pumpDCA Drain cooling approachDNI Direct Normal IrradiationEES Engineering equation solverEERE Energy Efficiency & Renewable energyEXP Expansion valveG GeneratorHPH High pressure feed water heatersHPT High pressure turbineLPT Low pressure turbineLPH Low pressure feed water heatersPTC Parabolic trough concentratorSTPP Solar thermal power plantPTCSTPP Parabolic trough concentrating solar thermal power plantTTD Terminal temperature difference

Appendix A. Thermal power plant key components exergeticanalysis

A.1 The exergy balance for boiler:

The exergy flow equation for boiler becomes:

0 ¼ _mtðJa �JbÞ � _m19ðJ1 �J19Þ � _m4ðJ5 �J4Þ � Ta _Sgen(29)

This gives:

Ta _Sgen ¼ ��_mtðha � hbÞ � _m19ðh1 � h19Þ � _m4ðh5 � h4Þ

��

Ta _mtðsa � sbÞ � _m19ðs1 � s19Þ � _m4ðs5 � s4Þ�

(30)

_Idestroyed ¼ Ta _Sgen (31)

The second law efficiency is:

hII;Boiler ¼ 1�_Idestroyed

_mf ðJa �JbÞ

¼ _m19ðJ1 �J19Þ � _m4ðJ5 �J4Þ_mf ðJa �JbÞ

(32)


A.2 The exergy balance for the high pressure turbine (HPT):

_WHPT ¼ _m1ðJ1 �J2Þ þ�_m1 � _m2

�ðJ2 �J3Þ � Ta _Sgen (33)

_Idestroyed ¼ Ta _Sgen ¼ Ta�_m1ðs2 � s1Þ þ

�_m1 � _m2

�ðs3 � s2Þ(34)


hII;HPT ¼ 1�_Idestroyed

_m1ðJ1 �J2Þ þ ð _m1 � _m2ÞðJ2 �J3Þ

¼_WHPT

_m1ðJ1 �J2Þ þ ð _m1 � _m2ÞðJ2 �J3Þ(35)

A.3 The exergy balance for the Low pressure turbine (LPT):

_WLPT ¼ _m5ðJ5 �J6Þ þ�_m5 � _m6

�ðJ6 �J7Þ ��_m5 � _m6

� _m7�ðJ7 �J8Þ �

�_m5 � _m6 � _m7 � _m8

�ðJ8 �J9Þ� �

_m5 � _m6 � _m7 � _m8 � _m9�ðJ9 �J10Þ � Ta _Sgen

(36)_Idestroyed ¼ Ta _Sgen ¼ Ta�_m5ðs6 � s5Þ þ

�_m5 � _m6

�ðs7 � s6Þ� �

_m5 � _m6 � _m7�ðs8 � s7Þ

� �_m5 � _m6 � _m7 � _m8

�ðs9 � s8Þ� �

_m5 � _m6 � _m7 � _m8 � _m9�ðs10 � s9Þ

(37)


hII;LPT ¼ 1�_Idestroyed

Exergy input¼

_WLPT

Exergy input(38)

A.4 The exergy balance for the condenser:

0 ¼ _m10ðJ10 �J11Þ �Xnk¼1

�1� Ta

Tk

�Qk � Ta _Sgen (39)

_Idestroyed ¼ Ta _Sgen ¼ �_m10ðh10 � h11Þ � Ta

�_m10ðs10 � s11Þ

��

Xnk¼1

�1� Ta

Tk

�_Qk (40)


hII;Con ¼ 1�_Idestroyed

_m10ðJ10 �J11Þ(41)

A.5 The exergy balance for the condensate extract pump (CEP):

� _WCEP ¼ _m11ðJ11 �J12Þ � Ta _Sgen (42)

_Idestroyed ¼ Ta _Sgen ¼ _m11ðJ11 �J12Þ þ _WCEP

¼ Ta�_m11ðs12 � s11Þ

(43)


hII;CEP ¼ 1�_Idestroyed

_WCEP¼ _m11ðJ11 �J12Þ

_WCEP(44)

A.6 The exergy balance for the boiler feed water pump (BFP):

� _WBFP ¼ _m16ðJ16 �J17Þ � Ta _Sgen (45)

_Idestroyed ¼ Ta _Sgen ¼ _m16ðJ16 �J17Þ þ _WBFP

¼ Ta�_m17ðs17 � s16Þ

(46)


hII;BFP ¼ 1�_Idestroyed

_WBFP¼ _m16ðJ16 �J17Þ

_WBFP(47)

A.7 The exergy flow equation for the high presure feed water heater(HPH1) system:

0 ¼ _m2ðJ2 �J20Þ � _m18ðJ19 �J18Þ � Ta _Sgen (48)

_Idestroyed ¼ Ta _Sgen ¼ ��_m2ðh2 � h20Þ � _m18ðh19 � h18Þ

�� Ta

�_m2ðs2 � s20Þ � _m18ðs19 � s18Þ

�(49)


hII;HPH1 ¼ 1�_Idestroyed

_m2ðJ2 �J20Þ¼ _m18ðJ19 �J18Þ

_m2ðJ2 �J20Þ(50)

A.8 The exergy flow equation for the high presure feed water heater(HPH2) system:

0 ¼ _m3ðJ3 �J22Þ þ _m21ðJ21 �J22Þ� _m17ðJ18 �J17Þ � Ta _Sgen (51)

_Idestroyed ¼ Ta _Sgen ¼ ��_m3ðh3 � h22Þ þ _m21ðh21 � h22Þ

� _m17ðh18 � h17Þ�� Ta

�_m3ðs3 � s22Þ

þ _m21ðs21 � s22Þ � _m17ðs18 � s17Þ�

(52)


hII;HPH2 ¼ 1�_Idestroyed

_m3ðJ3 �J22Þ þ _m21ðJ21 �J22Þ

¼ _m17ðJ18 �J17Þ_m3ðJ3 �J22Þ þ _m21ðJ21 �J22Þ

(53)

A.9 The exergy flow equation for the low presure feed water heater(LPH1) system:



� _m12ðh13 � h12Þ�� Ta

�_m9ðs9 � s28Þ

þ _m27ðs27 � s28Þ � _m12ðs13 � s12Þ�

(55)


hII;LPH1 ¼ 1�_Idestroyed

_m9ðJ9 �J28Þ þ _m23ðJ23a �J28Þ


(56)





� _m14ðh14 � h13Þ�� Ta

�_m8ðs8 � s26Þ

þ _m25ðs25 � s26Þ � _m14ðs14 � s13Þ�

(58)



_m8ðJ8 �J26Þ þ _m25ðJ25 �J26Þ


(59)


0 ¼ _m7ðJ7 �J24Þ � _m14ðJ15 �J14Þ � Ta _Sgen (60)

_Idestroyed ¼ Ta _Sgen

¼ ��_m7ðh7 � h24Þ � _m14ðh15 � h14Þ

�� Ta

�_m7ðs7 � s24Þ � _m14ðs15 � s14Þ

�(61)



_m7ðJ7 �J24Þ¼ _m14ðJ15 �J14Þ

_m7ðJ7 �J24Þ(62)

A.12 The exergy flow equation for the deaerator

It is an adiabatic mixing chamber where a hot streams 23, 6 aremixed with a cold stream 15, forming a mixture 16, the exergysupplied is the sum of the exergies of the hot and cold streams, andthe exergy recovered is the exergy of the mixture. The exergy flowequation for the dearetor system becomes:

0 ¼ _m6J6 þ _m23J23 þ _m15J15 � _m16J16 � Ta _Sgen (63)

where

_m16 ¼ _m23 þ _m15 þ _m6 (64)

_Idestroyed ¼ Ta _Sgen ¼ Ta�_m16s16 � _m15s15 � _m23s23 � _m6s6

(65)


hII;Der ¼ 1� Ta _Sgen_m6J6 þ _m23J23 þ _m15J15

¼ _m16J16_m6J6 þ _m23J23 þ _m15J15

(66)

A.13 The exergy flow equation for the expansion valve EXP1:

0 ¼ _m20ðJ20 �J21Þ � Ta _Sgen (67)

_Idestroyed ¼ Ta _Sgen ¼ Ta _m20ðs21 � s20Þ (68)

The second law efficiency is

hII;EXP1 ¼ 1� Ta _Sgen_m20ðJ20 �J21Þ

(69)


0 ¼ _m22ðJ22 �J23Þ � Ta _Sgen (70)




(72)


0 ¼ _m24ðJ24 �J25Þ � Ta _Sgen (73)




(75)


0 ¼ _m26ðJ26 �J27Þ � Ta _Sgen (76)




(78)


0 ¼ _m28ðJ28 �J29Þ � Ta _Sgen (79)




(81)


Appendix B

Formulas used for finding incidence angle (q) for a plane rotatedabout a horizontal north-south axis with continuous east westtracking are given below.

B.1 The incidence angle (q) for a plane rotated about a horizontalnorth-south axis with continuous east west tracking is given by[23]:

cos q ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffihcos q2z þ cos2 d sin2 u

ir(82)

The zenith angle (qz) is the angle between the line of sight to thesun and the vertical. The zenith angle is related to both the decli-nation angle and the hour angle by the following relationship [23]:

cos qz ¼ ðsin F sin dþ cos F cos d cos uÞ (83)

The declination angle (d) is the angular position of the sun atsolar noon, with respect to the plane of the equator. The followingexpression for declination angle was developed by Cooper in 1969(Cooper, as cited by [23]):

d ¼ 23:45 sin�360

284þ n365

�(84)

The position of the sun depends on the hour angle (u), or theangular displacement of the sun east or west of the local meridian.The hour angle comes as a result of the rotation on the earth, whichspins on its axis at a rate of 15� per hour:

u ¼ ðSolar Time� 12Þ � 15 (85)

The relationship between solar time and standard time, inhours, is: [24]:

Solar Time ¼ Standard Time þ ðLst � LlocÞ15

þ E60

(86)

Equation of time ðEÞ ¼229:19ð0:000075þ 0:001868� cos Be0:032077� sin Be0:014615� cos 2Be0:04089� sin 2BÞ (87)

Where

B ¼ ðne1Þ � 360365

(88)

Appendix C

Formulas used for finding outside/inside convective heattransfer coefficient of the absorber/receiver tube are given below.

C.1 To determine the outside convective heat transfer coefficientby wind hw the following correlations recommended by McAdams[23] for the flow of air across a tube can be used:

hwDco=kair ¼ 0:40þ 0:54ðrairVwDco=mairÞ0:52/for 0:1

< rairVwDco=mair < 1000 (89)

hwDco=kair ¼ 0:30ðrairVwDco=mairÞ0:6/for 1000

< rairVwDco=mair < 50000 (90)

C.2 The convection heat transfer coefficient hf for the insidesurface of the absorber/receiver tube and thermic fluid is evaluatedbased on the flow.

The properties of thermic fluid in the Eqs. (91)e(96) are evalu-ated at the mean temperature of fluid for the segmental length ofPTC.

If the flow is laminar flow then hf is calculated from thefollowing equation

Nu ¼ hfDi=kf ¼ 3:66 (91)

For fully developed turbulent flow the hf is calculated by

Nu ¼ hfDi=kf ¼ 0:023�rfVfDi=mf

�0:8�Prf

�0:4(92)

The average velocity Vf of thermic fluid in the receiver tube

Vf ¼ mf=�p4D2i rf

�(93)

The pressure loss Dpf of thermic fluid through the receiver tube

Dpf ¼ 4fLV2f rf=2Di (94)

Laminar flow coefficient of friction is calculated by

f ¼ 16=Ref (95)

Turbulent flow coefficient of friction is calculated by

f ¼ 0:0791�Ref

��0:25(96)

C.3 The power (P) required to pump the fluid through a pipewhose pressure drop is Dpf is

P ¼ mf � Dpfrf � hp

(97)

References

[1] Vogel W, Henry K. Large-scale solar thermal power: technologies, costs anddevelopment. Weinheim: WILEY-VCH Verlag GmbH & Co. KGaA; 2010.

[2] Wittmann M, Ecka M, Paalb RP, Steinhagen HM. Methodology for optimizedoperation strategies of solar thermal power plants with integrated heatstorage. Solar Energy 2011;85(4):653e9.

[3] Quaschning V, Rainer K, Ortmanns W. Influence of direct normal Irradiancevariation on the Optimal parabolic trough field size: a Problem Solved withTechnical and Economical Simulations. ASME Journal of Solar Energy Engi-neering 2002;124:160e4.

[4] Birnbaum J, Feldhoff JF, Fichtner M, Hirsch T, Jocker M, Paal RP, et al. Steamtemperature stability in a direct steam generation solar power plant. SolarEnergy 2011;85(4):660e8.

[5] Gaul HW, Rabl A. Incidence-angle modifier and average optical efficiency ofparabolic trough collectors. ASME Journal of Solar Energy Engineering 1980;102:16e21.

[6] Kaushik SC, Siva Reddy V, Tyagi SK. Energy and exergy analysis of thermalpower plants: a review. Renewable and Sustainable Energy Reviews 2011;15:1857e72.

[7] Siva Reddy V, Kaushik SC, Tyagi SK, Panwar NL. An approach to analyse energyand exergy analysis of thermal power plants: a review. Smart Grid andRenewable Energy 2010;1:143e52.

[8] Kaushik SC, Misra RD, Singh N. Second law analysis of a solar thermal powersystem. International Journal of Solar Energy 2000;20:239e53.

[9] Gupta MK, Kaushik SC. Exergy analysis and investigation for various feedwater heaters of direct steam generation solarethermal power plant.Renewable Energy 2010;35(6):1228e35.

[10] Palenzuela P, Zaragoza G, Alarcon-Padilla DC, Guillen E, Ibarra M, Blanco J.Assessment of different configurations for combined parabolic-trough (PT)solar power and desalination plants in arid regions. Energy 2011;36(8):4950e8.

[11] Blanco-Marigorta AM, Victoria Sanchez-Henríquez M, Pena-Quintana JA.Exergetic comparison of two different cooling technologies for the powercycle of a thermal power plant. Energy 2011;36(4):1966e72.

[12] Kopac M, Hilalci A. Effect of ambient temperature on the efficiency of theregenerative and reheat catalagzı power plant in turkey. Applied ThermalEngineering 2007;27:1377e85.

[13] Aljundi I. Energy and exergy analysis of a steam power plant in Jordan.Applied Thermal Engineering 2009;29:324e8.


[14] Energy Efficiency & Renewable energy (EERE): (http://apps1.eere.energy.gov/buildings/energyplus/cfm/weather_data3.cfm/region¼2_asia_wmo_region_2/country¼IND/cname¼India http://www.eere.energy.gov).

[15] Klein SA, Alvarado F. Engineering equation solver, Version 8.629. Middleton,WI: F Chart Software; 2010.

[16] Bartlett RL. Steam turbine performance and economics. New York: McGraw-Hill; 1958.

[17] Lippke F. Simulation of the part-load behaviour of a 30 MWe SEGS plant.Report No. SAND95-1293. Alburquerque, NM, USA: SNL; 1995.

[18] Patnode AM. Simulation and Performance Evaluation of Parabolic Trough SolarPower Plants. Master. Thesis, University of Wisconsin-Madison, USA: 2006.

[19] Petela R. Exergy of heat radiation. ASME Journal of Heat Transfer 1964;86:187e92.

[20] Geyer M, Lupfert E, Osuna R, Zarza E, Nava P, Langenkamp J, et al. EURO-TROUGH e parabolic trough collector developed for cost efficient solar powergeneration. Zurich, Switzerland. In: Proceedings of 11st InternationalSymposium on concentrating solar power and Chemical energy Technologies;2002.

[21] Montes MJ, Abanades A, Martinez-Val JM, Valdes M. Solar multiple optimi-zation for a solar-only thermal power plant, using oil as heat transfer fluid inthe parabolic trough collectors. Solar Energy 2009;83:2165e76.

[22] Odeh SD, Morrison GL, Behnia M. Modeling of parabolic trough direct steamgeneration solar collectors. Solar Energy 1998;62:395e406.

[23] Duffie John A, Beckman William A. Solar engineering of thermal processes.2nd ed. New York: John Wiley and Sons, Inc.; 1991.

[24] Stine William B, Harrigan RaymondW. Solar energy fundamentals and design,with computer applications. John Wiley & Sons, Inc; 1985.

[25] Lupfert E, Geyer M, Schiel W, Esteban A, Osuna R, Zarza E, Nava P. EURO-TROUGH design issues and prototype testing at PSA. Proc. of ASME interna-tional solar energy conference-forum, solar energy: the power to choose,Washington, DC; April 21e25, 2001. 389e394.

[26] Price H, Eckhard LP, David K, Zarza E, Gilbert C, Randy G, et al. Advances inparabolic trough solar power Technology. Journal of Solar Energy Engineering2002;124:109e25.

[27] Xu C, Wang Z, Li X, Sun F. Energy and exergy analysis of solar power towerplants. Applied Thermal Engineering 2011;31:3904e13.

http://apps1.eere.energy.gov/buildings/energyplus/cfm/weather_data3.cfm/region=2_asia_wmo_region_2/country=IND/cname=India






http://www.eere.energy.gov