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Solar Energy 86 (2012) 531–540

Parabolic-trough solar thermal power plant simulation scheme,multi-objective genetic algorithm calibration and validation

Javier Bonilla a,⇑, Luis Jose Yebra a, Sebastian Dormido b, Eduardo Zarza a

a PSA-CIEMAT, Plataforma Solar de Almerıa – Centro de Investigaciones Energeticas, MedioAmbientales y Tecnologicas, Crta. de Senes s/n,

04200 Tabernas, Almerıa, Spainb UNED, Universidad Nacional de Educacion a Distancia, Escuela Tecnica Superior de Ingenierıa Informatica, 28040 Madrid, Spain

Received 25 May 2011; received in revised form 25 October 2011; accepted 28 October 2011Available online 6 December 2011

Communicated by: Associate Editor Robert Pitz-Paal

Abstract

The dynamic simulator design and development of a direct steam generation parabolic-trough solar thermal power plant is detailed inthis paper. The dynamic simulator is not only the equation-based object-oriented model but also includes features to facilitate the sim-ulation process. A whole simulator scheme has been developed for that purpose. This simulator scheme considers the issues of fetchingand converting sensors data to model inputs and obtaining suitable initial values for the boundary condition problem in the numericalintegration. The calibration and validation processes have been tackled, using Matlab as the primary tool. However, several tools werestudied and tested. A multi-objective genetic algorithm approach has been chosen for calibrating the dynamic model.� 2011 Elsevier Ltd. All rights reserved.

Keywords: Dynamic simulation; Calibration and validation; Direct steam generation; Parabolic-trough solar thermal power plant; Multi-objective geneticalgorithm calibration

1. Introduction

The focus of this paper is the development of a simulatorscheme for a direct steam generation parabolic-trough solarthermal power plant. It is important to note that the simula-

0038-092X/$ - see front matter � 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2011.10.025

⇑ Corresponding author. Tel.: +34 950 014084; fax: +34 950 365015.

Abbreviations: DISS, DIrect Solar Steam; PTC, Parabolic-Trough Col-lector; EOO, Equation-based Object-Oriented; HTF, Heat Transfer Fluid;DSG, Direct Steam Generation; BOP, Balance Of Plant; IDE, IntegratedDevelopment Environment; CSV, Comma-Separated Value; PRE, Per-centage Relative Error; IAM, Incidence Angle Modifier; HEM, Homo-geneous Equilibrium Model; FVM, Finite Volume Method; HTC, HeatTransfer Coefficient; DSI, Direct Solar Irradiance; DNI, Direct NormalIrradiance.

E-mail addresses: javier.bonilla@psa.es (J. Bonilla), luis.yebra@psa.es(L.J. Yebra), sdormido@dia.uned.es (S. Dormido), eduardo.zarza@psa.es(E. Zarza).

tor scheme, apart from the Equation-based Object-Oriented(EOO) dynamic model, includes several features to facilitatethe simulation, calibration and validation processes. Thesimulator scheme also considers important numericalaspects, such as boundary conditions fulfillment. Fetching,converting and comparing real data to simulated resultshas been taken into account. Several tools to perform the cal-ibration and validation process have been studied and aappropriate framework has been defined for this task. Amulti-objective genetic algorithm approach was eventuallyused to calibrate the dynamic model.

The real system, under study in this work, is the CIE-MAT-PSA (Centro de Investigaciones Energeticas Medio-ambientales y Tecnologicas – Plataforma Solar de Almerıa,a Spanish government research and test center) DISS(DIrect Solar Steam) test facility, a parabolic-trough solarthermal power plant.

532 J. Bonilla et al. / Solar Energy 86 (2012) 531–540

This paper presents in detail the latest improvementsmade in a dynamic equation-based object-oriented simula-tor to study the DISS test facility behavior, this dynamic sim-ulator is primarily intended to be used for the developmentof advanced control systems. A fair amount of researchhas been devoted to study this thermal power plant, first ofall the study of its feasibility, erection and safe operationin the DISS project (Zarza et al.,2004; Eck et al., 2003). Con-sidering modelling and simulation of the DISS solar thermalpower plant are worth mentioning (Eck and Hirsch, 2007;Yebra, 2006).

2. The DISS parabolic-trough solar thermal power plant

The DISS (DIrect Solar Steam) test facility is a para-bolic-trough solar thermal power plant owned by CIE-MAT-PSA (see Fig. 1). The parabolic-trough technologyis one of the several different solar thermal concentratingtechnologies available. The aim of the DISS facility is todevelop a new generation of solar power plants using Par-abolic-Trough Collectors (PTCs) to produce high pressuresteam in the absorber tubes. Their high working tempera-ture makes PTCs suitable for supplying heat to industrialprocesses, replacing traditional fossil fuels (Kutshceret al., 1982; Zarza, 2000 ). The Heat Transfer Fluid(HTF) used in the DISS test facility is the two-phase-flowsteam–water, which circulates in three different states, sub-cooled liquid, steam–water mixture and superheated steam.This technology, known as direct steam generation (DSG),increases overall system efficiency while reducing invest-ment costs, by eliminating the oil previously used as aheat-transfer medium between the solar field and the Bal-ance Of Plant (BOP), and thereby also eliminating the needfor a heat exchanger.

2.1. Main features of the DISS facility

The DISS plant consists of two subsystems, the solarfield of PTCs and the BOP. In the solar field, feed wateris preheated, evaporated and converted into superheated

Fig. 1. General view of the DISS test facility, a parabolic-trough solarthermal power plant owned by Plataforma Solar de Almerıa (CIEMAT).

steam as it circulates through the absorber tubes of a665-m-long row of PTCs with a total solar collecting sur-face of 3838 m2. Superheated steam generated in the solarfield is condensed, processed and reused again as feed waterfor the solar field (closed-circuit operation) in the BOP.The BOP consists of water/steam separators, condensers,chemical dosing system, preheaters, deaerators and waterpumps. Fig. 2 shows a simplified diagram of the DISS loop.

3. DISS facility model

A DISS solar thermal power plant EOO model (Yebra,2006; Yebra et al., 2006) was developed to study the behav-ior of the real plant, the DISS model only considers theonce-trough operation mode.

An EOO methodology allows to describe the system as aset of equations which are acausal, maintaining its mathe-matical meaning. Moreover, a object-oriented methodol-ogy allows to define basic models of components whichcan be reused to develop new complex models withoutadditional effort. This methodology allows to develop reus-able and easy to maintain components. The modelling lan-guage chosen was Modelica 2.2.1 (Modelica Association,2007) which is a equation-based object-oriented modellinglanguage. Modelica is developed and maintained by theModelica Association. The Integrated Development Envi-ronment (IDE) chosen, which supports the Modelica lan-guage, has been Dymola 6.0b (Dynasim, 2006).

Fig. 3 shows the DISS test facility Modelica componentdiagram which has 11 PTC components. The model inputsare the following, the ambient temperature (Tamb), theDirect Solar Irradiance (DSI) (Rad), with regards to theHTF, the inlet temperature (inletTemp), the inlet pressure(inletPres) and the mass flow rate (mdot_ws), the three lastinputs are also provided for the last collector injector, sincethis model only supports the once-through operation mode.From the DSI, the Direct Normal Irradiance (DNI) is com-puted using the incidence angle. The PSA algorithm (Blanco-Muriel et al., 2001) is used to calculate the solar vector, thePTCs are considered to properly follow the sun trajectory.

The PTC thermal potency is computed using the DNI,the PTC area and the thermal, geometrical and opticallosses. A experimental global thermal losses model for thiskind of PTC, proposed by Ajona (1999) is considered. Thegeometrical losses are included in the experimental Inci-dence Angle Modifier (IAM) model, also for this kind ofPTC, proposed by Gonzalez et al. (2001). The optical lossesmodel is described in this manuscript, in Section 5. Theabsorber tube, located in the geometrical focal line of theparabolic-trough receiver, is composed of a steel pipe anda glass cover. Conduction in the steel pipe has beenneglected in the model.

The two-phase flow is modelled as a discretized or distrib-uted-parameter model, using a Homogeneous EquilibriumModel (HEM), which contains mixture equations for themass, momentum and energy balances, described in (Bonillaet al., 2011a). The Finite Volume Method (FVM) (Patankar,

Fig. 2. Diagram of the DISS loop (Zarza, 2000).

Cont...

Water...

Tpb...cl...p0...

Con

t...

Water...T

pb...cl...p0...

CCP_diss

Tamb Rad

CCP_diss

Tamb Rad

CCP_diss

Tamb Rad

CCP_diss

Tamb Rad

CCP_diss

Tamb Rad

CCP_diss

Tamb Rad

CCP_diss

Tamb Rad

CCP_diss

Tamb Rad

CCP_diss

Tamb Rad

CCP_diss

Tamb Rad

CCP_diss

Tamb Rad

Water...

T pb...cl...p0...

Tamb

Rad

InletTe...

InletPr...

mdot_...

Outle...

pout

Tout

mdotout

is_liquid

Tmout

pinIn

letT

emp_

inj

Inle

tPre

ssur

...

mdo

t_in

j...

Fig. 3. DISS test facility Modelica model (Yebra, 2006).

J. Bonilla et al. / Solar Energy 86 (2012) 531–540 533

1980), the staggered grid method (Harlow and Welch, 1965)and the upwind scheme (Jensen, 2003) are used to discretizedthe model. In order to close the equation system, heat trans-fer and wall friction equations are required. Heat transfer ismodelled using a heat transfer coefficient (HTC). In themodel, the HTCs can be considered constant for each flow

state or different correlations can be used, such as Gnielinski(Gnielinski, 1976) correlation for the single phase orGungor–Winterton (Gungor and Winterton, 1986) for thetwo phase. The wall friction is modelled using a friction fac-tor, the friction factor is considered constant as its value hasbeen calibrated using experimental data.

534 J. Bonilla et al. / Solar Energy 86 (2012) 531–540

One of the improvements is the automatization of theinitial parameter assignments which are provided usingan automatically generated input file (described in Section4). For instance, the initial date and time parameters usedto calculate the solar vector are in that input file and it isnot necessary to set those values in the model itself. Theinitial condition values (such as the outlet pressure) arealso obtained automatically from this input file, thereforethe user does not have to set those values manually foreach simulation run.

4. DISS facility simulator

This section presents the developed DISS facility simula-tor which is not only the model itself but it also facilitatessolving the initial condition problem, the calibration andvalidation processes. Fig. 4 shows the DISS facility simula-tor scheme, the following paragraphs describe each elementin detail.

4.1. DISS test facility

The DISS test facility has several sensors distributedalong the whole plant, the number of sensors and it loca-tion was discussed in the DISS project (Zarza, 2000). Thisproject was set with the aim of studying the direct steamgeneration in parabolic-trough solar thermal power plantsunder real solar conditions. Several kind of sensors areavailable, such as temperature, pressure and flow sensors.

4.2. Data Acquisition System (DAS)

It stores, for each experiment, sensors data in a databasewhich was designed and implemented for the DISS project.The most important DISS database tables are the sensor andseason tables. The sensor table stores all the information

Fig. 4. DISS test facilit

about each sensor including name, description and units.The season table establishes which sensors all available foreach season. The data of each experiment is stored individ-ually in one table per day due to the large amount of data.

4.3. Web application

It was developed to easily access to the experimentaldata. The user can define profiles, each profile includes anumber of selected sensors, therefore every time the userneeds to extract data it is not necessary to select every sin-gle sensor, instead the profile can be loaded. The date andtime range must be also provided by the user. The outputcan be a graph or a data file. Graphs can be in bitmap orvectorial format whereas data files are stored in plain textfiles in Comma-Separated Value (CSV) format which canbe optionally compressed in a ZIP-format file.

4.4. File conversion application

With the aim of using the output data files in the DISSModelica model through the Dymola IDE, a file conver-sion computer program was developed. This computer pro-gram converts a CSV format text file to a trajectory file,which is the required input file format in the DymolaIDE. This conversion is performed preserving the originalname, description and units of the sensors.

4.5. Initial values library

A Modelica library was developed in order to facilitatethe process of obtaining some parameters to solve the ini-tial condition problem. This library automatically retrievesthe suitable values (such as inlet temperature and inlet andoutlet pressure). The only required inputs are the trajectory

560

540

520

500

480

460

440

420

Tsal_CCP2_Medida Tsal_CCP2_Simulada

[K]

y simulator scheme.

J. Bonilla et al. / Solar Energy 86 (2012) 531–540 535

file and the initial simulation time to obtain the propervalues.

4.6. The DISS Modelica model

The model receives the input data, the real data for com-parison purposes, the values to solve the initial conditionproblem, the parameter values and also the selection ofthe parametrizable classes to configure the model. Themodel is highly configurable, allowing to set the steam–water heat transfer coefficient model between different cor-relations, the thermodynamic properties computationmethod (Mean Densities (Bonilla et al., 2010), HeuristicApproach (Bonilla et al., 2011b) or Modelica.Media(Modelica Association, 2007) among other options. All thisconfiguration is done graphically through the Dymola userinterface.

5. Calibration

Several calibration tools were analyzed and tested. Thefirst attempt was to use the Dymola Design library (Dyna-sim, 2006), unfortunately the model was to complex andthe calibration could not been performed. Secondly, theJModelica.org platform and the Optimica compiler (Akes-son et al., 2010) were considered, but unfortunately againthis environment only works with Modelica 3 whereasthe DISS model is implemented in Modelica 2.2.1. How-ever, positive feedback was obtained from the authors ofthis tool, and it seems to be a suitable one to take underconsideration for future developments. Finally, Matlab7.8.0 (MathWorks, Inc., 2009) was chosen as a tool forthe calibration process, Dymola includes mechanisms toexport Modelica models to Simulink in an easy and directway, using a Simulink block where the model, parametersand inputs can be specified. Moreover, Matlab is a widelyused tool and provides a toolbox to perform parallel cali-brations, using the Parallel Computing Toolbox and theMatlab Distributed Computing Server, this is a future goalin order to take advantage of a 12-node cluster in the cal-ibration process.

5.1. Genetic algorithm

The multi-objective heuristic genetic algorithm function,GAMULTIOBJ, from the Matlab Genetic AlgorithmToolbox (Chipperfield et al., 1994) has been used for thecalibration. This function uses a controlled elitist geneticalgorithm, a variant of NSGA-II (Deb, 2001) widely usedin optimization. A controlled elitist genetic algorithmfavors individuals that can help increase the diversity ofthe population even if they have a lower fitness valuewhereas an elitist genetic algorithm always favors individu-als with better fitness value. It is important to maintain thediversity of population for convergence to an optimal Par-eto front. This is done by controlling the elite members ofthe population using two options to control the elitism.

The Pareto fraction option limits the number of individualson the Pareto front and the distance function helps tomaintain diversity on a front by favoring individuals thatare relatively far away on the front. To form the next gen-eration, the algorithm combines the current population andits offspring generated with the standard bimodal crossover(Beyer and Deb, 2001) and polynomial mutation operators.Finally, the best individuals in terms of non-dominanceand diversity are chosen. This new version of NSGA hasa low time complexity. For more information about themulti-objective genetic algorithm see Chipperfield et al.(1994) and for the calibration of Modelica models usinggenetic algorithms in Matlab together with a practicalexample, see Hongesombut et al. (2002).

5.2. Optimization variables

The DISS Modelica model is highly sensitive to the opti-cal efficiency of the PTCs. The optical efficiency must beproperly estimated in order to obtain good approxima-tions. The estimated optical efficiency value for a modifiedLS-3 PTC is 75%. However, this value can considerablydecrease daily due to the soiling of the collectors (Zarza,2000). The nominal estimated optical efficiency value mustbe then estimated particularly for each experiment in orderto obtain accurate results.

Although there are other uncertainties in the model,such as the thermal losses, the fluid heat transfer coeffi-cients, and the wall friction. All of them have been mod-elled using experimental correlations, as mentioned inSection 3. Moreover, the optical efficiencies of each PTCmust be properly estimated because the model is highlysensitive to them, for that reason the optical efficiencieshave been chosen as the optimization variables in thiswork.

The optical efficiency of the ith PTC ðgoptiÞ is defined as a

function of the peak optical efficiency ðgopti ;0�Þ, which con-

siders a 0� incidence angle, and as a function of the IAM,Eq. (1), where hi is the incidence angle. Whereas the peakoptical efficiency is defined in Eq. (2) by the reflectivity(ri), the intercept factor (ci), the absorptivity (ai), the trans-missivity (si) and the soiling factor ðF eiÞ. Therefore, thevalue to be estimated is the peak optical efficiency, due tothe IAM model implemented is defined by Eq. (3). TheIAM model was proposed in (Gonzalez et al., 2001) for amodified LS-3 PTC and it also considers geometrical losses(Zarza, 2000).

gopti¼ gopti;0

� � KðhiÞ; ð1Þ

gopti ;0�¼ ri � ci � ai � si � F ei; ð2Þ

KðhiÞ ¼ 1� 2; 23073� 10�4 � hi � 1:1� 10�4 h2i

þ 3; 18596� 10�6 � h3i � 4; 85509� 10�8 � h4

i

ð0� 6 hi < 80�Þ;KðhiÞ ¼ 0 ð80� P hi 6 90�Þ: ð3Þ

Fig. 5. DISS model calibration in Matlab.

3 3.5 4 4.5 5 5.5x 104

0

200

400

600

800

1000

Time (s)

Irrad

ianc

e (W

/m2 )

Fig. 6. Direct solar irradiance for the 9th July 2001.

536 J. Bonilla et al. / Solar Energy 86 (2012) 531–540

5.3. Fitness function

Eq. (4) shows the Percentage Relative Error (PRE),�riðgopti

; jÞ, considering the ith PTC and the jth sampledvalue, where T siðgopti

; jÞ is the simulated output tempera-ture, T riðjÞ is the real temperature, n is the number of PTCsand m the number of samples.

�riðgopti; jÞ ¼ 100 �

T siðgopti; jÞ � T riðjÞ

T riðjÞ;

i 2 ½1; n�; j 2 ½1;m�: ð4Þ

The multi-objective approach minimizes the cumulativePRE, �þri

ðgoptiÞ, between the real and simulated output tem-

peratures for each PTC, according to Eq. (5).

�þriðgoptiÞ ¼

Xm

j¼1

j�riðgopti; jÞj; i 2 ½1; n�: ð5Þ

Other metrics, used in Section 5.4, are the following, themean PRE, ��riðgopti

Þ, the maximum PRE, ��riðgoptiÞ, and a

vector of PREs, �riðgoptiÞ, described by Eqs. (6)–(8) respec-

tively. Fig. 5a shows the DISS Simulink block andFig. 5b shows the model used for calibration.

��riðgoptiÞ ¼

�þriðgoptiÞ

n; i 2 ½1; n�; ð6Þ

��riðgoptiÞ ¼ max

j2½1;m�j�riðgopti

; jÞj; i 2 ½1; n�; ð7Þ

�riðgoptiÞ ¼

[m

j¼1

�riðgopti; jÞ; i 2 ½1; n�: ð8Þ

5.4. Calibration results

The model has been calibrated using experimental datafrom the real plant following the scheme shown in Section

3 3.5 4 4.5 5 5.5x 104

450

500

550

600

650

700

Time (s)

Tem

pera

ture

(K) Real temperature

Simulated temperature

Fig. 7. Real and simulated output 11th PTC temperatures in the calibration process for the 9th July 2001.

Table 1Calibrated peak optical efficiencies for the 9th July 2001.

ith PTC 1 2 3 4 5 6

gopti ;0� 0.630456 0.628347 0.627592 0.628347 0.628519 0.623357

7 8 9 10 11 Mean

gopti ;0� 0.624095 0.626673 0.626451 0.623447 0.622733 0.626355

Table 2Mean and maximum PREs between real and simulated output temper-atures for the 9th July, 2001.

ith PTC 1 (%) 2 (%) 3 (%) 4 (%) 5 (%) 6 (%)

��ri ðgoptiÞ 0.41 0.40 0.67 0.28 0.42 0.44

��riðgopti

Þ 2.59 2.58 3.13 2.00 2.04 2.05

7 (%) 8 (%) 9 (%) 10 (%) 11 (%) Mean (%)

��ri ðgoptiÞ 0.43 0.45 0.64 1.29 1.57 0.64

��riðgopti

Þ 2.07 4.09 4.53 6.82 10.72 3.59

J. Bonilla et al. / Solar Energy 86 (2012) 531–540 537

4. With the aim of comparing the new calibration schemewith the previous one, the calibration process describedhere is analogous to the described in (Yebra et al., 2006)by means of using the same real data, corresponding tothe calibration for the 9th July 2001, this day was selectedin order to properly calibrate the model because there weresolar radiation perturbations during the operation day, asit can be seen in Fig. 6 which shows the DSI (Ed). The

3 3.5 4−12−10

−8−6−4−2

02468

101212

Ti

ε r 11 (%

)

Fig. 8. �r11ðgopt11

Þ between the real and simulated output 11th PTC

calibration involves the estimation of the peak optical effi-ciency of each collector ðgopti ;0�

Þ.The calibrated parameters for the 9th July 2001 are

shown in Table 1, it can be seen how the calibrated peakoptical efficiency values are close to 63%. The calibratedpeak optical efficiency values are low in comparison tothe theoretical peak optical efficiency of 75%. The maincauses for the decrease in the optical efficiency are prob-lems related to the PTC tracking systems when the experi-ments were performed, the soiling of the PTCs can alsoconsiderably affect.

The mean and maximum PREs between real and simu-lated output temperatures for each collector, according toEqs. (6) and (7) respectively, are shown in Table 2. Fig. 7shows the real and simulated output temperatures for thelast PTC (11th PTC) where the continuous line is the realoutput temperature and the dashed line is the simulated out-put temperature, it can be seen that there is a delay not con-sidered in the simulated output temperature, this might berelated to the neglection of modelling the interconnectionsbetween PTCs which implies neglecting length of pipe,valves and 90� elbows have also been neglected. The maxi-mum PRE for the 11th PTC has decreased, consideringthe previous DISS model, from 12.7% to 10.7% (not consid-ering the initialization in the previous DISS model, wherelarge errors were obtained, up to 27.1%). The global meanPRE and the mean maximum PRE have also decreased from0.79% to 0.64% and from 7.31% to 3.59% respectively. Fig. 8shows the PRE for the 11th PTC during the simulation.Modelling the delay might reduce the error further.

4.5 5 5.5x 104

me (s)

temperature in the calibration process for the 9th July 2001.

3.5 4 4.5 5 5.5 6 6.5x 104

450

500

550

600

650

Time (s)

Tem

pera

ture

(K)

Fig. 10. Real and simulated output 11th PTC temperatures in the validation process for the 10th July 2001.

3.5 4 4.5 5 5.5 6 6.5x 104

−4

−3

−2

−1

0

1

22

Time (s)

ε r 11

(%)

Fig. 11. �r11ðgopt11

Þ between the real and simulated output 11th PTC temperatures in the validation process for the 10th July 2001.

3.5 4 4.5 5 5.5 6 6.5x 104

500

600

700

800

900

1000

Time (s)

Irrad

ianc

e (W

/m2 )

Fig. 9. Direct solar irradiance for the 10th July 2001.

Table 3Mean and maximum PREs between real and simulated output temper-atures for the 10th July 2001.

ith PTC 1 (%) 2 (%) 3 (%) 4 (%) 5 (%) 6 (%)

��ri ðgoptiÞ 0.50 0.51 0.79 0.32 0.35 0.48

��riðgopti

Þ 5.27 5.29 6.10 3.66 2.97 2.28

7 (%) 8 (%) 9 (%) 10 (%) 11 (%) Mean (%)

��ri ðgoptiÞ 0.47 0.44 0.63 1.51 0.99 0.63

��riðgopti

Þ 2.35 2.29 3.09 4.99 3.19 3.77

538 J. Bonilla et al. / Solar Energy 86 (2012) 531–540

6. Validation

.With the aim of validating the previously calibratedparameters shown in Table 1, the same parameters were usedfor a different operation day. The operation day selected wasthe 10th July 2001, because as mentioned earlier, the DISSmodel is highly sensitive to the optical efficiency. In order

to used the most accurate optical efficiency values, the fol-lowing day to the calibration day was selected. The DSI(Ed) is shown in Fig. 9.

Fig. 10 shows the real and simulated output last PTC(11th PTC) temperatures where the continuous line is thereal output temperature and the dashed line is the simulatedoutput temperature, it can be seen how the simulated tem-perature follows the real temperature dynamic accuratelyand the delay is observed again. The output temperatureis only slightly overestimated when the injecting steam fromthe 11th PTC injector increases the input mass flow andtemperature (56,000 s time instant in simulation), as it canbe seen in Fig. 12. In Table 3, the mean and maximum PREsfor each PTC and the mean values for the field are shown.Fig. 11 shows the PRE for the 11th PTC during the simula-tion. The error obtained is low, being the global mean PRE0.63% and the mean maximum PRE 3.77%.

3.5 4 4.5 5 5.5 6 6.5 70

0.02

0.04

0.06

0.08

Mas

s flo

w (k

g/s)

Time (s)

200

300

400

500

600

Tem

pera

ture

(K)Injector 11th PTC Mass flow

Injector 11th PTC Temperature

x 104

Fig. 12. Input mass flow and temperature of the 11th PTC injector in the validation process for the 10th July 2001.

J. Bonilla et al. / Solar Energy 86 (2012) 531–540 539

7. Conclusions and future work

The most remarkable conclusions are the following:

� A DISS simulator scheme has been developed in orderto facilitate the calibration, validation and simulationprocesses, fetching and converting easily real data forcomparison purposes, using a web application and aconversion computer program respectively.� The initial condition problem has also been taken into

account facilitating the process of obtaining the initialvalues.� A calibration and validation scheme has been defined,

using the Matlab Genetic Algorithm Toolbox to developa multi-objective calibration process, minimizing PREsbetween real and simulated output temperatures in eachPTC.

As future work it would be worth dealing with the fol-lowing issues:

� Study in depth the delay in the system.� Study the increase of the error when increases the 11th

PTC injector input mass and temperature flow.� Consider to develop a framework to perform parallel

calibrations in Matlab using the Parallel ComputingToolbox and the Matlab Distributed Computing Serverin order to take advantage of a 12-node cluster.

Acknowledgments

This work has been financed by CIEMAT research cen-tre, by the INNPACTO Project, Hibridacion de tecnologıas

renovables en una planta de generacion de energıa, IPT-440000-2010-004 and the National Plan Project, Predictive

COntrol techniques for efficient management of reneWable

Energy micro-gRids (POWER), DPI2010-21589-C05-04 ofthe Spanish Ministry of Science and Innovation and FED-ER funds. This support is gratefully acknowledged by theauthors.

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