Available online at www.sciencedirect.com

www.elsevier.com/locate/solener

ScienceDirect

Solar Energy 105 (2014) 381–389

Balancing heat transfer fluid flow in solar fields

Mohammad Abutayeh ⇑, Anas Alazzam, Bashar El-Khasawneh

Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates

Received 23 September 2013; received in revised form 5 March 2014; accepted 21 March 2014

Communicated by: Associate Editor Yogi Goswami

Abstract

Proper distribution of heat transfer fluid in solar fields remains an issue for the concentrated solar power industry. Balancing fluidflow in solar fields is very challenging due to their complex piping networks. It is further exacerbated by the instantaneously and spatiallyvarying solar radiation necessitating continuous flow adjustments to control heat transfer fluid temperature. Poorly balanced solar fieldsentail over and under heating of a fairly costly heat transfer fluid; thus, shortening its life span and the life span of equipment handling itdue to frequent thermal shocks. Proper distribution of heat transfer fluid will eventually minimize equipment malfunction, maximizesolar power generation, and improve operational safety. A flow control strategy aimed at properly distributing heat transfer fluid in solarfields has been developed along with a model for the proposed strategy. The strategy consists of manipulating solar field valve positionsto control flow distribution and modulating pump speed to control flow rate in response to a continually varying solar radiation in orderto attain a set temperature for heat transfer fluid exiting the solar field.� 2014 Elsevier Ltd. All rights reserved.

Keywords: Concentrated solar power; Parabolic trough collector; Heat transfer fluid; Solar field

1. Introduction

Parabolic trough collector (PTC) is the most economicaland commercially available concentrating solar power(CSP) technology. PTC systems include numerous para-bolic trough mirrors tracking the sun on a single axis. Aheat transfer fluid (HTF) flows in the focal line of thetroughs collecting solar heat that is transferred to highpressure water generating high pressure steam. The solar-generated steam is then used to propel a steam turbine con-nected to a generator producing electricity (Schindwoffet al., 1980).

A streamlined schematic of a generic PTC type CSPplant is shown in Fig. 1. The Plant includes two segregatedloops: an HTF loop collecting solar heat in a solar field(SF) and a water loop receiving that collected solar heat

http://dx.doi.org/10.1016/j.solener.2014.03.025

0038-092X/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +971 2 501 8470; fax: +971 2 447 2442.E-mail address: mohammad.abutayeh@kustar.ac.ae (M. Abutayeh).

to process it in a Rankine cycle power block (PB). Theloops of a SF are structurally identical; therefore, HTFneeds to be distributed equally among the loops to opti-mize solar energy collection during normal operating con-ditions. So, a manual control valve is typically placed at theentrance of each loop to manage the distribution of HTFamong the loops of the SF.

HTF absorbs solar heat by flowing inside blackenedpipes placed inside vacuumed envelops running in the focalline of the sun-tracking collectors. HTF exit temperature iscontrolled by manipulating its residence time in SF loopsby adjusting its flow rate. Consequently, total HTF flowis determined by the speed of its circulation pump, whereasHTF loop flow is determined by pressure drop across theloop that can be adjusted by varying loop inlet valve posi-tion. A simplified SF layout of a PTC type CSP plant isshown in Fig. 2.

A robust heat exchanger train (HXT) made up of aneconomizer, an evaporator, and a super heater is connected

Nomenclature

a azimuth angle, radiansA area, m2

AT altitude transverse, radiansAW PTC aperture width, mC PTC mirror cleanliness, percentCv valve flow coefficientCSP concentrating solar powerD diameter, mDay day of year, dayDCS distributed control systemDII direct incident insolation, W/m2

DNI direct normal insolation, W/m2

f friction factorFC flow controllerFL PTC focal length, mFT flow transmitterG generatorh enthalpy, kJ/kgHA hour angle, radiansHour hour of day, hHTF heat transfer fluidHXT heat exchanger trainIA incident angle, radiansIAM incident angle modifier, percent‘ longitude angle, degreesL length, mm mass flow rate, kg/sn counterN countNPSH net positive suction head, mOrientation PTC orientation angle, radians

P pressure, barPB Power blockPTC parabolic trough collectorq heat flow, WRD PTC row distance, mRe Reynolds numberS speed, m/sSA shadow argumentSD solar day, daySF solar fieldSG specific gravitySH solar hour, hSP set pointT temperature, �CTC temperature controllerTC time correction term, minuteTilt PTC tilt angle, radiansTT temperature transmitterTZ time zone, hU overall heat transfer coefficient, W/m2-�Cv volumetric flow, m3/sVFD variable frequency driveVP valve positiona altitude angle, radiansd declination angle, radianse pipe roughness, mg efficiency, percentk latitude angle, radiansl viscosity, cPq density, kg/m3

382 M. Abutayeh et al. / Solar Energy 105 (2014) 381–389

in series where water and HTF flow in a counter-currentpattern. High pressure water enters the economizer to beheated to near saturation then evaporated to steam in theevaporator then turned into superheated steam in the superheater before it is forwarded to a steam turbine to generatepower. Hot HTF coming from the SF flows through theHXT giving up its heat to the water loop to produce thedesired high pressure steam before it is pumped back tothe SF. An expansion vessel is placed before the HTFpump to accommodate extra HTF volume produced byits thermal expansion in the SF and to provide the neces-sary elevation head for the HTF pump to overcome itsnet positive suction head (NPSH).

Typically, SF header pipes resemble an H shape withloops branching out in opposite directions forming a geo-metrically symmetrical layout. The PB is usually placedin the middle of the SF to simplify HTF distribution, min-imize pump load, and minimize the amount of HTF neededto fill the piping network. The PB zone includes the HTFexpansion vessel, HTF circulation pump, HXT, and other

auxiliary equipment as well as the Rankine cyclecomponents such as the turbine, condenser, feedwaterpump, deaerator, and others. A typical H-shaped SFlayout of a PTC type CSP plant is shown in Fig. 3.

2. Background

A few researchers investigated the issue of HTF flowbalance in solar fields for the purpose of controlling its out-let temperature. A computer simulation of HTF tempera-ture control has been carried out by Schindwoff(Schindwoff et al., 1980) where strict control requirementswere included in the control logic. A feedback controlscheme was developed where a flow control valve wasmanipulated based on HTF temperature in each row ofcollectors. Another computer simulation of HTF tempera-ture control via flow manipulation was set up by Zunft(Zunft, 1995) where the dynamics of a collector loop weremodeled by a set of nonlinear first order hyperbolic partialdifferential equations. A feedforward controller was

Fig. 1. Schematic of a PTC type CSP plant.

Fig. 2. SF layout of a PTC type CSP plant.

PB

Fig. 3. H-shaped SF layout of a PTC type CSP plant.

M. Abutayeh et al. / Solar Energy 105 (2014) 381–389 383

included in the simulation to mitigate the effect of irregularsolar radiation.

A linear model of a predictive controller has been devel-oped to regulate HTF outlet temperature in SEGS VI,which is a 30 MWe PTC type CSP plant (Stuetzle et al.,2004). The performance of the controller and its influenceon power output have also been examined. In addition, adetailed list of different automatic control schemes appliedto regulate HTF outlet temperature from solar fields wascompiled in a two part comprehensive review (Camachoet al., 2007a,b).

3. Objective

The amount of power generated in a concentrated solarpower plant is directly proportional to the amount andenergy of steam expanding through the turbine. Theamount and energy of solar steam generated depends onthe magnitude of heat transfer from the HTF loop intothe water loop. The temperature gradient between theHTF and water is the driving force for that heat transfer;therefore, maximizing the outlet HTF temperature fromthe solar field entails maximizing solar power generation.

384 M. Abutayeh et al. / Solar Energy 105 (2014) 381–389

Poor distribution of HTF among loops causes tube rup-tures due to over-heating, underperformance due to under-heating, and equipment malfunction due to thermal shocksbrought by oscillating fluid temperatures. Better control ofHTF flow and distribution would result in safer operation,increased electric generation, and decreased equipmentbreakdown.

The purpose of this endeavor is to develop a flow bal-ance strategy to regulate HTF flow so as to maximize itsSF outlet temperature by using solar radiation as a feedfor-ward signal and outlet temperature as a feedback signal toa closed loop controller. HTF has a large residence time inSF loops due to their outsized structure making sole feed-back control inadequate; therefore, feedforward controlhas to be incorporated into the sought after HTF flow bal-ance strategy.

4. Calculation

Initially, solar heat input into each loop is calculatedbased on weather data and loop characteristics. HTFflow rate in each loop is then calculated based on solarheat input and desired exit temperature. Total HTFflow rate in the SF is subsequently calculated by sum-ming up all of the loop flow rates. Pressure at eachnode of the SF is calculated next based on HTF prop-erties and pipe characteristics. Finally, the valve positionof each loop inlet valve can be determined based onloop inlet and outlet pressures to produce the pressuredrop necessary to attain the calculated HTF flow ratein each loop.

The following solar calculations were presented in ear-lier work concerning solar thermal power plant simulation(Abutayeh et al., 2012) and are taken from research find-ings done at Sandia National Laboratories (Lippke, 1995;Cohen et al., 1999).

TC is a time correction term needed to adjust regulartime to solar time. TC is a function of time zone, longitudeangle, and day of year and is estimated by

TC ¼ 4 15TZ� ‘ð Þ þ 9:87 sin4p365� ðDay � 81Þ

� �� 7:53

� cos2p365� ðDay � 81Þ

� �� 1:5

sin2p365� ðDay � 81Þ

� �ð1Þ

IA ¼ cos�1ðffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ðcosð�� TiltÞ � cosðTiltÞ � cosð�Þ � ð1� cosða�OrientationÞÞÞ2

qÞ ð11Þ

SD is the solar day which is also needed to adjust regulartime to solar time and is given by

SD ¼

Day; 0 � Hour þ TC=60 � 24

Day � 1;Hour þ TC=60 < 0 AND Day > 1

Day þ 364;Hour þ TC=60 < 0 AND Day � 1

Day þ 1;Hour þ TC=60 > 24 AND Day < 365

1;Hour þ TC=60 > 24 AND Day � 365

8>>>>>><>>>>>>:ð2Þ

SH is the solar hour used to calculate the annual solarhour and is given by

SH ¼Hour þ TC=60; 0 � Hour þ TC=60 � 24

24þ Hour þ TC=60;Hour þ TC=60 < 0

Hour þ TC=60� 24;Hour þ TC=60 > 24

8><>: ð3Þ

Declination, hour, altitude, azimuth, and altitude trans-verse solar angles are given by

d ¼ sin�1 0:39795 � cos 0:98563 p=180ð Þ SD� 173ð Þð Þ½ � ð4ÞHA ¼ ðp=180Þ � 15 � ðSH� 12Þ ð5Þa ¼ sin�1 sinðdÞ � sinðkÞ½ � þ cosðdÞ � cosðHAÞ � cosðkÞ ð6Þ

a ¼

p� sin�1ð� cosðdÞ � sinðHAÞ= cosðaÞÞ; cosðHAÞ� tanðdÞ= tanðTCÞ

2pþ sin�1ð� cosðdÞ � sinðHAÞ= cosðaÞÞ; cosðHAÞ< tanðdÞ= tanðTCÞ

8>>><>>>: ð7Þ

AT ¼a; a� pj j < 1

tan�1 tan að Þcos p=2það Þj j

� �; a� pj j � 1

(ð8Þ

SA is the shadow argument needed to evaluate shadoweffects on incident solar radiation. SA is a function of PTCrow distance and aperture width plus the altitude trans-verse solar angle

SA ¼ RD

AW� cosðp=2�ATÞ ð9Þ

Shadow efficiency is a multiplier used to adjust incidentsolar radiation to account for PTC shadow eclipsing the SFaround sunrise and sunset

gShadow ¼1; SA � 1

0; SA < 0

SA; 0 � SA < 1

8><>: ð10Þ

IA is the incident angle defined as the angle betweensolar beams and the line normal to the PTC aperture. Itis constantly changing and can be calculated by

IAM is the incident angle modifier multiplier used to

adjust incident solar radiation to account for direct and

M. Abutayeh et al. / Solar Energy 105 (2014) 381–389 385

indirect losses due to incident angle. IAM can be estimatedby the following correlation

IAM ¼ cosðIAÞ � 0:0300802842443682 � IA

� 0:0938882616103359 � IA2 ð12Þ

End loss efficiency is a multiplier used to adjust incidentsolar radiation to account for radiation incident on andreflected off PTC periphery that does not land on theabsorber

gEnd Loss ¼ 1� FLPTC

LPTC

� tanðIAÞ ð13Þ

Absolute efficiency is the overall multiplier used toadjust incident solar radiation given by

gAbsolute ¼ gOptical � gShadow � gEnd Loss � CMirror � IAM ð14Þ

Solar radiation sensors measure direct normal irradi-ance (DNI) and forward its value to the distributed controlsystem (DCS) to be used for control purposes. Directincident irradiance (DII) represents the solar radiationavailable for exploitation. It is a ration of DNI and canbe determined by

DII ¼ gAbsolute �DNI ð15Þ

If spatial variation of solar radiation is not an issue,DNI and DII given above pertain to all of the SF loops.CSP plants usually have a few weather stations measuringDNI and their output is averaged to yield a DNI valueintended for the entire SF. This will result in an evendistribution of HTF among all of the loops since they arestructurally identical and are exposed to equal amountsof solar radiation.

If spatial variation of solar radiation is significant due tofrequent cloud covers, DNI and DII given above pertain toindividual loops. If that is the case, CSP plants need toinstall DNI sensors on all the loops to give individualizedDNI readings. This will result in an uneven distributionof HTF among the loops since they are structurallyidentical but are exposed to different amounts of solarradiation.

The above DII equation reflects the first scenario whereDNI applies to all of the SF loops. If the second scenario isdesired, then the above DII equation needs to be writtenfor each loop. Explicitly: DIILoop 1 = gAbsolute�DNILoop 1,DIILoop 2 = gAbsolute�DNILoop 2, . . ., DIILoop n = gAbsolute-

�DNILoop n

. This will depict the spatial variation of solarradiation within the SF and will result in different HTFflow rates in SF loops, as will be evident later, to attain aset temperature for HTF exiting the solar field.

Solar heat absorbed in one loop can be calculated by

qDIILoop ¼ NPTC per Loop � LPTC � AW PTC �DII ð16Þ

HTF flow required to attain that set HTF exit tempera-ture in each loop is calculated by

mLoop ¼qDII

Loop � qPipe LossLoop � qPTC Loss

Loop

1000 � ðhOutHTF � hIn

HTFÞð17Þ

HTF enthalpy is a function of its temperature, hHTF =f(THTF), and that function is usually provided by theHTF manufacture. Outlet HTF enthalpy is evaluated atits desired set exit temperature, while inlet HTF enthalpyis evaluated at its SF inlet temperature which is a knowndesign parameter. Pipe heat loss applies to the insulatedpipe portion of the loop and can be easily calculated using:qPipe Loss = UPipe�APipe�DT. PTC heat loss applies to theexposed portion of the loop, aka the absorber, and canbe estimated using functions usually provided by theabsorber manufacture. PTC heat loss is a function ofabsorber surface area, wind speed, and temperature gradi-ent, qPTC Loss = f (APTC, SWind, DT). The aforementionedtemperature gradient, DT, refers to the difference betweenthe average HTF temperature and ambient temperature.

Total HTF mass flow rate provided by the HTF pump iscalculated by summing up all loop flows

mPump ¼X

mLoop ð18Þ

Loop HTF volumetric flow is needed to calculate inletvalve flow coefficient and is calculated by

vLoop ¼ mLoop=qInHTF ð19Þ

Total HTF volumetric flow is needed to calculate HTFinlet pressure and is calculated by

vPump ¼ mPump=qInHTF ð20Þ

HTF density is a function of its temperature, qHTF =f(THTF), and that function is usually provided by theHTF manufacture. Inlet HTF density is evaluated at itsSF inlet temperature which is a known design parameter.

Next, the piping network of the SF will be divided intonodes where calculations will be performed at each node todetermine loop inlet and outlet conditions. A node is apoint in the piping network where HTF flow either splitsor merges. A node can also represent a point where pipediameter changes; however, that usually happens at pointswhere HTF flow either splits or merges anyway. HTF flowsplits from a supply header to feed SF loops and mergeswith a return header to bring solar heat to the PB as illus-trated in Fig. 2. To flow the right amount of HTF througheach loop, pressure should be calculated at all the nodes ofthe piping network. The resultant pressure drop acrosseach loop is subsequently used to find all loop inlet valvepositions.

The diameter and total length of all the different parts ofthe SF need to be obtained beforehand. Diameter refers topipe internal diameter, while total length refers to actualplus equivalent lengths. Equivalent lengths for elbows, U-turns, T-intersections, and others are widely available in lit-erature. Pipe fittings and geometry should also be obtainedbeforehand from detailed SF drawings and their equivalent

386 M. Abutayeh et al. / Solar Energy 105 (2014) 381–389

lengths added to actual lengths to get total lengths. Loopsconsist of varying pipe segments; however, it is reasonableto assume an average loop diameter since all loops areidentical.

Total length of each pipe segment between nodes alongthe supply and return headers is given by

LTotal ¼ LActual þX

LEquivalent ð21Þ

HTF mass flow rate of each pipe segment between nodesalong the supply header is calculated by

mnSupply Header ¼ mPump �

Xn�1

1

mLoop ð22Þ

For example, HTF mass flow rate at the node feedingLoop 48 is equal to the total HTF mass flow rate providedby the HTF pump minus the sum of HTF mass flow ratesin Loop 1 though Loop 47.

HTF mass flow rate of each pipe segment between nodesalong the return header is calculated by

mnReturn Header ¼

XLast

n

mLoop ð23Þ

For example, HTF mass flow rate at the node reclaimingLoop 48 is equal to the sum of HTF mass flow rates inLoop 48 though the last loop.

It is worth mentioning that HTF mass flow rate at cor-responding nodes on the supply and return header pipesare equal. For example, HTF mass flow rate at the nodefeeding Loop 48 equals HTF mass flow rate at the nodereclaiming Loop 48. Therefore, it is sufficient to computeHTF mass flow rate along just one of the header pipes thenequate the results to the corresponding nodes of the otherheader pipe. Explicitly

mnSupply Header ¼ mn

Return Header ð24Þ

HTF flow in the SF has to always remain turbulent inorder to have a uniform HTF temperature in the axialdirection. Uniform axial mixing will bring about theaccurate temperature measurement needed for optimumcontrol. Absorber manufactures specify a minimum HTFflow rate to protect against tube ruptures due to overheat-ing, which is caused by the low flow arising from erroneousunderestimated temperature measurement.

Reynolds number of each pipe segment between nodesalong the supply header pipe is calculated by

RenSupply Header ¼

4 � 1000 � mnSupply Header

p � DSupply Header � lInHTF

ð25Þ

Reynolds number of each pipe segment between nodesalong the return header pipe is calculated by

RenReturn Header ¼

4 � 1000 � mnReturn Header

p � DReturn Header � lOutHTF

ð26Þ

HTF viscosity is a function of its temperature, lHTF =f(THTF), and that function is usually provided by theHTF manufacture. Outlet HTF viscosity is evaluated at

its desired set exit temperature, while inlet HTF viscosityis evaluated at its SF inlet temperature which is a knowndesign parameter.

HTF pressure decreases along its header pipes and in SFloops due to wall friction. The magnitude of this pressuredrop, also known as head loss, depends on average HTFvelocity and can be estimated using the Darcy–Weisbachphenomenological equation. Furthermore, the Darcy–Weisbach equation includes a dimensionless friction factorthat denotes pipe resistance to flow. That friction factorcan be estimated by various empirical and theoretical rela-tions available in literature or it may be obtained from pub-lished charts. The Moody approximation of theColebrook–White equation is chosen to find the frictionfactor along HTF header pipes for its simplicity.

Friction factor of each pipe segment between nodesalong the supply header pipe is calculated at turbulent con-ditions by

f nSupply Header ¼ 0:0055þ 0:0055

� 20; 000 � �Pipe

DnSupply Header

þ 1; 000; 000

RenSupply Header

" #13

ð27Þ

Friction factor of each pipe segment between nodesalong the return header pipe is calculated at turbulent con-ditions by

f nReturn Header ¼ 0:0055þ 0:0055

� 20; 000 � �Pipe

DnSupply Header

þ 1; 000; 000

RenReturn Header

" #13

ð28Þ

e is pipe absolute roughness, while e/D is pipe relativeroughness. Pipe roughness can be thought of as a flowresistance and its value is widely available in literaturefor different pipe materials. The piping network of the SFis made up of the same material; therefore, the same piperoughness would be used for all of the different pipesegments.

Pressure drop of each pipe segment between nodes alongthe supply header pipe is calculated by the Darcy–Weis-bach equation

DP nSupply Header ¼

f nSupply Header � Ln

Supply Header � mnSupply Header

2

qInHTF � Dn

Supply Header5 � 105

ð29Þ

where LSupply Header refers to the total length, actual plusequivalent, of pipe segments between nodes along the sup-ply header pipe.

Pressure drop of each pipe segment between nodes alongthe return header pipe is calculated by the Darcy–Weisbachequation

M. Abutayeh et al. / Solar Energy 105 (2014) 381–389 387

DP nReturn Header ¼

f nReturn Header � Ln

Return Header � mnReturn Header

2

qInHTF � Dn

Return Header5 � 105

ð30Þ

where LReturn Header refers to the total length, actual plusequivalent, of pipe segments between nodes along thereturn header pipe.

HTF pressure at each node of the supply header pipeequals HTF pressure at the previous node minus the pres-sure drop of the pipe segment upstream of the current node

P nSupply Header ¼ P n�1

Supply Header � DP nSupply Header ð31Þ

HTF pressure at each node of the return header pipeequals HTF pressure at the previous node minus the pres-sure drop of the pipe segment upstream of the current node

P nReturn Header ¼ P n�1

Return Header � DP nReturn Header ð32Þ

The previous two equations show that a starting point isneeded to initiate the calculation of HTF pressure at all SFnodes. HTF pressure at the first node of the supply headerpipe equals HTF pump outlet pressure which is a functionof its volumetric flow as given by its system curve,PPump = f(vPump).

The system curve function is usually provided by thepump manufacture. On the other hand, HTF pressure atthe first node of the return header pipe equals HTF pres-sure at the last node of the supply header pipe minus thepressure drop across the last SF loop. The inlet valve ofthe last loop is fully open because no HTF is neededbeyond that point; therefore, its pressure drop contributioncan be ignored. Thus, the initial HTF pressure at the firstnode of both header pipes can be found by

P 1Supply Header ¼ P Pump ¼ f ðvPumpÞ ð33Þ

P 1Return Header ¼ P Last

Supply Header � DP LastLoop ð34Þ

HTF pressure at each SF node has been expressed; thus,loop inlet and outlet HTF pressures are now known. Sub-sequently, the pressure drop across SF loops should becomputed then used to find the desired pressure dropacross their inlet valves, PSupply Header � PReturn Header =DPLoop + DPValve. The proper valve position of each loopinlet valve can then be determined via its Cv curve.

Average Reynolds number of each SF loop is calculatedby

RenLoop ¼

4 � 1000 � mnLoop

p � bDLoop � l̂HTF

ð35Þ

Friction factor of each SF loop is calculated at turbulentconditions by the Moody approximation of the Cole-brook–White equation

f nLoop ¼ 0:0055þ 0:0055

� 20; 000 � �PipebDLoop

þ 1; 000; 000

RenLoop

" #13

ð36Þ

Pressure drop across each SF loop is calculated by theDarcy–Weisbach equation

DP nLoop ¼

f nLoop � LLoop � mLoop2

q̂HTF � bD5Loop � 105

ð37Þ

Average values for diameter, density, and viscosity areused in the above loop calculations; however, that is con-sidered sufficient since all SF loops are structurally identi-cal. Diameter may slightly change within a loop due topipe connections between absorbers; therefore, an averagevalue is used to simplify calculations. HTF temperature,and subsequently its density and viscosity, will be varyingwithin a SF loop as the HTF picks up solar heat while flow-ing in the focal line of the collectors. Consequently, HTFdensity and viscosity averaged between loop inlet and out-let temperatures are used in the above loop calculations.

Desired pressure drop across each loop inlet valve is cal-culated by

DP nValve ¼ P n

Supply Header � P nReturn Header � DP n

Loop ð38Þ

The flow coefficient of each loop inlet valve can be cal-culated by definition

CvnValve ¼ 4162 � vn

Loop �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiSGIn

HTF

DP nValve

sð39Þ

Finally, the valve position of each loop inlet valve can beobtained from the value of its flow coefficient via a so-called Cv curve function supplied by the valve manufacture

VPnValve ¼ f ðCvn

ValveÞ ð40Þ

Note that the valve position of the last loop is set as fullyopen because no HTF is needed beyond the last loop;therefore, CvValve and VPValve of last loop valve need notto be calculated. Based on the equation expressing the ini-tial HTF pressure at the first node of the return header pipegiven above, DPValve of the last loop valve will be zeroresulting in infinity CvValve and fully open VPValve.

5. Procedure

One of the most important measures in optimizing theperformance of PTC type CSP plants is proper distributionof HTF within their SF. Poor HTF distribution results infrequent thermal shocks of HTF equipment due to oscillat-ing HTF temperatures caused by poor control of its flow inresponse to changing DNI. In addition, poor HTF distri-bution among SF loops will force the DCS to defocus somePTC collectors to mitigate solar heat input so as to avoidHTF overheating. Unnecessary defocusing amounts to fueldumping; therefore, proper HTF distribution among SFloops is top priority for CSP plant operators in order toget the most out of available solar radiation.

The DCS seeks to maximize outlet HTF temperaturefrom the SF to maximize power generation as was men-tioned earlier. This is very difficult to accomplish via a sim-ple feedback control loop due to the large HTF residence

DNI mPump

FT

VFD

Model

FC + TC

TT

SP

Fig. 4. HTF distribution control adapted for SF with no spatial variation.

388 M. Abutayeh et al. / Solar Energy 105 (2014) 381–389

time in the SF caused by its enormous size; therefore, feed-forward control needs to be integrated into the outlet HTFtemperature control logic. Solar radiation level is the vari-able that determines how much heat is going to beabsorbed by the HTF; hence, it will be input into the feed-forward controller. Moreover, maximizing outlet HTFtemperature from the SF will be sought after by maximiz-ing outlet HTF temperature from each SF loop. The outletHTF temperature control logic depends on the spatial var-iation of solar radiation within the SF.

If spatial variation of solar radiation within the SF isnot an issue, a single DNI value is obtained for the entireSF. HTF flow rate per loop is then obtained using theabove calculations. HTF flow rate in the entire SF isobtained by multiplying its flow rate per loop with thenumber of SF loops since HTF flow rate is identical inevery loop. HTF flow rate, Reynolds number, friction fac-tor, and pressure drop along both header pipes are calcu-lated using relations given above. Pressure at each nodealong both header pipes is calculated progressively startingwith the initial HTF pressure at the first node of bothheader pipes as detailed above. Finally, the valve positionof each loop inlet valve is obtained using its Cv value thatwas obtained via the desired pressure differential acrosseach loop inlet valve. These valve positions remain thesame irrespective of solar radiation levels; therefore, man-ual balancing valves can be used to regulate HTF flowamong loops since their valve position need to be set onlyonce. A variable frequency drive (VFD) connected to the

TC

DNI

FC +FT

Model

Fig. 5. HTF distribution control adap

HTF pump can be used to modulate HTF total flow inorder to attain a set temperature for HTF exiting the SF.Fig. 4 illustrates the HTF distribution control adaptedfor a SF with no special DNI variation. Measured DNIis used to generate the set point for the HTF flow feedfor-ward controller using the above calculations, while adesired HTF exit temperature is used as a set point for atemperature feedback controller. The output of both con-trollers are added and used to adjust the speed of theHTF pump.

If spatial variation of solar radiation within the SF is anissue, a unique DNI value is obtained for each loop withinthe SF. HTF flow rate per loop is then obtained using theabove calculations. HTF flow rate in the entire SF isobtained by summing up all of the loop flow rates. HTFflow rate, Reynolds number, friction factor, and pressuredrop along both header pipes are calculated using relationsgiven above. Pressure at each node along both header pipesis calculated progressively starting with the initial HTFpressure at the first node of both header pipes as detailedabove. Finally, the valve position of each loop inlet valveis obtained using its Cv value that was obtained via thedesired pressure differential across each loop inlet valve.These valve positions are constantly varying due to the spa-tially varying solar radiation; therefore, automatic balanc-ing valves need to be used to regulate HTF flow amongloops since their valve position need constant adjustment.A VFD connected to the HTF pump can be used to mod-ulate HTF total flow in order to provide the necessary total

TT

SP

mPump

FCFT

VFD

ted for SF with spatial variation.

M. Abutayeh et al. / Solar Energy 105 (2014) 381–389 389

flow. Fig. 5 illustrates the HTF distribution controladapted for a SF with spatial DNI variation. Locally mea-sured DNI is used to generate the set point for the HTFloop flow feedforward controller using the above calcula-tions, while a desired HTF loop exit temperature is usedas a set point for a temperature feedback controller. Theoutput of both controllers are added and used to adjustthe loop inlet valve position. The generated set points forall HTF loops are totalized to generate a set point forthe HTF flow feedforward controller to adjust the speedof the HTF pump.

6. Conclusion

A flow control strategy has been developed to properlydistribute HTF among the SF loops of a PTC type CSPplant. The strategy entails manipulating inlet valve posi-tions of SF loops to control flow distribution and modulat-ing HTF pump speed to control flow rate in response to acontinually varying solar radiation in order to attain a settemperature for HTF exiting the SF. The above equationsdetail how measured solar radiation along with other fixedvariables can be used to calculate an optimum inlet valveposition for all SF loops.

If spatial variation of solar radiation within the SF isnot an issue, manual balancing valve positions are set onceand kept constant at all times because those valve positionswill guarantee even HTF distribution among all of the SFloops irrespective of the magnitude of solar radiation. Out-let HTF temperature from the SF is then regulated via aHTF pump control logic comprising a DNI-driven flowfeedforward controller trimmed by a temperature feedbackcontroller. Hence, a process control loop is applied aroundthe entire SF as one global system with fixed inlet loopvalve positions.

If spatial variation of solar radiation within the SF is anissue, automatic balancing valves are used because theirvalve positions can be varied independently to controlHTF distribution among SF loops. Outlet HTF tempera-ture from each SF loop is regulated via an inlet loop valvecontrol logic comprising a DNI-driven flow feedforwardcontroller trimmed by a temperature feedback controller.

Hence, a process control loop is independently appliedaround each SF loop to manipulate its inlet loop valveposition. Furthermore, the HTF flow signals generatedby all the loops are totalized to generate a set point forthe flow feedforward controller of the HTF pump controllogic. This proposed HTF pump control logic does notrequire a feedback controller since temperature is locallycontrolled in SF loops.

HTF pump control logic will obviously include upperand lower flow limits corresponding to pump and PTCabsorber limitations. Reaching the upper flow limit willinvolve PTC defocusing to limit solar heat input, whilereaching the lower flow limit will result in reduced HTFexit temperature. Spreadsheet simulations showed thatHTF flow varies linearly with solar radiation, m = a �DII + b, while pressure drop across the entire SF variesparabolically with solar radiation, DP = a � DII2 + b �DII + c.

References

Abutayeh, M., Goswami, D.Y., Stefanakos, E.K., 2012. Solar thermalpower plant simulation. Environ. Progr. Sust. Energy J. 32, 417–424.

Camacho, E.F., Rubio, F.R., Berenguel, M., Valenzuela, L., 2007a. Asurvey on control schemes for distributed solar collector fields. Part I:Modeling and basic control approaches Original Research Article.Solar Energy 81 (10), 1240–1251.

Camacho, E.F., Rubio, F.R., Berenguel, M., Valenzuela, L., 2007b. Asurvey on control schemes for distributed solar collector fields. Part II:Advanced control approaches Original Research Article. Solar Energy81 (10), 1252–1272.

Cohen, G.E., Kearney, D.W., Kolb, G.J., 1999. Final Report on theOperation and Maintenance Improvement Program for ConcentratingSolar Power Plants. SAND99-1290. Sandia National Laboratories;Livermore, CA.

Lippke, F., 1995. Simulation of the Part Load Behavior of a 30 MWeSEGS Plant. Sandia National Laboratories, Albuquerque, NM,SAND95-1293.

Schindwoff, R., 1980. Fluid Temperature Control for Parabolic TroughSolar Collectors. Joint Automatic Control Conference, San Francisco,CA.

Stuetzle, T., Blair, N., Mitchell, J.W., Beckman, W.A., 2004. Automaticcontrol of a 30 MWe SEGS VI parabolic trough plant OriginalResearch Article. Solar Energy 76 (1-3), 187–193.

Zunft, S., 1995. Temperature control of a distributed collector field. SolarEnergy 55 (4), 321–325.