1-s2.0-S0038092X11002350-main

Optimal time-invariant operation of a power and water

cogeneration solar-thermal plant

Amin Ghobeity a ,Corey J.Noone a ,Costas N.Papanicolas b ,Alexander Mitsos a ,?

Department of Mechanical Engineering,Massachusetts Institute of Technology,77Massachusetts Avenue,Cambridge,MA 02139,USA

The Cyprus Institute (CyI),15Kypranoros Street,Nicosia 1061,Cyprus

Received 22July 2010;received in revised form 11January 2011;accepted 20June 2011

Available online 19July 2011

Communicated by:Associate Editor Robert Pitz-Paal

Abstract

Conceptual design,system-level models,and optimization of operation are presented for a cogeneration solar-thermal plant.The solar-thermal energy collected and concentrated in a salt pond is used in a regenerative Rankine steam cycle with an extraction turbine to produce electricity and process steam.The desalination system is based on reverse osmosis (RO)and multi-e?ect distillation (MED).An equation-oriented modeling environment is used for the development of time-dependent system-level models required for optimiza-tion of the plant.A meteorological radiation model is used to estimate the hourly distribution of beam radiation as a function of time (day and hour),location,and local weather (mainly visibility and humidity).A recently developed model is used to estimate the ?eld e?ciency,including projection losses and shading/blocking for a given heliostat layout.Time-invariant optimal operating conditions are presented for a summer day,considering Cyprus as a case study.Seawater desalination processes,RO and MED,are modeled by adapting and extending models from the literature.A control-volume model is developed for the steam cycle based on the ?rst and sec-ond law,with given isentropic e?ciencies,turbine leaks,and a detailed model for thermodynamic properties of steam/water.This model is validated and allows for optimization over a wide range of operating conditions,e.g.,various extraction pressures.The optimization problem is formulated as a nonlinear program (NLP)with dynamics embedded and a heuristic global optimization approach is used.The sequential method of optimization is used,decoupling the simulation from the optimization.The results show that for the plant size con-sidered (4MW e equivalent nominal capacity)and the MED design chosen based on the literature and industry practice,RO is preferred over MED from an energy point of view.In addition,under the current feed-in tari?(FiT)and water prices in Cyprus,extracting steam for MED is not recommended.In contrast,if current market prices for electricity and water in Cyprus are used,i.e.,FiT is neglected,with a typical steam cycle design,extracting steam for MED at low pressures yields maximum income.A new process con?guration is presented based on the ?ndings from the case studies,resulting in signi?cantly higher income and exergetic e?ciencies.ó2011Elsevier Ltd.All rights reserved.

Keywords:Solar-thermal cogeneration plant;Concentrating solar power;Seawater desalination by solar power;MED and RO;System-level optimization of solar plants

1.Introduction

Combined electricity generation and seawater desalina-tion via solar-thermal energy sources is considered.Seawa-

ter desalination is being increasingly considered in various parts of the world as a viable method to address the shortage of potable water.However,seawater desalination methods are energy intensive and indirectly (or even directly)contribute to CO 2emission (Darwish et al.,2009).Desalting seawater using renewable energy sources (RES)is a promising alternative,particularly for islands and remote areas,and has recently received considerable

?Corresponding author.Tel.:+16173246768.

E-mail address:amitsos@https://www.360docs.net/doc/934883900.html, (A.Mitsos).

https://www.360docs.net/doc/934883900.html,/locate/solener

Solar Energy 85(2011)

2295–2320

Nomenclature

English Symbols

A perm membrane’s permeability to water(m3/m2/s/bar) C c concentration of solute in brine(g/L)

C f concentration of solute in feedwater(g/L)

C H pump’s non-dimensional head

C p concentration of solute in permeate(g/L)

C Q pump’s non-dimensional capacity

C W pump’s non-dimensional power

D pump’s impeller diameter(m)

E?net speci?c energy consumption(kWh/m3)

E net net energy consumption rate(kWh)

g gravity(m/s2)

H pump’s head(m)

L binary variable de?ning operation mode(0=no operation,1=operating)

N pump shaft frequency(Hz)

N Max maximum frequency of variable frequency drive (100%rated speed)

N e total number of elements in system

N epv number of elements per vessel

P f feed pressure at the inlet of the vessel(bar)

P atm atmospheric pressure(bar)

P conc pressure of the concentrate stream(bar)

P in pressure at the suction of high-pressure pump (bar)

P net net driving pressure(bar)

PF concentration polarization factor

Q pump’s capacity(m3/s)

Q pw permeate water production rate per element(m3/ day)

Q T pw total volumetric permeate water production(m3)

r membrane salt rejection factor

S e membrane’s active surface area(m2)

t time(s)

T w feedwater temperature(°C)

TCF temperature correction factor

W power requirement of pump(W)

Y recovery ratio

TDS total concentration of dissolved solids

heat transfer rate from heat source i to the steam

cycle(kW)

W e?net equivalent power produced from the plant (kWh)

T i temperature of heat source i in steam cycle(K) T c temperature of heat sink in steam cycle(K)

C wàe constant to convert water production to an

equivalent electricity production(kWh/m3)

I b beam solar radiation(kW/m2)

I0solar constant(kW/m2)

I ex extraterrestrial solar radiation(kW/m2)C a Mie scattering(aerosol absorption)correction

factor

C r Rayleigh scattering(molecules absorption)cor-

rection factor

C o ozone absorption correction factor

C w water vapor absorption factor

C mg mixed gases absorption correction factor

M optical airmass

M0pressure-corrected optical airmass

P atm atmospheric pressure(assumed 1.01325bar) (bar)

P amb ambient pressure(bar)

X o total column of ozone in the atmosphere(cm) X w total column of precipitable water in the atmo-sphere(cm)

e m partial pressure o

f water in air(bar)

N day the number of the day in year(1=January1, 365=December31)

H site elevation(m)

d1to d7constants used for calculation of total column of ozone

t sh total hours of sunshine per day(h)

t time(s)

E in energy concentrated into the pond(kW)

F se view factor from the pond(i.e.,the surface of the

salt)to the environment

A h total re?ecting area of the heliostats(m2)

M salt total mass of salt mixture in the pond(kg)

C salt

average speci?c heat capacity of salt mixture kJ/

(kg K)

T salt temperature of salt mixture in the pond(K)

_E pond

the energy extracted from the pond for producing

steam(kW)

_E lid

the energy extracted from the lid for producing

steam(kW)

M lid mass of the lid(kg)

C lid

average speci?c heat capacity of the lid kJ/(kg K) T lid temperature of the lid(K)

A a total area of the aperture(m2)

C w

average speci?c heat capacity of water kJ/(kg K) _M

MED

mass?ow rate of the feedwater to MED(kg/s) _M

mass?ow rate of the feedwater to RO(kg/s)

_E lid

loss

total energy losses from the lid through radiation

and convection(kW)

h x speci?c enthalpy at port x(inlet,extraction,or

exhaust)of the turbine(kJ/kg)

P x pressure at port x(inlet,extraction,or exhaust) of the turbine(MPa)

T x temperature at port x(inlet,extraction,or ex-haust)of the turbine(K)

2296 A.Ghobeity et al./Solar Energy85(2011)2295–2320

s x speci?c entropy at port x(inlet,extraction,or ex-haust)of the turbine kJ/(kg.K)

_m x mass?ow rate at port x(inlet,extraction,or ex-haust)of the turbine(kg/s)

W e gross electricity generated by the generator(kW) Q c heat transferred from steam to cooling water of the condenser in steam cycle(kW)

cooling water?ow rate of the condenser in the

steam cycle(kg/s)

T cw out outlet temperature of cooling of the condenser in steam cycle(K)

T cw in inlet temperature of cooling of the condenser in steam cycle(K)

T steam temperature of charge steam to MED(K) N e?ects number of e?ects in MED

C feed feedwater salinity(g/L)

T MED w feedwater temperature to MED(K)

C max brine maximum allowable brine concentration(g/L)

TBT top brine temperature(K) BPE boiling point elevation(K)

_M s charge steam?ow rate in MED(kg/s)

_D F i water production rate through?ashing in e?ect i of MED(kg/s)

_D E i water production rate through evaporation in ef-fect i of MED(kg/s)

_F i feedwater?ow rate to e?ect i of MED(kg/s)

brine?ow rate from e?ect i of MED(kg/s) GOR gained output ratio of MED(kg/kg)

X b brine salinity of MED(g/L)

X f feedwater salinity of MED(g/L)

T b i temperature of brine in e?ect i of MED(K)

C f concentration of solute in feedwater(g/L)

T RO w temperature of feedwater to RO(K)

S e active surface area of RO membranes(m2)

A perm permeability of RO membranes to water(m3/m2/

s/bar)

FF fouling factor of RO membranes

r salt rejection of RO membranes

P in pressure at the suction of RO’s high-pressure pump(bar)

P f feed pressure at the inlet of the vessel(bar) Greek Symbols

D P fc pressure loss across one vessel(bar)

g e?ciency

P osmotic pressure in the concentrate?ow(bar)

U electricity tari?rate($/kWh)

U T total electricity cost per day($)

p osmotic pressure of feedwater(bar)

h z solar zenith angle(rad)

d declination angle,angular position of th

e sun at

solar noon(rad)

/solar latitude(rad)

x hour angle(rad)k1,k2constants used for calculation of aerosol optical thickness d a

a,b constants used for calculation of aerosol optical thickness d a

d a aerosol optical thickness

x ss sunset hour angle(rad)

g?eld heliostat?eld e?ciency

lid emissivity of the lid

salt average emissivity of the salt mixture

D T MED temperature raise of the MED feedwater through

heating at the lid(K)

D T RO Temperature raise of the RO feedwater through

heating at the lid(K)

D T average temperature drop across MED e?ects

(K)

D h vap average enthalpy of vaporization(kJ/kg)

g x e?ciency of component x(pump,VFD,PX,etc.)

in RO

g I?rst law e?ciency of the steam cycle(energetic

e?ciency)

g II second law e?ciency of the steam cycle(exergetic

e?ciency)

D P fc pressure loss across one vessel(bar) Subscripts and Superscripts

bp superscript denoting booster pump

cp superscript denoting circulating pump

hp superscript denoting high-pressure pump

m subscript denoting electric motor

p subscript denoting pump

px subscript denoting pressure exchanger

VFD subscript denoting variable frequency drive

in inlet to turbine

exh.turbine’s exhaust

ext.i extraction port i of the turbine

turb.turbine

PFD process?ow diagram

gear gearbox

gen.generator

sg.steam generator

pw process water(condensed steam returned from MED)

OFWH open feedwater heater

CFWH closed feedwater heater

salt salt pond

lid lid

RO reverse osmosis

MED multi-e?ect distillation

cond.condenser

SSR seal steam regulator

hp high-pressure pump

px pressure exchanger

VFD variable frequency drive

m electric motor

A.Ghobeity et al./Solar Energy85(2011)2295–23202297

attention(Blanco et al.,2009;Alarco′n-Padilla et al.,2008; Garcia-Rodriguez,2002;de la Nuez Pestana et al.,2004; Miranda and In?eld,2003).Utilization of concentrating solar power(CSP),in particular,for large-scale seawater desalination has been considered by several investigators, most notably,at the German Aerospace Center(DLR) (Trieb et al.,2009),and at the Plataforma Solar de Almer?′a (PSA)(Alarco′n-Padilla et al.,2008)in Spain(e.g.,the AQUASOL project).The Acquasol1project(Hardiman et al.,2009),a large-scale CSP-desalination plant currently under development in Australia,is also noteworthy.PSA has been perhaps the most active institution in designing system and demonstrating the feasibility of utilizing solar energy for combined power and water cogeneration plants. AQUASOL at PSA is a demonstration plant in which large-scale seawater desalination via solar energy is demon-strated.In AQUASOL,compound parabolic concentrators (CPCs)and fossil-?red boilers provided the energy required for simultaneous power generation and seawater desalina-tion by a multi-e?ect distillation(MED)system.Solar energy was also utilized in a solar dryer to produce salt from the brine.POWERSOL(Garcia′-Rodr?′guez and Blanco-Ga′lvez,2007)and MEDESOL(Blanco-Ga′lvez et al.,2009)are two other concepts for power and water cogeneration via solar energy that are developed at PSA and both consider membrane distillation technologies for seawater desalination.Previously developed conceptual designs and/or the pilot plants for the combined power generation and seawater desalination via solar energy have considered conventional solar collection designs,namely CPCs in AQUASOL(Alarco′n-Padilla et al.,2008);para-bolic troughs in“Acquasol1”(Hardiman et al.,2009);?at panel and one-axis sun tracking parabolic trough collectors in POWERSOL(Garcia′-Rodr?′guez and Blanco-Ga′lvez, 2007).A new solar-thermal cogeneration concept is consid-ered in this paper.The proposed plant stores energy ther-mally at two temperatures.The high exergy heat collected is used for power generation,while the low exergy heat collected by the system is used for preheating feedwater of seawater desalination as well as preheating in power cycle.Herein,a cogeneration plant is considered,i.e.,one producing both electricity and desalinated water.Another term used in the literature to describe this concept is dual-purpose plant.A non-conventional solar energy collection and storage system is considered in the present study.The energy collection and storage used herein provides the possibility of using low-exergy heat collected in the solar-thermal energy receiver system.Also,the focus of prior work is on feasibility of using solar energy for large-scale desalination,whereas the present study focuses on systematic modeling and optimization of a cogeneration concept.In particular,the focus of the present study is on system-level models,novel systems integration,dynamic simulation,and systematic optimization of a novel conceptual design for combined electricity generation and seawater desalination via solar-thermal energy.In addition, the concept considers a recently developed design as the thermal energy storage(Slocum et al.,2011)of the plant.

The conceptual design for the plant includes three major sub-systems:the solar energy collection and storage,the electricity and process steam generation,and the seawater desalination.Fig.1depicts the conceptual process?ow dia-gram.As shown in Fig.1,the CSP system con?guration considered here is di?erent from the conventional central tower systems(e.g.,Solar One(Alpert and Kolb,1988), Solar Two(Apacheco et al.,2000),Solar Tres(Ortega et al.,2008),and PS10(Romero et al.,2002),or the alter-native con?guration with secondary re?ectors and concen-trators(“beam-down”con?guration)(Yogev and Epstein, 2003;Blackmon et al.,2005;Segal and Epstein,2008). Here,the design known as CSPonD(Slocum et al.,2011) is used.In this concept,heliostats strategically positioned on a hillside re?ect light directly into a salt pond.A single storage tank?lled with a nitrate salt(60wt%NaNO3, 40wt%KNO3)is the volumetric receiver combined with thermal energy storage.The energy collected by this system is used for seawater desalination and electricity generation.

Section2brie?y describes the motivations for selecting Cyprus for the case studies presented here;the objectives of the study and the methodology used are described in Section3;details of technologies selected,system con?gu-ration,and system-level models to simulate the subdivi-sions of the plant are brie?y described in Sections4and 5.Several optimization case studies and the results are pre-sented in Sections6and7.

2.Case study of Cyprus

Cyprus is considered as the case study for the solar models and optimization problems presented here.The shortage of both electricity(Zachariadis,2010)and water(Tsiourtis, 2001)in Cyprus,as well as the need to move towards cleaner power generation systems(Poullikkas et al.,2010; Poullikkas,2009a)makes Cyprus a suitable case study for cogeneration of power and water through RES.Currently, Cyprus is almost entirely dependent on imported petroleum products(Zachariadis,2010;Poullikkas,2009a).However, the country is set to meet an ambitious target of13%contri-bution from RES by2020(Poullikkas,2009a;European Commission:Directorate-General for Energy and Trans-port,2008).Solar energy has great potentials in Cyprus (Poullikkas et al.,2010;Poullikkas,2009a)and as such, solar-thermal technologies are being considered as a viable solution to meet future energy needs,while moving towards meeting the target set by the EU(Poullikkas et al.,2010; Poullikkas,2009a).Seawater desalination is considered the most reliable solution to address shortages of water in Cyprus(Tsiourtis,2001).Seawater desalination,however, puts further stress on an already strained energy system in Cyprus.The collective e?ect of the signi?cant energy requirements of desalination,the dependency of the island on imported oil,the shortage of both water and energy, and the need to generate power via RES encourages cogen-

2298 A.Ghobeity et al./Solar Energy85(2011)2295–2320

eration via RES.While direct desalination using solar energy for Cyprus has been considered previously(e.g.,Kalogirou, 1997),no system-level conceptual design and optimization of cogeneration considering recent energy policies,e.g.,the feed-in tari?(FiT),has been performed so far.

3.Goals and methodology

The goal of the study is optimization of operation for a cogeneration solar-thermal plant that uses CSPonD (Slocum et al.,2011)as the energy collection and storage,a regenerative Rankine steam cycle for power gen-eration,and a hybrid seawater desalination based on reverse osmosis(RO)and multi-e?ect distillation(MED). Semi-detailed physics-based models,required for optimiza-tion,are developed for all major elements of the plant. Although time-invariant operating conditions are sought, time-dependent models are required rather than steady-state models due to,most importantly,the inherent time-dependency of solar irradiance and the heliostat?eld e?ciency,further explained in Section A.2.The models developed are detailed,allowing for optimization of oper-ation and implementing possible operation alternatives.

An integrated model of the entire plant,including heliostats,receiver,heat storage,power generation and desalination is developed in an equation-oriented simula-tor,JACOBIAN(Numerica Technology,2009).The mod-els are validated with measurements,available models in the literature,and/or commercial software packages (including STEAM PRO Thermo?ow,2010models devel-oped by the authors’collaborators at the Electricity Authority of Cyprus The Cyprus Institute,2010).The sequential method of optimization is used,where the optimization is decoupled from the simulation,resulting in relatively small optimization problems with relatively expensive function evaluations.Heuristic global optimiza-tion is performed,by combining a multistart procedure with IPOPT(Wa¨chter and Biegler,2006)and SNOPT(Gill et al.,2005)as the gradient-based local solvers.This procedure is parallelized in a distributed-memory PC clus-ter.SNOPT(Philip and Walter,2002),a commercial code is a Fortran77implementation of a sparse successive quadratic programming algorithm with limited-memory quasi-Newton approximations to the Hessian of the Lagrangian.IPOPT(Wa¨chter and Biegler,2006)is an open-source code implemented in C++.It is an interior point method intended for large-scale optimization and can use?rst-and second-order derivatives of the objective function and constraints with respect to the optimization variables.Herein,only?rst derivatives are returned

by Fig.1.Conceptual process?ow diagram.

JACOBIAN and IPOPT uses an approximation for the Hessian.

4.Technology

Solar-thermal power plants utilize the sun’s energy to generate electricity.The energy stored from converting solar energy to thermal energy is used in a power cycle to generate electricity.The main components of a solar-ther-mal power plant are the energy collection system,the recei-ver system,the thermal energy storage,and the typical components used in conventional power cycles(e.g.,steam turbines and generators).The receiver system converts the solar energy intercepted and re?ected by the collection sys-tem.In systems with energy storage capabilities,such as the one proposed,the solar radiation received is?rst stored into a thermal energy storage medium to manage the variations in the solar energy in?ux.The storage system handles?uctuations in solar energy in?ux(e.g.,clouds passing Herrmann and Lippke,1999).It may also contain su?cient thermal energy to continue the power generation overnight,or during days with overcast weather.A heat transfer?uid(HTF),possibly di?erent from the heat stor-age medium,transfers the energy from the storage medium to the power cycle.A Rankine steam cycle described in Section A.4is considered here.Hence,the energy extracted from the energy storage system is used to generate steam in a steam generator.

The solar energy received by the collectors is only a few kWh/m2/day.To achieve higher intensities and ultimately higher operating temperatures and high exergy storage, CSP technologies are used.In CSP systems,the surface area from which the heat losses occur,i.e.,the receiver aperture,is signi?cantly less than the total surface area of the collectors.Solar towers,parabolic troughs,and dish/ Stirling systems are the main CSP technologies.The concentrating systems may also be classi?ed based on the nominal focusing geometry:point(solar towers and dish systems)and line(parabolic and Fresnel troughs).Descrip-tion and technical speci?cation of CSP systems is beyond the scope of the present section;they are explained elsewhere, e.g.,(Luzzi and Lovegrove,2004;Romero et al.,2002;Kaltschmitt et al.,2007).A point focusing sys-tem where heliostats concentrate light onto a receiver is considered here.The energy diverted and concentrated by heliostats is received by the receiver system,which is a crit-ical subsystem as it greatly a?ects the allowable operating temperatures and the overall e?ciency.Traditional receiver systems are brie?y discussed in the following.The receiver systems are classi?ed by their geometry(e.g.,tubular, volumetric)as well as the heat transfer medium(e.g.,air, molten salt,water/steam).The receiver system used in Solar One(10MW e)is an example of the vertical tubular receivers with water/steam as the heat transfer medium (Alpert and Kolb,1988;Kaltschmitt et al.,2007).CESA-1(0.875MW e tower system)also used vertical tubes with the heated steam charging the energy storage system(a 2-tank nitrate molten salt system).The di?culties faced in operating Solar One led to replacement of water/steam with molten salt in Solar Two(10MW e)(Kaltschmitt et al.,2007).In Solar Two,a nitrate molten salt was pumped from the“cold”tank of a two-tank storage system to the receiver system where it was heated up and then pumped to the hot tank,from which the required energy for the power cycle was withdrawn.The receiver system considered for“Solar Tres”(Ortega et al.,2008)is a new cylindrical molten salt receiver.Major outstanding techni-cal issues associated with the conventional receiver systems used with the tower systems are:(a)The entire system con-taining the salt(pumps,pipes,etc.)must be well insulated and kept warm overnight or during extended overcast,or ?ushed down to prevent salt from freezing in pipes and pumps.(b)Creation of large temperature gradients or local hot or cold spots due to uneven distribution of the solar in?ux to the receiver system is problematic.Such variations in temperature are created mainly by tracking errors.In addition to material challenges,uneven distribution could cause salt freezing in a short portion of tube,disrupting the plant’s operation(in the worst cases,for several hours) (Apacheco et al.,2000).The receiver system in Solar TRES is designed with the aim to better handle such problems (Ortega et al.,2008).A large cylindrical molten salt receiver designed“to minimize thermal stress and to resist inter-granular stress corrosion cracking”using nickel alloy mate-rials is considered for Solar TRES(Ortega et al.,2008). However,very little is published about the technical aspects of the receiver system considered for Solar TRES,and the concept has yet to be demonstrated and tested.Volumetric receivers are an alternative to surface receivers.There are two types of volumetric receivers:open volumetric receiv-ers and closed volumetric receivers.Closed volumetric receivers often have a quartz window in front of a cavity receiver(Buck et al.,2002).The cavity receiver transfers heat to the working?uid.In general,volumetric receivers have been shown to handle solar?uxes5–10times higher than that of tubular receivers.An example of the closed volumetric air receivers is Solgate which was a pilot hybrid solar-fossil fuel power system with direct solar heating of pressurized air charging a down stream gas turbine(Buck et al.,2002).In closed volumetric air receivers,air is trapped in a closed system and heated under pressure. The concentrated light transmits through a fused quartz window which encloses the air receiver.The outlet air tem-perature from this system is slightly above1270K(Buck et al.,2002).In open volumetric air receivers,a porous sur-face receiver intercepts the concentrated solar energy re?ected by the heliostats.The surrounding air is sucked into the system through the absorber surface.While pass-ing the absorber’s surface,the air temperature rises.Porous ceramics and wire mesh systems have been previously used as the absorber.An example of demonstrated open volumetric air receivers is TSA(3MW th–hybrid with gas burners Haeger et al.,1994).In general,air systems reach high temperatures(1270K);however,they have sev-

2300 A.Ghobeity et al./Solar Energy85(2011)2295–2320

eral major disadvantages such as low speci?c heat capacity and signi?cant heat losses.Furthermore,the high-tempera-ture air receivers are prone to frequent hardware damage. Surface oxidation of the absorber surface and frequent rup-tures in the high-temperature wire mesh absorber surface of the volumetric air receivers are examples of the di?cul-ties associated with high-temperature concentrating sys-tems using air systems(Romero et al.,2002).

There has been a great deal of research concerning the development of di?erent type of receiver systems to mini-mize the heat losses,and ultimately higher capture e?cien-cies.For instance,Yeda Research and Development Company Ltd.,the commercial arm of the Weizmann Institute of Science(WIS)owns a patent(Karni and Bertocchi,2006)in which they present a unique receiver design to minimize solar radiation heat losses.

Yeda Research and Development Company Ltd. patented the“beam-down”system as an alternate to the traditional central receiver system to reduce the signi?cant costs of the tower and pumping(Yogev and Epstein,2003; Blackmon et al.,2005;Luzzi and Lovegrove,2004;Segal and Epstein,2008).In beam-down systems,a secondary mirror is mounted at the top of the tower to re?ect the con-centrated rays from the heliostats to the receiver system on the ground.Although this approach reduces the construc-tion cost of the plant and eliminates the need for pumping salt to high altitudes,additional optical losses are intro-duced to the system by the secondary re?ector mirror and concentrators on the ground above the receiver.

CSPonD(Slocum et al.,2011)is the CSP technology considered in this study.A brief description of the CSPonD suitable for the development of system-level models is given here.In this concept,heliostats positioned on a south-fac-ing hill re?ect the light directly into the receiver on the ground(close to the base of the hill).The potential advan-tages of this concept include the elimination of the tower and the salt pumping system to transport salts to relatively high altitudes.The receiver in the CSPonD design is a salt pond which also acts as the energy storage medium.The energy storage is designed such that the radiation heat losses from the salt are predominantly absorbed by a dome structure(the lid)covering the salt pond.The lid has an opening(the aperture)that the concentrated light passes through before it is absorbed by the salt pond.The concept is further described in Slocum et al.(2011).Models devel-oped to calculate the temperature in the pond and heat losses from the system are further described in Section A.3.The heat collected at the lid is considered for pre-heat-ing the desalination feedwater(Fig.1).In Section7,an alternative use of this relatively low-grade heat is presented.

The power cycle assumed is a regenerative Rankine cycle consisting of a steam generator,an extraction turbine,a condenser,and an open feedwater heater(OFWH) (Poullikkas et al.,2009)(Fig.1).Heat is withdrawn from the pond to generate steam in the steam generator of the steam cycle.Steam is extracted from the turbine at two pressures,one for MED and another for the OFWH.The extraction pressures will be optimized.

Hybrid desalination based on RO and MED is consid-ered for seawater desalination.Although MED is the old-est known large-scale seawater desalination technology,it is not as widespread as multi-stage?ash(MSF).The inter-est in MED has been recently renewed due to technological advances such as reduced scaling,which is the deposition of heat resistant materials on heat transfer surfaces,and the development of advanced heat exchangers(Shannon et al.,2008).Similarly,RO is rapidly gaining popularity for seawater desalination mostly due to reductions in mem-brane cost and development of energy recovery units. Hence,a hybrid RO/MED desalination is assumed here. The electricity requirements of RO have been reported to be lower than equivalent electricity requirements of MED in both single-purpose(water only)and cogeneration (water and power)plants(Semiat,2008).However,the availability of low grade heat from the lid as well as by extraction steam from the turbine makes the selection of the most suitable desalination system for the proposed plant a non-trivial problem.Further potential advantage of having a hybrid RO/MED is blending of the product water from a single-stage RO,that results in low capital cost and relatively low water quality,with the product water from an MED system.For instance,the product of RO system in Mediterranean regions may need expensive post-treatment to reduce the Boron level to an acceptable level(Koutsakos et al.,2007;Ludwig,2004).Blending the permeate from these two systems may eliminate the need for such post-treatment and,in general,result in a better overall product quality(Ludwig,2004).Conse-quently,drinkable water standard qualities(World Health Organization,2008)can be met in a more e?cient way. Hamed(2005)concluded that blending of a low cost single stage RO,resulting in a high total dissolved solids(TDS)in the product water,with the product of MSF results not only in a lower total product cost and quality,but also in a lower membrane replacement cost as some stress is reduced from membranes to produce a high quality prod-uct water.Another advantage of a hybrid desalination sys-tem is operation?exibility as RO uses electricity and MED predominantly uses heat.

5.Modeling

System-level models are developed,using the equation-oriented modeling environment JACOBIAN,based on the best available models in the literature or from?rst principles.The models calculate the time-variable energy and mass balance in each sub-system.Most importantly, the models calculate the instantaneous solar energy in?ux to the receiver,the transferred energy to the power block,and the energy(thermal and electric)available to the desalination facility and provided to the power grid.Further,models are developed to calculate the energy consumption and production rate of the seawater

A.Ghobeity et al./Solar Energy85(2011)2295–23202301

RO and MED processes under a wide range of operating conditions and various heat integration schemes such as preheating feedwater for RO.The sub-models and design parameters used for beam solar radiation,MED,RO, and the steam cycle are based largely on the models available in the literature,and are described in Appendix A.The model used for solar radiation is based on Bird and Hulstrom(1981),Badescu(2008);the model for esti-mating the heliostat?eld e?ciency is described in Noone et al.(2011);the models for the receiver system and power cycle are based on heat transfer and thermody-namic principles and are provided in Appendix A;the model for RO is based on Ghobeity and Mitsos (2010),which is an extended model by DOW Chemical Company(DOW,2009);and the model for MED is based the models developed by Darwish et al.(2006, 2007,2008).An integrated plant model simulates the connection between sub-systems.

6.Optimization of short-term operation

A?xed plant size is considered for the case studies presented here.The estimates provided in the literature for the electricity and water consumption per capita(total of residential and industrial)in Cyprus are15.22kWh/day/ person(IEA,2008)and0.61m3/day/person(Donta et al., 2008)(total including domestic,irrigation,tourism,and industry),respectively.The required daily production of approximately5000persons(a design choice)is then estimated as76MWh e/day and3072m3/day,respectively. Hence,an RO system with64elements and nominal capac-ity of approximately1500m3/day is assumed.The balance of water demand for this population is expected to be pro-duced through MED.A?xed number of e?ects(8e?ects) with parallel feed con?guration is assumed for the MED design.An8-e?ect MED with an assumed gained output ratio(GOR),de?ned as the mass of product water per unit mass of charge steam,of6–7(note upper limit of GOR is the number of e?ects)will produce approximately2000–2400m3/day.The size of the MED system(i.e.,the size of heat exchangers),however,depends on the optimal operating conditions found from optimization.Speci?cally, the charge steam rate and the achieved GOR from the MED system determine the required heat transfer area for MED,which is ultimately determined after optimal operating conditions for the MED are found.The same also applies to the condenser as the size of the condenser depends on the steam extraction rate for both MED and OFWH,hence its size is calculated after optimal operating conditions are found.One should note that calculating the required heat transfer area and the cooling water for the MED and condenser after optimal operating conditions are found does not a?ect the optimization results.The objective of optimization is maximum income and not the net pro?t.

The operating challenges of the plant(and any solar-thermal plant)include short-term and long-term variations in the available solar irradiance.Short-term variation is due to the changes of radiation due to the position of the sun(e.g.,morning vs.noon vs.night)and weather?uctua-tions(e.g.,clouds reducing the direct irradiance Herrmann and Lippke,1999).Long-term variation refers to the di?er-ence of solar irradiance between summer and winter.The short-term variations are proposed to be addressed mainly by the energy storage.Long-term operation requires more complex solutions.The focus of the present study is on optimization of short-term operation on a summer day, when solar energy has highest potentials.

Optimal operation under constant operating conditions (i.e.,nominal optimum)is discussed in this section.The con-ditions considered include constant operation conditions, cloudless sky,and short-term optimization(24h)using a heuristic global optimization approach(multistart)with IPOPT(Wa¨chter and Biegler,2006)and SNOPT(Gill et al.,2005)as the nonlinear programming(NLP)local solv-ers.Design parameters,optimization variables,the objective function,the design constraints,and the results for three case studies are presented in the following.A mid-summer day, June21,is selected for all optimization case studies.

Three case studies are considered in the following:

1.Maximizing income using actual water and electricity

prices for RES(the FiT in Cyprus).Minimum allowable production rates for water and electricity are considered.

2.Maximizing a weighted energetic function.No minimum

allowable production rate for water nor electricity is considered.

3.Maximizing income using typical water and electricity

prices,neglecting all incentives.Selling price of0.92€/m3

(0.54Cyprus￡/m3Socratous,2010;Kalogirou,2001)is

assumed for water.Electricity market price in Cyprus strongly depends on fuel price(i.e.,imported petroleum), and as a result varies from about0.07€/kWh for fuel price of225€/MT to about0.17€/kWh for fuel price of600€/ MT(Poullikkas,2009b).An average purchasing tari?of

0.12€/kWh is assumed for this case study.

The optimization case studies presented here,as dis-cussed in the following,assume a?xed plant design.The fact that the electricity prices?uctuate signi?cantly with the?uctuations in oil prices emphasize the importance of optimizing the operation assuming a?xed plant design. Similar to the electricity market,FiT depends on parame-ters such as location,and is subject to uncertainties such as the change in renewable energy policies.Future work will consider simultaneous optimization of design and operation.

The optimization variables,objective functions,con-straints and the parameters(i.e.,constants)are discussed in the following sections.The optimization variables, objective functions and constraints are scaled to a range around1as gradient-based solvers,such as SNOPT(Gill et al.,2005)and IPOPT(Wa¨chter and Biegler,2006)that are considered solvers in this study,usually have di?culties

2302 A.Ghobeity et al./Solar Energy85(2011)2295–2320

in solving problems in which optimization variables have vastly di?erent orders of magnitude(Bhatti,2000).

6.1.Design parameters

The constants of the problem(key design parameters) are given in Table1.These parameters are selected based on either industry practice(e.g.,number of e?ects),a tech-nological limitation(maximum inlet temperature of540°C for the turbine),environmental requirement(e.g.,maxi-mum brine TDS of80,000ppm),or simply a design choice (day of the year).

6.2.Optimization variables

The optimization variables for the case studies presented here are shown in Table2.The optimization variables selected for the energy storage determine the optimal energy?ows for the salt pond and the lid,while the optimi-zation variables selected for power block determine optimal steam extraction conditions,and indirectly the optimal operating conditions for the MED system.The motivation for optimizing the RO’s high pressure pump shaft frequency,N,is to assess whether operating at an energy-wise sub-optimal condition is recommended,con-sidering the collective e?ect of preheating and various water and electricity prices.In addition,given the?uctua-tions in electricity demand and prices,it is desired to vary the RO’s production increase pro?t(Ghobeity and Mitsos, 2010)and/or more e?ciently meet the demand for electric-ity and water.Future work will focus on a time-variable operation and such options will be explored further.

The lower and upper bounds of the optimization vari-ables are selected based on either typical industry practice and/or technological limitations.Where such information is not available nor trivial,a relatively low value for the lower bound and a relatively high value for the upper bound is selected to ensure that the optimal solution is not restricted.

It should be noted that not all combinations are feasible due to additional constraints,which are explained in Section6.4.For instance,selecting the upper bound of D T lid

and the upper bound of the RO pump shaft frequency simultaneously results in an infeasible solution due to a constraint on RO feed pressure(CONS8in Table 3explained in Section6.4).The sensitivity of the objective function and constraints to state variables is required for gradient-based optimization and is calculated in JACOBIAN.

6.3.Objective function

Finding a suitable performance metric for power gener-ation is a relatively well-established process(e.g.,maximiz-ing energetic or exergetic e?ciency).The same however is not true for a cogeneration plant as the product of a cogen-eration plant is not simply the net power produced.Also, the performance metrics such as steam cycle e?ciency, for a cogeneration plant strongly depend on quantity and quality of the steam extracted for MED.The performance metrics selected for optimization of the plant should take into account both water and electricity production per unit energy or exergy consumed from the thermal energy stor-age.A suitable performance metric that would take into these two parameters is simply the net pro?t from selling the net electricity and water produced from a plant with ?xed design for both the energy collection and storage sys-tem.Alternatively,a weighted function independent of water and electricity prices can be considered accounting for both water and power production rate.Hence,two objective functions are selected for the optimization case studies:maximum income and a maximum weighted ener-getic function.A selling price of0.26€/kWh(Poullikkas, 2009a)for electricity(the current FiT in Cyprus)and 0.92€/m3(0.54Cyprus￡/m3Socratous,2010;Kalogirou, 2001)for water is used to calculate the income.The income here is expressed in the units of€per day:

Obj

?C1FtC2Ee1Twhere C1is the price of water(€/m3),F is the water produc-tion per day(m3/day),C2is the price of electricity(€/kWh), E is the electricity production(kWh/day).Optimization constraints enforce that the?nal temperatures in the pond and the lid are approximately equal to their initial temper-atures(T i6T f6T i+5).It should be noted that the initial temperature does not refer to the temperature after the process has been idle for a long time,but rather the temper-

Table1

Key design parameters.

Key

parameters

Value Comments

Heat collection

N day150June21st

g?eld(t)Calculated(see

Section A.2)Field e?ciency,product of cosine e?ciency,shading,blocking,and mirror re?ectivity

Power block

g isen(–)0.78Turbine’s isentropic e?ciency(assumed

constant across all stages)

T in813.15(K)Steam inlet temperature

P in40(bar)Steam inlet pressure

P exh.0.05(bar)Exhaust pressure

TDS42(g/L)Seawater’s total dissolved solids

r0.9975Membrane’s salt rejection

S e35(m2)E?ective area per membrane

N e64Total number of elements(membranes)

in system

MED

X max

B 80(g/L)Maximum allowable brine TDS

BPE0.7(K)Average boiling point elevation across

e?ects

D T2(K)Temperature drop across e?ects

N e?ects8Total number of e?ects

A.Ghobeity et al./Solar Energy85(2011)2295–23202303

ature at the beginning of the day.This is essentially the same from day to day.An alternate approach would be to consider a penalty for the net energy used from the en-ergy storage system and eliminating the constraint on the ?nal temperature of the salt and the lid.

A disadvantage of the objective function de?ned by Eq.(1)is its dependency on the regional water and electricity prices (or FiT),which also may vary with time and loca-tion.De?ning an objective function for maximizing the production independently of the price is relatively simple

for a single-purpose plant (i.e.,water or power)is relatively simple (i.e.,maximizing kWh of electricity produced or m 3of water produced).In contrast,in cogeneration there is tradeo?between the two products,and a single metric needs to be de?ned.As such,a weighted energetic function,which also takes into account the production rate of both water and electricity,is de?ned as Obj 2?E tC w àe F

e2T

Table 2

Optimization variables.Optimization variable

Description

Lower bound

Upper bound Energy storage (salt pond and the lid)

D T lid MED (K)

Di?erence between the inlet and outlet temperature of seawater in the MED feedwater preheater at the lid 0.0050.00D T lid RO (K)Di?erence between the inlet and outlet temperature of seawater in the RO feedwater preheater at the lid 0.0010.00D T lid

SG (K)Di?erence between the inlet and outlet temperature of seawater in CFWH at the lid

0.00250.00D T PB

MED (K)Di?erence between the inlet and outlet temperature of seawater

the MED feedwater preheater between

MED steam extraction and the ?rst evaporator of MED 0.0010.00T lid (t =0)(K)

Initial temperature of the lid 450753T salt (t =0)(K)Initial temperature in the salt pond 820873Power block _m

in (kg/s)Inlet steam rate of the turbine

0.25 3.50_m

ext :1(kg/s)Steam extraction rate for MED

0.25 3.50P ext :1(bar)Extraction pressure of MED extraction port 0.25 2.00P ext :2(bar)Extraction pressure of OFWH extraction port

1.0 6.00T FWH out (K)

Temperature of the condensed steam after the OFWH

337.15474Reverse osmosis (RO)N (Hz)High pressure pump shaft frequency (see Ghobeity and Mitsos,2010)

Table 3

Key constraints of optimization.Identi?er Name

Constraint Lower bound Upper bound Description of the constraint

CONS 1Salt temperature T salt (K)818

873Minimum and maximum allowable temperature of the salt mixture

CONS 2MED production R 24

0Q MED dt (m 3)1000for case study 1and 0for case study 2and 3

–Minimum allowable water production from MED

CONS 3RO production R 240

Q RO dt (m 3)

1500for case study 1and 0for case study 2and 3

–Minimum allowable water production from RO

CONS 4Power production R 24

W net e dt (MWh)

48for case study 1and 0for case study 2and 3

–Minimum allowable power production CONS 5Water production Q pwt +Q distitateT (m 3/s)0.0087for case study 1and 0for case study 2and 3

–Minimum allowable water production rate CONS 6Power production rate

W net e (MW) 1.0for case study 1and 0for case study 2and 3–Minimum allowable electricity generation rate CONS 7RO’s feedwater temperature T RO w (K)298308Maximum allowable feedwater temperature in RO

CONS 8RO’s feedwater pressure

P f (bar)6583Allowable operating pressure in RO

CONS 9MED’s feedwater temperature T MED f

(K)–

T B N eff à2Maximum allowable feedwater temperature in MED

CONS 10Lid temperature T lid (K)

–

723

Maximum lid temperature

CONS 11Salt’s ?nal temperature T salt (t =24h )(K)

T salt (t =0)T salt (t =0)+5Minimum and maximum allowable ?nal temperature of the salt mixture CONS 12Lid’s Final Temperature

T lid (t =24h )(K)T lid (t =0)T lid (t =0)+5Minimum and maximum allowable temperature of the lid

CONS 13Turbine’s inlet ?ow _m

in (kg/s) 2.10 4.172Turbine’s inlet steam ?ow rate

CONS 14

Turbine’s exhaust ?ow

_m exhaust à0:05_m in (kg/s)

–

The exhaust ?ow should be at least 5%of the inlet ?ow

2304

A.Ghobeity et al./Solar Energy 85(2011)2295–2320

where C wàe=4kWh/m3is a constant used to convert the water produced per day(m3/day)to an equivalent electric-ity production(kWh/day).This objective aims at eliminat-ing the dependence on electricity and water prices as well as on FiT.The disadvantage of using such a weighted ener-getic function is neglecting economical parameters such as capital,operation and maintenance cost.

6.4.Optimization constraints

The optimization constraints are derived from either a technological limitation(e.g.,a maximum allowable feed pressure in RO),a design requirement(e.g.,a minimum daily power or water production),or simply a requirement to ensure feasible operation(e.g.,minimum allowable approach temperature between a hot and cold stream in the steam generator,i.e.,feasible pinch point temperature di?erence).The constraints stemmed from the design requirements are derived largely based on the desired plant speci?cations,while the optimization constraints due to technological limitations are identi?ed from industry knowledge and literature review of the technologies used. For instance,a maximum allowable top brine temperature (TBT)for the MED system is an optimization constraint that is identi?ed based on literature review and understand-ing of the details of the particular technology considered.

The constraints of the problem are shown in Table3and explained in the following.The most important constraint of the problem,which puts a limitation on heat withdrawn from the pond,as well as indirectly on the heat withdrawn from the lid,is the temperature of the pond.The salt used as the heat storage medium has a freezing temperature around530K and decomposes at a temperature around 875K.The minimum allowable temperature in the pond is however subject to another constraint,that the salt tem-perature should be higher than the desired steam tempera-ture produced by the steam generator plus the pinch (minimal approach temperature)of10K.The temperature of the salt is time dependent,and consequently,care must be exercised to ensure that any constraint on the salt tem-perature is met for any given time throughout the day. Termed path constraints such as T min

Z24 0maxeT saltetTàT maxT;0;eT minàT saltetTT

f g

? 2dt6

where is a constraint violation tolerance(10à3here).The constraints identi?ed by CONS2to CONS6ensure minimum allowable instantaneous production rate and to-tal daily production of power and water in the plant. CONS7ensures that the temperature of the feedwater to RO must be lower than a maximum allowable temperature de?ned by membrane manufacturer to prevent membrane compaction(Wilf,2007).Similarly,the vessel containing the RO membranes has a pressure rating that must be en-sured(CONS8).As described in Section A.6,the tempera-ture and pressure in MED evaporators drops successively from the?rst e?ect to the last e?ect.As a result,pre-heating the MED feedwater is limited by the brine temperature in the last e?ect,which itself depends on optimal operating conditions.This constraint is shown as CONS9in Table3,in which an upper bound of2°C(a design choice) plus the brine temperature in the last e?ect is selected for the temperature of feedwater to MED.A path constraint (CONS10)ensures that the temperature of the lid is below a maximum allowable temperature(a design choice).Con-straints11and12in Table3enforce the?nal temperature of the salt and the lid to temperatures approximately equal to the initial temperatures in the pond and the lid.In par-ticular,they ensure that under ideal weather conditions (clear and cloudless sky)the optimal operating conditions selected does not use the energy stored in the pond or the lid.Also,the upper bound of these two temperatures ensure that the energy storage(salt pond as well as the lid)is not over-charged.Finally,the last two constraints in Table3ensure reliable and e?cient operation of the tur-bine.The isentropic e?ciency of steam turbines is fairly uniform between50%part-load and full-load operation, and drops sharply below50%part-load(Savola et al., 2007).The amount of steam extracted from the turbine should not be such that the exhaust?ow rate is less than 5%of the inlet?ow rate(Thermo?ow,2010)(CONS14).

https://www.360docs.net/doc/934883900.html,putational infrastructure

A parallelized Linux cluster with32nodes was used for optimization.Four DELL PCs(each with an Intel Core2 Quad Processor at2GHz processor speed)form the cluster.An in-house code links the simulator(JACOBIAN) to the local solver(IPOPT or SNOPT).

6.6.Optimal operating conditions

The optimal conditions are found using a heuristic global optimization approach(multistart)with IPOPT (Wa¨chter and Biegler,2006)and SNOPT(Gill et al., 2005)as the gradient-based local solvers.The results are the best found,but global optimality is not guaranteed. Optimal operating conditions for the three case studies are discussed in the following.

6.6.1.Case study1:Maximum income

Electricity and water prices of0.26€/kWh and0.92€/m3 results in minimum allowable water production through the MED.The optimizer chooses minimum extraction pressure for both the OFWH and the MED.The optimal steam extraction rate for MED is the lowest steam extraction rate that results in the minimum allowable water production from the MED.The optimal steam extraction rate is not the selected lower bound of steam extraction rate,i.e.,the lower bound selected for steam extraction rate is not too high.Hence,the conclusion is that under the values used

A.Ghobeity et al./Solar Energy85(2011)2295–23202305

for the electricity and water prices,and the technology con-sidered,water production through the MED system selected is not economically favorable.Note that the objective func-tion used here accounts for income from operating a?xed design.

The optimizer chooses operating conditions for RO that might seem unexpected,and hence explained further in the following.The optimizer chooses maximum possible pre-heating for RO at a rather low production rate.The system selected for RO is capable of operating between approxi-mately1400–1600m3/day through adjusting the high pres-sure pump shaft frequency and preheating.The resulting speci?c electricity consumption with maximum preheating

(i.e.,feedwater temperature of308K)is between3.2and

3.7kWh/m3,depending on shaft frequency and preheating. Hence,given the electricity and water prices used,one expects the optimizer to choose a shaft frequency close to maximum water production.The optimizer in contrast chooses the minimum shaft frequency that results in water production through RO barely higher than the speci?ed minimum allowable water production from RO.The pro?t from RO,OBJ RO

,is calculated from

OBJ RO

?F RO C1àE RO C2

where F RO and E RO are the production(m3)and energy consumption[kWh]of RO,respectively;and C1and C2 are the constants given in Eq.1.The production through RO is optimized by adjusting the shaft frequency N (Ghobeity and Mitsos,2010)and preheating.The e?ect of increasing the shaft frequency on pro?t is found from

@OBJ RO

1 @N ?

@F RO

C1à

@E RO

Considering the relations between production and energy consumption of an RO with a variable frequency drive (VFD)from(Ghobeity and Mitsos,2010),one can show that

@OBJ RO

1?F nom:

nom:

C1à

3N2

nom:

E nom:

where F nom:

RO and E nom:

are the nominal production rate and

energy consumption of RO,respectively.Hence,increasing N will increase the objective function only if

C1F nom:eC2E nom:T>

3N2

nom:

;

which under the conditions used is not satis?ed.Therefore, since the production rate of the system increases linearly with increasing shaft frequency N,while the power con-sumption increases as N2,increasing shaft frequency(i.e., increasing water production from a?x design RO)is not economical under the electricity and water prices used.

An interesting scenario arises in operation of cogenera-tion plants that use renewable energy sources.The income found from optimal operating conditions can be further increased through selling the renewable electricity to the grid at the FiT and purchasing back the required electricity for desalination from the grid at the electricity market price,which is lower than the FiT.The signi?cant di?er-ence between the FiT and the purchase rate for buying electricity o?the grid does not promote the direct use of RES for producing water.This point is further discussed in Section6.6.3.

6.6.2.Case study2:Maximum weighted-average energetic function

Optimal operation using the weighted energetic objective function,as de?ned above by Obj2,with no constraints for the water or electricity produced is considered in this section. As mentioned previously,RO uses electricity exclusively (with optional preheating of feedwater)whereas MED uses both electricity and process steam at temperatures around 338–358K.The advantage of this objective function is that it provides results to compare the energetics of MED vs. RO,assuming RO uses approximately4kWh/m3.

The results of this case study suggest no water produc-tion through MED.Optimizing for maximum income using a price of0.26€/kWh for electricity and0.92€/m3 for water with no constraint for the water production resulted in same conclusion,i.e.,zero steam extraction for MED.To further discuss the?ndings of this case study, the penalty paid(i.e.,less electricity produced)for extract-ing steam at a?xed pressure of0.5bar,as an example,and variable steam rate is studied in the following.Fig.2shows the produced electricity as a function of the extracted steam for MED.Under no steam extraction,the power produced is approximately3.8MW e.With increasing steam extrac-tion,the power produced decreases due to(a)a lower steam rate exits the turbine exhaust at exhaust pressure of0.05bar,and(b)the higher steam extraction rate for MED,the higher water production from MED,and consequently the higher MED electrical power require-

2306 A.Ghobeity et al./Solar Energy85(2011)2295–2320

ment.The resulting power reduction from steam extraction for MED is only economical if the pro?t from the water production outweighs the penalty(i.e.,less pro?t due to selling less power)from extracting steam(Fig.2).This is a strong function of the GOR achieved with the MED sys-tem as well as the water and electricity prices used.Fig.3 shows the achieved weighted sum of electricity and water as a function of GOR,steam extraction and assuming a (rather small)electricity consumption of1kWh per m3of the MED product.This shows that signi?cantly higher GORs are required for making steam extraction for MED attractive from an energy point of view,even with a low electricity requirement.These?ndings are in accor-dance with Semiat(Semiat,2008)who reports a penalty of 5.2–10kWh e/m3for a water and power cogeneration(i.e., dual-purpose desalination)plant.Considering the penalty paid for extracting steam at various pressures(i.e.,produc-ing less electricity),the minimum required GOR number that would support co-generation using MED can be found approximately as follows:for an extraction pressure of 0.25bar,the minimum required GOR number is calculated as12.7;for an extraction pressure of0.50bar,the mini-mum required GOR number calculated is18.5;and for an extraction pressure of1.0bar,the minimum required GOR number calculated is25.9.The high GOR values required at these low pressures are high given the small MED scale.Note again that a constant electricity con-sumption of1kWh/m3was assumed.

The electricity consumption of MED can be reduced using steam ejectors.Brie?y,steam ejectors use the energy contained in a high pressure stream(“a motive?uid”)to cre-ate a low pressure zone that draws in and entrains a?uid (here non-condensible gases from the last e?ect of MED) (Al-Juwayhel et al.,1997;El-Dessouky and Ettouney, 1999).In other words,steam ejectors create the required par-tial vacuum in all MED evaporators,e?ectively reducing the power requirement of MED signi?cantly.Moreover,the entrained steam from the last e?ect is added to the charge steam,resulting into a signi?cant increase in the heat avail-able to evaporate seawater in the?rst e?ect of MED.Hence, in addition to lower electricity cost,a much higher GOR can also be achieved,but at a higher energetic penalty as steam needs to be extracted at a higher pressure.On the other hand, the added product water,due to a higher GOR,is achieved at a relatively small added capital,maintenance and operation cost as steam ejectors are relatively inexpensive and operate reliably,owing to their simple design and absence of moving part(Kamali et al.,2009).Motive steam of steam ejectors, based on the values in the open literature,has typically a pressure in the order of a few bar(Kamali et al.,2009)to as high as45bar(Temstet et al.,1996).Future study will examine the thermoeconomics of using steam ejector with MED.

6.6.3.Case study3:Maximum income neglecting feed-in tari?

Given the signi?cant e?ect of FiT on optimal operating conditions,the case of maximizing income,neglecting the incentives for power produced by RES,is studied in this section.A water price of0.92€/m3and a electricity price of0.12€/kWh is assumed for this case study.The goal of this case study is twofold:(a)assessing the pro?tability of cogeneration(power and water through extracting steam for MED)under typical electricity and water price ratios, and(b)investigating whether considering an incentive for water proportional to the incentive considered for electric-ity(i.e.,FiT)will make extracting steam for MED a prof-itable option or not.The case of optimizing the operation for maximum income neglecting FiT is equivalent to the case of optimizing the operation considering incentives for water produced by RES,where the incentive is exactly proportional to the incentives considered for the electricity produced by RES,i.e.,the FiT.

The optimizer chooses similar optimal operating condi-tions as in the previous case studies,with the di?erence being in the steam extraction rate.Similar to previous case studies,the steam extraction rate for both MED and the OFWH are the lowest allowable.The temperature after the OFWH is also the lowest allowable.The di?erence here is the amount of steam extracted from the turbine for MED.Under the electricity and water prices used here, cogeneration through MED is indeed favored over power production.Speci?cally,the results show that for this case study,extracting steam at0.25bar and at the maximum allowable rate yields maximum pro?t.This shows that under typical electricity and water market prices,cogenera-tion through MED is economical despite the loss in electricity production.One should note that water to elec-tricity price ratio of6–10is a typical ratio seen in most of the regions of the world that use desalination to meet the potable water demand.Therefore,this case study demon-strates that the current energy policies in Cyprus,and most of the countries in Mediterranean region,fail to address the use of RES for cogeneration processes,or in this particular study cogeneration of water and power by solar energy.

A.Ghobeity et al./Solar Energy85(2011)2295–23202307

Incentives,designed considering current unincentivised water and electricity price and the FiT,must be considered for water produced by renewable energy sources.The opti-mal operating conditions for RO are those resulting in maximum water production,achieved through preheating and a low high pressure shaft frequency.RO is energeti-cally favorable to MED,and economically favorable to power production.As such,had the total number of mem-branes been included in the optimization (i.e.,optimization of design),the optimizer would have chosen the largest number of elements allowed.7.Revised heat integration scheme

The results of the three case studies presented in the pre-vious section indicate that selecting the lowest possible extraction pressures for both the OFWH and MED results in maximum income.Furthermore,in all three case studies,the optimal temperature after the OFWH of the steam cycle is the lowest allowed.A low steam extraction pressure in combination with a low exit temperature for the feed-water heater results in the lowest steam extraction rate from the turbine.Therefore,although extracting steam

for the OFWH increases the cycle e?ciency,it does not maximize the income.This motivates using the heat col-lected at the lid for preheating the feedwater of the steam generator in the steam cycle.The process ?ow diagram of Fig.1is modi?ed as shown in Fig.4to include the option of preheating feedwater at the lid.

Operation of the plant is re-optimized in the following,considering the process ?ow diagram given in Fig.4under three possible operating strategies (labeled as A–C in the following).Maximum income (obj 1)with a constant elec-tricity price of 0.12€/kWh and water price of 0.92€/m 3is considered in the following.The constraints of optimiza-tion are relaxed to allow zero steam extracting from the turbine to the OFWH.

The main goal of the following case studies is under-standing the e?ect of di?erent heat integration schemes such as comparing the use of extracted steam for the OFWH with the use of heat from the pond for all stages of steam generation from the condensate return,i.e.,pre-heating/evaporating/superheating.It is also of interest to compare the case of using the lid for pre-heating and the salt pond for evaporation/superheating to the case of using the energy from the salt pond for pre-heating as well as

W turb

W RO

W e

W pump

Q exchanger

W pump First Effect

Second Effect

Third Effect

Condenser

Seawater

Brine

Product water

Steam Condensate

Feed water Heater

High Pressure Feed Pump

Permeate Flow

Pressure Exchanger (PX)

Seawater

Concentrate Flow

Q solar Q absorbed

Q lost

Q solar

Q c

o n c e n t r

a t e d

Salt Pond

Steam Generator (Heat Exchanger)

Heat Collection and Storage

Power Cycle

Reverse Osmosis

MED

Q RO, MED

Feed water Heater

W MED

Booster Pump

Condenser

Pre-heater (open)

(cooling water)

W pump

MED feedwater (from the condenser in

power block)

P r e -h e a t e r (c l o s e d )

Q steam generator

Feed water Heater

Fig.4.The revised conceptual process ?ow diagram.The changes are inclusion of a closed feedwater heater (CFWH)(highlighted)in the steam cycle and elimination of the MED preheater that decreased the temperature of the extracted steam temperature before the MED.

2308 A.Ghobeity et al./Solar Energy 85(2011)2295–2320

evaporation/superheating.To investigate these,three sce-narios are considered in the following:

Case A,Most General Case:The operation is optimized considering all operating options including the use of the heat collected at the lid for pre-heating in the steam cycle(i.e.,considering all options shown in the process ?ow diagram(PFD)of Fig.4).

Case B,Using Low Grade Heat for Desalination Only: The operation is optimized disallowing the use of the

heat collected at the lid for pre-heating water in the steam cycle(i.e.,same as case A,but eliminating the closed feedwater heater in the steam cycle).

Case C,Using Low Grade Heat for Desalination Only and Restricting Steam Cycle Design:The operation is optimized disallowing the use of the heat collected at the lid for pre-heating condensed steam in the steam cycle

(i.e.,initially considered PFD as shown in Fig.1).A min-

imum exit temperature of100 C and extraction pressure of1bar are considered for the OFWH to investigate the e?ect of imposing such conditions.

Another process?ow con?guration that could be con-sidered is a reheat Rankine cycle,in which steam from exhaust of an intermediate pressure(IP)stage of the tur-bine is heated before entering subsequent lower pressure (LP)stages of the turbine.This option is not investigated here mainly because the steam turbine considered is rela-tively small(4MW e nominal power rating)and typically not suitable for a reheat Rankine cycle.

These three operating strategies are feasible under di?er-ent operating temperature ranges.Finding the feasible operating range for di?erent operating strategies is di?cult, considering the?nal constraints of

T saltet?t fTP T saltet?0Tt5K

and

T lidet?t fTP T lidet?0Tt5K

Finding initial temperatures for the pond and the lid by trial and error such that all constraints of the problem are satis?ed is very di?cult,if not impossible.The con-straints on the?nal temperature of the pond and the lid, in particular,are the hardest constraints to satisfy.Hence, initial temperatures of the pond and the lid are also opti-mized to ensure feasibility.

7.1.Optimal operating conditions for Case studies A–C

The main plant speci?cations under optimal operating conditions of case studies A–C are provided in Table4, and discussed in the following.The objective of optimiza-tion for these three case studies(A–C)is maximum income (i.e.,Obj2).The value of Obj2is also given in Table4,and as shown,Case A results in the highest value for the weighted energetic function used.The income in Case A is the highest and Case C the lowest,with a di?erence of approximately2%.A major di?erence between the optimal operating conditions in cases A and B with case C is the steam extraction rate for MED.Speci?cally,whether or not steam extraction for MED yields more income strongly depends on the heat integration scheme and the constraint, if any,imposed on the temperature after the OFWH.This is true even if the price of0.12€/kWh for electricity and 0.92€/m3for water are used.Enforcing a minimum allow-able temperature after the OFWH,i.e.,case study C, makes steam extraction for MED economical.In particu-lar,the economical advantages of steam extraction(i.e., additional pro?t from water production and a lower steam extraction rate for the OFWH)outweigh the economical disadvantages(i.e.,lower power production from steam extraction and MED power use)of steam extraction for MED.In contrast,for cases A and B,in which no exit tem-perature for the OFWH is enforced,steam extraction for MED yields slightly less income.It should be noted that for cases A and B even higher values for income are obtained if the constraint on minimum water production from MED is removed from optimization.

To further understand the di?erence between these three cases,the key optimal energy?ows and operating temper-atures are provided in Table5.Given the di?erence between these heat integration schemes,the discussion of the cycle e?ciency bares interesting results.

Two e?ciencies,analogous to the?rst and second law e?ciencies of a power cycle,are de?ned for the plant and used to further compare these cases.Considering both water and power production of the plant,these two e?-ciencies are de?ned by Eqs.3and4as follows:

g I?

W eff

Q i

e3Tg IIetT?

W eff

Q i1àT c

T ietT

e4TTable4

Results of optimization:Case studies A–C.

Case

C Power to the grid(MW e) 3.38 3.35 2.89 Water produced by MED(m3/day)144715071503 Water produced by RO(m3/day)100010002217 Obj1(total income)($)11,99011,94811,737 Obj2(total weighted energetic function)

(MWh)

90.9590.3784.17

Table5

Cycle e?ciency:Case studies A–C.

Case A Case B Case C Heat extracted from the pond(MW)9.0713.9513.00 Heat extracted from the lid(MW) 6.100.000.00 Average temperature of the pond(K)835843843 Average temperature of the lid(K)563785757

g I de?ned by Eq.(3)0.220.240.25 Average g II de?ned by Eq.(4)0.3890.3720.388

A.Ghobeity et al./Solar Energy85(2011)2295–23202309

where W e?is the net equivalent power produced from the plant.Water production rate in unit of m3/h is converted to an equivalent MW e using the constant C wàe=4kWh/m3._Q i is the heat input by source i at T i to the cycle.The Second law e?ciency considers the temperature of the heat sources T i,and therefore takes into account the availability of the thermal storage,i.e., exergy of the storage.

The second law e?ciency is time-dependent as the tem-perature of the pond and the lid change with time.Fig.5 shows how this e?ciency changes throughout the day. The cycle e?ciency is calculated for a similar steam extrac-tion rate for all cases.As shown in Table5,although Case A results in a higher energy consumption(9+6MW th compared to13MW th for Case C and14MW th for Case

B),it results in a lower heat extraction from the high exergy storage(energy storage with high temperature).As a result, Case A yields highest exergy e?ciency,as de?ned by g II, even though it results in lowest?rst law e?ciency.High-temperature exergy storage has higher availability and hence higher value;therefore,Case A results in a better operating strategy than both Case B and C as it results in both higher income and higher second law e?ciency in the steam cycle.The optimal operating conditions for the three case studies A–C result in di?erent daily distributions of operating temperatures in the pond and at the lid.As shown in Fig.6,the optimal operating conditions from Case A result in a lower temperature range for both the lid and the pond.The maximum temperature reached in the salt pond under optimal operating conditions of Case A is below the maximum allowable temperature in the salt pond.Hence,under the optimal operating conditions found from Case A,a larger heliostat?eld can be used with the same mass of salt and salt pond geometry.The ultimate e?ect is better utilization of the energy stored and higher capture e?ciency by the pond.

Hence,the optimal heat integration scheme that resulted in the highest income and also highest exergetic e?ciency (without explicitly exergetic e?ciency)is the use of the thermal energy collected at the lid for preheating purposes in the steam cycle and the thermal energy collected at the pond for evaporation and superheating.The consequence of this operating strategy is a lower?rst law e?ciency, however higher second law e?ciency and better use of the exergy storage.In particular,the optimal use of energy with high availability(i.e.,high exergy)collected in the salt pond is in evaporating and superheating.The use of ther-mal with low availability for preheating is preferred over extracting steam for preheating.

Fig.7shows the energy?ow diagram in the plant and major plant speci?cations.The conditions used for the?g-ure are those found from Case study A.

7.2.E?ect of steam extraction

A?nding of the study is the strong e?ect of non-trivial design constraints and parameters on the energetics of steam extraction for MED.For instance,under current electricity and water prices(i.e.,neglecting FiT)the use of an OFWH with its exit temperature enforced results in making steam extraction for MED more pro?table.On the other hand,if a CFWH is used with the required heat for preheating provided by the thermal energy collected at the lid,then steam extraction for MED is less pro?table

2310 A.Ghobeity et al./Solar Energy85(2011)2295–2320

than letting the entire steam exhaust the turbine and pro-duce more power.

The results show that for small scale (e.g.,4MW)MED with a typical design has too low GOR and too high elec-tricity consumption to be competitive with RO on an ener-getic basis.Alternatively,a more advanced heat integration scheme beyond simple pre-heating is required to improve GOR at small-scale considered here.One should note how-ever that comparing MED with RO only from energetic point of view does not necessarily mean that cogeneration by MED is less pro?table than using electricity for RO.Capital and operating and maintenance costs beyond elec-tricity are required to make such an analysis,which will be the focus of future research.

An option that is not considered here is the use of a back pressure turbine and eliminating the need for the condenser in the steam cycle.The resulting advantage is a lower cap-ital cost for the plant,while the disadvantages are lower electricity production due to higher exhaust pressures (0.25bar vs.0.05bar here)and less operation ?exibility.

Herein,technical performance metrics are considered.A forthcoming publication will present a detailed economic model addressing the ?nancial aspects of the technology presented.Moreover,future work will consider time-vari-able operation as well as optimization of economic objectives.8.Conclusions

System-level models are developed for dynamic simu-lation and optimization of a plant that utilizes solar energy for combined electricity generation and water pro-duction.Dynamic simulations are quite useful tools as they provide insight into the challenges involved in oper-ation of the proposed plant.The sequential method of optimization is employed with IPOPT and SNOPT as the local solvers,and JACOBIAN as the simulator.Time-invariable short-term operation of the plant is opti-mized to maximize the pro?t for selling the electricity and water produced.The optimal operating conditions

7.2 G J /d a y (2.0 M W h /d a y )

17.2 G J /d a y (4.8 M W h /d a y )

292 GJ/day (81.2 MWh/day)

121 GJ/day to RO

3880 G J /d a y

Salt Pond

Change in Storage Capacity

<1 MJ/day

914 G J /d a y

980 G J /d a y

1985 GJ/day

1895 G J /d a y

790

J /d a y

124

G J /d a y 63

J /

d a

Power Block

4 MW e Nominal Capacity (78% Isentropic Efficiency)Rankine Cycle with One Closed Feedwater Heater

Change in lid’s temperature over 1

day:<1 K

362 G J /d a y

37 G J /d a y 112 G J /d a y

MED

TOTAL BEAM RADIATION

FIELD’S

LOSSES

DIRECTED INTO THE POND

RADIATION LOSSES FROM THE POND

LOSSES TO

THE

ENVIRONMENT ABSORBED BY THE LID

LOSSES TO

THE

ENVIRONMENT

WITHDRAWN FROM THE POND

LOSSES TO

THE

ENVIRONMENT

CONDENSER REJECT (PARTAILLY )

TO THE GRID

ELECTRICITY

EXTRACTED STEAM

MED RETURN

HELIOSTATS

FIELD

2079 m 3/day (feed)

1000m 3/day (product)

1079m 3/day (brine)

533 G J /d a y

91 G J /d a y

CONDUCTION

LOSSES FROM THE POND

78 GJ/day to MED

STEAM GENERATOR

283 GJ/day

833 G J /d a y

3410 m 3/day (feed)

1447m 3/day (product)

1963m 3/day (brine)

527 GJ/day

PRE-HEATER

447 G J /d a y

80 GJ/day Fig.7.Energy ?ow diagram under optimal operating conditions of Case A.

A.Ghobeity et al./Solar Energy 85(2011)2295–2320

2311

strongly depend on the FiT and the price of fresh water. The current energy policies in Cyprus,and most of Med-iterranean region,do not re?ect the fact that the water produced by RES should also be considered for incen-tives.The results show that for a typical steam cycle design,under current electricity and water prices(i.e., no subsidy considered for electricity or water produced by RES),extracting steam at low extraction pressures yields the highest income.Hence,to encourage direct application of RES,it is recommended to consider incen-tives for producing water by direct application of RES. Optimizing for a weighted energetic function of electric-ity and water production,with no constraint considered for minimum allowable water production,shows that for the small-scale MED design selected,suitable for the small-scale power plant considered(4MW e equiva-lent nominal capacity),the MED equivalent energy requirements are much higher than typical RO energy requirements.In all case studies,the optimizer chooses the lowest allowable extraction pressure for MED.The optimal water temperature after the OFWH is also the lowest allowable.To meet this temperature,the optimizer selected extracting at the lowest extraction pressure. Based on these?ndings,an alternate process?ow con?g-uration is developed considering which signi?cantly improved operating conditions are achieved.In particu-lar,the optimal operating conditions result in highest income while ensuring the most e?cient use of both the low and high exergy heat.

Acknowledgments

The work presented in this paper is part of an interdis-ciplinary collaboration between the Cyprus Institute,the University of Illinois at Urbana Champaign,the Electricity Authority of Cyprus,and the Massachusetts Institute of Technology.We would like to particularly thank Dr.An-dreas Poullikkas and Dr.Constantinos Rouvas for provid-ing the initial power cycle design,Prof John G.Georgiadis for various fruitful discussions,and Danny Codd and Prof. Alex Slocum for sharing the CSPonD concept.Amin Ghobeity gratefully acknowledges his postdoctoral fellow-ship through the Natural Science and Research Council of Canada(NSERC).Funding from the Cyprus Research Promotion Foundation for the Cyprus Institute MIT Alli-ance under account number6918992is gratefully acknowledged.

Appendix A.System-level sub-models

System-level models developed or adopted from litera-ture for the present study and presented in this Appendix. Each sub-model is brie?y described,and wherever appropriate the model validation is also provided.The model formulation is provided only if the formulation is not available from the literature in a concise and/or complete form.A.1.Solar irradiance

Beam radiation is required to calculate the energy input to CSPonD.Meteorological data,if available for the time and location of interest,can be used as an input to the JACOBIAN model of the plant.For more general case studies,theoretical radiation models are required.Herein, a detailed model(Bird and Hulstrom,1981;Badescu, 2008)is used to calculate the hourly distribution of solar irradiance.The beam(direct),di?use,and global irradiance (sum of direct and di?use)on the earth surface are calcu-lated.However,only the beam radiation is required here. The beam radiation normal to a horizontal plane,I b,on the ground is calculated using the extraterrestrial solar radiation,I ex,and a set of correction factors.The correc-tion factors account for scattering and optical transmit-tance;namely,Mie scattering(aerosol absorption)C a, Rayleigh scattering(molecules absorption)C r,ozone absorption C o,absorption by water vapor C w,and?nally absorption by mixed gases C mg.

I b?0:975I ex sin

àh z

C a C r C o C w C mg

where h z is the solar zenith angle.The correction factors are calculated using the following equations:

C a?expàd0:873

1td aàd0:7088

àá

M00:9108

àá

C r?expà0:0903M00:84

àá

C o?1à0:1611X oe1t139:48X oTà0:3035

0:002715X o

1t0:0440X ot0:0003X2

C w?1à

2:4959X w

e1t79:034X wT0:6828t6:385X w

C mg?expeà0:0127M00:26T

where M and M0are the optical and pressure-corrected optical airmass,respectively,found from(Badescu,2008): M?sin

àh z

t0:1593:885àh z

eTà1:253

à1

M0?M

P amb

P atm

The solar zenith angle h z is a function of time and location, and calculated by:

h z?arccosesin d sin/tcos d cos/cos xT

where d is the declination angle(i.e.,angular position of the sun at solar noon),/is the solar latitude,and x is the hour angle.The aerosol optical thickness,d a is estimated by:

d a?0:2758

k a

t0:3500

k a

where k1=0.38,k2=0.50,a=1.3(based on its typical value Badescu,2008),and Angstrum’s turbidity parameter b depends on visibility:b=0.05for visibility of340km (clean atmospheric condition),b=0.1for visibility of

2312 A.Ghobeity et al./Solar Energy85(2011)2295–2320

28km(clear atmospheric condition),b=0.2for visibility of11km(turpid atmospheric condition),and b= 0.4à0.5for visibility of less than5km(very turpid atmo-spheric condition).Finally,X o and X w are the total column of ozone and precipitable water in the atmosphere and approximated from:

X o?ed1ted2td3sined4eN dayà30TT

td5sined6ehtdTTTsined7/T2TAM

X w?0:23Me m10àH=22000

where d1–d7are constants given in Badescu(2008).The distance between the sun and the earth changes as the earth revolves on an ellipsoidal orbit around the sun,causing a daily change in the distance between the earth and the sun,and consequently daily average solar radiation and the sunrise and sunset time.Also,the angular position of the sun with respect to the plane of equator,i.e.,solar dec-lination angle d,is a function of time and changes through-out the year as Kalogirou(2009),Sukhatme and Nayak (2008):

d?23:45sin

360

365

eN dayt284T

where N day=1corresponds to the?rst day of the year, January1st,and N day=365corresponds to the last day of the year.Daily variation in the extraterrestrial irradiance is found from:

I ex?I01t0:035cos

2peN dayà4T

366

where I0=1366.1(kW/m2)is the solar constant.

The total number hours of sunshine in the plant is found from:

t sh?2

x ss

where x ss is the sunset hour angle(15°is equivalent to1h) and found from

x ss?arccoseàtan d tan/T

The sunrise and sunset hour angle are1x ss before and after,respectively,of the solar noon angle.The inputs used to calculate the beam,di?use,and global irradiance in Cyprus are shown Table6.

The model is validated with the measurement on the ground.As shown in Fig.8,there is a good agreement between the model predictions and measurements(Mete-orological Data,2005)on the ground in Cyprus.The models predictions also agree well with the published data for the daily global radiation on a horizontal plane in Cyprus(Petrakis et al.,1998;Kalogirou,2003).It should be noted that the model is not based on?tted parameters on measurements,i.e.,the parameters used in the solar radiation model are based on the location and weather conditions listed in Table6.The model has been tested under various conditions and the results show that it captures the e?ect of seasonal changes,the weather conditions and location on the beam irradiance very well.The model e?ectively provides the necessary tools to accurately simulate the input solar power to sys-tem.Furthermore,several weather scenarios and seasonal changes can be easily modeled and the corresponding operation strategies can be studied.

A.2.Heliostats and?eld e?ciency

Heliostats are re?ecting mirrors that track the sun in two directions throughout the day.A drive system adjusts the orientation of individual heliostats continuously to ensure that the re?ected sun’s rays that bounce o?the mir-ror are directed towards the receiver system.

Shading and blocking,and the size of the re?ected image from the heliostats put design limits on the heliostats’lay-out.Shading refers to the blockage of the incoming rays from receiving the heliostats,and blocking refers to the blockage of the re?ected rays from one heliostat by another heliostat.Hence,shading and blocking put limits on the usage of the ground.As a result of these design limits, the ground usage,de?ned as the ratio of the total area of heliostats to the total area of the heliostats?eld,is around Table6

Key inputs used with the solar irradiance model.

Parameter Value

Geographic longitude h33°E

Geographical latitude/35°N

A coe?cient required to calculate

aerosol scattering a

1.3(the suggested typical value) Turbidity coe?cient b0.1(the suggested value for

visibility of29km)

Solar constant I01366.1W/m2

Relative humidity RH70%

Site’s elevation H50m

Temperature T298

A.Ghobeity et al./Solar Energy85(2011)2295–23202313

0.3–0.5for traditional central receiver systems on?at land (Howell et al.,1982).Ray-tracing methods are commonly used for optical analysis of the heliostats(Garcia et al., 2008).

The four most important parameters required to calcu-late the energy re?ected onto the receiver are:(a)the mir-rors’re?ectivity,(b)the so-called“cosine e?ciency”(Yao et al.,2009),(c)the shading and blocking e?ects,and(d) spillage.The model(Noone et al.,2011)to estimate these parameters is brie?y described in the following section. A.2.1.Heliostat?eld e?ciency

Brief overview of the model used(Noone et al.,2011) for the calculation of annual average?eld e?ciency for an arbitrary heliostat con?guration in three dimensions is presented.Unlike existing software packages for evaluating central receiver applications,where the heliostat?eld is assumed planar,the model used(Noone et al.,2011)calcu-lates?eld e?ciency accounting for variations in terrain, allowing for the evaluation of concepts such as utilizing hillsides as sites for heliostat?elds.As mentioned brie?y in previous section,calculating the e?ciency of a heliostat ?eld requires evaluating the most signi?cant factors in?u-encing the performance of the heliostat?eld:cosine losses, shading and blocking,and heliostat re?ectivity,each of which are discussed below.

Cosine e?ciency,i.e.,the ratio of projected heliostat area in the direction of beam irradiation to the heliostat surface area,is one of the largest losses in any central recei-ver solar thermal application.In order to calculate these projection losses throughout the day and year,a solar model is necessary to calculate the sun’s position as a func-tion of time.To accomplish this,the model uses an open source library,Solar Positioning Algorithm(SPA)(Reda and Andreas,2004).

Another factor in heliostat?eld performance is the e?ect of shading and blocking.Shading refers to a scenario where a heliostat obstructs part or all of the solar radiation incident to a neighboring heliostat,and blocking is similar but between a neighboring heliostat and the receiver.Like cosine losses,shading and blocking losses are also depen-dent on the sun’s position and vary throughout the day and year.For the purpose of the model,shading and block-ing is calculated as one term,the ratio of shaded or blocked heliostat area to the total heliostat surface area.The imple-mentation of shading and blocking calculations involves projecting heliostats areas from the direction of the sun and receiver onto the plane of the heliostat being evaluated and calculating the area of intersection.The heliostat sur-face is modeled as?at because the e?ect of heliostat rota-tion on?eld e?ciency far outweighs the e?ect of the surface curvature.Taking cosine losses for example,the result of the heliostat alignment assuming a?at surface is far more signi?cant than the variation in facet normal direction.

The last factor a?ecting the heliostat?eld e?ciency cal-culation is the heliostat re?ectivity.This value accounts for the re?ectivity of the surface material and imperfections. Usually provided by the manufacturer,typical values range from0.90to0.95(Mancini,2000).For the purpose of the model,a conservative value of0.90is used.It should be noted that since heliostat re?ectivity only a?ects the total required heliostat area.More speci?cally,the conservative choice of0.9for the heliostat re?ectivity does not a?ect the optimal operating conditions of the plant.

In general,the calculations are performed over an entire year,but herein only the e?ciency for the chosen day is needed.At every time instance in the analysis,the main factors described above are calculated for each heliostat; the average instantaneous heliostat?eld e?ciency is then simply the average instantaneous e?ciency of all the helio-stats.Additionally,the time-averaged instantaneous e?-ciency is weighted by solar?ux.To account for the time and seasonal variation of solar irradiation,the model uses the Meteorological Radiation Model(MRM V1)(Bird and Hulstrom,1981;Badescu,2008)to estimate hourly irradiation and is found to correspond well with local mea-surements from several test locations.The result is an irra-diation-weighted average annual heliostat?eld e?ciency used to evaluate the potential of heliostat?eld con?gura-tions in three dimensions.For the present study,an idealized heliostat?eld was assumed placing heliostats on a hillside with a constant35°slope in a radially staggered pattern with concentric elevation contours.The hillside angle selected is such that re?ection losses from the salt surface,calculated using the Fresnel equations,are small. The size of the?eld was chosen to approximate the size of a heliostat?eld required for a4MW e nominal power requirement and the receiver was placed200m from,at the same elevation as,the base of the hillside.Fig.9shows the hourly and mean daily distribution of?eld e?ciency, calculated based on Noone et al.(2011)and used in present study.

A.3.Receiver

The receiver system considered is a salt pond that receives the concentrated solar energy through the aper-ture.The net energy collected in the pond is the energy re?ected into the pond from all heliostats minus the radia-tion and conduction losses.Following the CSPonD con-cept(Slocum et al.,2011),the receiver system(the salt pond)is the energy storage medium too.The temperature distribution in the pond is assumed approximately uni-form;however,the salt temperature changes with time as a function of the energy withdrawal rate from the pond, the heat losses,and mass of the salt in pond.The salt pond also has a lid(i.e.,a dome structure with the aperture open-ing covering the pond).The lid captures the energy con-tained in the salt evaporated from the pond.The radiation heat losses from the pond captured by the lid is a function of geometry and size determining the view factor between the pond and the lid.The view factor from the pond(i.e.,the surface of the salt),F se,to the environment

2314 A.Ghobeity et al./Solar Energy85(2011)2295–2320