design study of a stand-alone desalination system powered by renewable energy sources and a pumped...

Desalination 257 (2010) 137–149

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Desalination

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Design study of a stand-alone desalination system powered by renewable energysources and a pumped storage unit

Ioannis D. Spyrou, John S. Anagnostopoulos ⁎School of Mechanical Engineering/Fluids Section, National Technical University of Athens, 9 Heroon Polytechniou ave., Zografou, 15780 Athens, Greece

⁎ Corresponding author. Tel.: +30 2107721080.E-mail address: [email protected] (J.S. Ana

0011-9164/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.desal.2010.02.033

a b s t r a c t
a r t i c l e i n f o
Article history:Received 12 December 2009Received in revised form 20 February 2010Accepted 23 February 2010Available online 29 March 2010

Keywords:Stand-alone desalinationWind powerPhotovoltaicsPumped storagePlant operation simulationDesign optimization

The aim of this work is to investigate in detail the optimum design and operation strategy of a stand-alonehybrid desalination scheme, capable to fulfill the fresh water demand of an island or other remote coastalregions. The scheme consists of a reverse-osmosis desalination unit powered by wind and solar electricityproduction systems and by a pumped storage unit.A specific computer algorithm is developed to simulate in detail the entire plant operation and also toperform economic evaluation of the investment. A stochastic optimization software based on evolutionaryalgorithms is implemented to accomplish design optimization studies of the plant for various objectives, likethe minimization of fresh water production cost or the maximization of water needs satisfaction.Miscellaneous parametric studies are also conducted in order to analyze the effects of various criticalparameters, as population, water pricing, water demand satisfaction rate and photovoltaics cost are.The results demonstrate not only the performance, the role and the contribution of each subsystem but alsothe production and economic results of the whole plant. An optimally designed scheme is found to beeconomically viable investment, although energy rejections are significant and there is a clear need for betterexploitation of renewable energy production surplus.

gnostopoulos).

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© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Nowadays it is observed, globally, an extensive phenomenon ofdrought. Especially in Greece, many isolated areas, such as Aegeanislands, suffer from drought [1]. The problem becomes worse insummer when the water demand increases up to 4–5 times comparedto winter because of tourism [2]. In most islands the existing waterstocks cannot satisfy such increasing demand; thus the problem thatcomes up must be solved with permanent and viable solutions. Atpresent, this water demand is being satisfied by tank transportationwith the considerably high cost of about 5–8€/m3 for Cyclades andDodecanese complex [1].

Seawater desalination can play an important role towards apermanent confrontation of the problem [2]. The installation ofdesalination units is a common solution throughout the world, inareas with drought. In the last decades the number of desalinationapplications has greatly increased, while desalination is the subject ofseveral research works. As a result, new desalination methods havebeen developed, experience has been gained, system operation hasbeen amended and the equipment production has become massive[3]. Thus, the two most important performance characteristics of such

applications, which are the quality of produced water and the waterproduction cost are continuously being improved.

A critical technical parameter of desalination applications is theway the system is powered. This decision is taken according to theselected method of desalination and the characteristics of thecandidate area [4]. Nowadays the method of reverse osmosisdominates globally; it requires only electricity, has a quite lowspecific energy demand, and can cooperate with technologies ofrenewable energy sources (RES) such as wind turbines and photo-voltaics [4–7]. Concerning Aegean islands that suffer from drought,most of them are isolated and the electricity is provided by localconventional power stations operating at very high production costs.In addition, the power demand of large desalination units may not besatisfied by the existing power stations. On the other hand, Aegeanislands feature an abundance of RES like solar and wind energy.Consequently, a desalination system powered by hybrid renewableenergy technologies would be a very promising solution for thoseregions.

Several simulation studies of desalination units cooperating withRES and conventional thermal units have already taken place [8–11].Stand-alone reverse-osmosis desalination units powered by windturbines and/or photovoltaics and supported by batteries have beenthe research topic of several works that have shown that such systemscould be a viable solution at present conditions [12–14]. Energystorage is an important aspect of such autonomous systems, althoughsome systems without storage have been simulated and tested

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138 I.D. Spyrou, J.S. Anagnostopoulos / Desalination 257 (2010) 137–149

[15,16]. Because of the stochastic and intermittent nature of RES, astorage system is usually required in order to avoid excessiverejection of the energy production, as well as to guarantee thedesalination unit operation during unfavorable weather conditions.The most common system for energy storage are batteries which areincluded in most studies. The use of batteries has the disadvantages ofshort life cycle, high-cost maintenance and environmentally un-friendly content [17,18]. As a result, batteries have been proposedonly for small-scale plants.

The present work aims to study an alternative means of energystorage, a pumped storage subsystem, in stand-alone desalinationplants, and to investigate its role on the operation of the wholescheme. Pumped storage in hybrid wind-hydro power productionplants has been studied applying numerical design optimizationmethodologies in some previousworks [19,20]. The optimum sizing ofall desalination system components that maximize its energy and/oreconomic results for small to large islands constitutes an objective ofthe present work, as well.

2. System description

The considered system is schematically shown in Fig. 1. The stand-alone desalination unit is powered by a hybrid RES system (wind-photovoltaics), and includes a fresh water tank to provide autonomyto the area for a determinate time period, in case that the system is outof order for some reason (e.g. maintenance, failure).

Due to the intermittent nature of those RES and the difficulty inpredicting the energy production rate, a means of energy storage isrequired to operate the desalination unit even during unfavorableweather conditions. A pumped storage subsystem is considered, as an

Fig. 1. Sketch of the examined d

alternative to batteries. A typical pumped storage unit consists of apumping and a turbining station, two water reservoirs at differentaltitude, and the necessary pipelines (Fig. 1). A number of pumps areusually installed in parallel operation, equipped with variable speedmotors in order to be able to absorb the fluctuating production of RESwith nopower gaps [19]. On the other hand, the type of hydroturbine(s)depends mainly on the available head between the reservoirs.

During periods of excessive RES production, the power surplus isused to operate the pumps and store hydraulic (dynamic) energy inthe upper reservoir (Fig. 1). On the other hand, when the primaryenergy production cannot satisfy the desalination demands, then thehydroturbine re-transforms the stored energy into electricity, whichpowers the desalination unit. Details on the energy transfer rules andconstrictions are given in Section 3.

3. Algorithm description

In order to simulate the entire system operation and itssubsystems interaction, a specific computer algorithm is developed.The software makes also an economic evaluation of the system, basedon empirical cost relations for all its main components (pumps, hydroand wind turbines, photovoltaics, pipelines, etc.) [19,20]. Thealgorithm is divided into three sections: data input, application ofsystem's logic operation, and techno-economic evaluation. Theseparts are described in more detail in the present section.

3.1. Data input

Data needed for the simulation of system's operation are either fixedor free variables, the valueor the range ofwhich is predeterminedby the

esalination system set-up.

Table 1Typical specific water consumption data.

Daily water consumption (l/day/person)

Population type Winter SummerResident, RWC 150 250Seasonal, SWC 200 300

139I.D. Spyrou, J.S. Anagnostopoulos / Desalination 257 (2010) 137–149

user. In the present study fixed quantities include the hydraulic head(here 400 m), the pipeline dimensions, the number of pumps andturbines, and the time-variation curves of wind speed and solarradiation. On the other hand, the size of all main system components(desalination unit,wind andphotovoltaic parks, pumping and turbiningsystems, reservoirs and fresh water tank), constitutes the free designvariables. Finally, some critical parameters like the resident population,the water demand satisfaction rate and the photovoltaics (PV) cost arealso introduced and examined in the presentwork. Detailed descriptionof the main system parameters, along with their technical andoperational constrictions, is given below.

3.1.1. Water demandCalculation of the hourly water demand of a candidate area is

based on an ideal island of constant resident population, RP. Theseasonal population, SP, of the island is assumed here to follow amonthly variation curve like the one drawn in Fig. 2, which is typicalfor a Greek island at the Aegean Sea: population in summer monthsmay increase due to tourism up to 3 or 4 times [1]. The residentpopulation is a major parameter of the system, and usually dependson the island size.

Assuming a seasonally varying specific daily consumption, SWC forseasonal population and RWC for resident population (Table 1), thetotal daily fresh water demand, DWD (m3), is obtained as:

DWD = RP⋅SWC + SP⋅RWC: ð1Þ

Then, based on typical fresh water demand variation curves [21],as shown in Fig. 3, a percentage of daily water demand, WDP,corresponds to every hour i of the day. As a result, the hourly waterdemand, HWD (m3), of the entire population is calculated as:

HWD = WDP⋅DWD: ð2Þ

3.1.2. Desalination unitThe correlation between hourly water demand, and the

corresponding power for desalination, PDEM (or the hourly energydemand, EDEM) is given by Eq. (3), assuming an average specificenergy consumption for desalination, SDC. Today, reverse-osmosisdesalination units require 2–4 kW h to produce 1 m3 of fresh water[5], and a value of 3 kW h/m3 is taken in the present study to stand forthe entire desalination process and apparatus (pumps, membranesand energy recovery systems).

PDEM = EDEM = HWD⋅SDC: ð3Þ

Fig. 2. Monthly variation of seasonal, in respect to resident population.

The desalination unit installed power, PD,I, is considered as asystem free variable. Thus, desalination water production capabilityper day, DFC, can be computed from the relation:

DFC = 24⋅ PD = SDCð Þ: ð4Þ

The reverse osmosis unit can operate between its nominal and aminimum load, PMD, because of membrane's characteristic curve [22]:

PMD≤PDES≤PD;I ð5Þ

where PDES is the instant power consumed by desalination unit. Thelower operation limit corresponds to theminimum required pressure toovercome the osmotic pressure and to set desalination unit up.Workingin partial loads may affect the quality of the produced fresh water, butthis is not a subject of the present work. In the present simulation, thetechnical minimum is taken at 25% of the nominal power.

The desalination system includes a fresh water tank, the capacityof which is proportional to the island size (or to the residentpopulation). A period of two summer days (August) was consideredas the desirable autonomy of the system. Thus, the capacity of thefresh water tank, VTC, is:

VTC = 2⋅DWD: ð6Þ

In order to conserve the above autonomy throughout the year, thehydroturbine is put in operation when the content of the tank dropsbelow 90%, providing that there exist available storage in the upperreservoir.

3.1.3. RES features and productionHourly energy production by wind turbines and photovoltaics is

being calculated using the corresponding meteorological data forwind speed, V, and solar radiation, G (Fig. 4). Specific data time seriesare used for all cases examined here, assuming that they arerepresentative of the Aegean islands complex [1].

Concerning the calculation of wind farm production, the powercurve of a typical wind turbine of specific nominal power, PMWT, isused. The installed wind power, PW,I, is a free variable of the system.For every hour the given wind speed corresponds to a specific power

Fig. 3. Typical hourly variation of water consumption during a day.

Fig. 4. Indicative meteo data time series (typical week of August).


production, PNWT, and the total wind farm production, PWT (or EWT inkW h), is calculated by the following equations, where ηWT is the windfarm's total efficiency:

PWT = EWT = ηWT⋅k⋅PNWT ð7Þ

k =PW;I

PMWT: ð8Þ

On the other hand, the power production by the PV array, PPV (orEPV in kW h), is computed by Eq. (9), assuming that there are NPV

identical PV panels of a specific nominal power PNPV each, averageefficiency ηPV, and panel's area A.

PPV = EPV = ηPV⋅NPV⋅A⋅G: ð9Þ

The total installed photovoltaic power is considered as a freevariable of the system and is given by:

PPV;I = NPV⋅PNPV: ð10Þ

In every time-step of the plant operation simulation, the total RESproduction, PRES, is the sum of wind turbines and PV production:

PRES = ERES = PPV + PWT: ð11Þ

The time-step used in the present study was always 1 h, hence thevalues of the produced energy ERES (in kW h), and power PRES (in kW)are exactly the same, allowing the treatment of even the energyquantities in terms of power. This practice is followed throughout thiswork.

3.1.4. Pumped storage subsystemThe pumping station is consisted by a number of variable speed

pumps in parallel operation, with total installed power PP,I. The pumpsoperate only when the available RES power exceeds a technicalminimum, which is taken 15% of the installed power. This correspondsto a number of at least 4 pumps, with the capability of reduction oftheir rotation speed by about 15%. For any available wind power, PPS,the hourly water flow, QP, from the lower to the upper reservoir is

given by the following relation, where HP is the pumping head and ηPis the total efficiency of the pumps:

QP =PPS⋅ηP

g⋅HP⋅3600 ð12Þ

PMP≤PPS≤PP;I: ð13Þ

Hydroturbines can operate at variable power load, PHT, in order tosupplement the RES production. However, operation at partial loadsmay affect efficiency. In this work the latter follows a typicalcharacteristic curve of Pelton turbines, the technical minimum ofwhich is taken 20% of the nominal power load, PMT. Therefore, thehourly water flow, QT (m3), through the hydroturbine is computed as:

QT =PHT

ηT⋅g⋅HT⋅3600 ð14Þ

PMT≤PHT≤PT;I ð15Þ

where HT is the net head and ηT is the turbine efficiency. The upperand lower reservoirs have equal useful capacity, which is a system'sdesign parameter.

3.2. System operation strategy

The basic power/energy balance relations for every time-step (1 h)are given below. The first stands for the RES produced power, whichcan be spent for desalination, PAD, or for pumping, PPS, while theremaining (if any), PREJ, is rejected

PRES = PAD + PPS + PREJ: ð16Þ

The desalination unit can be powered by RES, PAD, or hydroturbinepower, PHT, or both:

PDES = PAD + PHT: ð17Þ

Finally, if the existing water in the tank, along with the additionalproduction from RES and hydroturbine, cannot satisfy the waterdemand, then there is a desalination power shortage, PN:

PN = PDEM− PTANK + PAD + PHTð Þ; PTANK = VT ⋅SDC ð18Þ

where PTANK is the desalination power equivalent (in kW) of the freshwater tank content VT (in m3).

The fresh water demand is always being fed through the tank.Desalination unit operates in order to replace the consumed waterand to retain a 90% minimum fulfillment of this tank. The unit, as alsothe pumps and hydroturbines does not operate if the available poweris below its corresponding technical minima. In addition, desalinationstops when the water tank is full, and the same is done for the pumpsif the upper reservoir is full.

Following the above constrictions, the operation strategy of theentire system is presented in the flow chart of Fig. 5. The diagramconsists of two parts, explaining the management of RES and ofhydroturbine production, respectively.

In the first part of Fig. 5, the power produced by the primarygenerators (wind turbines and photovoltaics) can be used either fordesalination or for pumping storage. Priority is given to desalination

Fig. 5. Flow chart of the plant operation algorithm.



unit, provided that there is an empty space in the fresh water tank,namely PTANK,FN0, where:

PTANK;F = VTC−VTð Þ⋅SDC: ð19Þ

When the upper reservoir is full (PUPR,F=0 or VR=VRC), where:

PUPR;F = g⋅ VRC−VRð Þ⋅HT⋅ηT ð20Þ

and VR is the current water volume content, then the RES energysurplus is rejected, as also when PRES exceeds the installed pumpingpower.

On the other hand, the hydroturbine is set to operate in case ofdesalination power shortage (PNN0), but also when the fresh waterlevel in the tank drops below the limit VTG=0.9⋅VTC, namely:

PTANK;G = VTG−VTð Þ⋅SDC N 0: ð21Þ

The latter condition always happens first, hence it controls thesecond flow chart diagram of Fig. 5. Finally, the hydropower stopswhen the upper reservoir reaches its lowest acceptable level, herePUPR=0, or VR=0.

3.3. Techno-economic evaluation

At the end of the simulated period of plant operation (one year) alltechnical and economic evaluation indicators are computed. At thissection, the most important and those that will be presented anddiscussed in the results are defined.

3.3.1. Technical evaluationSystem's first priority is to satisfy the island's water needs at a

predetermined percentage limit. Consequently, in terms of desalina-tion power, we define an indicator of demand satisfaction rate, FDS

FDS = 1−∑8760

j = 1PN∑8760

j = 1PDEMð22Þ

where the summation is over the hours of a year (24×365). In orderto assess the hydroturbine contribution to the desalination powerfeed, the next indicator gives the ratio of the hydropower productiondivided by the total desalination energy absorbed during the year:

FHT =∑8760

j = 1PHT∑8760

j = 1PDES: ð23Þ

Also, an important energy indicator is defined to express theportion of RES production that cannot be exploited and it is finallyrejected.

FREJ =∑8760

j = 1PREJ∑8760

j = 1PRES: ð24Þ

Finally, the capacity factors of the three power generationsubsystems (PV, wind turbines, and hydroturbine) are computed bythe following relations and constitute the sizing indicators of this stand-alone system.

CFP =∑8760

j=1

PPVPRES

� �⋅ PAD + PPSð Þ

PPV;I⋅8760ð25Þ

CFW =∑8760

j=1

PWT

PRES

� �⋅ PAD + PPSð Þ

PW;I⋅8760ð26Þ

CFT =∑8760

j = 1PHTPT;IT8760

ð27Þ

where PPV,I, PW,I and PT,I are the corresponding installed power,respectively, and the rest power symbols represent hourly values.

3.3.2. Economic evaluationThe developed algorithm includes empirical equations from the

literature [23–25] (some of them updated using recent available data),in order to calculate the investment cost (purchase and construction) ofeach subsystem, as well as the operation and maintenance cost of theplant. Each cost depends either on a parameter's value or an operationquantity that comes up from the simulation. In the following relationspower is measured in kW, water volume in m3 and costs in €.

Wind turbines

Investment cost: ICW=1300⋅PW,I

O&M cost: OMW=0.02⋅ ICW

Photovoltaics

Investment cost: ICPV=6000 ⋅PPV,IO&M cost: OMPV=0.02⋅ ICPV

Desalination (reverse osmosis)

Unit investment cost: ICD=2270·DFC0.875

Tank cost: ICT=1090.8·VTC0.61

Investment cost: ICDES= ICT+ ICDO&M cost: OMDES=0.6·WAP

Where WAP is the total fresh water production:

WAP =∑8760

j = 1PDESSDC

: ð28Þ

Pumped storage subsystem

Hydroturbine investment cost: ICHT=18,000 ⋅PT,I0.48

Pumps investment cost: ICP=NP·1700·PP,I0.82

Reservoirs investment cost: ICR=2·420· VRC0.7.

The pipe investment cost, ICPIPE, is considered as the summary ofmaterial, welding, and coating costs, which are computed as functionof the pipe dimensions, whereas the latter is optimally selected fromstandardized tables depending on the water flow rate and head.

Other costs (electric and electronic equipment, unpredictables, etc.):

ICOTHER = 0:2⋅ ICHT + ICP + ICR + ICPIPEð Þ:

Pumped storage subsystem total cost: ICPS= ICHT+ ICP+ ICR+ ICPIPE+ICOTHER

O&M cost: OMPS=0.02· ICPS.

Total costs of the plant

System investment cost: ICSYSTEM= ICW+ ICPV+ ICDES+ ICPSSystem O&M cost: OMSYSTEM=OMW+OMPV+OMDES+OMPS.


The economic evaluation of the investment is based on the specificwater production cost and the dynamic index of Internal Return Rate(IRR). The annual water production cost is obtained as the sum of theannual depreciation, DA, of the total investment costs plus the totalO&M cost. Then, the specific water cost is computed as:

WPC =DA + OMSYSTEM

WAPð29Þ

DA =ICSYSTEM⋅r

1− 1 + rð Þ−n ð30Þ

where r is the discount rate and n is the plant's life cycle. The specificwater cost will be compared to the current water transportation cost.

IRR index is obtained as the solution of the equation:

∑n

j=0

Bj

1 + IRRð Þj = ICSYSTEM + ∑n

j=1

Cj

1 + IRRð Þj ð31Þ

where the annual incomes Bj and expenses Cj are:

Bj = Bj−1·e; B0 = WAP·FWP ð32Þ

Cj = Cj−1⋅e; C1 = OMSYSTEM: ð33Þ

In the above relations, e is the average inflation rate and FWP thesell price of the produced fresh water. Every value is converted topresent.

4. Results and discussion

This section is devoted to the presentation of results from theoperation simulation and optimal sizing of the examined hybridsystem. Firstly, a reference system with reasonable design isexamined and the results are analyzed in order to acquire a detailedview of the plant operation and the subsystems' interaction. Then,various single and double-objective optimization studies take place,and some general conclusions are deduced.

4.1. Reference plant simulation

The various design parameters of an indicative desalination systemtaken as reference are selected according to the following reasoning:The system is installed in a medium size island of 5000 residents.Having in mind the water consumption profiles in Section 3.1.1, ayearly average hourly fresh water demand would be 160 m3. Thus, a

Table 2Dimensioning of the examined systems.

Design parameter Symbol Referencesystem

OptimumSystem A

OptimumSystem B

1 Island resident population(people)

RP 5000 5000 5000

2 Tank capacity (m3) VTC 8.500 8500 85003 Desalination installed power (kW) PD,I 480 498 6124 Wind turbines installed power

(kW)PW,I 800 1210 1500

5 Photovoltaics installed power(kW)

PPV,I 200 0 0

6 Hydroturbine installed power(kW)

PHT,I 480 127 326

7 Pumps installed power (kW) PP,I 600 386 5938 Storage reservoir capacity (m3) VRC 40.000 12.120 56.900

desalination power of 480 kW is needed (3 kW h/m3). Also, a freshwater tank of 8500 m3 capacity in order to provide 2 days ofautonomy in August is included (Eq. (5)). Then, because of thestochastic nature of RES, the cumulative installed power of windturbines and PV is taken about two times greater than the desalinationunit power, namely 800 kW and 200 kW, respectively.

On the other hand, hydroturbine installed power is taken equal tothe desalination power (480 kW), in order to provide sufficient power

Fig. 6. Plant monitoring during a winter week: a) energy production, b) water needssatisfaction, c) energy consumption, d) tank and reservoir content.


even in the most adverse case of simultaneous apnea, cloudiness andempty fresh water tank. Pumping station installed power is takenbetween hydroturbine and total RES power (wind plus PV), at600 kW. Concerning the reservoirs, a net capacity of 40,000 m3 waschosen that corresponds to about 3 days of continuous turbineproduction. All the above data are tabulated in Table 2 (Referencesystem).

Fig. 7. Plant monitoring during a summer week: a) energy production, b) water needssatisfaction, c) energy consumption, d) tank and reservoir content.

Graphs of plant performance during a typical winter week and atypical summer week are presented in Figs. 6 and 7, showing theenergy production and exploitation and the water needs satisfactionby desalination.

In the winter the energy is produced mostly by wind turbines(Fig. 6a), whereas hydroturbine does not operate at all. Water needsare small and they are fully satisfied even in periods of lowdesalination production (Fig. 6b), while the fresh water tank remainsalmost full (Fig. 6d). As a result, a large percentage of RES productioncannot be either used or stored, and it is rejected (Fig. 6c).

On the other hand, during the summer-week results of Fig. 7 thewater demand is higher, and the hydroturbine is continuously used tosupplement the desalination power (Fig. 7a), as long as there isavailable hydraulic energy stored in the upper reservoir (Fig. 7d).Nevertheless, the water needs are not totally satisfied, and there existcertain hours every day when the fresh water tank empties (Fig. 7band d). This problem becomes worse towards the end of the week,due to the reduced wind production (Fig. 7a). The only positive effectis that energy rejections are now minimal, since the RES productionsurplus can be pumped and stored to the upper reservoir (Fig. 7c).

From quantitative point of view, the performance of the referencesystem can be evaluated from the results in the corresponding columnof Table 3,whichwere obtained by the simulation algorithm for a yearlyoperation of the system. It is concluded that the examined system iscapable to satisfy the island's water demand at a high degree (90.3%),but not fully. Also, a considerable part (39.5%) of the RES productioncannot either be consumed for desalination or stored, and the capacityfactors of all three generators are low. Hydroturbine participation indesalination powering is not so strong (18.1%) but justifies itsimplementation in the system. Concerning the economic results, theestimated specific production cost of thewater is 2.53€/m3,much lowerthan the current transportation cost (5–8€/m3). Using the former asinitial (first year's) sell price for the system, the obtained IRR index valueexceeds 14%, for a depreciation period of 20 years.

4.2. System optimal design

The values of the system free design variables are numericallyoptimized for various objectives. Towards this purpose a generaloptimization software was used, which is developed and brought tomarket by the Lab. of Thermal Turbomachinery, NTUA [26]. Thesoftware performs stochastic optimization based on evolutionaryalgorithms, and it is very effective for multi-parametric and multi-objective optimization of complex and discontinuous cost functions,like in the present simulation. The optimization algorithmworks withpopulations of candidate solutions and in order to create the nextimproved generation it mimics the biological evolution of speciesgenerations, using processes like cross-over and mutation [26]. It has

Table 3Systems energy and financial results.

Description Referencesystem

OptimumSystem A

OptimumSystem B

1 Water demand satisfaction, FDS (%) 90.3 90.0 99.52 Energy rejection, FREJ (%) 39.5 57.2 58.13 Capacity factors (%)

Wind turbines, CFW 21.5 15.7 14.8Photovoltaics, CFPV 13.2 0 0Hydroturbine, CFT 6.7 19.1 12.8

4 Hydroturbine contribution, FHT (%) 18.1 13.8 21.55 Water production, WAP (m3/year) 516.070 514.000 568.5006 Pumped storage unit cost, ICPS (K€) 2.070 897 2.3897 System investment cost, ICSYSTEM (K€) 7.729 6.010 8.5308 System O&M cost, OMSYSTEM (K€) 396.6 359 429.49 Water production cost, WPC (€/m3) 2.53 2.07 2.5210 Internal Return Rate, IRR (%) 14.2 18.9 14.2


been successfully used by one of the authors in various previousstudies [19,20].

4.2.1. Single-objective optimizationDuring preliminary tests it resulted that the water production cost

reduces increasing the hydroturbine power up to a limit, beyondwhich a minor further decrease in production cost is possible, but therequired hydroturbine power exhibits an abrupt and undesirablefurther increase. After repeated computations for a range of differentpopulations and water demand satisfaction limits, a maximumeffective and reasonable size of the hydroturbine in relation to thedesalination unit power is extracted and tabulated, in order to be usedas additional constriction in all subsequent evaluations.

At first, the desalination system for 5000 residents is optimized soas to minimize the specific water production cost, WPC, while thecoverage of the annual water needs is kept almost equal to thereference system performance (90%). The convergence rate of theoptimizer is shown in Fig. 8. Wide variation limits were used for alldesign variables, and for this reason a great number of about 15,000evaluations is required to minimize the cost function value. A singleevaluation is taken after simulating the entire system operation for aperiod of one year. The obtained optimal values of the designparameters, as well as the most important performance and economicindexes of the so-called System A are concentrated in Tables 2 and 3,respectively, in comparison to the reference system results.

The optimal system exhibits a considerably reduced waterproduction cost (2.07€/m3), compared to the reference designcorresponding cost (2.53€/m3, Table 3). This gain comes mainlyfrom the smaller installed size of the pumped storage system(Table 2), which is now much better exploited (capacity factor ofhydroturbine, Table 3). On the other hand, the optimum power of thewind farm is 50% increased, but its capacity factor reduces. Hence,from the energy point of view the optimum system exhibits less RESexploitation and increased energy rejections (Table 3).

In a second optimization study the desired water demandsatisfaction limit for the same population is set at a much higherlevel, 99.5%, and the results are also given in the last columns ofTables 2 and 3 (System B). Compared to the previous optimal SystemA, the obtained System B configuration has a larger desalination unitand wind farm power. Moreover, in order to guarantee the abovefresh water sufficiency, the optimal size of both hydraulic turbine andreservoirs are now obtained much larger (Table 2). As a result, thecapacity factors of generators (wind and hydroturbines) are notsatisfactory. In other words, the system is rather oversized, but this isnecessary in order to achieve the high demand satisfaction require-ment, especially during summer. However, compared to the initialnon-optimal system, the new design still achieves a slightly lessproduction cost of fresh water (2.5€/m3), in spite of its higher total

Fig. 8. Indicative convergence history of the optimization algorithm.

investment cost (Table 3), thanks to the better energy managementamong its subsystems.

On the other hand, a remarkable result is that both optimalSystems A and B do not include photovoltaics at all, because of thehigh investment cost of the latter. Consequently, wind turbines arethe primary power generators of an economically optimized invest-ment, at least for the current cost-effectiveness of PV units.

4.2.2. Parametric studiesAiming to analyze further the system performance and results, a

parametric study of the effect of island size (resident population) iscarried out. A single-objective optimization is performed for everydifferent size examined hence the results always correspond tooptimal systems.

Thegraphs in Fig. 9 depict theminimumachievablewaterproductioncost for two different acceptable limits of water demand satisfaction, asfunction of the island's resident population. For 90% satisfaction thespecific cost of produced water ranges from about 2.4€/m3 for a smallisland of 1000 residents, to about 1.8€/m3 for a large island (20,000residents). The production cost becomes, as expected, quite higher for99% satisfaction requirement (Fig. 9), because the entire systemmust beoversized to cover also the peak water demand periods.

This is evident also in the comparative results of Fig. 10a and b. Analmost linear dependence on the population for all subsystems installedpower can be observed in these results. The optimum wind powerremains 2 to 2.5 times greater than the desalination power, whereas thepumping station power is almost equal to the difference between them,in order to store the RES production surplus (Fig. 10a,b). Also, theoptimal hydroturbine has only about half of the desalination power,since the former is used as an auxiliary and supplementary powersource. As it can be seen in Fig. 11, hydroturbine participates indesalination unit feeding at a percentage in the range of 13 to 16% for90% demand satisfaction. Its contribution increases for higher coveringlimits (18 to 23% for 99% satisfaction, Fig. 11), in order to fulfill theincreased needs for guaranteed power. Photovoltaics are again notincluded in the optimum systems configuration.

The optimal capacity of the energy storage reservoirs (not shownin figure), increases also linearly with the population, e.g. from about2000 m3 for 1000 residents to 65,000 m3 for 20,000 residents and for90% satisfaction of demands. The above values become 4 times largerfor 99% satisfaction limit (from 8000 to 265,000 m3, respectively).

The capacity factors of the two powering units of the desalinationsystem are drawn in Fig. 12. Their values are low and exhibit only asmall increase with the population, indicating that they are at certaindegree oversized. As a result, a significant portion of the primaryenergy production that ranges between 55 and 60% is rejected. The

Fig. 9. Water production cost for various island sizes.

Fig. 12. Capacity factor of main power generators for various populations and waterdemand satisfaction limits.

Fig. 10. Optimal subsystems size for various populations, and demand satisfaction limit:a) 90%, and b) 99%.


capacity factor of the primary energy source, wind turbines, does notchange much for the high demand covering (99%). On the contrary, inthat case the hydroturbine capacity factor reduces substantially(Fig. 12), as the machine becomes larger to cover the peak demandneeds. A possibility to exploit the rejected energy to other consump-tions or sell it to an electric grid appears to be the only way to increasethe capacity factors and to reduce energy rejections.

Fig. 11. Hydroturbine contribution to desalination.

In a second parametric study the sell price of the produced freshwater is considered as a parameter to assess the economic feasibilityof the investment. In this case the objective of system optimizations isto maximize the IRR value. The obtained results for a small and a largeisland and for two demand satisfaction limits are plotted in Fig. 13. Itcan be observed that systems designed for larger islands and lowerdemand satisfaction are the most attractive for an investor, exhibitingmuch higher IRR values for a given water pricing.

Considering a typical IRR threshold value of the order of 10%, theresults in Fig. 13 show that for all cases the investment becomeseconomically viable for water present price above 2.5€/m3, which ismuch smaller than the current purchase cost (5–8€/m3). Moreover,the economic results could be even better under more favorablefinancial strategies (e.g. subsidy), or by further exploitation of thestored energy.

4.2.3. Double-objective optimizationsAccording to the results of single-optimization studies, the low

water production cost, the small pumped storage unit size, and thehigh demand satisfaction rate are competitive objectives among eachother. Consequently, simultaneous optimization of them would be oftechnical and economic importance.

The first such optimization study concerning the minimization ofboth hydroturbine power and water production cost, is carried out forvarious populations and demand satisfaction limits. In this case theoptimizer converges to a series of optimum solutions distributed on

Fig. 13. Effect of water pricing on the IRR value of the investment.

Fig. 14. Two-objective optimization results for various populations, and 99.5% demandsatisfaction limit.

Fig. 16. Effect of demand satisfaction limit on the water production cost.


curves, called Pareto Fronts [26], which are illustrated in Figs. 14 and15. As expected due to economy of scale, the water production costreduces as population and plant size increase (Fig. 14). However, in allcases there is an upper limit of normalized hydroturbine size, abovewhich the production cost reduction becomes negligible. For largeislands and/or for high demand satisfaction rates this limit is in therange of 0.4–0.5 of the installed desalination power (Figs. 14 and 15,respectively), whereas for small populations and/or reduced satisfac-tion rates it becomes lower: about 0.3 for 1000 residents (Fig. 14), andabout 0.2 for demand satisfaction 90% or lower (Fig. 15).

A remarkable result is that for reduced water needs satisfactionrequirements the energy storage unit may not be included at all,because its incorporation only slightly decreases thewater productioncost (Fig. 15). More detailed computations for the present datashowed that optimal systems obtained for populations larger than5000 residents always include a pumped storage unit for any demandsatisfaction. However, for smaller islands the energy storage becomesunnecessary when the water demand satisfaction limit is below 75%.

A more comprehensive picture of the effect of demand satisfactionlimit on the water production cost is given in Fig. 16 that containsPareto Fronts obtained from corresponding two-objective optimiza-

Fig. 15. Two-objective optimization results for various demand satisfaction limits and5000 residents.

tions, for various populations. In all the three curves the productioncost increases almost linearly with the satisfaction limit, and only forhigh percentage rates, above 95%, it rises more steeply, due to theneed of larger-sized power production and pumped storage units.Consequently, the optimum selection of this limit depends on thelocal conditions and the adopted strategy in order to cover the totalwater demand needs of an island, that may include penalty prices forinsufficient production or shipping transportation cost of supplemen-tary water.

4.2.4. Photovoltaic productionAs mentioned before, all previously obtained lowest production

cost systems do not incorporate photovoltaics, due to the highinvestment cost of this technology that makes it non-competitivecompared to wind turbines for such stand-alone desalination plants.However, in the last decade this cost has been considerably decreasedand is expected to keep reducing in the next years. Consequently, weare approaching to a threshold, below which the solar energyproduction will be economically favorable. In order to estimate thatvalue for the hybrid desalination units examined here, a parametricstudy of the influence of PV investment cost on the optimum unitconfiguration is performed.

The results for two different demand satisfaction limits are plottedin Fig. 17, for an indicative number of 5000 residents, and they aresimilar for smaller or larger populations. The photovoltaic productionunit becomes part of the optimal system when its installation costreduces below 3000€/kW. As the cost is further reduced, the PVoptimal size increases linearly, and exceeds the wind farm power inthe range between 1500 and 2000€/kW, depending on the demandsatisfaction limit (Fig. 17). This PV cost is quite higher than the

Fig. 17. Effect of investment cost on PV participation in hybrid desalination units.

Fig. 18. Power generators capacity factor for optimum system with photovoltaics.


corresponding wind generators cost (taken 1300€/kW, Section 3.3.2).The reason is that the entire solar production is available during thedaytime, namely within the high water demand hours, in contrast tothe wind power, a considerable part of which may be generatedduring the night. This advantageous feature reduces the need forenergy storage, resulting in smaller optimum reservoirs size andpumped storage machinery. The latter compensates the higherinstallation cost of photovoltaics compared to wind generators.

On the other hand, the optimum relation between hydroturbineand desalination installed power, discussed in Section 4.2.3, is notaffected by the PV production, because it is mainly associated withperiods of peak water demand and/or insufficient RES production.

For the optimal systems obtained without photovoltaics, the windfarm and hydroturbine capacity factors are always below 20%, evenfor lower satisfaction limits than those shown in Fig. 12. This picturechanges when the cost of PV system is reduced, allowing it to be partof the optimum hybrid unit. Assuming an investment cost forphotovoltaics of the order of 1800€/kW, for which the optimumsize of both RES units (wind and solar) are about the same (Fig. 17),the corresponding capacity factors for 5000 resident population areillustrated in Fig. 18.

The values for all three generators increase as demand satisfactionlimit decreases, because smaller satisfaction needs can be fulfilledwith smaller installed power. Compared to Fig. 12, the exploitation ofthe wind farm production is remarkably improved by introducing thePV unit, which reduces the optimum wind farm size. On the otherhand however, hydroturbine capacity factor exhibits a considerabledrop for demand satisfaction rates above 80% (Fig. 18). This happensbecause part of its duty during daytime hours is now replaced by PVproduction, whereas its installed power remains high in order to beable to provide the required power for desalination at periods ofinsufficient RES production.

5. Conclusions

A numerical algorithm is developed and applied in order toinvestigate in detail the operation and performance of a hybrid stand-alone desalination system. The results of the various parametric andoptimum design studies of the system carried out in this work aresummarized below.

The studied stand-alone hybrid desalination system is capable tofulfill the water demand of areas such as Greek islands, having anattractive specific water production cost (1.5–3.0€/m3), which is muchcompetitive to the present water transportation pricing (5–8€/m3).

A pumped storage subsystem is necessary to guarantee the desiredfresh water production throughout the year. Its contribution to thedesalination power feed varies between 13% and 23%, and itsoptimum installed power becomes greater for larger islands or higherwater demand satisfaction requirements.

Photovoltaics are still non-competitive solution for the studiedhybrid system. However, PV production pattern fits well with the dailywater consumption needs, and such units are expected to become basiccomponent of hybrid desalination systems in the forthcoming years,when their investment costs will drop below 3000€/kW.

The capacity factor of the primary and secondary power generatorsof an optimally designed system(RES and hydroturbine, respectively) isrelatively low in all cases, while a significant portion of the RESproduction is rejected. Consequently, the capability of exploiting thepumped storage unit to produce electricity for other parallel usagesprovides to be the only effectiveway to improve the capacity factor of allsubsystems. This would also minimize the amount of rejected energy,and improve the economic results of the entire desalination plant.

List of symbols

CFP
Capacity factor of pumps, % CFT Capacity factor of hydroturbines, % CFW Capacity factor of wind turbines, % DWD Daily fresh water demand, m3
FDS
Water demand satisfaction rate, 0–1 or % FHT Hydroturbine contribution indicator, 0–1 or % FREJ Energy exploitation indicator, 0–1 or % G Hourly solar radiation, kW h/m2
g
Gravity acceleration, m/s2
HP
Pumping head, m HT Hydroturbine net head, m HWT Hourly fresh water demand, m3
ICSYSTEM
Total investment cost of the hybrid system, €
OMSYSTEM
Annual operation and maintenance costs, €
PAD
RES production spent for desalination kW PD,I Desalination unit installed power, kW PDEM Hourly power demand for desalination, kW PDES Desalination unit consumption, kW PHT Hydroturbine production, kW PMD Technical minimum of desalination unit, kW PMP Technical minimum of hydroturbines, kW PMT Technical minimum of pumping station, kW PN Desalination power shortage, kW PP,I Pumping station installed power, kW PPS Pumping absorbed power, kW PPV Photovoltaics production, kW PPV,I Photovoltaics installed power, kW PREJ Rejected power, kW PRES Cumulative RES production, kW PT,I Hydroturbine installed power, kW PTANK Power equivalent of water tank content, kW PWT Wind turbines production, kW PWT,I Wind turbine installed power, kW QP Pumped water flow rate, m3/h QT Water flow rate through hydroturbine, m3/h RP Monthly island resident population, people RWC Water consumption of resident population, l/day/human SDC Specific desalination consumption, kW h/m3
SP
Monthly island seasonal population, people SWC Water consumption of seasonal population, l/day/human VR Water volume in the reservoir, m3
VRC
Reservoirs capacity, m3
VT
Water volume in the tank, m3
VTC
Water tank capacity, m3
WDP
Hourly percentage of daily water demand, % WPC Specific fresh water production cost, €/m3
ηP
Pumping efficiency, % ηT Hydro turbining efficiency, %
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