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

Desalination 257 (2010) 137–149

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Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l

Design study of a stand-alone desalination system powered by renewable energy sources 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

a r t i c l e

i n f o

Article history: Received 12 December 2009 Received in revised form 20 February 2010 Accepted 23 February 2010 Available online 29 March 2010 Keywords: Stand-alone desalination Wind power Photovoltaics Pumped storage Plant operation simulation Design optimization

a b s t r a c t The aim of this work is to investigate in detail the optimum design and operation strategy of a stand-alone hybrid desalination scheme, capable to fulfill the fresh water demand of an island or other remote coastal regions. The scheme consists of a reverse-osmosis desalination unit powered by wind and solar electricity production systems and by a pumped storage unit. A specific computer algorithm is developed to simulate in detail the entire plant operation and also to perform economic evaluation of the investment. A stochastic optimization software based on evolutionary algorithms is implemented to accomplish design optimization studies of the plant for various objectives, like the 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 critical parameters, 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 also the production and economic results of the whole plant. An optimally designed scheme is found to be economically viable investment, although energy rejections are significant and there is a clear need for better exploitation of renewable energy production surplus. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Nowadays it is observed, globally, an extensive phenomenon of drought. Especially in Greece, many isolated areas, such as Aegean islands, suffer from drought [1]. The problem becomes worse in summer when the water demand increases up to 4–5 times compared to winter because of tourism [2]. In most islands the existing water stocks cannot satisfy such increasing demand; thus the problem that comes up must be solved with permanent and viable solutions. At present, this water demand is being satisfied by tank transportation with the considerably high cost of about 5–8 €/m3 for Cyclades and Dodecanese complex [1]. Seawater desalination can play an important role towards a permanent confrontation of the problem [2]. The installation of desalination units is a common solution throughout the world, in areas with drought. In the last decades the number of desalination applications has greatly increased, while desalination is the subject of several research works. As a result, new desalination methods have been developed, experience has been gained, system operation has been amended and the equipment production has become massive [3]. Thus, the two most important performance characteristics of such

⁎ Corresponding author. Tel.: + 30 2107721080. E-mail address: anagno@fluid.mech.ntua.gr (J.S. Anagnostopoulos). 0011-9164/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2010.02.033

applications, which are the quality of produced water and the water production cost are continuously being improved. A critical technical parameter of desalination applications is the way the system is powered. This decision is taken according to the selected method of desalination and the characteristics of the candidate area [4]. Nowadays the method of reverse osmosis dominates globally; it requires only electricity, has a quite low specific energy demand, and can cooperate with technologies of renewable energy sources (RES) such as wind turbines and photovoltaics [4–7]. Concerning Aegean islands that suffer from drought, most of them are isolated and the electricity is provided by local conventional power stations operating at very high production costs. In addition, the power demand of large desalination units may not be satisfied by the existing power stations. On the other hand, Aegean islands feature an abundance of RES like solar and wind energy. Consequently, a desalination system powered by hybrid renewable energy technologies would be a very promising solution for those regions. Several simulation studies of desalination units cooperating with RES and conventional thermal units have already taken place [8–11]. Stand-alone reverse-osmosis desalination units powered by wind turbines and/or photovoltaics and supported by batteries have been the research topic of several works that have shown that such systems could be a viable solution at present conditions [12–14]. Energy storage is an important aspect of such autonomous systems, although some systems without storage have been simulated and tested

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[15,16]. Because of the stochastic and intermittent nature of RES, a storage system is usually required in order to avoid excessive rejection of the energy production, as well as to guarantee the desalination unit operation during unfavorable weather conditions. The most common system for energy storage are batteries which are included in most studies. The use of batteries has the disadvantages of short life cycle, high-cost maintenance and environmentally unfriendly content [17,18]. As a result, batteries have been proposed only for small-scale plants. The present work aims to study an alternative means of energy storage, a pumped storage subsystem, in stand-alone desalination plants, and to investigate its role on the operation of the whole scheme. Pumped storage in hybrid wind-hydro power production plants has been studied applying numerical design optimization methodologies in some previous works [19,20]. The optimum sizing of all desalination system components that maximize its energy and/or economic results for small to large islands constitutes an objective of the present work, as well.

2. System description The considered system is schematically shown in Fig. 1. The standalone desalination unit is powered by a hybrid RES system (windphotovoltaics), and includes a fresh water tank to provide autonomy to the area for a determinate time period, in case that the system is out of order for some reason (e.g. maintenance, failure). Due to the intermittent nature of those RES and the difficulty in predicting the energy production rate, a means of energy storage is required to operate the desalination unit even during unfavorable weather conditions. A pumped storage subsystem is considered, as an

alternative to batteries. A typical pumped storage unit consists of a pumping and a turbining station, two water reservoirs at different altitude, and the necessary pipelines (Fig. 1). A number of pumps are usually installed in parallel operation, equipped with variable speed motors in order to be able to absorb the fluctuating production of RES with no power 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 is used to operate the pumps and store hydraulic (dynamic) energy in the upper reservoir (Fig. 1). On the other hand, when the primary energy production cannot satisfy the desalination demands, then the hydroturbine re-transforms the stored energy into electricity, which powers the desalination unit. Details on the energy transfer rules and constrictions are given in Section 3. 3. Algorithm description In order to simulate the entire system operation and its subsystems interaction, a specific computer algorithm is developed. The software makes also an economic evaluation of the system, based on empirical cost relations for all its main components (pumps, hydro and wind turbines, photovoltaics, pipelines, etc.) [19,20]. The algorithm is divided into three sections: data input, application of system's logic operation, and techno-economic evaluation. These parts are described in more detail in the present section. 3.1. Data input Data needed for the simulation of system's operation are either fixed or free variables, the value or the range of which is predetermined by the

Fig. 1. Sketch of the examined desalination system set-up.

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user. In the present study fixed quantities include the hydraulic head (here 400 m), the pipeline dimensions, the number of pumps and turbines, and the time-variation curves of wind speed and solar radiation. On the other hand, the size of all main system components (desalination unit, wind and photovoltaic parks, pumping and turbining systems, reservoirs and fresh water tank), constitutes the free design variables. Finally, some critical parameters like the resident population, the water demand satisfaction rate and the photovoltaics (PV) cost are also introduced and examined in the present work. Detailed description of the main system parameters, along with their technical and operational constrictions, is given below. 3.1.1. Water demand Calculation of the hourly water demand of a candidate area is based on an ideal island of constant resident population, RP. The seasonal population, SP, of the island is assumed here to follow a monthly variation curve like the one drawn in Fig. 2, which is typical for a Greek island at the Aegean Sea: population in summer months may increase due to tourism up to 3 or 4 times [1]. The resident population is a major parameter of the system, and usually depends on the island size. Assuming a seasonally varying specific daily consumption, SWC for seasonal population and RWC for resident population (Table 1), the total 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 water demand, HWD (m3), of the entire population is calculated as: HWD = WDP ⋅DWD :

ð2Þ

3.1.2. Desalination unit The correlation between hourly water demand, and the corresponding power for desalination, PDEM (or the hourly energy demand, EDEM) is given by Eq. (3), assuming an average specific energy consumption for desalination, SDC. Today, reverse-osmosis desalination 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 for the entire desalination process and apparatus (pumps, membranes and energy recovery systems). PDEM = EDEM = HWD ⋅SDC :

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

ð3Þ

139

Table 1 Typical specific water consumption data. Daily water consumption (l/day/person) Population type Resident, RWC Seasonal, SWC

Winter 150 200

Summer 250 300

The desalination unit installed power, PD,I, is considered as a system free variable. Thus, desalination water production capability per day, DFC, can be computed from the relation: DFC = 24⋅ðPD = SDC Þ:

ð4Þ

The reverse osmosis unit can operate between its nominal and a minimum load, PMD, because of membrane's characteristic curve [22]: PMD ≤PDES ≤PD;I

ð5Þ

where PDES is the instant power consumed by desalination unit. The lower operation limit corresponds to the minimum required pressure to overcome the osmotic pressure and to set desalination unit up. Working in partial loads may affect the quality of the produced fresh water, but this is not a subject of the present work. In the present simulation, the technical minimum is taken at 25% of the nominal power. The desalination system includes a fresh water tank, the capacity of which is proportional to the island size (or to the resident population). A period of two summer days (August) was considered as the desirable autonomy of the system. Thus, the capacity of the fresh water tank, VTC, is: VTC = 2⋅DWD :

ð6Þ

In order to conserve the above autonomy throughout the year, the hydroturbine is put in operation when the content of the tank drops below 90%, providing that there exist available storage in the upper reservoir. 3.1.3. RES features and production Hourly energy production by wind turbines and photovoltaics is being calculated using the corresponding meteorological data for wind speed, V, and solar radiation, G (Fig. 4). Specific data time series are used for all cases examined here, assuming that they are representative of the Aegean islands complex [1]. Concerning the calculation of wind farm production, the power curve of a typical wind turbine of specific nominal power, PMWT, is used. 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.

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

QP =

PPS ⋅ηP ⋅3600 g⋅HP

PMP ≤PPS ≤PP;I :

ð12Þ

ð13Þ

Hydroturbines can operate at variable power load, PHT, in order to supplement the RES production. However, operation at partial loads may affect efficiency. In this work the latter follows a typical characteristic curve of Pelton turbines, the technical minimum of which is taken 20% of the nominal power load, PMT. Therefore, the hourly water flow, QT (m3), through the hydroturbine is computed as:

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

PHT ⋅3600 ηT ⋅g⋅HT

PMT ≤PHT ≤PT;I production, PNWT, and the total wind farm production, PWT (or EWT in kW h), is calculated by the following equations, where ηWT is the wind farm's total efficiency: PWT = EWT = ηWT ⋅k⋅PNWT

ð14Þ

ð15Þ

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

ð7Þ 3.2. System operation strategy

PW;I : k= PMWT

ð8Þ

On the other hand, the power production by the PV array, PPV (or EPV in kW h), is computed by Eq. (9), assuming that there are NPV identical PV panels of a specific nominal power PNPV each, average efficiency ηPV, and panel's area A. PPV = EPV = ηPV ⋅NPV ⋅A⋅G:

ð9Þ

The total installed photovoltaic power is considered as a free variable of the system and is given by: PPV;I = NPV ⋅PNPV :

ð10Þ

In every time-step of the plant operation simulation, the total RES production, 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 the values of the produced energy ERES (in kW h), and power PRES (in kW) are exactly the same, allowing the treatment of even the energy quantities in terms of power. This practice is followed throughout this work. 3.1.4. Pumped storage subsystem The pumping station is consisted by a number of variable speed pumps in parallel operation, with total installed power PP,I. The pumps operate only when the available RES power exceeds a technical minimum, which is taken 15% of the installed power. This corresponds to a number of at least 4 pumps, with the capability of reduction of their rotation speed by about 15%. For any available wind power, PPS, the hourly water flow, QP, from the lower to the upper reservoir is

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

ð16Þ

The desalination unit can be powered by RES, PAD, or hydroturbine power, PHT, or both: PDES = PAD + PHT :

ð17Þ

Finally, if the existing water in the tank, along with the additional production from RES and hydroturbine, cannot satisfy the water demand, then there is a desalination power shortage, PN: PN = PDEM −ðPTANK + PAD + PHT Þ; PTANK = VT ⋅ SDC

ð18Þ

where PTANK is the desalination power equivalent (in kW) of the fresh water 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 water and to retain a 90% minimum fulfillment of this tank. The unit, as also the pumps and hydroturbines does not operate if the available power is below its corresponding technical minima. In addition, desalination stops when the water tank is full, and the same is done for the pumps if the upper reservoir is full. Following the above constrictions, the operation strategy of the entire system is presented in the flow chart of Fig. 5. The diagram consists of two parts, explaining the management of RES and of hydroturbine production, respectively. In the first part of Fig. 5, the power produced by the primary generators (wind turbines and photovoltaics) can be used either for desalination or for pumping storage. Priority is given to desalination

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

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unit, provided that there is an empty space in the fresh water tank, namely PTANK,F N 0, where: PTANK;F = ðVTC −VT Þ⋅SDC :

ð21Þ

The latter condition always happens first, hence it controls the second flow chart diagram of Fig. 5. Finally, the hydropower stops when the upper reservoir reaches its lowest acceptable level, here PUPR = 0, or VR = 0. 3.3. Techno-economic evaluation At the end of the simulated period of plant operation (one year) all technical and economic evaluation indicators are computed. At this section, the most important and those that will be presented and discussed in the results are defined. 3.3.1. Technical evaluation System's first priority is to satisfy the island's water needs at a predetermined percentage limit. Consequently, in terms of desalination power, we define an indicator of demand satisfaction rate, FDS

FDS = 1−

∑8760 j = 1 PN ∑8760 j = 1 PDEM

ð22Þ

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

FHT =

∑8760 j = 1 PHT ∑8760 j = 1 PDES

:

ð23Þ

Also, an important energy indicator is defined to express the portion of RES production that cannot be exploited and it is finally rejected. FREJ =

∑8760 j = 1 PREJ ∑8760 j = 1 PRES

:

CFW =

CFT =

ð20Þ

and VR is the current water volume content, then the RES energy surplus is rejected, as also when PRES exceeds the installed pumping power. On the other hand, the hydroturbine is set to operate in case of desalination power shortage (PN N 0), but also when the fresh water level in the tank drops below the limit VTG = 0.9 ⋅ VTC, namely: PTANK;G = ðVTG −VT Þ⋅SDC N 0:

∑

ð19Þ

When the upper reservoir is full (PUPR,F = 0 or VR = VRC), where: PUPR;F = g⋅ðVRC −VR Þ⋅HT ⋅ηT

8760

ð24Þ

j=1



 PWT ⋅ðPAD + PPS Þ PRES PW;I ⋅8760

∑8760 j = 1 PHT PT;I T8760

ð26Þ

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 evaluation The 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) of each subsystem, as well as the operation and maintenance cost of the plant. Each cost depends either on a parameter's value or an operation quantity that comes up from the simulation. In the following relations power 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,I O&M cost: OMPV = 0.02 ⋅ ICPV Desalination (reverse osmosis) Unit investment cost: ICD = 2270 · D0.875 FC Tank cost: ICT = 1090.8 · V0.61 TC Investment cost: ICDES = ICT + ICD O&M cost: OMDES = 0.6·WAP Where WAP is the total fresh water production:

WAP =

∑8760 j = 1 PDES : SDC

ð28Þ

Pumped storage subsystem Hydroturbine investment cost: ICHT = 18,000 ⋅ P0.48 T,I Pumps investment cost: ICP = NP · 1700 · P0.82 P,I Reservoirs investment cost: ICR = 2 · 420 · V0.7 RC . The pipe investment cost, ICPIPE, is considered as the summary of material, welding, and coating costs, which are computed as function of the pipe dimensions, whereas the latter is optimally selected from standardized tables depending on the water flow rate and head. Other costs (electric and electronic equipment, unpredictables, etc.): ICOTHER = 0:2⋅ðICHT + ICP + ICR + ICPIPE Þ:

Finally, the capacity factors of the three power generation subsystems (PV, wind turbines, and hydroturbine) are computed by the following relations and constitute the sizing indicators of this standalone system. 8760

∑

CFP =

j=1



 PPV ⋅ðPAD + PPS Þ PRES PPV;I ⋅8760

Pumped storage subsystem total cost: ICPS = ICHT + ICP + ICR + ICPIPE + ICOTHER O&M cost: OMPS = 0.02 · ICPS. Total costs of the plant

ð25Þ

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

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

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

WPC =

DA =

DA + OMSYSTEM WAP

ð29Þ

ICSYSTEM ⋅r 1−ð1 + r Þ−n

143

desalination power of 480 kW is needed (3 kW h/m3). Also, a fresh water tank of 8500 m3 capacity in order to provide 2 days of autonomy in August is included (Eq. (5)). Then, because of the stochastic nature of RES, the cumulative installed power of wind turbines and PV is taken about two times greater than the desalination unit power, namely 800 kW and 200 kW, respectively. On the other hand, hydroturbine installed power is taken equal to the desalination power (480 kW), in order to provide sufficient power

ð30Þ

where r is the discount rate and n is the plant's life cycle. The specific water cost will be compared to the current water transportation cost. IRR index is obtained as the solution of the equation: n

Bj

j=0

ð1 + IRRÞ

∑

j

n

Cj

j=1

ð1 + IRRÞj

= ICSYSTEM + ∑

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 the sell price of the produced fresh water. Every value is converted to present. 4. Results and discussion This section is devoted to the presentation of results from the operation simulation and optimal sizing of the examined hybrid system. Firstly, a reference system with reasonable design is examined and the results are analyzed in order to acquire a detailed view 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 system taken 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, a yearly average hourly fresh water demand would be 160 m3. Thus, a

Table 2 Dimensioning of the examined systems. Design parameter 1 Island resident population (people) 2 Tank capacity (m3) 3 Desalination installed power (kW) 4 Wind turbines installed power (kW) 5 Photovoltaics installed power (kW) 6 Hydroturbine installed power (kW) 7 Pumps installed power (kW) 8 Storage reservoir capacity (m3)

Symbol Reference Optimum Optimum system System A System B RP

5000

5000

5000

VTC PD,I PW,I

8.500 480 800

8500 498 1210

8500 612 1500

PPV,I

200

0

0

PHT,I

480

127

326

PP,I VRC

600 40.000

386 12.120

593 56.900

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

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even in the most adverse case of simultaneous apnea, cloudiness and empty fresh water tank. Pumping station installed power is taken between hydroturbine and total RES power (wind plus PV), at 600 kW. Concerning the reservoirs, a net capacity of 40,000 m3 was chosen that corresponds to about 3 days of continuous turbine production. All the above data are tabulated in Table 2 (Reference system).

Graphs of plant performance during a typical winter week and a typical summer week are presented in Figs. 6 and 7, showing the energy production and exploitation and the water needs satisfaction by desalination. In the winter the energy is produced mostly by wind turbines (Fig. 6a), whereas hydroturbine does not operate at all. Water needs are small and they are fully satisfied even in periods of low desalination production (Fig. 6b), while the fresh water tank remains almost full (Fig. 6d). As a result, a large percentage of RES production cannot be either used or stored, and it is rejected (Fig. 6c). On the other hand, during the summer-week results of Fig. 7 the water demand is higher, and the hydroturbine is continuously used to supplement the desalination power (Fig. 7a), as long as there is available hydraulic energy stored in the upper reservoir (Fig. 7d). Nevertheless, the water needs are not totally satisfied, and there exist certain hours every day when the fresh water tank empties (Fig. 7b and d). This problem becomes worse towards the end of the week, due to the reduced wind production (Fig. 7a). The only positive effect is that energy rejections are now minimal, since the RES production surplus can be pumped and stored to the upper reservoir (Fig. 7c). From quantitative point of view, the performance of the reference system can be evaluated from the results in the corresponding column of Table 3, which were obtained by the simulation algorithm for a yearly operation of the system. It is concluded that the examined system is capable 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 production cannot either be consumed for desalination or stored, and the capacity factors of all three generators are low. Hydroturbine participation in desalination powering is not so strong (18.1%) but justifies its implementation in the system. Concerning the economic results, the estimated specific production cost of the water is 2.53 €/m3, much lower than the current transportation cost (5–8 €/m3). Using the former as initial (first year's) sell price for the system, the obtained IRR index value exceeds 14%, for a depreciation period of 20 years.

4.2. System optimal design The values of the system free design variables are numerically optimized for various objectives. Towards this purpose a general optimization software was used, which is developed and brought to market by the Lab. of Thermal Turbomachinery, NTUA [26]. The software performs stochastic optimization based on evolutionary algorithms, and it is very effective for multi-parametric and multiobjective optimization of complex and discontinuous cost functions, like in the present simulation. The optimization algorithm works with populations of candidate solutions and in order to create the next improved generation it mimics the biological evolution of species generations, using processes like cross-over and mutation [26]. It has

Table 3 Systems energy and financial results.

1 2 3

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

4 5 6 7 8 9 10

Description

Reference system

Optimum System A

Optimum System B

Water demand satisfaction, FDS (%) Energy rejection, FREJ (%) Capacity factors (%) Wind turbines, CFW Photovoltaics, CFPV Hydroturbine, CFT Hydroturbine contribution, FHT (%) Water production, WAP (m3/year) Pumped storage unit cost, ICPS (K€) System investment cost, ICSYSTEM (K€) System O&M cost, OMSYSTEM (K€) Water production cost, WPC (€/m3) Internal Return Rate, IRR (%)

90.3 39.5

90.0 57.2

99.5 58.1

21.5 13.2 6.7 18.1 516.070 2.070 7.729 396.6 2.53 14.2

15.7 0 19.1 13.8 514.000 897 6.010 359 2.07 18.9

14.8 0 12.8 21.5 568.500 2.389 8.530 429.4 2.52 14.2

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

4.2.1. Single-objective optimization During preliminary tests it resulted that the water production cost reduces increasing the hydroturbine power up to a limit, beyond which a minor further decrease in production cost is possible, but the required hydroturbine power exhibits an abrupt and undesirable further increase. After repeated computations for a range of different populations and water demand satisfaction limits, a maximum effective and reasonable size of the hydroturbine in relation to the desalination unit power is extracted and tabulated, in order to be used as additional constriction in all subsequent evaluations. At first, the desalination system for 5000 residents is optimized so as to minimize the specific water production cost, WPC, while the coverage of the annual water needs is kept almost equal to the reference system performance (90%). The convergence rate of the optimizer is shown in Fig. 8. Wide variation limits were used for all design variables, and for this reason a great number of about 15,000 evaluations is required to minimize the cost function value. A single evaluation is taken after simulating the entire system operation for a period of one year. The obtained optimal values of the design parameters, as well as the most important performance and economic indexes 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 water production cost (2.07 €/m3), compared to the reference design corresponding cost (2.53 €/m3, Table 3). This gain comes mainly from the smaller installed size of the pumped storage system (Table 2), which is now much better exploited (capacity factor of hydroturbine, Table 3). On the other hand, the optimum power of the wind farm is 50% increased, but its capacity factor reduces. Hence, from the energy point of view the optimum system exhibits less RES exploitation and increased energy rejections (Table 3). In a second optimization study the desired water demand satisfaction limit for the same population is set at a much higher level, 99.5%, and the results are also given in the last columns of Tables 2 and 3 (System B). Compared to the previous optimal System A, the obtained System B configuration has a larger desalination unit and wind farm power. Moreover, in order to guarantee the above fresh water sufficiency, the optimal size of both hydraulic turbine and reservoirs are now obtained much larger (Table 2). As a result, the capacity factors of generators (wind and hydroturbines) are not satisfactory. In other words, the system is rather oversized, but this is necessary in order to achieve the high demand satisfaction requirement, especially during summer. However, compared to the initial non-optimal system, the new design still achieves a slightly less production cost of fresh water (2.5 €/m3), in spite of its higher total

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

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investment cost (Table 3), thanks to the better energy management among its subsystems. On the other hand, a remarkable result is that both optimal Systems A and B do not include photovoltaics at all, because of the high investment cost of the latter. Consequently, wind turbines are the primary power generators of an economically optimized investment, at least for the current cost-effectiveness of PV units. 4.2.2. Parametric studies Aiming to analyze further the system performance and results, a parametric study of the effect of island size (resident population) is carried out. A single-objective optimization is performed for every different size examined hence the results always correspond to optimal systems. The graphs in Fig. 9 depict the minimum achievable water production cost for two different acceptable limits of water demand satisfaction, as function of the island's resident population. For 90% satisfaction the specific cost of produced water ranges from about 2.4 €/m3 for a small island of 1000 residents, to about 1.8 €/m3 for a large island (20,000 residents). The production cost becomes, as expected, quite higher for 99% satisfaction requirement (Fig. 9), because the entire system must be oversized to cover also the peak water demand periods. This is evident also in the comparative results of Fig. 10a and b. An almost linear dependence on the population for all subsystems installed power can be observed in these results. The optimum wind power remains 2 to 2.5 times greater than the desalination power, whereas the pumping station power is almost equal to the difference between them, in order to store the RES production surplus (Fig. 10a,b). Also, the optimal hydroturbine has only about half of the desalination power, since the former is used as an auxiliary and supplementary power source. As it can be seen in Fig. 11, hydroturbine participates in desalination unit feeding at a percentage in the range of 13 to 16% for 90% demand satisfaction. Its contribution increases for higher covering limits (18 to 23% for 99% satisfaction, Fig. 11), in order to fulfill the increased needs for guaranteed power. Photovoltaics are again not included in the optimum systems configuration. The optimal capacity of the energy storage reservoirs (not shown in figure), increases also linearly with the population, e.g. from about 2000 m3 for 1000 residents to 65,000 m3 for 20,000 residents and for 90% satisfaction of demands. The above values become 4 times larger for 99% satisfaction limit (from 8000 to 265,000 m3, respectively). The capacity factors of the two powering units of the desalination system are drawn in Fig. 12. Their values are low and exhibit only a small increase with the population, indicating that they are at certain degree oversized. As a result, a significant portion of the primary energy production that ranges between 55 and 60% is rejected. The

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

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

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

In a second parametric study the sell price of the produced fresh water is considered as a parameter to assess the economic feasibility of the investment. In this case the objective of system optimizations is to maximize the IRR value. The obtained results for a small and a large island and for two demand satisfaction limits are plotted in Fig. 13. It can be observed that systems designed for larger islands and lower demand satisfaction are the most attractive for an investor, exhibiting much higher IRR values for a given water pricing. Considering a typical IRR threshold value of the order of 10%, the results in Fig. 13 show that for all cases the investment becomes economically viable for water present price above 2.5 €/m3, which is much smaller than the current purchase cost (5–8 €/m3). Moreover, the economic results could be even better under more favorable financial strategies (e.g. subsidy), or by further exploitation of the stored energy.

capacity factor of the primary energy source, wind turbines, does not change much for the high demand covering (99%). On the contrary, in that case the hydroturbine capacity factor reduces substantially (Fig. 12), as the machine becomes larger to cover the peak demand needs. A possibility to exploit the rejected energy to other consumptions or sell it to an electric grid appears to be the only way to increase the capacity factors and to reduce energy rejections.

4.2.3. Double-objective optimizations According to the results of single-optimization studies, the low water production cost, the small pumped storage unit size, and the high demand satisfaction rate are competitive objectives among each other. Consequently, simultaneous optimization of them would be of technical and economic importance. The first such optimization study concerning the minimization of both hydroturbine power and water production cost, is carried out for various populations and demand satisfaction limits. In this case the optimizer converges to a series of optimum solutions distributed on

Fig. 11. Hydroturbine contribution to desalination.

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

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

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

curves, called Pareto Fronts [26], which are illustrated in Figs. 14 and 15. As expected due to economy of scale, the water production cost reduces as population and plant size increase (Fig. 14). However, in all cases there is an upper limit of normalized hydroturbine size, above which the production cost reduction becomes negligible. For large islands and/or for high demand satisfaction rates this limit is in the range of 0.4–0.5 of the installed desalination power (Figs. 14 and 15, respectively), whereas for small populations and/or reduced satisfaction rates it becomes lower: about 0.3 for 1000 residents (Fig. 14), and about 0.2 for demand satisfaction 90% or lower (Fig. 15). A remarkable result is that for reduced water needs satisfaction requirements the energy storage unit may not be included at all, because its incorporation only slightly decreases the water production cost (Fig. 15). More detailed computations for the present data showed that optimal systems obtained for populations larger than 5000 residents always include a pumped storage unit for any demand satisfaction. However, for smaller islands the energy storage becomes unnecessary when the water demand satisfaction limit is below 75%. A more comprehensive picture of the effect of demand satisfaction limit on the water production cost is given in Fig. 16 that contains Pareto Fronts obtained from corresponding two-objective optimiza-

Fig. 15. Two-objective optimization results for various demand satisfaction limits and 5000 residents.

tions, for various populations. In all the three curves the production cost increases almost linearly with the satisfaction limit, and only for high percentage rates, above 95%, it rises more steeply, due to the need of larger-sized power production and pumped storage units. Consequently, the optimum selection of this limit depends on the local conditions and the adopted strategy in order to cover the total water demand needs of an island, that may include penalty prices for insufficient production or shipping transportation cost of supplementary water. 4.2.4. Photovoltaic production As mentioned before, all previously obtained lowest production cost systems do not incorporate photovoltaics, due to the high investment cost of this technology that makes it non-competitive compared to wind turbines for such stand-alone desalination plants. However, in the last decade this cost has been considerably decreased and is expected to keep reducing in the next years. Consequently, we are approaching to a threshold, below which the solar energy production will be economically favorable. In order to estimate that value for the hybrid desalination units examined here, a parametric study of the influence of PV investment cost on the optimum unit configuration is performed. The results for two different demand satisfaction limits are plotted in Fig. 17, for an indicative number of 5000 residents, and they are similar for smaller or larger populations. The photovoltaic production unit becomes part of the optimal system when its installation cost reduces below 3000 €/kW. As the cost is further reduced, the PV optimal size increases linearly, and exceeds the wind farm power in the range between 1500 and 2000 €/kW, depending on the demand satisfaction limit (Fig. 17). This PV cost is quite higher than the

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

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A pumped storage subsystem is necessary to guarantee the desired fresh water production throughout the year. Its contribution to the desalination power feed varies between 13% and 23%, and its optimum installed power becomes greater for larger islands or higher water demand satisfaction requirements. Photovoltaics are still non-competitive solution for the studied hybrid system. However, PV production pattern fits well with the daily water consumption needs, and such units are expected to become basic component 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 generators of an optimally designed system (RES and hydroturbine, respectively) is relatively low in all cases, while a significant portion of the RES production is rejected. Consequently, the capability of exploiting the pumped storage unit to produce electricity for other parallel usages provides to be the only effective way to improve the capacity factor of all subsystems. This would also minimize the amount of rejected energy, and improve the economic results of the entire desalination plant. Fig. 18. Power generators capacity factor for optimum system with photovoltaics. List of symbols

corresponding wind generators cost (taken 1300 €/kW, Section 3.3.2). The reason is that the entire solar production is available during the daytime, namely within the high water demand hours, in contrast to the wind power, a considerable part of which may be generated during the night. This advantageous feature reduces the need for energy storage, resulting in smaller optimum reservoirs size and pumped storage machinery. The latter compensates the higher installation cost of photovoltaics compared to wind generators. On the other hand, the optimum relation between hydroturbine and desalination installed power, discussed in Section 4.2.3, is not affected by the PV production, because it is mainly associated with periods of peak water demand and/or insufficient RES production. For the optimal systems obtained without photovoltaics, the wind farm and hydroturbine capacity factors are always below 20%, even for lower satisfaction limits than those shown in Fig. 12. This picture changes when the cost of PV system is reduced, allowing it to be part of the optimum hybrid unit. Assuming an investment cost for photovoltaics of the order of 1800 €/kW, for which the optimum size of both RES units (wind and solar) are about the same (Fig. 17), the corresponding capacity factors for 5000 resident population are illustrated in Fig. 18. The values for all three generators increase as demand satisfaction limit decreases, because smaller satisfaction needs can be fulfilled with smaller installed power. Compared to Fig. 12, the exploitation of the wind farm production is remarkably improved by introducing the PV unit, which reduces the optimum wind farm size. On the other hand however, hydroturbine capacity factor exhibits a considerable drop for demand satisfaction rates above 80% (Fig. 18). This happens because part of its duty during daytime hours is now replaced by PV production, whereas its installed power remains high in order to be able to provide the required power for desalination at periods of insufficient RES production.

5. Conclusions A numerical algorithm is developed and applied in order to investigate in detail the operation and performance of a hybrid standalone desalination system. The results of the various parametric and optimum design studies of the system carried out in this work are summarized below. The studied stand-alone hybrid desalination system is capable to fulfill the water demand of areas such as Greek islands, having an attractive specific water production cost (1.5–3.0 €/m3), which is much competitive to the present water transportation pricing (5–8 €/m3).

CFP CFT CFW DWD FDS FHT FREJ G g HP HT HWT ICSYSTEM OMSYSTEM PAD PD,I PDEM PDES PHT PMD PMP PMT PN PP,I PPS PPV PPV,I PREJ PRES PT,I PTANK PWT PWT,I QP QT RP RWC SDC SP SWC VR VRC VT VTC WDP WPC ηP ηT

Capacity factor of pumps, Capacity factor of hydroturbines, Capacity factor of wind turbines, Daily fresh water demand, Water demand satisfaction rate, Hydroturbine contribution indicator, Energy exploitation indicator, Hourly solar radiation, Gravity acceleration, Pumping head, Hydroturbine net head, Hourly fresh water demand, Total investment cost of the hybrid system, Annual operation and maintenance costs, RES production spent for desalination Desalination unit installed power, Hourly power demand for desalination, Desalination unit consumption, Hydroturbine production, Technical minimum of desalination unit, Technical minimum of hydroturbines, Technical minimum of pumping station, Desalination power shortage, Pumping station installed power, Pumping absorbed power, Photovoltaics production, Photovoltaics installed power, Rejected power, Cumulative RES production, Hydroturbine installed power, Power equivalent of water tank content, Wind turbines production, Wind turbine installed power, Pumped water flow rate, Water flow rate through hydroturbine, Monthly island resident population, Water consumption of resident population, Specific desalination consumption, Monthly island seasonal population, Water consumption of seasonal population, Water volume in the reservoir, Reservoirs capacity, Water volume in the tank, Water tank capacity, Hourly percentage of daily water demand, Specific fresh water production cost, Pumping efficiency, Hydro turbining efficiency,

% % % m3 0–1 or % 0–1 or % 0–1 or % kW h/m2 m/s2 m m m3 € € kW kW kW kW kW kW kW kW kW kW kW kW kW kW kW kW kW kW kW m3/h m3/h people l/day/human kW h/m3 people l/day/human m3 m3 m3 m3 % €/m3 % %

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