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An optimization model for the production of desalinated water using photovoltaic systems
Desalination 258 (2010) 100–105
Contents lists available at ScienceDirect
Desalination j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / d e s a l
An optimization model for the production of desalinated water using photovoltaic systems Andreas Poullikkas ⁎ Electricity Authority of Cyprus, P.O. Box 24506, 1399 Nicosia, Cyprus
a r t i c l e
i n f o
Article history: Received 2 January 2010 Received in revised form 15 March 2010 Accepted 16 March 2010 Available online 18 April 2010 Keywords: Desalination Reverse osmosis Solar energy Photovoltaics Renewable energy sources
a b s t r a c t In this work, an optimization model using a genetic algorithm technique is developed for the desalinated water production cost using photovoltaics (PVs). In order to demonstrate the applicability of the method a parametric study is carried out for the optimum reverse osmosis (RO) desalinated water cost. In particular, taking into account various RO plant capacities the desalinated water cost have been determined for various scenarios from which the requirements in electrical energy are covered partly (25%, 50%, 75%) and/or fully (100%) from PVs. Based on the data and the assumptions used, the results indicate that the production cost of desalinated water is increased with the degree of integration of PVs for partial and/or total electricity requirements of the RO plant. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The world demand of desalination equipment is expected to grow by more than 10% annually in the next two decades. This demand is derived by the reduced per capita share of fresh water in the world and by the increasing concern for water quality, which is based on the increasing water pollution [15]. Reverse Osmosis (RO) is the only process that can be competitive for most kinds of water at any capacity. RO desalination is well developed and has been in commercial use for three decades for desalting low salinity brackish water. RO use for seawater desalting is becoming increasingly more reliable and cost competitive. The cost of RO desalination has been going down and will continue to do in the future because of technology improvements and market forces. The cost of RO desalination depends on many variables including feed water salinity and quality, plant size, finance cost, energy cost, process type, infrastructure requirements, intake type, plant reliability and operation and maintenance (O&M) requirements [9]. In order to obtain the desired plant life and reliability with minimum cost, proper cost analysis should be performed. In recent years the photovoltaic (PV) industry has been experiencing a dramatic growth at a global level. Continuous increase of conventional fuel costs as well as growing pressure to turn towards renewable energy sources are the main drivers behind this rapidly expanding industry which since the start of the decade has achieved continuous annual growth of around 30% [13,14]. An important PVs
⁎ Fax: +357 22 201809. E-mail address: [email protected]. 0011-9164/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2010.03.036
application, which is currently emerging in the Mediterranean region, is the operation of RO desalination plants integrated with PV systems in order to satisfy the RO requirements in electrical energy either partly or fully. In this work, an optimization model is developed using a genetic algorithm (GA) for the calculation of both the cost of electricity produced from the PV system and the desalinated water production cost. The algorithm combines the CAROC software [9–11], for the optimum desalinated water production cost and the IPP v2.1 software [8,12] for the optimum cost of electricity produced from the PV system. In order to demonstrate the applicability of the method a parametric study is carried out for the optimum reverse osmosis (RO) desalinated water cost. In particular, the operation of a RO desalination plant and the electricity requirements which are partly and/or fully covered by PVs are simulated. Taking into account various RO plant capacities the desalinated water cost is determined for various scenarios from which the requirements in electrical energy are covered partly (25%, 50%, 75%) and/or fully (100%) from PVs. In Section 2, the least energy consumption desalination technology for integration with PVs is selected. The optimization model developed is presented in Section 3 and the results of the parametric analysis are discussed in Section 4. The conclusions are summarized in Section 5. 2. Desalination technology selection During the past ten years several countries facing water shortage problems have investigated and selected the least cost desalination technology in order to cover their needs. For example in [16], where a review of Morocco water policy is carried out, it was concluded that
A. Poullikkas / Desalination 258 (2010) 100–105
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seawater desalination with RO plants, compared to other desalting methods, is the most economical option. In [18], for the case of Spain, it was estimated that independent RO units for sea water desalination is the least cost option, compared to cogeneration and hybrid desalination systems. Also, a comparative study carried out by the International Atomic Energy Agency [5,6], concerning the use of various desalination technologies have demonstrated that in most cases the RO desalination units are the most economic option. Based on previous work [1,3,4,7,9–11,19], it can be concluded that RO desalination technology compared to other alternative desalting options is more economic in terms of capital cost, energy consumption and O&M cost. In the case of energy consumption RO technology requires less primary energy for the production of 1 m3 of desalinated water. This is illustrated in Table 1 in which a comparison is presented for the most commonly used desalting processes. The comparison is based on the equivalent electricity energy consumption required for the production of 1 m3 of desalinated water in kWh/ m3. We observe that when using a multi stage flash (MSF) desalination process the equivalent electricity energy consumption required is 13.7 kWh/m3 and in the case of multi effect distillation (MED) desalination process the equivalent electricity energy consumption is 10.8 kWh/m3. When a cogeneration (power-water production) scheme is used in conjunction with MSF desalination process the equivalent electricity energy consumption is 7.4 kWh/m3 and in the case when a cogeneration (power-water production) scheme is used in conjunction with MED desalination process the equivalent electricity energy consumption is 6.2 kWh/m3. When using a RO desalination process the equivalent electricity energy consumption required is 4 kWh/m3. Finally, current technological developments on RO systems, concerning the integration of pressure recovery units, already achieved a reduction of the RO energy consumption below 4 kWh/ m3. Additionally, in recent years the RO market has been experiencing a dramatic growth at a global level. This increase is a result of technological achievements enabling for the reduction of the membranes cost, which is a dominant cost component for the operation of RO plants.
3. Optimization model The optimization model developed uses a GA technique for the calculation of both the cost of electricity produced from the PV system and the desalinated water production cost. A review of the GA techniques used for RO desalination systems optimization is provided in [2]. A schematic diagram of the optimization flow chart is shown in Fig. 1. The algorithm combines the CAROC software [9– 11], for the optimum desalinated water production cost and the IPP v2.1 software [8,12] for the optimum cost of electricity produced from the PV system. Both have been used extensively during the past years for similar studies (e.g., [1,3]). A brief description of simulation software follows.
Fig. 1. Flow chart of the optimization model.
3.1. CAROC software
Table 1 Energy consumption comparison for different desalination technologies. Technology
Equivalent electricity energy consumption (kWh/m3)
Independent MSF plant Independent MED plant Cogeneration (Rankine power cycle and MSF plant) Cogeneration (Rankine power cycle and MED plant) Independent RO plant
13.7 10.8 7.4
The CAROC software [9,10] is used for the calculation of water production cost from various RO desalination schemes. The algorithm takes into account the capital cost, the energy consumption and, operation and maintenance requirements of each candidate scheme and calculate the least cost configuration and the ranking order of the candidate RO schemes. The technical and economic parameters of each candidate RO desalination plant are taken into account based on the cost function:
6.2 4.0
min
∂C ∂k
= min
∂CAS ∂ECS ∂OCS ∂MCS ∂HCS : + + + + ∂k ∂k ∂k ∂k ∂k
ð1Þ
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A. Poullikkas / Desalination 258 (2010) 100–105
Table 2 Parametric cost-benefit analysis data and assumptions. Parameter
Value
Technical data RO plant capacity RO plant specific energy consumption Annual solar potential PV PV PV PV
module module module module
type capacity area efficiency
20,000 m3/day–80,000 m3/day 4.2 kWh/m3 1970 kWh/m2 (south orientation at 28 degrees fixed angle) mono-Si 185 W 1.3 m2 14.2%
software tool takes into account the capital cost, the fuel cost and O&M requirements of each candidate scheme and calculates the least cost configuration and the ranking order of the candidate power technologies. A brief description of the optimization procedure is given below. The technical and economic parameters of each candidate power generation technology are taken into account based on the cost function:
Capital data RO plant specific capital cost PV system specific capital cost Batteries specific capital cost
see Fig. 2 2500€/kW 1500€/kW
Operation and maintenance data Cost of RO membranes Cost of RO plant membranes Annual PV system O&M
17.14€/m3/day 0.072€/m3 1% of capital cost
Other data Grid electricity tariff Discount rate Economic life of RO and PV plants Annual income tax rate
0.1272€/kWh 6% 20 years 10%
min
8 > > 2 > > ∂CCj > N > + > > > ∑ 4 ∂k > >
9 > 3> > ∂CFj ∂COMFj ∂COMVj > > > + ∂k + ∂k > ∂k 5> > > j > = ð1 + iÞ ; 3 2 > ∂Pj > > > N 6 7 > > ∂k 7 > ∑ 6 > 4ð1 + iÞj 5 > > j=0 > ;
∂c = min > ∂k > > > > > > > > > > :
ð3Þ
where c is the final cost of electricity in €/kWh, in real prices, for the candidate technology k, CCj is the capital cost function in €, CFj is the fuel cost function in €, COMFj is the fixed O&M cost function in €, COMVj is the variable O&M cost function in €, Pj is the total electricity production in kWh, j = 1,2,…N is the periods (e.g., years) of installation and operation of the power generation technology and i is the discount rate. The least cost solution is calculated by:
where C is the specific cost of water production in €/m3, in real prices, for the candidate RO technology k, CAS is the specific capital cost function in €/m3, ECS is the specific energy cost function in €/m3, OCS is the specific fixed O&M cost in €/m3, MCS is the specific membrane replacement cost in €/m3 and HCS is the specific cost of chemicals in €/m3. The least cost solution is calculated by: ∂C : ð2Þ least cost solution = min ∂k Details of the optimization algorithm implementing the above mathematical formulation can be found in [9,10]. 3.2. IPP software The cost of electricity produced from the PV system is estimated using the IPP v2.1 optimization software [8,12]. This user-friendly
least cost solution = min
∂c : ∂k
ð4Þ
Details of the optimization algorithm implementing the above mathematical formulation can be found in [8,12]. 4. Parametric analysis In order to demonstrate the applicability of the optimization model developed in Section 3 a parametric study is carried out for the optimum RO desalinated water cost for various RO plant capacities. The input data and assumptions used for the above analysis are tabulated in Table 2. For the purpose of this parametric study we assume the installation and operation of a RO desalination plant with energy consumption requirements of 4.2 kWh/m3 and an annual capacity factor of 90%. For the operation of the RO plant the cost of membranes is assumed at 17.14€/m3/day and the cost of chemicals at
Fig. 2. RO plant capital cost as a function of RO plant capacity [17].
A. Poullikkas / Desalination 258 (2010) 100–105
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Fig. 3. RO plant annual energy consumption as a function of RO plant capacity.
0.072€/m3 [10]. In the case of the PV system a typical mono-Si solar PV module has been selected with a capacity of 185 W, efficiency 14.2% and area of 1.3 m2. A south orientation is assumed at 28 degrees fixed angle with an annual solar potential of 1970 kWh/m2. More details on the PV system data used can be found in [13]. The annual O&M cost is assumed at 1% of the PV system capital cost and the grid electricity tariff in order to cover the additional requirements of the RO plant is assumed at 0.1272€/kWh. In this analysis the economic life of both RO plant and PV system are assumed at 20 years with a discount rate of 6%. The effect of the RO plant capacity cost is examined in this parametric analysis by varying the capacity from 20,000 m3/day, in steps of 10,000 m3/day, up to 80,000 m3/day. The capital cost of the various RO plant sizes from 20,000 m3/day up to 80,000 m3/day, were estimated using Thermoflow Suite 18 (module PEACE) [17] is illustrated in Fig. 2. These estimations are in good agreement with price quotes obtained from RO desalination plant manufacturers
[20,21]. Also the effect of the use of PVs degree of integration is examined by the use of various scenarios from which the requirements in electrical energy are covered partly (25%, 50%, 75%) and/or fully (100%) from PVs. The results concerning the annual energy (electricity) consumption are illustrated in Fig. 3. We observe that in the case of a RO desalination plant with a capacity of 20,000 m3/day the annual energy consumption requirements are 27 GWh and in the case of a RO desalination plant with a capacity of 80,000 m3/day the annual energy consumption requirements are 110 GWh. In Fig. 4 the results concerning the desalinated water production cost are presented. We observe that the cost increases with the use of the degree of PV system for the energy requirements of the RO plant. For example for a RO desalination plant of 40,000 m3/day the desalinated water production cost increases by approximately 9% with the use of PVs for the 25% coverage of the total electricity requirements of the RO plant. For the satisfaction of the total
Fig. 4. Desalinated water production cost as a function of RO plant capacity.
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Fig. 5. Expected PV system installed capacity as a function of RO plant capacity.
electricity requirements of the RO plant with PVs the desalinated water production cost increases by approximately 39%, e.g., from 0.87€/m3 to 1.21€/m3. The results obtained are in good agreement with those reported in [7]. The results concerning the required installed PVs capacity are illustrated in Fig. 5. We observe that in the case of a 60,000 m3/day capacity RO plant the required PV installed capacity in order to cover all electricity consumption should be 45 MWp. The associated land requirements for the installation of PVs are presented in Fig. 6, where, e.g., for the 80,000 m3/day capacity RO plant case approximately 600,000 m2 are required in order to cover all electricity consumption.
5. Conclusions In this work, an optimization model was developed using a GA technique for the calculation of both the cost of electricity produced from the PV system and the desalinated water production cost. The algorithm combines the CAROC software [9–11], for the optimum desalinated water production cost and the IPP v2.1 software [8,12] for the optimum cost of electricity produced from the PV system. In order to demonstrate the applicability of the method a parametric study was carried out for the optimum RO desalinated water cost. In particular, the operation of a RO desalination plant and the electricity requirements which are partly and/or fully covered by PVs were
Fig. 6. Expected PV system land requirements as a function of RO capacity.
A. Poullikkas / Desalination 258 (2010) 100–105
simulated. Taking into account various RO plant capacities the desalinated water cost have been determined for various scenarios from which the requirements in electrical energy are covered partly (25%, 50%, 75%) and/or fully (100%) from PVs. Based on the data and the assumptions used, the results indicated that the production cost of desalinated water is increased with the degree of integration of PVs for partial and/or total electricity requirements of the reverse osmosis plant. References [1] M. Afonso, J. Jaber, M. Mohsen, Brackish groundwater treatment by reverse osmosis in Jordan, Desalination 164 (2004) 157–171. [2] B. Djebedjian, H. Gad, I. Khaled, M.A. Rayan, Optimisation of reverse osmosis desalination system using genetic algorithms technique, Proceedings of the Twelfth International Water Technology Conference, IWTC12 (2008) 1047–1067. [3] S. Ghabayen, M. McKee, M. Kemblowski, Characterization of uncertainties in the operation and economics of the proposed seawater desalination plant in the Gaza Strip, Desalination 161 (2004) 191–201. [4] K. Glucina, J.M. Laine, Water desalination technologies, Sustainability assessment of water desalination technologies, UNESCO, 2000. [5] P. Gowin, T. Konishi, J. Kupitz, Nuclear and fossil seawater desalination— Economic evaluation methodology and results, International workshop on desalination technologies for small and medium plants with limited environmental impact, 1998. [6] P. Gowin, J. Kupitz, T. Konishi, Nuclear seawater desalination—IAEA activities and economic evaluation, Proceedings of the IDA World Congress on Desalination and Water Reuse, 1999.
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[7] I. Karagiannis, P. Soldatos, Water desalination cost literature: review and assessment, Desalination 223 (2008) 448–456. [8] A. Poullikkas, A decouple optimization method for power technology selection in competitive markets, Energy Sources, Part B 4 (2009) 199–211. [9] A. Poullikkas, Optimization algorithm for reverse osmosis desalination economics, Desalination 133 (2001) 75–81. [10] A. Poullikkas, “Optimization procedures for the selection of reverse osmosis desalination plants”, Chapter 15 in Desalination Research Progress, NOVA Publishers, ISBN: 978-1-60456-567-6, 2008. [11] A. Poullikkas, Technical and economic analysis for the integration of small reverse osmosis desalination plants into MAST gas turbine cycles for power generation, Desalination 172 (2005) 145–150. [12] A. Poullikkas, I.P.P. ALGORITHM v2.1, Software for power technology selection in competitive electricity markets, © 2000–2006, User Manual, 2006. [13] A. Poullikkas, Parametric cost-benefit analysis for the installation of photovoltaic parks in the island of Cyprus, Energy Policy 37 (2009) 3673–3680. [14] A. Poullikkas, Introduction to Power Generation Technologies, NOVA Science Publishers, Inc., New York, ISBN: 978-1-60876-472-3, 2009. [15] E. Russel, Drinking water from the sea, International Power Generation, July 1998. [16] K. Tahri, Desalination experience in Morocco, Desalination 136 (2001) 43–48. [17] Thermoflow Suite 18, Thermal engineering software for the power and cogeneration industries, 2008. [18] J. Uche, L. Serra, A. Valero, Hybrid desalting systems for avoiding water shortage in Spain, Desalination 138 (2001) 329–334. [19] M. Wittholz, B. O'Neill, C. Colby, D. Lewis, Estimating the cost of desalination plants using cost database, Desalination 229 (2008) 10–20. [20] www.ide-tech.com (IDE Technologies Ltd.). [21] www.cadagua.es (Gadagua S.A.).
Contents lists available at ScienceDirect
Desalination j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / d e s a l
An optimization model for the production of desalinated water using photovoltaic systems Andreas Poullikkas ⁎ Electricity Authority of Cyprus, P.O. Box 24506, 1399 Nicosia, Cyprus
a r t i c l e
i n f o
Article history: Received 2 January 2010 Received in revised form 15 March 2010 Accepted 16 March 2010 Available online 18 April 2010 Keywords: Desalination Reverse osmosis Solar energy Photovoltaics Renewable energy sources
a b s t r a c t In this work, an optimization model using a genetic algorithm technique is developed for the desalinated water production cost using photovoltaics (PVs). In order to demonstrate the applicability of the method a parametric study is carried out for the optimum reverse osmosis (RO) desalinated water cost. In particular, taking into account various RO plant capacities the desalinated water cost have been determined for various scenarios from which the requirements in electrical energy are covered partly (25%, 50%, 75%) and/or fully (100%) from PVs. Based on the data and the assumptions used, the results indicate that the production cost of desalinated water is increased with the degree of integration of PVs for partial and/or total electricity requirements of the RO plant. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The world demand of desalination equipment is expected to grow by more than 10% annually in the next two decades. This demand is derived by the reduced per capita share of fresh water in the world and by the increasing concern for water quality, which is based on the increasing water pollution [15]. Reverse Osmosis (RO) is the only process that can be competitive for most kinds of water at any capacity. RO desalination is well developed and has been in commercial use for three decades for desalting low salinity brackish water. RO use for seawater desalting is becoming increasingly more reliable and cost competitive. The cost of RO desalination has been going down and will continue to do in the future because of technology improvements and market forces. The cost of RO desalination depends on many variables including feed water salinity and quality, plant size, finance cost, energy cost, process type, infrastructure requirements, intake type, plant reliability and operation and maintenance (O&M) requirements [9]. In order to obtain the desired plant life and reliability with minimum cost, proper cost analysis should be performed. In recent years the photovoltaic (PV) industry has been experiencing a dramatic growth at a global level. Continuous increase of conventional fuel costs as well as growing pressure to turn towards renewable energy sources are the main drivers behind this rapidly expanding industry which since the start of the decade has achieved continuous annual growth of around 30% [13,14]. An important PVs
⁎ Fax: +357 22 201809. E-mail address: [email protected]. 0011-9164/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2010.03.036
application, which is currently emerging in the Mediterranean region, is the operation of RO desalination plants integrated with PV systems in order to satisfy the RO requirements in electrical energy either partly or fully. In this work, an optimization model is developed using a genetic algorithm (GA) for the calculation of both the cost of electricity produced from the PV system and the desalinated water production cost. The algorithm combines the CAROC software [9–11], for the optimum desalinated water production cost and the IPP v2.1 software [8,12] for the optimum cost of electricity produced from the PV system. In order to demonstrate the applicability of the method a parametric study is carried out for the optimum reverse osmosis (RO) desalinated water cost. In particular, the operation of a RO desalination plant and the electricity requirements which are partly and/or fully covered by PVs are simulated. Taking into account various RO plant capacities the desalinated water cost is determined for various scenarios from which the requirements in electrical energy are covered partly (25%, 50%, 75%) and/or fully (100%) from PVs. In Section 2, the least energy consumption desalination technology for integration with PVs is selected. The optimization model developed is presented in Section 3 and the results of the parametric analysis are discussed in Section 4. The conclusions are summarized in Section 5. 2. Desalination technology selection During the past ten years several countries facing water shortage problems have investigated and selected the least cost desalination technology in order to cover their needs. For example in [16], where a review of Morocco water policy is carried out, it was concluded that
A. Poullikkas / Desalination 258 (2010) 100–105
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seawater desalination with RO plants, compared to other desalting methods, is the most economical option. In [18], for the case of Spain, it was estimated that independent RO units for sea water desalination is the least cost option, compared to cogeneration and hybrid desalination systems. Also, a comparative study carried out by the International Atomic Energy Agency [5,6], concerning the use of various desalination technologies have demonstrated that in most cases the RO desalination units are the most economic option. Based on previous work [1,3,4,7,9–11,19], it can be concluded that RO desalination technology compared to other alternative desalting options is more economic in terms of capital cost, energy consumption and O&M cost. In the case of energy consumption RO technology requires less primary energy for the production of 1 m3 of desalinated water. This is illustrated in Table 1 in which a comparison is presented for the most commonly used desalting processes. The comparison is based on the equivalent electricity energy consumption required for the production of 1 m3 of desalinated water in kWh/ m3. We observe that when using a multi stage flash (MSF) desalination process the equivalent electricity energy consumption required is 13.7 kWh/m3 and in the case of multi effect distillation (MED) desalination process the equivalent electricity energy consumption is 10.8 kWh/m3. When a cogeneration (power-water production) scheme is used in conjunction with MSF desalination process the equivalent electricity energy consumption is 7.4 kWh/m3 and in the case when a cogeneration (power-water production) scheme is used in conjunction with MED desalination process the equivalent electricity energy consumption is 6.2 kWh/m3. When using a RO desalination process the equivalent electricity energy consumption required is 4 kWh/m3. Finally, current technological developments on RO systems, concerning the integration of pressure recovery units, already achieved a reduction of the RO energy consumption below 4 kWh/ m3. Additionally, in recent years the RO market has been experiencing a dramatic growth at a global level. This increase is a result of technological achievements enabling for the reduction of the membranes cost, which is a dominant cost component for the operation of RO plants.
3. Optimization model The optimization model developed uses a GA technique for the calculation of both the cost of electricity produced from the PV system and the desalinated water production cost. A review of the GA techniques used for RO desalination systems optimization is provided in [2]. A schematic diagram of the optimization flow chart is shown in Fig. 1. The algorithm combines the CAROC software [9– 11], for the optimum desalinated water production cost and the IPP v2.1 software [8,12] for the optimum cost of electricity produced from the PV system. Both have been used extensively during the past years for similar studies (e.g., [1,3]). A brief description of simulation software follows.
Fig. 1. Flow chart of the optimization model.
3.1. CAROC software
Table 1 Energy consumption comparison for different desalination technologies. Technology
Equivalent electricity energy consumption (kWh/m3)
Independent MSF plant Independent MED plant Cogeneration (Rankine power cycle and MSF plant) Cogeneration (Rankine power cycle and MED plant) Independent RO plant
13.7 10.8 7.4
The CAROC software [9,10] is used for the calculation of water production cost from various RO desalination schemes. The algorithm takes into account the capital cost, the energy consumption and, operation and maintenance requirements of each candidate scheme and calculate the least cost configuration and the ranking order of the candidate RO schemes. The technical and economic parameters of each candidate RO desalination plant are taken into account based on the cost function:
6.2 4.0
min
∂C ∂k
= min
∂CAS ∂ECS ∂OCS ∂MCS ∂HCS : + + + + ∂k ∂k ∂k ∂k ∂k
ð1Þ
102
A. Poullikkas / Desalination 258 (2010) 100–105
Table 2 Parametric cost-benefit analysis data and assumptions. Parameter
Value
Technical data RO plant capacity RO plant specific energy consumption Annual solar potential PV PV PV PV
module module module module
type capacity area efficiency
20,000 m3/day–80,000 m3/day 4.2 kWh/m3 1970 kWh/m2 (south orientation at 28 degrees fixed angle) mono-Si 185 W 1.3 m2 14.2%
software tool takes into account the capital cost, the fuel cost and O&M requirements of each candidate scheme and calculates the least cost configuration and the ranking order of the candidate power technologies. A brief description of the optimization procedure is given below. The technical and economic parameters of each candidate power generation technology are taken into account based on the cost function:
Capital data RO plant specific capital cost PV system specific capital cost Batteries specific capital cost
see Fig. 2 2500€/kW 1500€/kW
Operation and maintenance data Cost of RO membranes Cost of RO plant membranes Annual PV system O&M
17.14€/m3/day 0.072€/m3 1% of capital cost
Other data Grid electricity tariff Discount rate Economic life of RO and PV plants Annual income tax rate
0.1272€/kWh 6% 20 years 10%
min
8 > > 2 > > ∂CCj > N > + > > > ∑ 4 ∂k > >
9 > 3> > ∂CFj ∂COMFj ∂COMVj > > > + ∂k + ∂k > ∂k 5> > > j > = ð1 + iÞ ; 3 2 > ∂Pj > > > N 6 7 > > ∂k 7 > ∑ 6 > 4ð1 + iÞj 5 > > j=0 > ;
∂c = min > ∂k > > > > > > > > > > :
ð3Þ
where c is the final cost of electricity in €/kWh, in real prices, for the candidate technology k, CCj is the capital cost function in €, CFj is the fuel cost function in €, COMFj is the fixed O&M cost function in €, COMVj is the variable O&M cost function in €, Pj is the total electricity production in kWh, j = 1,2,…N is the periods (e.g., years) of installation and operation of the power generation technology and i is the discount rate. The least cost solution is calculated by:
where C is the specific cost of water production in €/m3, in real prices, for the candidate RO technology k, CAS is the specific capital cost function in €/m3, ECS is the specific energy cost function in €/m3, OCS is the specific fixed O&M cost in €/m3, MCS is the specific membrane replacement cost in €/m3 and HCS is the specific cost of chemicals in €/m3. The least cost solution is calculated by: ∂C : ð2Þ least cost solution = min ∂k Details of the optimization algorithm implementing the above mathematical formulation can be found in [9,10]. 3.2. IPP software The cost of electricity produced from the PV system is estimated using the IPP v2.1 optimization software [8,12]. This user-friendly
least cost solution = min
∂c : ∂k
ð4Þ
Details of the optimization algorithm implementing the above mathematical formulation can be found in [8,12]. 4. Parametric analysis In order to demonstrate the applicability of the optimization model developed in Section 3 a parametric study is carried out for the optimum RO desalinated water cost for various RO plant capacities. The input data and assumptions used for the above analysis are tabulated in Table 2. For the purpose of this parametric study we assume the installation and operation of a RO desalination plant with energy consumption requirements of 4.2 kWh/m3 and an annual capacity factor of 90%. For the operation of the RO plant the cost of membranes is assumed at 17.14€/m3/day and the cost of chemicals at
Fig. 2. RO plant capital cost as a function of RO plant capacity [17].
A. Poullikkas / Desalination 258 (2010) 100–105
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Fig. 3. RO plant annual energy consumption as a function of RO plant capacity.
0.072€/m3 [10]. In the case of the PV system a typical mono-Si solar PV module has been selected with a capacity of 185 W, efficiency 14.2% and area of 1.3 m2. A south orientation is assumed at 28 degrees fixed angle with an annual solar potential of 1970 kWh/m2. More details on the PV system data used can be found in [13]. The annual O&M cost is assumed at 1% of the PV system capital cost and the grid electricity tariff in order to cover the additional requirements of the RO plant is assumed at 0.1272€/kWh. In this analysis the economic life of both RO plant and PV system are assumed at 20 years with a discount rate of 6%. The effect of the RO plant capacity cost is examined in this parametric analysis by varying the capacity from 20,000 m3/day, in steps of 10,000 m3/day, up to 80,000 m3/day. The capital cost of the various RO plant sizes from 20,000 m3/day up to 80,000 m3/day, were estimated using Thermoflow Suite 18 (module PEACE) [17] is illustrated in Fig. 2. These estimations are in good agreement with price quotes obtained from RO desalination plant manufacturers
[20,21]. Also the effect of the use of PVs degree of integration is examined by the use of various scenarios from which the requirements in electrical energy are covered partly (25%, 50%, 75%) and/or fully (100%) from PVs. The results concerning the annual energy (electricity) consumption are illustrated in Fig. 3. We observe that in the case of a RO desalination plant with a capacity of 20,000 m3/day the annual energy consumption requirements are 27 GWh and in the case of a RO desalination plant with a capacity of 80,000 m3/day the annual energy consumption requirements are 110 GWh. In Fig. 4 the results concerning the desalinated water production cost are presented. We observe that the cost increases with the use of the degree of PV system for the energy requirements of the RO plant. For example for a RO desalination plant of 40,000 m3/day the desalinated water production cost increases by approximately 9% with the use of PVs for the 25% coverage of the total electricity requirements of the RO plant. For the satisfaction of the total
Fig. 4. Desalinated water production cost as a function of RO plant capacity.
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Fig. 5. Expected PV system installed capacity as a function of RO plant capacity.
electricity requirements of the RO plant with PVs the desalinated water production cost increases by approximately 39%, e.g., from 0.87€/m3 to 1.21€/m3. The results obtained are in good agreement with those reported in [7]. The results concerning the required installed PVs capacity are illustrated in Fig. 5. We observe that in the case of a 60,000 m3/day capacity RO plant the required PV installed capacity in order to cover all electricity consumption should be 45 MWp. The associated land requirements for the installation of PVs are presented in Fig. 6, where, e.g., for the 80,000 m3/day capacity RO plant case approximately 600,000 m2 are required in order to cover all electricity consumption.
5. Conclusions In this work, an optimization model was developed using a GA technique for the calculation of both the cost of electricity produced from the PV system and the desalinated water production cost. The algorithm combines the CAROC software [9–11], for the optimum desalinated water production cost and the IPP v2.1 software [8,12] for the optimum cost of electricity produced from the PV system. In order to demonstrate the applicability of the method a parametric study was carried out for the optimum RO desalinated water cost. In particular, the operation of a RO desalination plant and the electricity requirements which are partly and/or fully covered by PVs were
Fig. 6. Expected PV system land requirements as a function of RO capacity.
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simulated. Taking into account various RO plant capacities the desalinated water cost have been determined for various scenarios from which the requirements in electrical energy are covered partly (25%, 50%, 75%) and/or fully (100%) from PVs. Based on the data and the assumptions used, the results indicated that the production cost of desalinated water is increased with the degree of integration of PVs for partial and/or total electricity requirements of the reverse osmosis plant. References [1] M. Afonso, J. Jaber, M. Mohsen, Brackish groundwater treatment by reverse osmosis in Jordan, Desalination 164 (2004) 157–171. [2] B. Djebedjian, H. Gad, I. Khaled, M.A. Rayan, Optimisation of reverse osmosis desalination system using genetic algorithms technique, Proceedings of the Twelfth International Water Technology Conference, IWTC12 (2008) 1047–1067. [3] S. Ghabayen, M. McKee, M. Kemblowski, Characterization of uncertainties in the operation and economics of the proposed seawater desalination plant in the Gaza Strip, Desalination 161 (2004) 191–201. [4] K. Glucina, J.M. Laine, Water desalination technologies, Sustainability assessment of water desalination technologies, UNESCO, 2000. [5] P. Gowin, T. Konishi, J. Kupitz, Nuclear and fossil seawater desalination— Economic evaluation methodology and results, International workshop on desalination technologies for small and medium plants with limited environmental impact, 1998. [6] P. Gowin, J. Kupitz, T. Konishi, Nuclear seawater desalination—IAEA activities and economic evaluation, Proceedings of the IDA World Congress on Desalination and Water Reuse, 1999.
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