**4. RE/DES systems**

Many different renewable energy desalination systems are technically feasible (Kalogirou, 2005). Fig.5 presents the possible combinations between desalination processes and RE technologies.

A methodology for selecting the most appropriate combination between desalination technologies and renewable energies for a given site based on different criteria was developed (Setiawan et al., 2009). Desalination systems are energy intensive, and their energy consumption is a driving factor in determining their economic feasibility when they are coupled to RES. Typical energy consumptions for different desalination processes are shown in Table 1.

Optimization of Renewable Energy Systems: The Case of Desalination 97

Solar/ MSF (6%)

Wind/ MVC (5%)

PV/ ED (6%)

Fig. 6. Breakdown of renewable energy powered desalination system technologies

consumption (Table 1) and little need for maintenance (Weiner et al., 2001).

commercial small plant 48 kW is required to produce 450 L/day in three stages.

to 2.39 \$/m3 for desalination systems with a capacity of 300 m3/day.

**4.2 Multiple-effect distillation driven by solar energy** 

Reverse Osmosis (RO) is the desalination process which can be coupled, in reliable and economic way, with RES. The suitability of renewable energy technologies, especially wind turbines and photovoltaics, for RO desalination systems is due to the convenience of RO for desalinating small quantity of water for remote and isolated areas; it has low energy

Solar-powered MSF plants can produce 6–60 L/m2/day, in comparison with the 3–4

The use of solar troughs for MSF desalination was tested mainly in the USA. In a typical

In Szacsvay et al. (1999), a Solar/MSF system using an Atlantis autoflash multistage stage desalination unit is described. Since the standard MSF process is not able to operate coupled to any variable heat source, an adapted MSF system called "Autoflash" was developped. Performance and layout data were obtained both from computer simulation and experimental results with a small-sized Solar/MSF systems in Switzerland. The system had been in operation for 9 years. From these studies it was shown that the cost of distillate could be reduced from 5.48 \$/m3 for small desalination system with a capacity of 15 m3/day

Several multiple-effect distillation (MED) plants of medium capacity powered by solar energy were built worldwide. One MED-plant designed for a maximum capacity of 120 m3/day with 18 stack type stages and pre-heaters was analyzed in UAE (El-Nashar and Samad, 1998). Evacuated-tube solar collectors of 1862 m2 were used with water as heat carrying medium. It had a heat accumulator of 300 m3 capacity. Specific heat consumption of the plant was 43.8 kcal/kg with performance ratio of 12.4. Due to heat accumulator the

Wind/RO (19%)

Solar/MED (13%)

implemented worldwide (Forstmeier, 2007).

**4.1 MSF desalination plants driven by solar energy** 

L/m2/day typical of solar stills (Block, 1989)).

Other (15%)

Hybrid (4%)

PV/RO (32%)

Fig. 5. Technological combinations of the main renewable energies and desalination methods


Table 1. Energy consumption and electric power cogeneration (Bilton et al., 2011)

In table 1 the energy requirements are separated into thermal energy which is used to heat the seawater and electrical energy which is used to drive pumps, compressors and auxiliary equipment. For seawater desalination, reverse osmosis requires the least amount of overall energy. However, if thermal energy is inexpensive (the case of Middle East), a thermal desalination process like multi-effect distillation can be practical.

Fig.6 illustrates the breakdown of renewable energy powered desalination system technologies implemented worldwide in 2007 (Forstmeier, 2007). It shows that the most used RES/Desalination systems are RES/RO (51% of the total worldwide installed RES/DES plants).

**Renewable Energies** (ER)

Shaft Electricity**Geothermal Solar Wind**

Geotherm ie So la ire Eolienne

SD

H D MED MSF TVC M D

sola ires

C ollectors

(kJ/kg)

R O MVC

M eca niq ue Electricite

R O ED MVC

Electrical Energy (kWh/m3)

Procede direct

Direct Processes

Electricite Ca pteurs

ElectricitySo la r

therm ique

a l

H D MED TVC M D

methods

**Seawater** 

**Brackish water** 

RES/DES plants).

R O MVC

H D: Air H um id ifica tion a n d Dehu m id ifica tio n

M ED: M ultiple-Effect Distilla tion M SF: M ultista ge Fla sh TVC : Th erm a l Va po r C o m pression M VC : M ech a nica l Va po r C om pression

SD: So la r Distilla tio n

R O: R ev erse Osm o sis ED: Electrod ia lysis *2. M embrane Techniq ues*

*1. Distilla tion Techniq ues*

C ha leur Electricite PV Sola ire

Heat Electricityr

ED H D

Fig. 5. Technological combinations of the main renewable energies and desalination

Desalination Process Thermal Energy

Multi-Stage Flash (MSF) 190-290 4-6 Multi-Effect Distillation (MED) 150-290 2.5-3 Vapor Compression (VC) - 8-12 Reverse Osmosis (RO) without Energy Recovery - 7-10 Reverse Osmosis (RO) with Energy Recovery - 3-5

Reverse Osmosis (RO) without Energy Recovery 1-3 Reverse Osmosis (RO) with Energy Recovery 1.5-4 Electrodialysis 1.5-4 Table 1. Energy consumption and electric power cogeneration (Bilton et al., 2011)

desalination process like multi-effect distillation can be practical.

In table 1 the energy requirements are separated into thermal energy which is used to heat the seawater and electrical energy which is used to drive pumps, compressors and auxiliary equipment. For seawater desalination, reverse osmosis requires the least amount of overall energy. However, if thermal energy is inexpensive (the case of Middle East), a thermal

Fig.6 illustrates the breakdown of renewable energy powered desalination system technologies implemented worldwide in 2007 (Forstmeier, 2007). It shows that the most used RES/Desalination systems are RES/RO (51% of the total worldwide installed

Fig. 6. Breakdown of renewable energy powered desalination system technologies implemented worldwide (Forstmeier, 2007).

Reverse Osmosis (RO) is the desalination process which can be coupled, in reliable and economic way, with RES. The suitability of renewable energy technologies, especially wind turbines and photovoltaics, for RO desalination systems is due to the convenience of RO for desalinating small quantity of water for remote and isolated areas; it has low energy consumption (Table 1) and little need for maintenance (Weiner et al., 2001).

#### **4.1 MSF desalination plants driven by solar energy**

Solar-powered MSF plants can produce 6–60 L/m2/day, in comparison with the 3–4 L/m2/day typical of solar stills (Block, 1989)).

The use of solar troughs for MSF desalination was tested mainly in the USA. In a typical commercial small plant 48 kW is required to produce 450 L/day in three stages.

In Szacsvay et al. (1999), a Solar/MSF system using an Atlantis autoflash multistage stage desalination unit is described. Since the standard MSF process is not able to operate coupled to any variable heat source, an adapted MSF system called "Autoflash" was developped. Performance and layout data were obtained both from computer simulation and experimental results with a small-sized Solar/MSF systems in Switzerland. The system had been in operation for 9 years. From these studies it was shown that the cost of distillate could be reduced from 5.48 \$/m3 for small desalination system with a capacity of 15 m3/day to 2.39 \$/m3 for desalination systems with a capacity of 300 m3/day.

#### **4.2 Multiple-effect distillation driven by solar energy**

Several multiple-effect distillation (MED) plants of medium capacity powered by solar energy were built worldwide. One MED-plant designed for a maximum capacity of 120 m3/day with 18 stack type stages and pre-heaters was analyzed in UAE (El-Nashar and Samad, 1998). Evacuated-tube solar collectors of 1862 m2 were used with water as heat carrying medium. It had a heat accumulator of 300 m3 capacity. Specific heat consumption of the plant was 43.8 kcal/kg with performance ratio of 12.4. Due to heat accumulator the

Optimization of Renewable Energy Systems: The Case of Desalination 99

incorporated in the system is computed such that the daily variations of the solar radiation are compensated. On the other hand, up to now the design process does not include the optimization of the components' number and type and the minimization of the total system

Since the coastal areas present a high availability of wind power resources, wind powered desalination represents a promising alternative of renewable energy desalination (Gracia-Rodriguez et al., 2002). Wind-powered RO plants have been implemented on the islands of the County of Split and Dalmatia (Croatia), on the island Utsira in Norway, and in remote

A prototype wind-powered RO desalination system was constructed and tested on Coconut Island off the northern coast of Oahu, Hawaii, for brackish water desalination (Liu et al., 2002). The system has four major subsystems: multivaned windmill/pump, flow/pressure stabilizer, RO module, and control mechanism. It was shown that the flow rate of 13 l/min could be processed for an average wind speed of 5 m/s, and a brackish feed water at a total dissolved solids concentration of 3000 mg/l. The average rejection rate and recovery ratio were 97% and 20%, respectively. Energy efficiency equal to 35% was shown to be comparable to the typical energy efficiency of well-operated multi-vaned

A prototype of a fully autonomous wind powered desalination system has been installed on the island of Gran Canaria in the Canarian Archipelago (Carta et al., 2003). The system consists of a wind farm, made up of two wind turbines and a flywheel, which supplies the energy needs of a group of eight RO modules throughout the complete desalination process (from the pumping of seawater to the storage of the product water), as well as the energy requirements of the control subsystems. It was highlighted that this system can be applied to seawater desalination, both on a small and large scale, in coastal regions with a scarcity of

The economic feasibility of a wind-powered RO plant was evaluated by mathematical modelling analysis (Forstmeier et al., 2007). It was shown that the costs of a windpowered RO desalination system are in line with what is expected for a conventional desalination system, proving to be particularly cost-competitive in areas with good wind resources that have high costs of energy. The unit cost of freshwater production by a conventional RO plant can be reduced up to 20% for regions with an average wind speed

In order to optimize the design of Wind/RO systems Kiranoudis et al. (1997) considered desalination plants power-supplied by one Wind Generator (W/G). The optimal design objectives are the determination of the optimum size and type of the W/G and the optimum structure of the RO desalination unit membranes, such that the system total annual cost is minimized, with respect to certain product quality and quantity demand constraints. This procedure is implemented using a successive quadratic optimization algorithm. The W/Gdesalination systems investigated do not incorporate either electric energy, or produced

cost.

**4.4 Reverse osmosis driven by wind energy** 

water for domestic and/or agricultural use.

communities in Australia.

windmills.

of 5 m/s or higher.

water storage units.

evaporator could run 24 h a day during sunny days producing freshwater of 85 m3/day. The plant was able to desalt seawater of 55,000 ppm. The total seawater requirement was 42.5 m3/h. The major problem was the maintenance of the pumps. It was shown that the acid cleaning and silt removal were extremely necessary for better performance of the plant.

A practical scale desalination system of three effects using only solar energy from solar collectors as the heat source and the electrical power from the PV-cells was investigated by Abu-Jabal et al. (2001). The unit was developed and manufactured by the Ebara Corporation (Tokyo) and tested at the Al Azhar University in Gaza. The average production rate was in the range of 6–13 L/m2/day.

Thomas (1997) carried several experiments on MED and MSF units driven by solar energy in Kuwait. He reported several difficulties operating under the variable conditions of solar insulation. Greater success has been found with self-regulating solar MSF plants than solar MED plants.

In Fiorenza et al. (2003) the water production cost for seawater desalination by MED powered by a solar thermal field has been estimated. The results obtained for plants of capacity varying between 500 and 5000 m3/d have shown that the cost of water produced can be reduced by increasing the plant capacity; i.e. 3.2 \$/m3 for the 500 m3/d plant capacity and 2 \$/m3 for the 5000 m3/d plant capacity.

#### **4.3 Reverse osmosis desalination driven by photovoltaic**

Photovoltaic (PV) powered RO systems have been implemented in different regions, i.e: remote areas of the Tunisia desert, rural areas of Jordan, remote communities in Australia, etc. Several investigations were carried to analyze the cost of PV/RO desalination systems (Kalogirou, 2001). If PV connected to a RO system is commercial nowadays, the main problem of this technology is reported to be the high cost of the PV cells. The distance at which the PV energy is competitive with conventional energy depends on the plant capacity, on the distance to the electric grid and on the salt concentration of the feed (Garzia-Rodriguez, 2002).

In Saudi Arabia, a PV/RO brackish water desalination plant was installed (Hasnain and Alajlan, 1998). It was connected to a solar still with 5 m3/d production. The feed water of the water still was the blowdown of the RO unit (10 m3/d). A detailed cost analysis was also reported.

Bourouni and Chaibi (2009) presented a PV/RO desalination plant, for supplying one village, in southern Tunisia. It uses solar energy to power a reverse osmosis brackish water desalination unit with a capacity of 15 m3/day. They present an analytical description of the plant components and reports experimental results for a 6-month operating period. Several problems were highlighted such as brine rejection, low efficiencies and high cost.

Several tools were developed to improve the design of PV/RO systems by using iterative procedure (Herbert et al., 2007). The size of the RO unit is computed according to the desalinated-water requirements, while the PV system nominal power rating is calculated such that the corresponding energy requirements of the RO unit are satisfied, taking into account the available solar radiation potential of the installation area. The size of the battery incorporated in the system is computed such that the daily variations of the solar radiation are compensated. On the other hand, up to now the design process does not include the optimization of the components' number and type and the minimization of the total system cost.

#### **4.4 Reverse osmosis driven by wind energy**

98 Modeling and Optimization of Renewable Energy Systems

evaporator could run 24 h a day during sunny days producing freshwater of 85 m3/day. The plant was able to desalt seawater of 55,000 ppm. The total seawater requirement was 42.5 m3/h. The major problem was the maintenance of the pumps. It was shown that the acid cleaning and silt removal were extremely necessary for better performance of the plant. A practical scale desalination system of three effects using only solar energy from solar collectors as the heat source and the electrical power from the PV-cells was investigated by Abu-Jabal et al. (2001). The unit was developed and manufactured by the Ebara Corporation (Tokyo) and tested at the Al Azhar University in Gaza. The average production rate was in

Thomas (1997) carried several experiments on MED and MSF units driven by solar energy in Kuwait. He reported several difficulties operating under the variable conditions of solar insulation. Greater success has been found with self-regulating solar MSF plants than solar

In Fiorenza et al. (2003) the water production cost for seawater desalination by MED powered by a solar thermal field has been estimated. The results obtained for plants of capacity varying between 500 and 5000 m3/d have shown that the cost of water produced can be reduced by increasing the plant capacity; i.e. 3.2 \$/m3 for the 500 m3/d plant capacity

Photovoltaic (PV) powered RO systems have been implemented in different regions, i.e: remote areas of the Tunisia desert, rural areas of Jordan, remote communities in Australia, etc. Several investigations were carried to analyze the cost of PV/RO desalination systems (Kalogirou, 2001). If PV connected to a RO system is commercial nowadays, the main problem of this technology is reported to be the high cost of the PV cells. The distance at which the PV energy is competitive with conventional energy depends on the plant capacity, on the distance to the electric grid and on the salt concentration of the feed (Garzia-

In Saudi Arabia, a PV/RO brackish water desalination plant was installed (Hasnain and Alajlan, 1998). It was connected to a solar still with 5 m3/d production. The feed water of the water still was the blowdown of the RO unit (10 m3/d). A detailed cost analysis was also

Bourouni and Chaibi (2009) presented a PV/RO desalination plant, for supplying one village, in southern Tunisia. It uses solar energy to power a reverse osmosis brackish water desalination unit with a capacity of 15 m3/day. They present an analytical description of the plant components and reports experimental results for a 6-month operating period. Several

Several tools were developed to improve the design of PV/RO systems by using iterative procedure (Herbert et al., 2007). The size of the RO unit is computed according to the desalinated-water requirements, while the PV system nominal power rating is calculated such that the corresponding energy requirements of the RO unit are satisfied, taking into account the available solar radiation potential of the installation area. The size of the battery

problems were highlighted such as brine rejection, low efficiencies and high cost.

the range of 6–13 L/m2/day.

and 2 \$/m3 for the 5000 m3/d plant capacity.

**4.3 Reverse osmosis desalination driven by photovoltaic** 

MED plants.

Rodriguez, 2002).

reported.

Since the coastal areas present a high availability of wind power resources, wind powered desalination represents a promising alternative of renewable energy desalination (Gracia-Rodriguez et al., 2002). Wind-powered RO plants have been implemented on the islands of the County of Split and Dalmatia (Croatia), on the island Utsira in Norway, and in remote communities in Australia.

A prototype wind-powered RO desalination system was constructed and tested on Coconut Island off the northern coast of Oahu, Hawaii, for brackish water desalination (Liu et al., 2002). The system has four major subsystems: multivaned windmill/pump, flow/pressure stabilizer, RO module, and control mechanism. It was shown that the flow rate of 13 l/min could be processed for an average wind speed of 5 m/s, and a brackish feed water at a total dissolved solids concentration of 3000 mg/l. The average rejection rate and recovery ratio were 97% and 20%, respectively. Energy efficiency equal to 35% was shown to be comparable to the typical energy efficiency of well-operated multi-vaned windmills.

A prototype of a fully autonomous wind powered desalination system has been installed on the island of Gran Canaria in the Canarian Archipelago (Carta et al., 2003). The system consists of a wind farm, made up of two wind turbines and a flywheel, which supplies the energy needs of a group of eight RO modules throughout the complete desalination process (from the pumping of seawater to the storage of the product water), as well as the energy requirements of the control subsystems. It was highlighted that this system can be applied to seawater desalination, both on a small and large scale, in coastal regions with a scarcity of water for domestic and/or agricultural use.

The economic feasibility of a wind-powered RO plant was evaluated by mathematical modelling analysis (Forstmeier et al., 2007). It was shown that the costs of a windpowered RO desalination system are in line with what is expected for a conventional desalination system, proving to be particularly cost-competitive in areas with good wind resources that have high costs of energy. The unit cost of freshwater production by a conventional RO plant can be reduced up to 20% for regions with an average wind speed of 5 m/s or higher.

In order to optimize the design of Wind/RO systems Kiranoudis et al. (1997) considered desalination plants power-supplied by one Wind Generator (W/G). The optimal design objectives are the determination of the optimum size and type of the W/G and the optimum structure of the RO desalination unit membranes, such that the system total annual cost is minimized, with respect to certain product quality and quantity demand constraints. This procedure is implemented using a successive quadratic optimization algorithm. The W/Gdesalination systems investigated do not incorporate either electric energy, or produced water storage units.

Optimization of Renewable Energy Systems: The Case of Desalination 101

the design of the overall plant. For these reasons we focus in this chapter on the

The operational performance and the reliability of the desalination systems driven by RES depend on their proper design and sizing. The optimal exploitation of the available RES

The objective of this chapter is to present a new methodology to optimize RO desalination system, which is power-supplied by hybrid Photovoltaic (PV) and Wind-Generator (W/G) energy sources. Compared to the past-proposed methodologies, which have been used in order to design water desalination systems driven by RES, the methodology presented in this chapter has the advantage to take into account all the critical operational parameters that affect both the resulting electric energy and desalinated-water production levels and the system capital and maintenance costs. The block diagram of the PV/Wind/RO system

The Battery bank is charged from the respective PV and W/G input power sources by using battery chargers, connected to a common DC bus. The power sources are usually configured in multiple power generation blocks according to the devices nominal power ratings and the redundancy requirements. The battery bank, which is usually of lead-acid type, is used to store the generated electric energy surplus and to supply the RO desalination units in case of low solar radiation and/or wind speed conditions. DC/AC converters are used to interface the DC battery voltage to the AC requirements of the RO desalination units. A water tank is used to store the produced desalinated water surplus, which is not directly

> *Battery Bank*

*DC/AC Inverters =/~* .

*RO Unit*

*Potable water for consumption*

> *Storage Tank*

*DC/AC Inverters =/~* .

The purpose of the proposed methodology is to derive, among a list of commercially available system devices, the optimal number and type of units such that the life time round total system cost (COTot) is minimized. At the same time the desalinated-water demand is

**5. New methodology of optimization hybrid PV/WIND/RO systems** 

potential is necessary in order to reduce the cost of the water produced.

optimization of this kind of systems.

considered in this study is illustrated in Fig.7.

consumed.

*Power Generation Blocks*

completely covered.

*PV*

*array Battery*

*W/G Battery Charger ~/=*

*Charger =/=*

.

.

.

.

Fig. 7. Block diagram of RO driven by Hybrid PV and W/G energy sources.

#### **4.5 Reverse osmosis desalination driven by hybrid pv/wind systems**

RO desalination units driven by hybrid PV/Wind power systems have been designed and implemented in different areas of the world (e.g. Sultanate of Oman, Israel, Mexico, Tunisia, etc.). The performances of these units were reported by Weiner et al. (2001), Peterson et al. (1981), Bourouni and Chaibi (2009) and Peterson et al. (1979).

Two RO desalination plants (Germany) using a plate module system supplied by a 6 kW wind energy converter and a 2.5 kW solar generator have been designed for remote areas (Peterson et al., 1979). Two of these prototypes were installed in the northern part of Mexico and in a small island on the German coast of the North Sea (Peterson et al., 1981).

The design of a stand-alone, hybrid PV/Wind system, used to power-supply a seawater RO desalination unit, based on a technoeconomic analysis, is proposed by Mohamed and Papadakis (2004). The system contains both a battery bank and a storage tank for the produced water, in order to cover the potable water demand during the days with negligible solar and/or wind energy production. The RO unit is designed to be able to cover the maximum daily water demand, dictating the corresponding maximum total power requirements. In the second step of the proposed methodology the number of PV modules is calculated such that the maximum energy requirements during the year are covered, taking into account the available solar radiation potential. The battery bank capacity is computed such that the electric energy required for two days can be stored. The volume of the water storage tank is calculated in such way that it provides two summer day autonomy. In order to minimize the total system cost, the developed software eliminates a part of the PV modules, determines the corresponding produced daily energy and replaces them by one or more W/G. This calculation is performed for various combinations of PV and W/G contribution percentages to the hybrid system total energy production. The combination achieving the minimum water production cost is selected as the final hybrid system configuration.

Manolakos et al. (2001) discussed the developed and the application a software tool for designing hybrid PV/Wind systems, which are used to cover the electricity and water demands of remote areas. The nominal power rating of the W/G and the number of the PV modules are determined through several program runs simulating the system operation, in order to satisfy the electric energy and water needs. The battery bank is sized taking into account several days of energy autonomy of the system, in order to ensure the uninterrupted power-supply during the time periods of low solar radiation and/or low wind speed. The volume of the desalinated-water tank is computed to satisfy the water demand, even during the time periods of low RES potential availability.

Voivontas et al. (2001) developed a computer-aided design tool for the preliminary design of desalination plants driven by RES and the evaluation of the corresponding water production cost. The RES power production capability is determined using an iterative procedure allowing an energy balance between the energy produced by the RES and the auxiliary energy sources (e.g. electric grid, diesel generators etc.) and the energy requirements of the desalination unit. However, this design method does not include the economic optimization of the resulting configurations. The investigations carried on RO desalination plants driven by hybrid PV/Wind systems showed that this kind of units is the most efficient compared to the other RES/DES technologies. Moreover, this technology can be improved by optimizing

RO desalination units driven by hybrid PV/Wind power systems have been designed and implemented in different areas of the world (e.g. Sultanate of Oman, Israel, Mexico, Tunisia, etc.). The performances of these units were reported by Weiner et al. (2001), Peterson et al.

Two RO desalination plants (Germany) using a plate module system supplied by a 6 kW wind energy converter and a 2.5 kW solar generator have been designed for remote areas (Peterson et al., 1979). Two of these prototypes were installed in the northern part of Mexico

The design of a stand-alone, hybrid PV/Wind system, used to power-supply a seawater RO desalination unit, based on a technoeconomic analysis, is proposed by Mohamed and Papadakis (2004). The system contains both a battery bank and a storage tank for the produced water, in order to cover the potable water demand during the days with negligible solar and/or wind energy production. The RO unit is designed to be able to cover the maximum daily water demand, dictating the corresponding maximum total power requirements. In the second step of the proposed methodology the number of PV modules is calculated such that the maximum energy requirements during the year are covered, taking into account the available solar radiation potential. The battery bank capacity is computed such that the electric energy required for two days can be stored. The volume of the water storage tank is calculated in such way that it provides two summer day autonomy. In order to minimize the total system cost, the developed software eliminates a part of the PV modules, determines the corresponding produced daily energy and replaces them by one or more W/G. This calculation is performed for various combinations of PV and W/G contribution percentages to the hybrid system total energy production. The combination achieving the minimum water production cost is selected as the final hybrid system

Manolakos et al. (2001) discussed the developed and the application a software tool for designing hybrid PV/Wind systems, which are used to cover the electricity and water demands of remote areas. The nominal power rating of the W/G and the number of the PV modules are determined through several program runs simulating the system operation, in order to satisfy the electric energy and water needs. The battery bank is sized taking into account several days of energy autonomy of the system, in order to ensure the uninterrupted power-supply during the time periods of low solar radiation and/or low wind speed. The volume of the desalinated-water tank is computed to satisfy the water

Voivontas et al. (2001) developed a computer-aided design tool for the preliminary design of desalination plants driven by RES and the evaluation of the corresponding water production cost. The RES power production capability is determined using an iterative procedure allowing an energy balance between the energy produced by the RES and the auxiliary energy sources (e.g. electric grid, diesel generators etc.) and the energy requirements of the desalination unit. However, this design method does not include the economic optimization of the resulting configurations. The investigations carried on RO desalination plants driven by hybrid PV/Wind systems showed that this kind of units is the most efficient compared to the other RES/DES technologies. Moreover, this technology can be improved by optimizing

demand, even during the time periods of low RES potential availability.

and in a small island on the German coast of the North Sea (Peterson et al., 1981).

**4.5 Reverse osmosis desalination driven by hybrid pv/wind systems** 

(1981), Bourouni and Chaibi (2009) and Peterson et al. (1979).

configuration.

the design of the overall plant. For these reasons we focus in this chapter on the optimization of this kind of systems.

### **5. New methodology of optimization hybrid PV/WIND/RO systems**

The operational performance and the reliability of the desalination systems driven by RES depend on their proper design and sizing. The optimal exploitation of the available RES potential is necessary in order to reduce the cost of the water produced.

The objective of this chapter is to present a new methodology to optimize RO desalination system, which is power-supplied by hybrid Photovoltaic (PV) and Wind-Generator (W/G) energy sources. Compared to the past-proposed methodologies, which have been used in order to design water desalination systems driven by RES, the methodology presented in this chapter has the advantage to take into account all the critical operational parameters that affect both the resulting electric energy and desalinated-water production levels and the system capital and maintenance costs. The block diagram of the PV/Wind/RO system considered in this study is illustrated in Fig.7.

The Battery bank is charged from the respective PV and W/G input power sources by using battery chargers, connected to a common DC bus. The power sources are usually configured in multiple power generation blocks according to the devices nominal power ratings and the redundancy requirements. The battery bank, which is usually of lead-acid type, is used to store the generated electric energy surplus and to supply the RO desalination units in case of low solar radiation and/or wind speed conditions. DC/AC converters are used to interface the DC battery voltage to the AC requirements of the RO desalination units. A water tank is used to store the produced desalinated water surplus, which is not directly consumed.

Fig. 7. Block diagram of RO driven by Hybrid PV and W/G energy sources.

The purpose of the proposed methodology is to derive, among a list of commercially available system devices, the optimal number and type of units such that the life time round total system cost (COTot) is minimized. At the same time the desalinated-water demand is completely covered.

Optimization of Renewable Energy Systems: The Case of Desalination 103

At the first step the RO plant is designed and optimized based on water demand, feed water characteristics and desalinated water specifications. One important outcome of this step is the determination of the energy required to operate the pumps and other auxiliaries. In the second step, special attention is paid to the design of energy systems related to the chosen technology and the arrangements of various components that can meet the goal of energy demand. In this step, the structure of the power unit, batteries, water storage and inverters are studied. Several Hybrid PV/Wind combinations are possible to power the designed RO plant. To validate the RES configuration, a simulation of the system operation is performed during the year in order to examine whether it fulfils the desalinated-water requirements. In the third step, a process employing GAs is executed, in order to dynamically search for the system configuration, which subject to the criterion set in the first step, results in

During the application of the proposed methodology, the system operation is simulated for one year with a time step of one hour. The power produced by the PV and W/G sources and the desalinated-water flow rate are assumed to be constant during that time step and they are arithmetically equal to the corresponding energy and water volume,

The equations of flow and salt distribution, used in the model, are similar to those provided

RO membranes are selected after checking the feed water characteristics. Hence, the number of membranes Nmb which is a function of unit capacity, the stream flow Qp and the

p

mb

mb

T

f.S (1)

<sup>N</sup> (2)

Q . . .. <sup>p</sup> *A S TCF F P mb* (3)

by the software for the design of RO membrane "FILMTEC-ROSA" (DOW, 2006).

mb

The number Ntp of pressure vessels in the system is calculated the following equation:

tp

Equation 3 is used to calculate the water flow rate produced by RO membranes.

The osmotic pressure in the different elements of RO unit is given by equation 4.

<sup>N</sup> <sup>N</sup>

A is the membrane pure water permeability, TCF is the temperature correction factor, F is the membrane fouling factor (0.8≤F≤ 1), ΔP is the applied transmembrane pressure and Δп

<sup>Q</sup> <sup>N</sup>

minimum total system cost.

**5.1 Modeling of the RO unit** 

membrane surface Smb is calculated as follows.

Where f is the pure water transport coefficient.

Where NT is the total number of membranes per unit.

is the transmembrane osmotic pressure.

respectively.

COTot is equal to the sum of the respective components capital and maintenance costs. The decision variables for the optimization are: (i) the number and the type of the membranes, (ii) the number and the type of the PV modules, (iii) the number and the type of the wind turbines, (iv) the batteries charger, (v) the DC/AC converters, (vi) the height of the turbines and the volume of the storage tank.

The minimization of the system total cost function has been implemented using genetic algorithms (GAs), which have the ability to attain the global optimum solution with relative computational simplicity. The scope of the GAs in the proposed methodology is the calculation of the optimum solutions in the overall state space of the desalination system sizing problem.

The block diagram depicted in Fig.8 summarizes the proposed optimization methodology. This methodology uses a database including: (i) the technical characteristics of commercially available system devices, (ii) their associated per unit capital and (iii) their maintenance costs. The input of the model are the: (i) feed and the desalinated water quality specifications (ii) water demand profile, (iii) daily solar irradiation on a horizontal plane, (iv) the hourly mean values of ambient temperature and wind speed.

Fig. 8. The flowchart of the proposed optimization methodology.

At the first step the RO plant is designed and optimized based on water demand, feed water characteristics and desalinated water specifications. One important outcome of this step is the determination of the energy required to operate the pumps and other auxiliaries. In the second step, special attention is paid to the design of energy systems related to the chosen technology and the arrangements of various components that can meet the goal of energy demand. In this step, the structure of the power unit, batteries, water storage and inverters are studied. Several Hybrid PV/Wind combinations are possible to power the designed RO plant. To validate the RES configuration, a simulation of the system operation is performed during the year in order to examine whether it fulfils the desalinated-water requirements.

In the third step, a process employing GAs is executed, in order to dynamically search for the system configuration, which subject to the criterion set in the first step, results in minimum total system cost.

During the application of the proposed methodology, the system operation is simulated for one year with a time step of one hour. The power produced by the PV and W/G sources and the desalinated-water flow rate are assumed to be constant during that time step and they are arithmetically equal to the corresponding energy and water volume, respectively.

#### **5.1 Modeling of the RO unit**

102 Modeling and Optimization of Renewable Energy Systems

COTot is equal to the sum of the respective components capital and maintenance costs. The decision variables for the optimization are: (i) the number and the type of the membranes, (ii) the number and the type of the PV modules, (iii) the number and the type of the wind turbines, (iv) the batteries charger, (v) the DC/AC converters, (vi) the height of the turbines

The minimization of the system total cost function has been implemented using genetic algorithms (GAs), which have the ability to attain the global optimum solution with relative computational simplicity. The scope of the GAs in the proposed methodology is the calculation of the optimum solutions in the overall state space of the desalination system sizing problem. The block diagram depicted in Fig.8 summarizes the proposed optimization methodology. This methodology uses a database including: (i) the technical characteristics of commercially available system devices, (ii) their associated per unit capital and (iii) their maintenance costs. The input of the model are the: (i) feed and the desalinated water quality specifications (ii) water demand profile, (iii) daily solar irradiation on a horizontal plane, (iv)

> Desalinated water specifications

Membranes specifications

> Battery Chargers Specs. PV Modules Specs.

> > W/G Specs.

Batteries Specs.

DC/AC Inverters Specs.

Different designs of RO units and determining their energy requirements

Select a combination of RO units, PV modules, battery chargers, W/G and DC/AC inverter types

Optimal sizing

All combinations optimized

Select the combination corresponding to the lowest cost

Yes

the hourly mean values of ambient temperature and wind speed.

No

Fig. 8. The flowchart of the proposed optimization methodology.

Feed water characteristics

and the volume of the storage tank.

Water demand

Daily irradiation and hourly mean values of temperature and wind speed

The equations of flow and salt distribution, used in the model, are similar to those provided by the software for the design of RO membrane "FILMTEC-ROSA" (DOW, 2006).

RO membranes are selected after checking the feed water characteristics. Hence, the number of membranes Nmb which is a function of unit capacity, the stream flow Qp and the membrane surface Smb is calculated as follows.

$$\mathbf{N}\_{\rm mb} = \frac{\mathbf{Q}\_{\rm p}}{\mathbf{f}.\mathbf{S}\_{\rm mb}} \tag{1}$$

Where f is the pure water transport coefficient.

The number Ntp of pressure vessels in the system is calculated the following equation:

$$\mathbf{N}\_{\rm tp} = \frac{\mathbf{N}\_{\rm mb}}{\mathbf{N}\_{\rm T}} \tag{2}$$

Where NT is the total number of membranes per unit.

Equation 3 is used to calculate the water flow rate produced by RO membranes.

$$\mathbf{Q\_p} = A.S\_{mb}.TCF.F.(\Delta P - \Delta \Pi) \tag{3}$$

A is the membrane pure water permeability, TCF is the temperature correction factor, F is the membrane fouling factor (0.8≤F≤ 1), ΔP is the applied transmembrane pressure and Δп is the transmembrane osmotic pressure.

The osmotic pressure in the different elements of RO unit is given by equation 4.

Optimization of Renewable Energy Systems: The Case of Desalination 105

It should be noted that many other parameters are considered in the model including estimation of the water needs, chemical analysis of the feed water and the choice of the membranes. The optimal system design is targeting towards the minimization of the RO

Each PV power generation block shown in Fig. 7, consists of NP PV modules connected in parallel and NS PV modules connected in series. On one day i (1≤i≤365) and at hour t (1≤t≤24) the maximum output power of each PV power generation block is determined. This calculation is based on the specifications of the PV module under Standard Test Conditions (STC, cell temperature=25 °C and solar irradiance=1 kW/m2), provided by the manufacturer, as well as the ambient temperature and solar irradiation conditions. The

( ) . . ( ). , . ( ) *<sup>i</sup> ii i P t N N V t I t FF t M s p OC SC*

<sup>20</sup> () () . (, ) <sup>800</sup> *i i i*

irradiance (W/m2) incident on the PV module placed at tilt angle β (°), KI is the short-circuit current temperature coefficient (A/°C), ( ) *<sup>i</sup> V t OC* is the open-circuit voltage (V), *VOC STC* , is the open-circuit voltage under STC (V), *Kv* is the open-circuit voltage temperature coefficient (V/°C), ( ) *<sup>i</sup> T t <sup>A</sup>* is the ambient temperature (°C), NOCT is the Nominal Operating Cell Temperature (°C), provided by the manufacturer and ( ) *<sup>i</sup> FF t* is the Fill Factor, (Markvart,

The number of PV modules connected in series in each PV power generation block, NS, is calculated according to the battery charger maximum input voltage, *<sup>m</sup> VDC* , and the PV

> *m DC <sup>s</sup> <sup>m</sup> OC*

*<sup>V</sup> <sup>N</sup> V*

The values of the daily solar irradiation on the horizontal plane are used to calculate the

according to the methodology analyzed by Lorenzo (1994).

*NOCT C Tt T t G t*

*i*

(13)

, ( ) ( ) 25 *i i V t V K Tt C OC OC STC v c* (14)

(15)

*G t*

*SC I t* 

(16)

 , , (, ) ( ) 25 . <sup>1000</sup>

(12)

is the PV module

is the global

energy consumption. In this frame energy recovery systems can be considered.

**5.2 Modeling of the photovoltaic PV panels** 

following equations (12-15) are used to design the PV modules:

modules maximum open-circuit voltage level, *<sup>m</sup> VOC* :

1994).

value of , *<sup>i</sup> G t*

*i i SC SC STC I c*

*c A*

Where ( ) *<sup>i</sup> P t <sup>M</sup>* is the maximum output power of the PV array, ( , ) *<sup>i</sup>*

short-circuit current (A), *SC STC* , *I* is the short-circuit current under STC, , *<sup>i</sup> G t*

*I t I K Tt C*

$$\Pi = 0.002654.(T + 273).\text{C.}\frac{1}{1000 - \frac{\text{C.}}{1000}}\tag{4}$$

Where C is the salt concentration.

The average pressure drop P between the first and the last element is given by equation 5.

$$
\Delta P = P\_f - \frac{1}{2} \Big/ \Delta P\_{\circ} \tag{5}
$$

ΔPfs represents the pressure drop between feed and discharge of a single element, it's given as follows:

$$
\Delta P\_{\circ} = 0.01. \overline{Q}\_{\circ}^{1.7} \tag{6}
$$

The efficiency (Yk) of the membrane is a function of the overall performance of the RO system Y and Nmb in the system (equation 7).

$$Y\_k = \mathbf{1} - (\mathbf{1} - \mathbf{Y})^{\mathbf{J}^{N\_{\text{obs}}}} \tag{7}$$

The product concentration CP is function of recovery rate and salt rejection (equation 8). The brine concentration Cc of RO element is calculated from the equation 9.

$$\mathbf{C}\_p = (\mathbf{1} - \mathbf{R}\_{mb}) \times \mathbf{C}\_{fc} \times p\_f \times \text{TCF} \times \frac{\mathbf{S}\_{mb}}{\mathbf{Q}\_p} \tag{8}$$

$$Q\_f.\mathcal{C}\_f = Q\_p.\mathcal{C}\_p + Q\_c.\mathcal{C}\_c\tag{9}$$

By applying equations (6), (7) and (8) the: flow rates and concentrations of permeate and concentrated brine in the first element are determined respectively. Thus, product water is collected in the central tube and the brine becomes feed to the second element. This process is repeated for all elements in series. To determine the feed pressure of the system, the model starts from last element for which the applied pressure Pa is calculated from equation (3).

The total water quantity QT produced by RO system is given by equation 10. Where Qk is the amount of water produced by the cell k. The desalinated water salinity concentration is deduced from equation 11.

$$Q\_T = \sum\_{k=1}^{N\_{mb}} Q\_k \tag{10}$$

$$C\_T = \frac{\sum\_{k=1}^{N\_{nb}} C\_k Q\_k}{Q\_T} \tag{11}$$

It should be noted that many other parameters are considered in the model including estimation of the water needs, chemical analysis of the feed water and the choice of the membranes. The optimal system design is targeting towards the minimization of the RO energy consumption. In this frame energy recovery systems can be considered.

#### **5.2 Modeling of the photovoltaic PV panels**

104 Modeling and Optimization of Renewable Energy Systems

<sup>1</sup> 0.002654. 273 . .

The average pressure drop P between the first and the last element is given by equation 5.

1

1.7

ΔPfs represents the pressure drop between feed and discharge of a single element, it's given

The efficiency (Yk) of the membrane is a function of the overall performance of the RO

The product concentration CP is function of recovery rate and salt rejection (equation 8). The

(1 ) *mb*

. .. *Q C QC QC f f pp c c* (9)

By applying equations (6), (7) and (8) the: flow rates and concentrations of permeate and concentrated brine in the first element are determined respectively. Thus, product water is collected in the central tube and the brine becomes feed to the second element. This process is repeated for all elements in series. To determine the feed pressure of the system, the model starts from last element for which the applied pressure Pa is calculated from equation

The total water quantity QT produced by RO system is given by equation 10. Where Qk is the amount of water produced by the cell k. The desalinated water salinity concentration is

1

*k k*

*C Q*

*T*

*Q* 

*Nmb T k k Q Q* 

> 1 .

*Nmb*

*k T*

*C*

brine concentration Cc of RO element is calculated from the equation 9.

*p mb fc f*

*T C <sup>C</sup>*

Where C is the salt concentration.

system Y and Nmb in the system (equation 7).

as follows:

(3).

deduced from equation 11.

1000

1000

<sup>2</sup> *PP P <sup>f</sup> fs* (5)

0.01. *P Q fs fc* (6)

<sup>1</sup> 1 (1 ) *Nmb Y Y <sup>k</sup>* (7)

*p <sup>S</sup> C R C p TCF <sup>Q</sup>* (8)

(10)

(11)

(4)

Each PV power generation block shown in Fig. 7, consists of NP PV modules connected in parallel and NS PV modules connected in series. On one day i (1≤i≤365) and at hour t (1≤t≤24) the maximum output power of each PV power generation block is determined. This calculation is based on the specifications of the PV module under Standard Test Conditions (STC, cell temperature=25 °C and solar irradiance=1 kW/m2), provided by the manufacturer, as well as the ambient temperature and solar irradiation conditions. The following equations (12-15) are used to design the PV modules:

$$P\_M^i(t) = N\_s.N\_p.V\_{OC}^i(t).I\_{SC}^i(t\_\prime \beta).F F^i(t) \tag{12}$$

$$I\_{SC}^{i}(t,\beta) = \left\{I\_{SC,STC} + K\_I \left[T\_c^i(t) - 25^{\circ}C\right]\right\} \frac{G^i(t,\beta)}{1000} \tag{13}$$

$$V\_{OC}^{i}(t) = V\_{OC,STC} - K\_v \left[ T\_c^i(t) - 25^{\circ}C \right] \tag{14}$$

$$T\_c^i(t) = T\_A^i(t) + \frac{NOCT - 20^{\circ}C}{800} \cdot G^i(t, \beta) \tag{15}$$

Where ( ) *<sup>i</sup> P t <sup>M</sup>* is the maximum output power of the PV array, ( , ) *<sup>i</sup> SC I t* is the PV module short-circuit current (A), *SC STC* , *I* is the short-circuit current under STC, , *<sup>i</sup> G t* is the global irradiance (W/m2) incident on the PV module placed at tilt angle β (°), KI is the short-circuit current temperature coefficient (A/°C), ( ) *<sup>i</sup> V t OC* is the open-circuit voltage (V), *VOC STC* , is the open-circuit voltage under STC (V), *Kv* is the open-circuit voltage temperature coefficient (V/°C), ( ) *<sup>i</sup> T t <sup>A</sup>* is the ambient temperature (°C), NOCT is the Nominal Operating Cell Temperature (°C), provided by the manufacturer and ( ) *<sup>i</sup> FF t* is the Fill Factor, (Markvart, 1994).

The number of PV modules connected in series in each PV power generation block, NS, is calculated according to the battery charger maximum input voltage, *<sup>m</sup> VDC* , and the PV modules maximum open-circuit voltage level, *<sup>m</sup> VOC* :

$$N\_s = \frac{V\_{DC}^m}{V\_{OC}^m} \tag{16}$$

The values of the daily solar irradiation on the horizontal plane are used to calculate the value of , *<sup>i</sup> G t* according to the methodology analyzed by Lorenzo (1994).

Optimization of Renewable Energy Systems: The Case of Desalination 107

*s BUS B*

The value of the battery bank nominal capacity, Cn (Ah), depends on the total number of batteries, NBAT, the number of series connected batteries and the nominal capacity of each

*n*

battery, CB (Ah):

calculated as follows:

*B V*

. *BAT n B S B <sup>N</sup> C C*

The maximum permissible battery depth of discharge, DOD (%) is specified by the system designer at the beginning of the optimal sizing procedure and it dictates the value of the minimum permissible battery bank capacity during discharging, Cmin (Ah), which is

During the desalination system operation the available battery bank capacity is modified according to the PV and W/G energy production levels and the power requirements of the

( ) ( ) ( 1) . .

where Ci (t), Ci (t−1) is the available battery capacity (Ah) at hour t and t−1, respectively, of day i, nB=80% is the battery round-trip efficiency during charging and nB=100% during discharging (Borowy and Salameh, 1996), VBUS is the nominal DC bus voltage (V), ( ) *<sup>i</sup> P t <sup>B</sup>* is the battery input/output power (W) ( ( ) *<sup>i</sup> P t <sup>B</sup>* <0 during discharging and ( ) *<sup>i</sup> P t <sup>B</sup>* >0 during

In order to avoid the battery performance degradation under practical operating conditions the maximum permissible battery bank charging or discharging current has been limited to (Cn/5) h. The initial capacity of the battery bank, C1 (0), is calculated using the following equation:

<sup>1</sup> <sup>1</sup> (0) . <sup>2</sup> *<sup>n</sup>*

The PV panels and W/G must be sized such that the produced energy during the year allows to completely satisfy the desalination system energy requirements. Hence, the remaining battery bank capacity at the end of the simulation period must be higher than its

*P t Ct Ct n t*

*i i B*

*i*

*B BUS*

desalination units. This variation is expressed by the following equation:

charging) and Δt is the simulation time step (Δt=1 h).

**5.5 Modeling of the global RE/DES system** 

initial value:

*<sup>V</sup>* (20)

*<sup>n</sup>* (21)

min . *C DOD C <sup>n</sup>* (22)

*<sup>V</sup>* (23)

<sup>1</sup> (24) (0) *i i C C* (24)

*DOD C C* (25)

365 1 *C C* (24) (0) (26)

The battery charger power conversion factor ns is defined as follows:

$$m\_s = \frac{P\_{PV}^i\left(t,\mathcal{J}\right)}{P\_M^i\left(t,\mathcal{J}\right)} = n\_1.n\_2\tag{17}$$

Where , *<sup>i</sup> P t PV* is the PV power really transferred to the battery bank by each PV power

generation block, n1 is the battery charger power electronic interface efficiency and n2 is a conversion factor, which depends on the battery charging algorithm executed during the charger operation and indicates the deviation of the actual PV power generated from the corresponding maximum power.

In case that the battery charger operates according to the Maximum Power Point Tracking (MPPT) principle (Esram and Chapman, 2007), n2 is approximately equal to 1, otherwise its value is much lower. The values of n1 and n2 are specified by the battery charger manufacturer.

#### **5.3 Modeling of wind generator W/G**

The variation of the W/G output power versus the wind speed is provided by the manufacturer. It usually indicates the actual power transferred to the battery bank from the W/G source, taking into account the effects of both the battery charger power electronic interface efficiency and the MPPT operation, if available. Thus, in the proposed methodology, the power transferred to the battery bank at hour t of day i, from each W/G power generation block, ( , ) *<sup>i</sup> P th WG* , is calculated using the following linear relation:

$$P\_{\rm WC}^i(t, h) = P\_1 + \left[\upsilon^i(t, h) - \upsilon\_1\right] \cdot \frac{P\_2 - P\_1}{\upsilon\_2 - \upsilon\_1} \tag{18}$$

where h (m) is the W/G installation height, ( , ) *<sup>i</sup> v th* is the wind speed (m/s) at height h (hlow≤h≤hhigh according to the limits hlow and hhigh specified by the W/G manufacturer) and (P1, v1), (P2, v2) are the W/G output power and wind speed pairs.

If the input wind speed data are measured at a different height than the desired W/G installation height, h, thus, (, ) *<sup>i</sup> v th* is corrected using the following exponential law:

$$\upsilon^i(t, h) = \upsilon^i\_{ref}(t). \left(\frac{h}{h\_{ref}}\right)^\alpha \tag{19}$$

where ( ) *<sup>i</sup> ref v t* is the reference (input) wind speed (m/s) measured at height href (m) and the exponent α ranges from 1/7 to 1/4.

#### **5.4 Modeling of batteries**

The number of batteries connected in series in each of the multiple, parallel-connected battery strings forming the battery bank, *<sup>s</sup> nB* , depends on the nominal DC bus voltage and the nominal voltage of each individual battery, *VB* (V):

generation block, n1 is the battery charger power electronic interface efficiency and n2 is a conversion factor, which depends on the battery charging algorithm executed during the charger operation and indicates the deviation of the actual PV power generated from the

In case that the battery charger operates according to the Maximum Power Point Tracking (MPPT) principle (Esram and Chapman, 2007), n2 is approximately equal to 1, otherwise its value is much lower. The values of n1 and n2 are specified by the battery charger manufacturer.

The variation of the W/G output power versus the wind speed is provided by the manufacturer. It usually indicates the actual power transferred to the battery bank from the W/G source, taking into account the effects of both the battery charger power electronic interface efficiency and the MPPT operation, if available. Thus, in the proposed methodology, the power transferred to the battery bank at hour t of day i, from each W/G

1 1

*P P P th P v th v*

where h (m) is the W/G installation height, ( , ) *<sup>i</sup> v th* is the wind speed (m/s) at height h (hlow≤h≤hhigh according to the limits hlow and hhigh specified by the W/G manufacturer) and

If the input wind speed data are measured at a different height than the desired W/G

( , ) ( ). *i i*

*<sup>h</sup> v th v t*

*ref*

The number of batteries connected in series in each of the multiple, parallel-connected battery strings forming the battery bank, *<sup>s</sup> nB* , depends on the nominal DC bus voltage and

power generation block, ( , ) *<sup>i</sup> P th WG* , is calculated using the following linear relation:

*WG*

(P1, v1), (P2, v2) are the W/G output power and wind speed pairs.

(, ) (, ) . *i i*

*i PV s i M P t n n n P t*

, . (, )

1 2

is the PV power really transferred to the battery bank by each PV power

2 1

(18)

(19)

2 1

*v v*

*<sup>i</sup> v th* is corrected using the following exponential law:

*ref*

 

*h*

*ref v t* is the reference (input) wind speed (m/s) measured at height href (m) and the

(17)

The battery charger power conversion factor ns is defined as follows:

Where , *<sup>i</sup> P t PV*

corresponding maximum power.

**5.3 Modeling of wind generator W/G** 

installation height, h, thus, (, )

exponent α ranges from 1/7 to 1/4.

the nominal voltage of each individual battery, *VB* (V):

**5.4 Modeling of batteries** 

where ( ) *<sup>i</sup>*

$$m\_B^s = \frac{V\_{BUS}}{V\_B} \tag{20}$$

The value of the battery bank nominal capacity, Cn (Ah), depends on the total number of batteries, NBAT, the number of series connected batteries and the nominal capacity of each battery, CB (Ah):

$$\mathbf{C}\_{n} = \frac{\mathbf{N}\_{BAT}}{n\_B^S} . \mathbf{C}\_B \tag{21}$$

The maximum permissible battery depth of discharge, DOD (%) is specified by the system designer at the beginning of the optimal sizing procedure and it dictates the value of the minimum permissible battery bank capacity during discharging, Cmin (Ah), which is calculated as follows:

$$\mathbf{C\_{min}} = DOD \mathbf{C\_{n}} \tag{22}$$

During the desalination system operation the available battery bank capacity is modified according to the PV and W/G energy production levels and the power requirements of the desalination units. This variation is expressed by the following equation:

$$\mathbf{C}^{i}(t) = \mathbf{C}^{i}(t-1) + n\_{B} \frac{P\_{B}^{i}(t)}{V\_{BUS}} \Delta t \tag{23}$$

$$\mathbf{C}^{i}(24) = \mathbf{C}^{i+1}(0) \tag{24}$$

where Ci (t), Ci (t−1) is the available battery capacity (Ah) at hour t and t−1, respectively, of day i, nB=80% is the battery round-trip efficiency during charging and nB=100% during discharging (Borowy and Salameh, 1996), VBUS is the nominal DC bus voltage (V), ( ) *<sup>i</sup> P t <sup>B</sup>* is the battery input/output power (W) ( ( ) *<sup>i</sup> P t <sup>B</sup>* <0 during discharging and ( ) *<sup>i</sup> P t <sup>B</sup>* >0 during charging) and Δt is the simulation time step (Δt=1 h).

In order to avoid the battery performance degradation under practical operating conditions the maximum permissible battery bank charging or discharging current has been limited to (Cn/5) h. The initial capacity of the battery bank, C1 (0), is calculated using the following equation:

$$\mathbf{C}^1(\mathbf{0}) = \left(\frac{1 - DOD}{2}\right) \mathbf{C}\_n \tag{25}$$

#### **5.5 Modeling of the global RE/DES system**

The PV panels and W/G must be sized such that the produced energy during the year allows to completely satisfy the desalination system energy requirements. Hence, the remaining battery bank capacity at the end of the simulation period must be higher than its initial value:

$$C^{365}(24) \ge C^1(0) \tag{26}$$

Optimization of Renewable Energy Systems: The Case of Desalination 109

problems with linear or non-linear cost functions, both accurately and efficiently and (ii) attain the global optimum solution with relative computational simplicity, without being

> *P* (*t*) *P* (*t*) *<sup>i</sup> <sup>T</sup> <sup>i</sup> RE*

*v* (*t*) *v* (*t*) *<sup>i</sup> <sup>D</sup> <sup>i</sup> RO*



*P* (*t*) *P* (*t*) *<sup>i</sup> <sup>T</sup> <sup>i</sup> RE V* (*t*) *V* (*t*) *<sup>i</sup> <sup>D</sup> <sup>i</sup> RO*

**No**

Fig. 9. The flowchart of energy and water flows among the components of the system.

maintenance costs evolving during the desalination system lifetime period:

( ) 20. ( 1) .(20 1)

. . .

*Aq RO M RO Aq INV INV M INV INV*

 

. . (20 1). )

*BAT Aq BAT BAT Aq BAT BAT M BAT*

*N CO CO CO*

Nmb ≥ 1; NPV ≥ 0; NWG ≥ 0; / 1 *<sup>s</sup> N n BAT B* ;VTANK ≥ 0;

. .. .

*f x CO CO CO CO*

The GA chromosomes are in the form of X = [Nmb, NPV, NWG, NBAT, h, β, WTANK]. The objective function to be minimized by the GA is equal to the sum of the capital and

*v* (*t*) *v* (*t*) *<sup>i</sup> <sup>D</sup> <sup>i</sup> RO* yes -*The water surplus Is stored in the tank*


yes

yes

No

( ) ( ) ( ) *v t v t v t i RO <sup>i</sup> D i Tank* 

**yes**

*P* (*t*) *P* (*t*) *<sup>i</sup> <sup>T</sup> <sup>i</sup> RE* -*The battery bank is charged by*

*PV Aq PV M PV WG Aq WG M WG Aq h M h*

*N CO CO N CO CO h CO h CO*

 

 . . . 1 .(20 1) . 20. *PV PV COM ch ch V CO CO TANK Aq Tank M TANK* 

(30)

. . . .. .

20. 20. . 20. .

*- The water demand is covered by the water stored in the tank*

*v* (*t*) *v* (*t*) *<sup>i</sup> <sup>D</sup> <sup>i</sup> RO*


*P* (*t*) *P* (*t*) *<sup>i</sup> <sup>T</sup> <sup>i</sup> RE*

*- The amount of the water stored remains constant*

**No**

**yes**

**No**


> 

( ) ( ) ( ) *v t v t v t i RO <sup>i</sup> D i Tank* 

**No**


**yes**

*P* (*t*) *P* (*t*) *<sup>i</sup> <sup>T</sup> <sup>i</sup> RE* -*The battery bank is charged by*

*- The water demand is covered by the water stored in the tank*

*P* (*t*) *<sup>i</sup> <sup>T</sup>* is determined

restricted by local optima (Michalewicz, 1994).

*The stored energy in the Battery bank is adequate* yes -*The battery bank is discharged by P* (*t*) *P* (*t*) *<sup>i</sup> RE <sup>i</sup> <sup>T</sup>*

*v* (*t*) *v* (*t*) *<sup>i</sup> <sup>D</sup> <sup>i</sup> RO* **yes** *The amount of the water stored remains constant*

*The RO desalination plant is turned off*

*v* (*t*) *v* (*t*) *<sup>i</sup> <sup>D</sup> <sup>i</sup> TANK* **yes** -*The Water Tank is discharged by* - *The battery bank is charged by* 

> *P* (*t*) *P* (*t*) *<sup>i</sup> FL <sup>i</sup> BAT* **yes**

*v* (*t*) *<sup>i</sup> D P* (*t*) *<sup>i</sup> RE*

*Flushing is processed Flushing is postponed*

.

*PV PV PV ch Aq ch ch*

.

with the following constraints :

hlow ≤ h ≤ hhigh; 0≤ β ≤ 90°.

*N CO*

**No**

**No**

**No**

When the necessary power for the RO operation is available, then the desalination process is performed and desalinated water is produced. Otherwise, the operation of the RO units is suspended. In this case, cleaning of each RO unit membranes should be performed, using flushing techniques. The total power produced by the PV and Wind Turbines at hour t of day i is calculated as follows:

$$P\_{RE}^{i}(t) = \mathbf{N}\_{ch}^{PV} \cdot \mathbf{n}\_{S}, P\_{M}^{i}(t, \mathcal{J}) + \mathbf{N}\_{\text{WG}}, P\_{\text{WG}}^{i}(t, h) \tag{27}$$

where *NWG* is the total number of W/G power generation blocks incorporated in the desalination system. At the hour t of the day i the total DC power input to the DC/AC inverters, ( ) *<sup>i</sup> P t <sup>T</sup>* (W), is related with the total AC power supplying the desalination units, ( ) *<sup>i</sup> P t RO* (W), according to the following equation:

$$P\_T^i(t) = \frac{P\_{RO}^i(t)}{n\_i} \tag{28}$$

where ni (%) is the power conversion efficiency of the DC/AC inverters. The minimum permissible amount of water stored in the tank, Vmin (m3), should be fixed (generally set equal to 25% to 30% of the tank total volume, VTANK (m3)).

The volume of the available water stored in the tank at hour t of day i, Vi(t) (m3), is modified during the desalination system operation, such that:

$$V\_{\min} \le V^i(\mathbf{t}) \le V\_{TANK} \tag{29}$$

When the desalinated water demand at hour t of day i ( ), *<sup>i</sup> V t <sup>D</sup>* (m3), is defined then the energy and water flows among the components of the system can be described by the Fig.9.

The developed desalination system model should be used to simulate the system operation on a yearly basis to check the feasibility of the proposed solution. The optimization of the whole system is achieved by using the Genetic Algorithms methods by considering potential solutions.

#### **5.6 System total cost minimization using gas**

The genetic algorithms (GAs) are used for designing and sizing a, through the calculation of optimum solutions in the overall state space. The role of the GA is to derive the optimal desalination system configuration by selecting chromosomes from the total state space of potential solutions, which minimize the problem's objective function and simultaneously lead to a successful system operation during the whole year.

GAs is an optimum search technique based on the concepts of natural selection and survival of the fittest individuals.

It works with a fixed-size population of possible solutions of a problem, which are evolving in time. A genetic algorithm utilizes three principal genetic operators; selection, crossover andmutation. Compared to conventional optimization methods, such as dynamic programming and gradient techniques, genetic algorithms are able to: (i) handle complex

When the necessary power for the RO operation is available, then the desalination process is performed and desalinated water is produced. Otherwise, the operation of the RO units is suspended. In this case, cleaning of each RO unit membranes should be performed, using flushing techniques. The total power produced by the PV and Wind Turbines at hour t of

where *NWG* is the total number of W/G power generation blocks incorporated in the desalination system. At the hour t of the day i the total DC power input to the DC/AC inverters, ( ) *<sup>i</sup> P t <sup>T</sup>* (W), is related with the total AC power supplying the desalination units,

> ( ) ( ) *i i RO*

*P t P t*

where ni (%) is the power conversion efficiency of the DC/AC inverters. The minimum permissible amount of water stored in the tank, Vmin (m3), should be fixed (generally set

The volume of the available water stored in the tank at hour t of day i, Vi(t) (m3), is

When the desalinated water demand at hour t of day i ( ), *<sup>i</sup> V t <sup>D</sup>* (m3), is defined then the energy and water flows among the components of the system can be described by the Fig.9. The developed desalination system model should be used to simulate the system operation on a yearly basis to check the feasibility of the proposed solution. The optimization of the whole system is achieved by using the Genetic Algorithms methods by considering

The genetic algorithms (GAs) are used for designing and sizing a, through the calculation of optimum solutions in the overall state space. The role of the GA is to derive the optimal desalination system configuration by selecting chromosomes from the total state space of potential solutions, which minimize the problem's objective function and simultaneously

GAs is an optimum search technique based on the concepts of natural selection and survival

It works with a fixed-size population of possible solutions of a problem, which are evolving in time. A genetic algorithm utilizes three principal genetic operators; selection, crossover andmutation. Compared to conventional optimization methods, such as dynamic programming and gradient techniques, genetic algorithms are able to: (i) handle complex

min ( )

*i*

*T*

*WG WG* (27)

*<sup>n</sup>* (28)

*<sup>i</sup> V Vt V TANK* (29)

() . . (, ) . (, ) *<sup>i</sup> PV i <sup>i</sup> P t N n P t N P th RE ch S M*

( ) *<sup>i</sup> P t RO* (W), according to the following equation:

**5.6 System total cost minimization using gas** 

lead to a successful system operation during the whole year.

equal to 25% to 30% of the tank total volume, VTANK (m3)).

modified during the desalination system operation, such that:

day i is calculated as follows:

potential solutions.

of the fittest individuals.

problems with linear or non-linear cost functions, both accurately and efficiently and (ii) attain the global optimum solution with relative computational simplicity, without being restricted by local optima (Michalewicz, 1994).

Fig. 9. The flowchart of energy and water flows among the components of the system.

The GA chromosomes are in the form of X = [Nmb, NPV, NWG, NBAT, h, β, WTANK]. The objective function to be minimized by the GA is equal to the sum of the capital and maintenance costs evolving during the desalination system lifetime period:

$$\begin{aligned} f(\mathbf{x}) &= \left[ \mathbf{CO}\_{Aq,RO} + 2\mathbf{0}\mathbf{CO}\_{M,RO} + \mathbf{CO}\_{Aq,inv}(\mathbf{r}\_{MV} + \mathbf{1}) + \mathbf{CO}\_{M,MV}, (20 - \tau\_{MV} - \mathbf{1}) \right] \\ &+ N\_{PV} \left( \mathbf{CO}\_{Aq,PV} + 2\mathbf{0}\mathbf{CO}\_{M,PV} \right) + N\_{\rm WG} \left( \mathbf{CO}\_{Aq,WG} + 2\mathbf{0}\mathbf{CO}\_{M,WG} + h\mathbf{C}\mathbf{O}\_{Aq,h} + 2\mathbf{0}h\mathbf{C}\mathbf{O}\_{M,h} \right) \\ &+ N\_{\rm RAT} \left[ \mathbf{CO}\_{Aq,RAT} + \tau\_{\rm RAT}\mathbf{CO}\_{Aq,RAT} + (20 - \tau\_{\rm RAT} - \mathbf{1})\mathbf{CO}\_{M,RAT} \right] \\ &+ N\_{\rm dr}^{PV} \left[ \mathbf{CO}\_{Aq,th}^{PV} + \left(\tau\_{\rm dr}^{PV} + \mathbf{1}\right) + \mathbf{CO}\_{M,dr}^{PV}, (20 - \tau\_{dr}^{PV} - \mathbf{1}) \right] + V\_{\rm TANK} \cdot \left[ \mathbf{CO}\_{Aq,Tnk} + 20\mathbf{C}\mathbf{O}\_{M,Tnk} \right] \end{aligned}$$

(30)

with the following constraints :

$$\begin{aligned} \mathsf{N}\_{\mathsf{m}\mathsf{b}} & \geq 1; \mathsf{N}\_{\mathsf{PV}} \geq 0; \mathsf{N}\_{\mathsf{WG}} \geq 0; \ N\_{\mathsf{B}AT} \;/\ n\_{\mathsf{B}}^{s} \geq 1; \mathsf{V}\_{\mathsf{TANK}} \geq 0; \\\ \mathsf{h}\_{\mathsf{low}} & \leq \mathsf{h} \leq \mathsf{h}\_{\mathsf{high}}; \ 0 \leq \beta \leq 90^{\circ}. \end{aligned}$$

Optimization of Renewable Energy Systems: The Case of Desalination 111

latitude=33.45°, longitude=9.02° and altitude=64 m above sea level. The average national water consumption in Tunisia is about 150 l/day/inhabitant. However, the RO unit is designed for primary needs consumption (drinking, cooking, etc.). Hence, a maximum daily water consumption of 50 l/day/inhabitant was assumed; giving 15m3/day as

To calculate the energy needs of the system, first we calculate the total power requirements for different subsystems, given the maximum operation hours of the RO system. In the

In the first iteration of the optimization methodology 20 individuals were generated. This population contains different PV/Wind combinations allowing to provide the water

The different characteristics of the components used in these simulations are summarized in

230 W Rotor diameter = 6.7 Nominal capacity = 200 Ah

4.7 US\$/W Acquisition cost = 760 US\$

10% Rated power = 7.5 ~ 10 kW DODmax = 40%

1.18 m² Efficiency = 80%

From the chromosomes generated in the first step a second generation is provided by using selection (30%), crossover (50%) and mutation (20%). We found that the minimum cost of water in the first generation was 3.56 \$/m3. It decreased to 3.12 \$/m3 in the second

The variation of the water cost during the GA-based optimization process evolution is

This figure shows a significant decrease of the objective function COTot for the first 30 generations and stabilizes around 2.62 \$/m3. This means that the optimal solution is

In the context of Ksar Ghilène Village the minimum cost corresponds to RO desalination plant driven by PV modules only. Fig.11 presents the variation of the charge and discharge

In the optimal solution no W/G is considered since the village of Ksar Ghilène does not

have a good potential for wind energy but a very interesting solar potential.

**RO Membranes Solar Generators Wind Turbines Batteries** 

Active surface = 37 m² Imax = 7.2 mA Heigh =18 ~ 43 m Nominal voltage = 12V

present case the total energy demand for the RO plant is 558.03 Wh.

required by the village and the power to drive the RO plant.

Acquisition cost =

state of the batteries during throughout the year.

Table 2. Characteristics of the different components used in the model

maximum total water needs.

Diameter = 8", Nominal power =

Recovery ~ 15%. Module efficiency =

Salt Reject = 99.5% Module Area =

table 2.

generation.

reached.

presented in Fig.10.

where *COAq*.*RO* , *COAq*.*PV* , *COAq*.*WG* , *COAq*.*BAT* , *COAq*.*INV* , . *PV COAq ch* , *COAq*.*Tank* and *COAq*.*<sup>h</sup>* are the capital costs of the RO desalination units, PV modules, W/Gs, batteries, DC/AC inverters, PV battery chargers, water storage tank (per m3), and W/G installation tower (per m), respectively. *COM*.*RO* ,*COM*.*PV* ,*COM*.*WG* ,*COM*.*BAT* ,*COM*.*INV* , . *PV COM ch* , *COM*.*TANK* and *COM*.*<sup>h</sup>* are the annual maintenance costs of the RO plant, PV modules, W/Gs, batteries, DC/AC inverters, PV battery chargers, water storage tank (per m3) and W/G installation tower (per m), respectively. BAT is the expected number of battery replacements during the 20-year system operation, because of limited battery lifetime and *PV ch* and INV are the expected numbers of PV battery chargers and DC/AC inverters replacements during the system 20-year lifetime period, which are equal to the system lifetime period (20 years) divided by the Mean Time Between Failures (MTBF) of power electronic converters. Each of the capital costs incorporated in Eq. (30) incorporates the market price and the installation cost of the respective device.

Initially, a population of chromosomes is generated randomly and the constraints described by the inequalities (Eq. 30) are evaluated for each chromosome. If any of the initial population chromosomes violates these constraints then it is replaced by a new, randomly generated chromosome, which fulfils these constraints. The first step of the GAbased optimal sizing algorithm iteration is the fitness function evaluation for each chromosome of the extracted population. If any of the resulting fitness function values is lower than the lowest value obtained at the previous iterations then this value is considered to be the optimal solution of the minimization problem and the corresponding chromosome's values are considered to be the desalination system's optimal sizing and operational parameters.

This optimal solution is replaced by better solutions, if any, produced in subsequent GA generations during the program evolution. The selection of the chromosomes which will be subject to the crossover andmutation operations, thus producing the next generation population, is based on the roulette wheel method (Michalewicz, 1994). The crossover mechanism uses the Simple Crossover, Simple Arithmetical Crossover and Whole Arithmetical Crossover operators. Next, the selected chromosomes are subject to the mutation mechanism, which is performed using the Uniform Mutation, Boundary Mutation and Non-Uniform Mutation operators. In case that the application of the crossover or mutation operators results in a chromosome which does not satisfy the optimization problem constraints, then a "repair" procedure is performed and that chromosome is replaced by the corresponding parent. In case of the Simple Crossover operation, where each new chromosome is generated by two parents, then the chromosome is replaced by the parent with the best fitness function value. The GA optimization process described above is repeated until a predefined number of population generations have been evaluated.

#### **6. Simulation results and discussion**

The proposed methodology, has been applied and tested for the design and optimal sizing of RO desalination systems power-supplied by PV and W/G energy sources, located in the area of Ksar Ghilène Village (300 inhabitants), southern Tunisia at:

are the capital costs of the RO desalination units, PV modules, W/Gs, batteries, DC/AC inverters, PV battery chargers, water storage tank (per m3), and W/G installation tower (per

*COM*.*<sup>h</sup>* are the annual maintenance costs of the RO plant, PV modules, W/Gs, batteries, DC/AC inverters, PV battery chargers, water storage tank (per m3) and W/G installation tower (per m), respectively. BAT is the expected number of battery replacements during the

expected numbers of PV battery chargers and DC/AC inverters replacements during the system 20-year lifetime period, which are equal to the system lifetime period (20 years) divided by the Mean Time Between Failures (MTBF) of power electronic converters. Each of the capital costs incorporated in Eq. (30) incorporates the market price and the installation

Initially, a population of chromosomes is generated randomly and the constraints described by the inequalities (Eq. 30) are evaluated for each chromosome. If any of the initial population chromosomes violates these constraints then it is replaced by a new, randomly generated chromosome, which fulfils these constraints. The first step of the GAbased optimal sizing algorithm iteration is the fitness function evaluation for each chromosome of the extracted population. If any of the resulting fitness function values is lower than the lowest value obtained at the previous iterations then this value is considered to be the optimal solution of the minimization problem and the corresponding chromosome's values are considered to be the desalination system's optimal sizing and

This optimal solution is replaced by better solutions, if any, produced in subsequent GA generations during the program evolution. The selection of the chromosomes which will be subject to the crossover andmutation operations, thus producing the next generation population, is based on the roulette wheel method (Michalewicz, 1994). The crossover mechanism uses the Simple Crossover, Simple Arithmetical Crossover and Whole Arithmetical Crossover operators. Next, the selected chromosomes are subject to the mutation mechanism, which is performed using the Uniform Mutation, Boundary Mutation and Non-Uniform Mutation operators. In case that the application of the crossover or mutation operators results in a chromosome which does not satisfy the optimization problem constraints, then a "repair" procedure is performed and that chromosome is replaced by the corresponding parent. In case of the Simple Crossover operation, where each new chromosome is generated by two parents, then the chromosome is replaced by the parent with the best fitness function value. The GA optimization process described above is repeated until a predefined number of

The proposed methodology, has been applied and tested for the design and optimal sizing of RO desalination systems power-supplied by PV and W/G energy sources, located in the area of Ksar Ghilène Village (300 inhabitants), southern Tunisia at:

*PV COAq ch* , *COAq*.*Tank* and *COAq*.*<sup>h</sup>*

*ch* 

*PV COM ch* , *COM*.*TANK* and

and INV are the

where *COAq*.*RO* , *COAq*.*PV* , *COAq*.*WG* , *COAq*.*BAT* , *COAq*.*INV* , .

m), respectively. *COM*.*RO* ,*COM*.*PV* ,*COM*.*WG* ,*COM*.*BAT* ,*COM*.*INV* , .

20-year system operation, because of limited battery lifetime and *PV*

cost of the respective device.

operational parameters.

population generations have been evaluated.

**6. Simulation results and discussion** 

latitude=33.45°, longitude=9.02° and altitude=64 m above sea level. The average national water consumption in Tunisia is about 150 l/day/inhabitant. However, the RO unit is designed for primary needs consumption (drinking, cooking, etc.). Hence, a maximum daily water consumption of 50 l/day/inhabitant was assumed; giving 15m3/day as maximum total water needs.

To calculate the energy needs of the system, first we calculate the total power requirements for different subsystems, given the maximum operation hours of the RO system. In the present case the total energy demand for the RO plant is 558.03 Wh.

In the first iteration of the optimization methodology 20 individuals were generated. This population contains different PV/Wind combinations allowing to provide the water required by the village and the power to drive the RO plant.

The different characteristics of the components used in these simulations are summarized in table 2.


Table 2. Characteristics of the different components used in the model

From the chromosomes generated in the first step a second generation is provided by using selection (30%), crossover (50%) and mutation (20%). We found that the minimum cost of water in the first generation was 3.56 \$/m3. It decreased to 3.12 \$/m3 in the second generation.

The variation of the water cost during the GA-based optimization process evolution is presented in Fig.10.

This figure shows a significant decrease of the objective function COTot for the first 30 generations and stabilizes around 2.62 \$/m3. This means that the optimal solution is reached.

In the context of Ksar Ghilène Village the minimum cost corresponds to RO desalination plant driven by PV modules only. Fig.11 presents the variation of the charge and discharge state of the batteries during throughout the year.

In the optimal solution no W/G is considered since the village of Ksar Ghilène does not have a good potential for wind energy but a very interesting solar potential.

Optimization of Renewable Energy Systems: The Case of Desalination 113

Several combinations for desalination processes driven by renewable energies (RE) can be proposed to provide water and energy in remote areas (Solar/MSF, Solar/MED, PV/RO, etc.). Reverse Osmosis (RO) is most often chosen as one of the most efficient desalination techniques in terms of energy consumption, flexibility, reliability, simple

There are a number of issues that should be taken into consideration while designing RES/RO systems as: the characteristics of water demand, the cost of water and fuel, the availability of renewable energy resources, the initial cost of the project, including the cost of each component required, the life time of the project, the interest rate subsidies, etc. A techno-economic comparison between different scenarios can be carried out to study the

In this chapter a new methodology to optimize RO desalination system driven by hybrid PV/Wind systems is presented. The proposed methodology is based on determining, among a list of commercially available system devices, the optimal number and type of units (PV modules, W/G, Batteries, etc.) such that the life time round total system cost is minimized, while simultaneously the desalinated-water demand is completely covered. The minimization of the system total cost function has been implemented using genetic

The proposed method has been applied and tested for the design of a desalination system, which cover the potable water demands of a small community in South Tunisia. The application of this methodology allows to reduce the cost of the produced water from 56 \$/m3 in the first generation to 2.62 \$/m3 for the optimal solution. The fluctuation of the

algorithms (GAs) that allows considering a large number of possible configurations.

Fig. 11. Variation of the Batteries charges for the optimal solution

**7. Conclusion** 

maintenance, etc.

feasibility of the project.

Fig. 11. Variation of the Batteries charges for the optimal solution
