Proposal of a Solar Thermal Power Plant at Low Temperature Using Solar Thermal Collectors

To this day, only two types of solar power plants have been proposed and built: high temperature thermal solar one and photovoltaic one. It is here proposed a new type of solar thermal plant using glass-top flat surface solar collectors, so working at low temperature (i.e., below 100˚C). This power plant is aimed at warm countries, i.e., the ones mainly located between −40˚ and 40˚ latitude, having available space along their coast. This land based plant, to install on the seashore, is technologically similar to the one used for OTEC (Ocean Thermal Energy Conversion). This plant, apart from supplying electricity with a much better thermodynamic efficiency than OTEC plants, has the main advantage of providing desalinated water for drinking and irri-gation. This plant is designed to generate electricity (and desalinated water) night and day and all year round, by means of hot water storage, with just a variation of the power delivered depending on the season.


Goal of the Presentation
The goal of this article is to describe a new type of power plant, taking its source in the difference in temperatures between hot water heated, up to about 77˚C, by glass-top flat surface solar collectors and the surface sea (or ocean) water. So a pipe is used to extract sea water from low depth. Another pipe forces the water back to the sea near the surface.
The power generation plant itself is similar to an OTEC plant.
In Figure 1, a simplified diagram of the plant layout is presented. Perough Rough electric power generated by the alternator (W). Ph Heat power consumed from the hot source by the thermal energy conversion unit (in W, Ph = Ph1 × Sco). Ph1 Heat power consumed from the hot source by the thermal energy conversion unit, for 1 m 2 of heat-absorbing surface collector (in W/m 2 ).

Phco
Heat power generated by a heat-absorbing surface collector Sco (in W, Phco = Phco1 × Sco). Phco1 Heat power generated by 1 m 2 of heat-absorbing surface collector (in W/m 2 ).

Phcodu
Heat power consumed from the hot source by the desalination unit (in W, Phcodu = Phcodu1 × Sco).
Phcodu1 Heat power consumed from the hot source by the desalination unit, for 1 m 2 of heat-absorbing surface collector (in W/m 2 ).

Qmdcw
Daily production of condensed water (in kg/day/m 2 ).

Rcw
Ratio between the heating power used for the desalination unit (Phcodu) and the available heat power (Phav).

T1
Liquid fluid temperature at the condenser outlet.

T2
Liquid fluid temperature at the compressor (circulation pump) outlet.

T3
Steam temperature at the turbine inlet.

T4
Saturated fluid temperature at the turbine outlet.

Ta
Mean ambient air temperature for the daylight period.

Tci
Cold temperature (at the condenser inlet) coming from the cold source (ocean). Tho Temperature (at the steam generator or evaporator outlet) returning to the hot source.

Tm
Mean water temperature inside the collectors.

Vt
Volume of water in the tank (in m 3 , with Vt = Vt1 × Sco). Vt1 Volume of water in the tank, for 1 m 2 of heat-absorbing surface collector (in m 3 /m 2 ).
The other variables are explained locally, but their mantissa (first letter) is, in general, generic: Δ (Delta) for a difference. Px for a power (W) or a power by surface unit (W/m 2 ), with the "x" relative to the source, as it can be a heat transfer rate from a hot or a cold source, or an electric power.  for 1 m 2 of heat-absorbing surface collector (for power variables only). a for "auxiliaries". av for "available". c for "cold" (sea water through the condenser). co for (solar thermal) "collectors". cw for "condensed water" (i.e. desalinated water). d for "daily". du for "desalination unit". e for "electric". h for "hot". i for "input" or "inlet". m for "mass" or for "mechanic". n for "net". o for "output" or "outlet".

Generalities and Concerned Areas
In different zones of the world, there are relatively great differences in temperature between the ambient air and the sea or ocean surface water for coastal areas. Moreover, if the latitude is low and the luminosity is high, the global horizontal irradiance is good, i.e., let's say superior or equal to 1500 kWh/m 2 per year. See [1] for estimates of the global horizontal irradiance in different places of the world. A priori, in many zones of the world, conditions would be favorable for such solar thermal power plants, i.e., part of Africa, Oceania and South America, Central America, south of California and South Asia coasts. A high mean ambient air permits to heat water by means of solar collectors with high efficiency.
Due to the difference in temperatures between the hot water at solar collectors output and the ocean temperature, it can be envisaged to set up plants generating electricity through a thermodynamic cycle.
See Figure 2, for the principle. Below, in Table 1, is an example taken from Nouakchott, capital of Mauritania where the global horizontal irradiance is very high, between 2150 and 2200 kWh/m 2 per year according to [2].
The ambient air and ocean temperatures (in ˚C) are issued from [3] and [4]. This example is very favorable because the mean ambient air temperature is high and the ocean is relatively cold.
Note that the surface ocean temperature and its temperature amplitude throughout the year depend on the latitude but also on the oceanic currents (cold or warm). Of course coasts swept by cold current are favorable. See the Figure 3 below.   From now on, this article will concentrate on the Nouakchott area, which is very favorable for such a type of power plant.

General Working
Based on Figure 1 where a simplified diagram of the plant layout is presented, the general working principle is the following:  Fresh water at about 71.2˚C extracted from the fresh water tank is heated by the solar irradiation inside the solar collectors. Then, the heated water at about 76.7˚C returns to the fresh water tank. This circuit is only in operation for the daylight period (cf. Section 6).  The fresh water at 76.7˚C is pumped towards the thermal energy conversion unit where it leaves heat to the refrigerant through a steam generator or an evaporator according to the cycle used (cf. Section 3). It is the "hot source" of the thermodynamic cycle.  In the thermal energy conversion unit, due to this hot source, steam is DOI: 10.4236/epe.2022.148019 350 Energy and Power Engineering produced which makes work a turbine-generator group generating electricity. The steam is condensed in a condenser cooled by the cold sea water ("cold source").  The sea water is filtered and pumped towards the condenser to cool the steam. Afterwards, the sea water returns to the sea. The sea water is pumped at a depth of about 20 or 30 m so to have an approximate constant sea temperature and to be sufficiently below the swell trough. The sea water is rejected just below the surface but far away from the water intake (at least 200 m, according to the current) to avoid to re-pump the rejected sea water.

Types of Thermal Energy Conversion Units and
Determination of the Thermodynamic Efficiency of These Units

Generalities about the Thermal Energy Conversion Units
See the location of the "Thermal energy conversion unit" in Figure 1. It works between the hot and the cold source to provide mechanical work which is transformed into electricity.
There are two types of units used in OTEC technology and used here:  One uses ammonia as a working fluid and works at relatively high pressure (i.e., around 8 bar) in a closed cycle. This cycle is called "Rankine" or "Rankine without superheating" or "Anderson". It will be called "Rankine" in what follows.  The other uses sea water as a working fluid and works in an open cycle at low pressure (i.e., under vacuum). This cycle is called "Claude". Note that for the proposed plant, the working fluid (refrigerant) will be fresh water and not sea water, this to avoid salt deposit inside the solar collectors.
For information about OTEC, see [5] and/or [6]. The goal here is to develop a simple equation to determine the net thermodynamic efficiency "ηnet" of these units, function of:  The hot temperature of the hot source called Thi  The cold temperature of the cold source called Tci.
Let's call "Pen" the net electric power provided to the grid net and "Ph'" the heat power consumed from the hot source. So

Diagram of the Thermal Energy Conversion Unit for a Rankine Cycle
The diagram of a machine based on the Rankine closed cycle is proposed below, in Figure 4. The refrigerant is usually ammonia (NH3, R717). Note 1: in Figure 4, "P" is worth for "Pressure", "v" for "specific volume", "T" for "Temperature" and "s" for "specific entropy".    ; for example the compression and the expansion are not really isentropic, there are losses  of heat along the cycle, etc. So the real efficiency is not as well as the ideal efficiency.
Compared to a true Rankine cycle, in Figure 4, it misses equipment such as a separator, different tanks and pumps, different systems relative to the turbine and the compressor, steam tapping from the turbine directed towards a heater, etc. It is not necessary to take into account this equipment as it will be indirectly considered in the real efficiency estimate (see §3.3).
Note: for this chapter and for all the calculations in this document, the thermodynamic data for R717 (NH3) comes from [7]. Note that the sole saturated state is given, so the enthalpy and density of the liquid in non-saturated state is taken from the liquid in saturated state considering the sole temperature. This introduces a very small error. The thermodynamic data for water comes from [8].

Determination of the Net Rankine Thermodynamic Efficiency
To determine this net efficiency, we are going to consider the study of an OTEC Rankine unit done by Creusot-Loire in 1980 and exposed in [6] pages 33 and 34. The previous Figure 4 represents Figure 8 of [6] (page 34), from which the temperatures and pressures can be extracted:  Tci = 4.8˚C, Tco = 9.05˚C. Tco − Tci = 4.25˚C, which depends on the condenser type, is supposed constant.
The heat transfer rate Ph (in W) from the hot source is equal to with Cp the specific heat capacity = 4200 J/(kg•˚K) at 25˚C. So Ph = 7.186E8 W. The theoretical Carnot efficiency ηCarnot between the high temperature at the steam generator output (T3 in ˚K) and the low temperature at the condenser temperature input (T4 in ˚K) is equal to: The rough electric power Perough generated is equal to 15E6 W according to (see [6] page 28).
With ηRankine the Rankine efficiency (compared to the Carnot efficiency). ηMachine is mainly the efficiency of the turbo generator but more generally the machine efficiency compared to an ideal Rankine efficiency. Here Finally the net efficiency ηnet is equal to with Thi and Tci in ˚C.
Note: for OTEC plants where the difference of temperature ΔThc between warm and cold sea temperatures (ΔThc = Thi -Tci) is about 22˚C, 12.21˚C represents a loss of a bit more than half of the initial ΔThc, which is relatively high. This relative loss in the proposed plant is only about the half due to a higher ΔThc (about 42˚C).  (14) for the example.

Estimation of the Different Components of Pea
The mechanical power Pmwf necessary for the compressor (Figure 4)

Diagram of the Thermal Energy Conversion Unit for a Claude Cycle and Determination of the Claude Thermodynamic Efficiency
The diagram of a machine based on the Claude cycle is proposed below in Figure 5. The working fluid circuit is connected by the fresh water circuit (in broad lines) instead of the sea (in OTEC plants). It is considered as an "open-cycle" contrary to the Rankine "closed-cycle" for which the same fluid circulates along the cycle.
The working fluid is condensed water under vacuum because under the pressure of one atmosphere, the boiling temperature is 100˚C, superior to the hot temperature targeted (T3 around 71˚C).
As for the Rankine cycle, this one is shown as ideal. Now, the cycle as shown is a pseudo cycle because the fluid circulation in the equipment is not always the same, as the fresh water entering the evaporator can become working fluid in the form of steam or can return to the fresh water tank. However, the matter being the same, the cycle can be represented as it was a closed cycle, so with the same flowrate all along the cycle.   Tco − Tci = 4.25˚C, which depends on the condenser type, is supposed constant.
 Thi = 26.8˚C, Tho = 21.34˚C (=T3), Phi is a bit superior to P3, to permit a flow rate (a precise determination being outside the scope of this article). The heat transfer rate Ph (in W) from the hot source is the same as for the Rankine cycle ( §3.2), equal to Ph = 7.186 E8 W.
Note: the altitude of the equipment (evaporator, turbine and condenser) under vacuum (P3 or P4) is such that the barometric static pressure of the working fluid corresponds to the vacuum pressure (so around 9 m).
In broad blue lines on Figure 5, it is symbolically displayed the evolution of the fresh water exchanging heat to make boil part of the flowrate. So the fresh water transfers, per second, the heat power.

Ph Qmh Hl Thi Phi Hls Tho Qmh Cp Thi Tho
with Hl for the liquid enthalpy in non saturated state and Hls for the liquid enthalpy in saturation state.
The steam flowrate Qmwf will be such that with Lv the heat of vaporization at Tho.
In our example, Thi = 26.8˚C, Tho = 21.34˚C, Lv(21.34˚C) = 2451 kJ/kg and Cp = 4200 J/kg. It can be deduced that So a big flow rate of hot water is necessary to produce a small flow rate of steam.
At the outlet (i.e. towards the fresh water tank), it appears a mixture at Tmix ( Figure 5), so that (considering a constant Cp): For the example, with 106.9 Qmh Qmwf = , Tmix = 21.25˚C which is very close to Tho (21.34˚C).
To be equivalent to the Rankine cycle, the total heat transfer (Ph) must be equal to 7.186E8 W, for our example. The heat is extracted from the evaporator and from the working fluid circuit, so that: The volume flow rate pumped by the extraction pump ( Figure 5) will be equal to: The Claude cycle is thermodynamically very close to the Rankine cycle, the slight difference being between the different behavior of the steam generator and the evaporator. The temperatures across the turbine (T3 and T4) being the same for both cycles, it is considered that Pen, Pea, ηCarnot, ηrough and ηnet are the same as the ones calculated for the Rankine cycle (cf. §3.3).
with Thi and Tci in ˚C.  Figure 5) is equal to 0.15 bar. Because P2 ≈ P3 + ΔPwf, the mechanical power Pmwf necessary for the working fluid circulation pump ( Figure 5) to pump the working fluid in a liquid state is equal to

Estimation of the Different Components of Pea
which is very weak, compared to the compressor in the Rankine cycle ( §3.3.1).
About the fresh water circuit towards the fresh water tank It is supposed that the pressure drop ΔPho through the pipes leading to the fresh water tank through the Tee (see Figure 5) is equal to 0.15 bar. The mechanical power Pmho necessary for the extraction pump ( Figure 5) to pump the fresh water is equal to: About the fresh water circuit from the fresh water tank It is supposed that the pressure drop ΔPhi through the pipes coming from the fresh water tank towards the evaporator is equal to 0.15 bar. The mechanical power Pmhi necessary for the fresh water circulation pump ( Figure 1) to pump the fresh water is equal to: About the sea water circuit The mechanical power Pmc necessary for the sea water circulation pump ( Figure 1) to pump the sea water through the condenser is the same as for the Rankine cycle ( §3.3.1) (i.e., Pmc = 1.56E6 W for the example).

Electric pumping power (Pep)
The sum of these 4 mechanical pumping powers is equal to Given a global efficiency of 0.85 for these pumps, the expected electric pumping power Pep is equal to: Power for vacuum (Pev) The necessary vacuum pumps and degassing units to trap dissolved gasses are supposed to consume Pev = 0.14% of Ph, so 1 MW in the example.
Reminder power (Per) The reminder equal to is intended to the different auxiliaries, control, light of the plant, etc. Pa, which is less penalizing.

Advantages of the Claude Cycle Compared to the Rankine Cycle
 With water as a working fluid, there is no toxic risk as with ammonia.
Even if the ammonia is well mastered by industry, the population could be reluctant toward this gas.  The cost of an evaporator is very inferior to the cost of a steam generator, due to a much smaller contact surface needed (see [6] p 73).  In the OTEC domain, the total cost of a Claude thermal energy conversion unit is a bit cheaper than the Rankine one according to [6] p 73.
 In fact, the evaporator needs a difference of temperature Thi − T3 of about 3.5˚C versus 5.5˚C for a steam generator, so the rough efficiency of a Claude cycle is better for an OTEC unit: 2.7% versus 2.11%, according to [6] page 70. However, for the plant proposed, this gain would be very small due to the yet relatively elevated difference in temperature T3 − T4 (about 42˚C).  The pressure being much smaller for the Claude cycle compared to the Rankine cycle (<1 bar versus 34 bar as given in §5.3), the mechanical sizing of pipes and equipment will probably be simpler and the cost weaker, due to a smaller thickness of the metal layer.

Common Advantage and Disadvantage
 For the sole thermal energy conversion unit, it is obvious that for the same electric power delivered, the cost will be much smaller than the cost of such a unit in the OTEC domain, simply because the net efficiency ηnet is roughly 5 times better. It means that for the same heat power from the hot source, it is delivered to the grid net, an electric power 5 times higher than an OTEC unit.  Now there will be the same problem of microbial fouling of the condenser  [5] for more details. It is a classical problem solved with filters of different kinds at the sea water inlet, the maintenance of the condenser being done, among others, by periodic mechanical and chemical (chlorination) treatments. This problem is outside the scope of this article.

Selection of the Best Solar Thermal Collector Type
There are 3 types of non-concentrating solar thermal collector heating water (see [9] and [10] for general information):  Unglazed liquid collectors are mainly used to heat water for swimming pools. They are simple and the cheapest among the collectors. The problem is their poor efficiency, which prevents any use for an application of solar thermal plant.  Evacuated tube collectors have the best efficiency. However, they use sophisticated technology (high vacuum) and they are the most expensive among the collectors. Their sophistication is an interrogation of competitive lifetime. Moreover, their relatively high cost will also prevent us from using them as a hot source for a solar thermal plant.  Glazed flat plate collectors (also called "glass-top flat surface solar collectors"). It is the best choice as they are simple, relatively cheap and efficient (with cost and efficiency between unglazed and evacuated collectors).

Description of the Hot Source
In Figure 6, it is shown the hot source formed by these collectors.
Fresh water is extracted at the temperature Tsi (about 71˚C), by the extraction pump from the inferior layer of the fresh water tank, a tank which is intended to supply the thermal energy conversion unit with hot water during the night period so as to provide a continuous working day and night, all year round.
Note 1: this tank is supposed thermally insulated to limit heat loss to the minimum, and covered by a roof to avoid evaporation. For the calculations, this tank is supposed thermally stratified, i.e., hot water (about 77˚C) remains in the superior layer and the "warm" water (about 71˚C) remains in the inferior layer.
However, it is not a requirement, as the water could be totally mixed.
To remain simple, the tank will have a small depth (let's say ≤ 10 m), and will look like a covered in-ground pool.  After heating by the collectors (up to Tso, about 77˚C) during the daylight period, the fresh water returns to the superior layer of the tank.

Mean Thermal Efficiency of the Glazed Flat Plate Collectors
From now on, only glazed flat plate collectors will be considered. They will be simply called "collectors".
The thermal power Phco generated by a heat-absorbing surface collector Sco (m 2 ) is equal to: With ηco the thermal collector efficiency and Ir the horizontal irradiation power (W/m 2 ).
According to [10] pages 121 and 122,  ηc0 is the thermal efficiency without heat loss (ideally it might be equal to 1).
 a1 is the linear coefficient of heat transfer (ideally it might be equal to 0).  a2 is the quadratic coefficient of heat transfer (ideally it might be equal to 0).

Tco Tm Ta
Tm is the mean temperature inside the collectors. For all collectors, it is supposed that Tm is the mean temperature between the inlet (Tsi) and the outlet (Tso) temperatures of the solar thermal collectors field: Roughly, the best equipment would be 15% better in term of efficiency (ηco) and the worst equipment would be 15% worse.

Goal and Hypothesis
The goal of this estimate is to assess the mean net electric power (Pen) delivered by this plant over one year, if located in the Nouakchott area. It will be supposed 1 m 2 of heat-absorbing surface collector, so the variable "Pen" will be replaced by "Pen1".
Note: the heat-absorbing surface collector is equal to about 91% of the total collector surface.
Of course, as the net electric power (Pen) is proportional to the heat power transferred (Ph, see §3.3 and §3.4) and, finally, to the effective surface of collectors (Sco), it will be, afterwards, enough to determine Sco from a targeted net electric power (Pen).
The first possibility of assessment would be to share the year in minutes, then to calculate the net electric power delivered during each minute and finally to calculate the mean value over the year. This would be possible but complex and over the scope of this article.
To limit the complexity of such estimate, it will be calculated a set of mean values, and on this basis, the estimate will be done. This method is simple but pessimistic.

Mean Values for the Continuous Working Estimate
It will be first determined by a meteorological set of data. From the Nouakchott data in §2.1, it can be deduced that:  The average "max air temperature" is equal to 31.75˚C.  The average "min air temperature" is equal to 23.08˚C.  The average "ocean temperature" (Tci) is equal to 22.0˚C. So according to §3.3, Tco = Tci + 4.25 = 26.25˚C and T4 = Tci + 6.75˚C = 28.75˚C. In saturated state for NH3 (Rankine cycle), P4 = f(T4) = 11.24 bar and for water (Claude cycle), P4 = f(T4) = 0.0395 bar. Note that P1 ≈ P4.
As the air temperature is minimum at the beginning of the day and maximum a bit before the end of the day, it will be considered that the average air temperature for the daylight period (Ta) is intermediate between both temperatures so 31.75 23.08 27. C 2 4 Even if the latitude of Nouakchott is not equatorial (18.1˚ North) it will be supposed that the mean daylight duration (Dp) is equal to 12 h (in fact very slightly superior to 12 h), and so corresponds to the March and September equinoxes (i.e., 20th of March and 23th of September in 2022).
According to [2], the GHI (global horizontal irradiance) is between 2150 and 2200 kWh/m 2 per year in the Nouakchott area. It will be considered 2175 kWh/m 2 per year.
So the mean horizontal irradiation power during daylight.

Determination of the Ideal Mean Hot Temperature Thi
Using the mean values, the mean hot temperature Thi at the steam generator or evaporator inlet (see Figure 4 and Figure 5) must be determined, using as criteria the maximum net electric power (Pen).
Below are reminded the Equation (13)  Dp, Tci, Ta, Ir are known, Thi is unknown. In a loop written in a computer program, it is easy to make slowly increase the Thi value. For each Thi, it will be successively found ηnet, ΔTco, ηco, Pen1.
The calculation will be stopped when the maximum value of Pen1 will be found.

Principle
The principle of continuous working is to store heat during the daylight in the form of a temperature rise of the water inside the fresh water tank, and to make "consume" half of this heat by the thermal energy conversion unit during the night; the other half being "consumed" during the day, as shown in Figure 7.
From the §5. 3  ( ) Half of this heat will be directly consumed by the thermal energy conversion unit and the other half will heat the fresh water inside the tank. To increase the tank temperature by ΔTt = 11˚C, the mass of water Mt1 by m 2 of the collector will be such that  Note: a more general but more complex equation Ir(w) = f(w), could be calculated for any latitude ρ and any declination of the Sun δ (between −23.43˚ and 23.43˚), taking into account the relative Earth orbit eccentricity factor (between −3.344% and 3.344%). It's not necessary here.

A More Precise Calculation of Phco1 and ΔTt
Daily ambient air temperature (Ta) according to the time (t) The daily temperature Ta can be approximated by a sinus function evolving between:  The average "max air temperature": 31.75˚C ( §5.2), supposed to be obtained at 18 h.  The average "min air temperature": 23.08˚C ( §5.2), supposed to be ob-   To simplify the calculation by ignoring the Ta and Tci influence, it will be considered that the worst and the best Pen1 are obtained respectively for the worst Ir and the best Ir. Ir depends on the horizontal irradiance at the top of the atmosphere (extraterrestrial solar irradiation) Ier and the luminosity (clearness index Cli). From [14] page 6, it can be observed that, at Nouakchott:  Ir is minimal in December with solar energy of 5023.07 Wh/m 2 /day,  Ir is maximal in April with solar energy of 7117.18 Wh/m 2 /day. Now, from Nouakchott data in §2.1, it can be observed that:  In December, the "max air temperature" is equal to 29˚C, the "min air temperature" is equal to 20˚C and the ocean temperature (Tci) is equal to 20.1˚C.  In April, the "max air temperature" is equal to 32˚C, the "min air temperature" is equal to 21˚C and the ocean temperature (Tci) is equal to 18.6˚C.
In the same way as explained in §5.2, it will be considered that the average air temperature (Ta) for the daylight period is intermediate between the "min air temperature" and the "max air temperature". So:

Solar Collectors Field Configuration
As shown in Figure 6, the collectors can be configured in series-parallel. They are supposed to be installed on a horizontal support, to remain with a simple (but pessimistic) calculation.
Note: of course, the installation of collectors could advantageously be done on inclined support, the best angle depending on the latitude, so as to improve the heat power output and to reduce the variation of net power output between the cold and the hot periods of the year. However, a calculation taking into account the azimuth and the inclination angle is beyond the objective of this article. Now In the case of Nouakchott, Ir becomes 522.4 W/m 2 instead 496.6 W/m 2 (so a gain of 5.2% on Ir). From the same type of calculation as in §5.3, it is found Pen1 = 7.89 W/m 2 instead 7.17 W/m 2 (so a gain of 10.0% on Pen1). Moreover, the variation of the generated net power throughout the year will be smaller, which is an advantage for the thermal energy conversion unit, because it will have to work with a reduced variation of the physical parameters. Let's suppose two collectors in parallel (4 m 2 ). The total volume flowrate will be the double for the same ΔP1co. So the mean mechanical power necessary will be the double (0.038 W for the example).
Let's suppose two collectors in series (4 m 2 ), as shown in Figure 6. In this case, for one collector: Let's suppose a configuration similar to the one shown in Figure 6:  All the collectors are grouped two by two in series.  All these groups of two collectors are in parallel.
Moreover, it will be supposed that the pressure loss in the pipes upstream and downstream the group of two collectors (4 m 2 ) will be equal to the pressure loss across this group. So 2 2 Ps P co ∆ = × ∆ if ΔTs increases. A "technical and economic" study will give the best configuration. For example, when Ir is close to the maximum, it would be possible to leave increase ΔTs up to a reasonable value, so as to limit the flow rate.
Note: there is no real limit to the dimensions of the solar thermal collectors field (which could also be seen as a fresh water system). Depth or width could reach kilometers or more. The sole constraints are:  To limit the heat loss from the pipes, with heat-insulation.
 To limit the pressure loss through the pipes, with sufficient pipe diameters.

Principle
It can be taken profit from the relatively high temperature Ts0 at the outlet of the collectors field ( Figure 6). In Figure 9, it is shown a vacuum distillation desalination unit. It is no more than a principle diagram. For more details about desalination units (for ETM), see [6] pages 114 and 115.
Note: as for the Claude cycle, the altitude of the equipment (steam generator and condenser) under vacuum is such that the barometric static pressure of the working fluid corresponds to the expected vacuum pressure (so around 7 m).

Estimation of the Electric Power Consumed for 1 m 2 of Heat-Absorbing Surface Collector (Peadu1)
About the fresh water circuit through the steam generator The fresh water mass flow rate through the desalination unit steam generator (Qmdu) is such that:  Electric pumping power (Pepdu1) The sum of these 3 mechanical pumping powers is equal to Power for vacuum (Pevdu1)

Example of Solar Thermal Power Plant
Further, it will be considered, as an example, a solar thermal power plant equivalent, in terms of electricity production, to the Seikh Zayed photovoltaic plant located at Nouakchott, which electricity production is equal to 25,409 MWh per year (cf. [11]).

Generalities about a Solar Thermal Power Plant Equivalent to the Seikh Zayed Photovoltaic Plant
The plant is supposed to be located at Nouakchott, it will be found for 1 m 2 of The expected Pen = 2.90E6 ( §9.1) will be really available if Peat (calculated) ≤ Peat max. If it is not the case (i.e., Peat > Peat max), Pen will have to be reduced by the difference Peat-Peat max.

Calculation of Pea for the Thermal Energy Conversion Unit
Supposing a Rankine Cycle It is reminded that:    It is supposed that the pressure drop ΔPwf through the pipes leading to the fresh water tank through the Tee (see Figure 5) is equal to 0.15 bar. So the mechanical power Pmwf is equal to 793 W for this example.
About the fresh water circuit towards the fresh water tank The mechanical power Pmho necessary for the extraction pump ( Figure 5)  It is supposed that the pressure drop ΔPho through the pipes leading to the fresh water tank through the Tee (see Figure 5) is equal to 0.15 bar. The mechanical power Pmho is equal to 2.76E4 W for the example.
About the fresh water circuit from the fresh water tank The mechanical power Pmhi necessary for the fresh water circulation pump ( Figure 1) to pump the fresh water through the evaporator is equal to: Pmhi Qvh Phi = × ∆ . It is supposed that the pressure drop ΔPhi through the pipes coming from the fresh water tank towards the evaporator is equal to 0.15 bar. So the mechanical power Pmhi = Pmho = 2.76E4 W for the example.
About the sea water circuit through the condenser The mechanical power Pmc necessary to pump the sea water through the condenser is the same as for the Rankine cycle ( §9.2.1) (i.e. Pmc = 8.93E4 W for the example).

Electric pumping power (Pep)
The sum of these 4 mechanical pumping powers is equal to

About the Desalination Unit
As calculated in §8.2, for 1 m 2 of heat-absorbing surface collector and for the ratio Rcw = 20%, the total expected consumed electric power (Peadu1) is equal to 0.101 W. So for Sco = 5.06E5 m 2 ( §9.1), the total expected consumed electric power Peadu is equal to 5.10E4 W.

About the Fresh Water Pumping Station Associated to the Solar Collectors Field
Let's suppose a solar collectors field configuration similar to the one shown in Figure 6. In Section 7, it has been determined that the mean mechanical power necessary for the fresh water extraction pump ( Figure 6) to pump the fresh wa-

Results and Discussion
It has been shown (in Section 2) that it exists, in different zones of the world, To take profit of the difference of temperatures between the fresh water heated by collectors (around 77˚C) and the surface sea water (around 22˚C), it has been studied (in Section 3) the OTEC Rankine and Claude cycles. Even if the Rankine cycle is better mastered than the Claude cycle, this last one has advantages, at least in the absence of toxicity risk.
In Section 4, the hot source (solar thermal collectors field) has been described and the type "glazed flat plate collectors" has been selected.
From the previous data, taking as example the Nouakchott area, the mean The continuous working (day and night, all year round) by means of a fresh water storage which acts as a thermal energy reserve is described in Section 6. In this chapter, it is shown that for Nouakchott two m 2 of solar collectors generate about the same average electricity production over the year than one m 2 of photovoltaic panel.
The solar collectors field configuration has been analyzed in Section 7.
The desalinated water production through a vacuum distillation desalination unit has been described in Section 8.
An example of solar thermal power plant has been proposed in Section 9. It takes as objective the same initial electric production as the Seikh Zayed photovoltaic plant located at Nouakchott, which corresponds to a mean net electric power to generate over a year equal to 2.90 MW. Moreover, it is produced 350 tons of desalinated water per day.
The Rankine and the Claude cycles have been considered. Compared to the Rankine cycle, the Claude has a better result, very close to the objective (see §9.2.5 and §9.2.6). Taking also into account the absence of toxicity of its working fluid (fresh water), it must be considered as the preferred cycle for this type of plant.
In Appendix, it is proposed the description of a small program able to calculate the net electric power provided to the grid net, for 1 m 2 of heat-absorbing surface collector. Three examples in different locations are given.
They show that, compared to collectors horizontally installed, the results are better when they are inclined by an angle equal to the latitude, above all for relatively high latitudes (see the third example in Appendix), in both aspects:  The net electric power averaged over the year is always superior,  The net electric power varies much less all along the year which is favorable for the machinery and for the electric net production management.
It must also be noted that if the collectors are horizontally installed, the main parameter is the latitude whereas if the collectors are inclined the main parameter is the clearness index.
Now the installation of such inclined collectors is obviously less simple and cheap than the installation of horizontal collectors.

Conclusions
It has been shown that this concept could work. Compared to a photovoltaic plant, the solar thermal power plant at low temperature has two main advantages:  It produces electricity continuously, all year round.
 It produces desalinated water for drinking and irrigation.
According to Section 10, the best configuration is: Moreover, the required technology for most of the equipment is relatively simple, so most of the repairs could be done locally.

Conflicts of Interest
The author declares no conflict of interest regarding the publication of this paper. Energy and Power Engineering December = 1.29/June = 7.97/Average over the year = 4.66.
Observations  The best configuration is the inclined collectors one: higher "Average over the year" net electric power and weaker differences between December/June/Equinoxes.  From these examples, it is obvious that the main parameter in the inclined collectors configuration is the clearness index which must be the highest possible. For example, the result from Lüderitz (9.31 W/m 2 ) is superior to the one from Nouakchott (8.53 W/m 2 ), even if the absolute latitude is not so favorable (27˚ versus 18˚), this because the clearness index is equal to 67.1% for Lüderitz versus 62.5% for Nouakchott. The result for Almeria (6.83 W/m 2 ) is not so good because the clearness index is not elevated (58.7%). Moreover, the advantage of this configuration compared to the horizontal installation increases with the latitude: the difference is small at Nouakchott (8.53 versus 8.29 W/m 2 ) but strong at Almeria (6.83 versus 4.66 W/m 2 ).  The two main parameters are the absolute latitude and the clearness index.
However, it can be observed that if the collectors are horizontally installed, the most influential parameter is the latitude, i.e. for a constant clearness index, the average net electric power decreases when the absolute latitude increases. Reversely if the collectors are inclined the most influential parameter is the clearness index.  Note that the extraterrestrial solar irradiation (Ier) is superior in December than in June, due a weaker distance from the Sun, which explains the better result in December than in June, in the inclined collectors configuration.