solar desalination management to fulfill greenhouse …

Actas de las XXXV Jornadas de Automática, 3-5 de septiembre de 2014, ValenciaISBN-13: 978-84-697-0589-6 © 2014 Comité Español de Automática de la IFAC (CEA-IFAC)

SOLAR DESALINATION MANAGEMENTTO FULFILL GREENHOUSE WATER DEMAND

USING PREDICTIVE CONTROL

Lidia Roca11CIEMAT - Plataforma Solar de Almerıa, ctra. de Senes km. 4,5 Tabernas (04200) Almerıa,

[email protected]

Jorge A. Sanchez2, Francisco Rodrıguez2, Javier Bonilla32 Universidad de Almerıa, ctra. Sacramento s/n, (04120) Almerıa, {jorgesanchez,frrodrig}@ual.es

3 CIEMAT - Plataforma Solar de Almerıa, [email protected]

Abstract

This paper proposes a control strategy for a solardesalination plant included in a micro-grid frame-work. The goal of the controller is to maintain avolume of distillate despite the water demanded bya greenhouse and taking into account solar irradi-ance disturbances. In a top layer, the temperaturesetpoints are calculated to assure enough energyand reach the water requirements. NMPC is usedto estimate the optimal solar field setpoints and aPI controller to choose the setpoint for the distil-late unit. In a second layer, these two tempera-tures are controlled by the solar field pump and bya three-way regulation valve respectively. Simula-tion results are included to compare the proposedstrategy with an open-loop operation.

Keywords: NEPSAC, feedback linearization,multi-effect plant.

1 INTRODUCTION

Modern agricultural systems are characterized bythe intensive and optimal use of land and wa-ter, turning agricultural exploitation into a semi-industrial concept. Greenhouses are systems suit-able both for zones with unfavorable climatic con-ditions - allowing crop growth regardless of theambient temperature, and for regions with less re-strictive weather - with the aim in this case ofincreasing crop productivity and improving fruitquality. The greenhouse environment is ideal forfarming because these variables can be manipu-lated to achieve optimal growth and plant devel-opment. This manipulation requires energy con-sumption, depending on the crop’s physiologicalrequirements and, additionally, depending on theproduction patterns adopted for yield quantityand timing. Crop growth is primarily determinedby climatic variables of the environment and theamount of water and fertilizers applied throughirrigation. Therefore, controlling these variablesallows the control of the growth. The produc-

tivity optimization through efficient and adequateirrigation is a basic objective in those countrieswith water limitations. Furthermore, this resourcelimitation is made worse due to the recent rapidexpansion of the surface area occupied by green-houses in the Mediterranean Basin. Consequently,this has also led to water becoming a more im-portant consideration in the sustainability of thegreenhouse-based system in south-eastern Spain.This water deficit has been progressively deplet-ing the aquifers in the area [19]. Eighty per centof the irrigation water used in Almerıa (Spain)comes from underground sources, leading to lo-calized overexploitation of aquifers [7]. Over thelast few years, as in other arid and semi-arid ar-eas of the world, it has been promoted the use ofalternative water sources such as purified water,rain and condensed water collection as a secondarysource, the reuse of drainage water, the develop-ment of new technologies related to water-use effi-ciency such as advanced irrigation controllers, andsea water desalination.

In this line, the idea of integrating solar desalina-tion systems in the agricultural environment hasbeen significantly considered with the aim of deal-ing with water limitations in some regions of theplanet. One of the most simple and cheap tech-niques, the solar stills [10], can be easily combinedwith greenhouses [4]. This kind of distillation pro-cesses are usually located on the roof of green-houses where a glass system is installed. Seawateris pumped to this cover where vapor is producedand raised by natural convection to the top glasswhere it condenses. The water falls down the roofbeing finally collected. As explained in [4], waterproduced by a solar still is not enough for grow-ing a crop. Moreover, operational reasons, such assalt accumulation, have lead to the non real appli-cability of this method. A relative new concept isthe use of seawater for cooling and humidification[8]. The purpose is to create adequate tempera-ture conditions for the crops. Solar energy is usedin an evaporation process to humidify water. Theprocess is explained in [12]. The air inside the


greenhouse is cooled due to a first evaporator lo-cated at the front wall of the greenhouse. Theair passes through the crops and reaches a sec-ond evaporator with hot water flowing inside it.Therefore, the air becomes hotter and more hu-mid. This air passes finally through a condenserobtaining water from the air stream. Based onthis concept, a new design has been recently pro-posed [27] which includes an improved solar waterheater.This paper deals with a different combination ofgreenhouse and solar desalination. It consists intaking advantage of the water produced in a so-lar multi-effect desalination, MED, plant to feeda greenhouse located in the southeast of Spain.The challenge is to properly operate the desalina-tion plant to produce the daily water demandedby the crop.Most of the optimization algorithms applied to de-salination processes deal with the design of cogen-eration plants [9, 18, 23, 26]. The objective func-tion includes thermodynamic and environmentalissues. However, few optimization problems arefocused on satisfying a variable water demand. In[22], for example, a nonlinear programming, NLP,problem is defined to reduce operating costs in areverse osmosis, RO, system. The outputs of theoptimization are the number of membranes usedin the operation, the feed pressure and the flow.In the present paper a Nonlinear Model Predic-tive Control, NMPC, is applied to find a propertemperature setpoint in a solar field coupled to adesalination process. The idea is to maintain adesired volume of distillate obtained with a MEDunit despite the water consumption by irrigationin a greenhouse.

2 CASE STUDY

The case study explored in this paper is a micro-grid framework in which two interconnectedplants must be managed; a greenhouse and asolar desalination plant (see Fig.1). On one hand,the greenhouse daily demands fresh water forirrigation purposes and, on the other hand, asolar desalination plant produces distillate waterin a multi-effect distillate unit. An intermediatestorage tank is assumed to be located betweenthe production process and the consumer system.

2.1 SOLAR DESALINATIONFACILITY

The desalination plant used in this study is theAQUASOL system sited at Plataforma Solar deAlmerıa in the southern of Spain. This pilot plantincludes a MED unit coupled with a solar collector

Figure 1: Solar desalination plant coupled with agreenhouse.

field1. As shown in Fig.1, seawater is pumped to-wards the first cell effect (or heater) of the MED.There, part of the water is evaporated and the restof the seawater goes down to the following cells bygravity (a detailed description of the MED unitcan be found in [11]). The required heat for theheater is provided by the solar field that suppliesenergy to the storage system (two 12 m3 waterstorage tanks). A three-way regulation valve, VM ,is used to reach the nominal temperature at theinlet of the first effect, by mixing water from theprimary tank with that returned from the heater.When the solar field temperature exceeds the onein the primary tank, the on-off valve position, Vt,is changed to connect these components. Other-wise, the solar field should be connected to thebottom part of the secondary water tank to avoidcooling down the primary water tank.

2.2 GREENHOUSE ENVIRONMENT

The research data used in this work have beenobtained from greenhouses located in the Exper-imental Station of the Cajamar Foundation, ElEjido, in the province of Almerıa, Spain (2o43’W, 36o48’ N, and at a 151-m elevation). Thetomato crops are grown in a multi-span ”Parral-type” greenhouse (Fig.2). The greenhouse has asurface area of 877 m2 (37.8 x 23.2 m) with apolyethylene cover. The daytime air temperatureand humidity are managed using the top and sidewindows which are controlled via a PI controller[17]. In addition, the biomass-based heating sys-tem allows one to control the night-time air tem-perature [20]. Setpoints for both systems are es-tablished at 24 ◦C, and 10 ◦C for the ventilationand heating, respectively. Throughout the experi-ments, the following inside climatic variables werecontinuously monitored: air temperature and rela-tive humidity (Vaisala HMP45A), solar radiation(Delta-Ohm LP PYRA 03), and photosynthetic

1Although the system was designed to operate alsowith fossil energies [1], this work only deals with thesolar operation mode.


Figure 2: Greenhouse facilities used for the experiences performed in this work. From left to right andfrom top to bottom: Greenhouse, Dropper, Solar and PAR radiation device at the outside, Irrigationsystem, Solar and PAR radiation device inside the greenhouse, and the tomato crop lines.

active radiation (PAR, Kipp&Zonen PAR-Lite).Outside the greenhouse a meteorological stationwas installed, in which air temperature, relativehumidity, solar and photosynthetic active radia-tion, rain detection, wind direction, and velocitymeasurements were taken. The crop was grownin coconut coir bags with six plants and threedroppers each. The irrigation is automated by ademand tray, which is formed by two crop bags.Drainage water is set at 20 % volume. All data arerecorded every minute with a personal computer.

3 SOLAR DESALINATIONPLANT MODEL

The model of the solar desalination plant is di-vided in three main components; the solar field,the storage system and the MED unit. Fig.3shows a diagram with the connections betweenthese models. A description of the variables in-volved is included in Table 1.

The solar field has been characterized using a con-centrated parameter model based on energy bal-ance, and the storage tanks have been charac-terized with models based on energy and massbalances. A description of these dynamic mod-els can be found in [16]. With the aim of reduc-ing the computational time of the whole model,a first-order model has been experimentally ob-tained to predict the distillate production (the dis-tillate flow rate, qd) as a function of the inlet MEDtemperature, TiM , and mass flow rate, mM ,:

qd(s) =0.07

120s+ 1e−100sTiM (s)+

0.021

60s+ 1e−40smM (s)

(1)

Figure 3: Connection between the submodels ofthe solar desalination plant.

Symbol Description Units

DVolume of water in

[m3]the distillate tank

I Irradiance [W/m2]m Mass flow rate [kg/s]tm Sampling time [s]T Temperature [℃]q Volumetric flow rate [m3/h]Sub. Description Sub. Description0 Initial value a Ambientd Distillate F Solar fieldi Inlet M MEDo Outlet p Primary tankSuperscript Description∗ Setpoint

Table 1: Nomenclature

4 CONTROL SYSTEM

The idea behind the controller proposed in thissection is to maintain a desired volume of distil-


late, D∗, by regulating the temperatures in thesolar field and in the MED heater.

This controller (see Fig. 4) includes two loops:

• Loop 1: To reach the desired distillate de-mand, the solar field must deliver enoughthermal energy. A NMPC is used to solve anoptimization problem, calculate a referencefor the outlet solar-field temperature and as-sure the required distillate production. Thiscontroller must be applied over the tempera-ture instead of the water flow rate to includethe following constraints:

1 ◦C ≤ T ∗oF − TiF ≤ 20 ◦C, (2)

Tp ≤ T ∗oF ≤ 95 ◦C. (3)

The solar-field outlet-inlet temperature dif-ference must be lower than 20 ◦C to avoidstress in the absorber tubes, a minimumtemperature difference must be guaranteedto avoid cooling down the water, ToF mustbe under 95 ◦C to avoid evaporation and itshould be higher than Tp to not to cool downthe stored water.

The outlet solar-field temperature, ToF , maybe controlled by varying the solar-field watermass flow rate, mF . Several algorithms havebeen tested in this plant, obtaining successfulresults [2, 13, 14, 15, 25, 21]. In this case, afeedback linearization control, FLC, is used[13].

• Loop 2: Since the distillate production de-pends mainly on the thermal energy deliveredto the first effect, if nominal conditions areassumed in the MED mass flow rate, mM ,a controller in TiM is required to reach thedesired demand. For this purpose, two con-secutive PI’s are included. The first one cal-culates a reference temperature for the MEDinlet water, T ∗

iM . This temperature is con-trolled with the second PI using the apertureof valve VM as control variable.

Notice that there is a maximum temperature,to avoid scale formation in the heater, 72 ◦C.

Figure 4: Control scheme

A minimum temperature is also defined to as-sure a minimum distillate production: 55 ◦C≤ T ∗

iM ≤ 72 ◦C.

4.1 NONLINEAR MPC

Model predictive control, MPC, is a typical con-trol methodology that uses a model of the pro-cess to estimate the outputs at future time valuesy(t+ k|t) and calculate the optimal future inputs.In general, MPC algorithms consist of applying acontrol sequence that minimizes a cost function:

J =

N2∑j=N1

δ(j)[y(t+ k|t)−

ω(t+ j)]2 +

Nu∑j=1

λ(j)[∆u(t+ j − 1)]2, (4)

where ω is the reference signal, ∆u is the controleffort obtained from cost function minimization,N1 is the minimum prediction horizon, N2 is themaximum prediction horizon, Nu is the controlhorizon and δ(j) and λ(j) are weighting sequencesthat penalize future tracking errors and controlefforts, respectively, along the horizons.

Although most of the MPCs are applied to linearmodels, some techniques have been developed toobtain the future control actions using a nonlin-ear model of the process [3]. In this work, theNEPSAC approach has been chosen [5] because ituses directly the nonlinear prediction model with-out local linearization and it solves the optimiza-tion problem in a low computational time. Theidea behind this technique is to use the nonlinearmodel to predict the base response and the stepresponse.For lineal systems, the superposition principle isvalid:

y(t+ k|t) = ybase(t+ k|t) + yopt(t+ k|t), (5)

where ybase(t + k|t) is the effect of a base controlsequence, and yopt(t+ k|t) is the effect of the op-timized future control actions. This second com-ponent is the result of unit impulse (hi) and stepresponses (gi):

yopt(t+ k|t) =hk∆u(t|t) + hk−1∆u(t+ 1|t) + ...

+ gk−Nu+1∆u(t+Nu − 1|t). (6)

Using matrix notation, the vector of outputs is,

Y = Y + GU, (7)

where Y, is the vector of base response outputsfrom t + N1 through t + N2, U is the vector offuture controls up to t + Nu − 1 and G is the(N2 − N1 + 1)xNu matrix with impulse and step


response coefficients. Minimizing the cost func-tion 4, a closed form solution can be obtained forthe unconstrained case [6]:

U∗ = (GTG + λI)−1GT(R− Y). (8)

The control input applied to the plant is,

u∗(t) = ubase(t|t) + ∆u(t|t) = ubase(t|t) + U∗(1).(9)

In the case of nonlinear systems, since the super-position principle is no longer valid, the NEPSACapproach proposes to find iteratively a control in-put ubase(t+k|t) as close as possible to u∗(t+k|t)so that yopt(t + k|t) ≈ 0 and the superpositionprinciple is not involved. The procedure is thefollowing one:

1. choose an initial ubase(t + k|t), for exampleubase(t+ k|t) = u∗(t+ k|t− 1),

2. calculate ∆u(t+ k|t) as explained for the lin-ear case,

3. if |∆u(t + k|t)| < ε, where ε is close enoughto zero, then u∗(t + k|t) = ubase(t + k|t) +∆u(t+ k|t) and the suboptimal control inputis u∗(t+k|t), otherwise make ubase(t+k|t) =u∗(t+ k|t) + ∆u(t+ k|t) and go to step 2.

4.2 FEEDBACK LINEARIZATIONCONTROL

The purpose of feedback linearization control isto transform a nonlinear system into a linear oneusing a nonlinear feedback that makes up for non-linearities in system behavior [24]. This techniquewas applied to AQUASOL solar field to track a de-sired temperature reference using the water massflow rate as the control signal [13]. Since experi-mental results showed successful results, this con-troller has been used in this work to follow theoptimal references estimated by the NMPC.

4.3 PI CONTROLLERS

The second loop includes two PI controllers withanti-windup. The first one is used as a referencegovernor to choose the inlet MED temperaturesetpoint, T ∗

iM . The parameters of this controllerare: Kp=20 ◦C/m3, Ti=1200 s and Tt=15 s. Thetemperature setpoint obtained with this controlleris reached using another PI controller that regu-lates the valve aperture, VM . In this case, the pa-rameters are: Kp=−2 %/◦C, Ti=60 s and Tt=8 s.

5 SIMULATION RESULTS

In this section, a simulation is included to demon-strate the advantages of using the controllers to

calculate the solar-field and MED temperaturesetpoints. The results are compared with the caseof using these setpoints fixed at 72℃ (which is themaximum value considered as input in the MEDunit).

With the aim of scaling the greenhouse water con-sumption to a real case, 6 greenhouses have beenconsidered in the simulation. Therefore, the realconsumption values obtained from the greenhousehave been multiplied for 6. Taking into accountthat typical daily consumption is around 1.3 m3,and assuming two days of storage capacity in caseof cloudy days, the setpoint in the distillate vol-ume has been established to D∗ = 6 · 1.3 · 2 =15.6 m3.

The NMPC strategy was tested using the follow-ing tuning parameters: tm = 300 s, N1 = 1 s, N2

= 600 s, δ = 0 and λ(j) = 10−6.

5.1 A TYPICAL OPERATION DAY

In this example the aim is to observe the controllerresponse when the output is near the referencelevel. Real irradiance and water consumption aredepicted in Fig.5, besides the volume of distillateobtained both with the controller and the openloop case.

At the beginning of the simulation, NMPC pre-dicts that the optimal temperature reference isthe minimum one (see Fig.6 (a)). Although thewater mass flow rate is saturated at its maximumvalue (Fig.6 (c)) trying to follow the reference, thesetpoint is not feasible with those conditions. Be-fore reaching the distillate reference, T ∗

oF starts toincrease and mF decreases. Therefore, distillateproduction is slightly reduced because less ther-mal power is being delivered to the storage system.Nevertheless, at time 50506 s, the greenhouse ir-rigation system is turned on and the volume ofstored distillate drastically decreases. For this rea-son, the optimal values obtained with NMPC areagain near the minimum one. This procedure isrepeated until the end of the simulation. For theopen-loop case, mF is saturated for most part ofthe time (Fig.6 (d)) trying to follow the tempera-ture setpoint (Fig.6 (b)).

The second control loop is shown in Fig.7.Whereas the MED setpoint is fixed for the caseof the open-loop case (Fig.7 (b)), this value variescontinually ((Fig.6 (a)) when the controller is ap-plied and the volume of distillate is near the de-sired value. The aperture of the valve decreaseswhen more water coming from the primary tankis needed to reach the desired temperature at theinlet of the MED unit.

Electricity consumption in the solar-field water


3.5 4 4.5 5 5.5 6

x 104

0

500

1000

1500

Irra

dia

nce

(W/m

2)

3.5 4 4.5 5 5.5 6

x 104

0

0.02

0.04

0.06

Gre

enhouse w

ate

r

consum

ption (

m3)

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x 104

10

15

20

Relative time (s)

Volu

me o

f

dis

tilla

te (

m3)

Setpoint Open loop Control

Figure 5: Irradiance and volume of distillate in a typical operation day.

3.5 4 4.5 5 5.5 6

x 104

1

1.5

2

2.5

3

3.5

Relative time (s)(c)

Wate

r m

ass

flow

rate

(kg/s

)

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x 104

1

1.5

2

2.5

3

3.5

Relative time (s)(d)

Wate

r m

ass

flow

rate

(kg/s

)

3.5 4 4.5 5 5.5 6

x 104

65

70

75

80

85

90

95

Relative time (s)(a)

Sola

r−field

outlet

tem

pera

ture

(oC

)

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x 104

65

70

75

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85

90

95

Relative time (s)(b)

Sola

r−field

outlet

tem

pera

ture

(oC

)

ToF

*T

oFT

oF(max)T

oF(min)T

oF

*T

oFT

oF(max)T

oF(min)

Figure 6: Solar-field temperature and water mass flow rate in a typical operation day. Control case (a)and (c). Open loop case (b) and (d).

pump is reduced as a consequence of using thecontroller to properly choose the setpoint valuesto maintain a desired volume in the distillate tank.Since less water flow rates are required, the pumpis working at lower power levels which reduces theelectricity costs.

6 CONCLUSIONS

For a specific greenhouse demanding water for ir-rigation purposes, to use distillate from a solar fa-cility is a feasible process that must be controlled.The use of appropriate control techniques couldnot only assure the water demand, but also re-duce electricity costs. The simulations shown in


3.5 4 4.5 5 5.5 6

x 104

55

60

65

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ME

D w

ate

r

tem

pera

ture

(oC

)

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x 104

0

20

40

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V2 v

alv

e

apert

ure

(%

)

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(oC

)

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x 104

0

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60

80

100

Relative time(c)

V2 v

alv

e

apert

ure

(%

)

T*iM

TiM

T*iM

TiM

Figure 7: MED temperature and V2 valve aperture in a typical operation day. Control case (a) and (c).Open loop case (b) and (d).

this paper deal only with a typical operating day,but more simulations are required to evaluate thecost throughout one year taking into account wa-ter dependence of crops along the different sea-sons. Future works will also include a model of thegreenhouse water consumption that will be usedwith two main purposes: i) use it as a load sim-ulator for an experimental campaign in the solardesalination facility to evaluate the controller ex-plained in this paper, ii) include it in the NMPCcost function to improve the estimations of thefuture control actions (the solar field temperaturesetpoints).

Acknowledgments

This work has been funded by project DPI2010-21589-C05-02 financed by the Spanish Ministry ofEconomy and Competitiveness and ERDF fundsand by the Controlcrop Project, P10-TEP- 6174,project framework, supported by the AndalusianMinistry of Economy,Innovation and Science (An-dalusia, Spain).

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