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Heat Transfer Fluid Temperature Control in a Thermoelectric Solar Power Plant Lourdes A. Barcia 1 , Rogelio Peon 2 , Juan Díaz 3, *, A.M. Pernía 3 and Juan Ángel Martínez 3 1 2 3

*

Normagrup Technology S.A., 33420 Llanera, Asturias, Spain; [email protected] Grupo TSK PCyT de Gijón, 33203 Gijón, Spain; [email protected] Department of Electrical Engineering, University of Oviedo, 33203 Gijón, Asturias, Spain; [email protected] (A.M.P.); [email protected] (J.A.M.) Correspondence: [email protected]; Tel.: +34-98-5182564

Received: 10 May 2017; Accepted: 21 July 2017; Published: 25 July 2017

Abstract: Thermoelectric solar plants transform solar energy into electricity. Unlike photovoltaic plants, the sun’s energy heats a fluid (heat transfer fluid (HTF)) and this, in turn, exchanges its energy, generating steam. Finally, the steam generates electricity in a Rankine cycle. One of the main advantages of this double conversion (sun energy to heat in the HTF-Rankine cycle) is the fact that it facilitates energy storage without using batteries. It is possible to store the heat energy in melted salts in such a way that this energy will be recovered when necessary, i.e., during the night. These molten salts are stored in containers in a liquid state at high temperature. The HTF comes into the solar field at a given temperature and increases its energy thanks to the solar collectors. In order to optimize the sun to HTF energy transference, it is necessary to keep an adequate temperature control of the fluid at the output of the solar fields. This paper describes three different algorithms to control the HTF output temperature. Keywords: thermal power plant; heat transfer fluid (HTF); process modeling; temperature control

1. Introduction The current increasing demand of energy requires the use of clean and renewable energies in order to prevent global warming. As it is well known, clean energies take advantage of different natural resources, such as wind, sun, tides, waves, geothermal, and different biofuels. The Kyoto Protocol evinces the world’s concern about using non-pollutant energies, regardless of the full compliance of it. The EU has set different goals for 2020: a 20% reduction of greenhouse gas emissions, 20% of the energy has to be produced using renewable energies, and a 20% efficiency improvement (20/20/20 goal [1]). Whatever the result, the world investment in this field was about 256,000 € in 2015, and it is expected to be increased in the near future [2]. One of the main drawbacks of these energies is their availability: as soon as they are generated, they have to be consumed, and the regulation is more complex than that in traditional energies, since natural resources are certainly unforeseeable. In this way, technology has evolved in such a way that different energy storage techniques have been proposed: chemical methods (batteries), flywheels—in which kinetic energy is stored—magnetic energy systems, compressed air storage, thermal storage, pumped hydro, and many others [3,4]. If renewable generation is combined with a clean storage method, the aforementioned problems are overcome, since it will be possible to generate energy even when the natural source is not available. The best example is the sun: it is evident that, during the night, it is impossible to obtain energy from it; however, it is possible to store the energy generated during sunny periods and consume it during the night. This is the case of solar thermal plants, such as the one that is the goal of this work: “La Africana”, located in Córdoba, in the south of Spain (Figure 1).

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Energies 2017, 1078 2 of 11 In this plant, the10,energy of the sun is transferred to the HTF (heat transfer fluid), and this fluid—usually a sort of oil—returns the energy back to two different systems [5,6]:

-

(Figure 1). In this plant, the energy of the sun is transferred to the HTF (heat transfer fluid), and this fluid—usually sort of oil—returns thebased energy two different [5,6]: The electricitya generation system, onback the to Rankine cycle:systems the HTF gives back its energy to

in ordergeneration to produce steam. -the water, The electricity system, based on the Rankine cycle: the HTF gives back its energy to The the energy storing system: the water, in order to produce HTF steam.returns the acquired energy in order to heat and melt salts. -These The energy thecontainers HTF returnsand the maintain acquired energy in order to heat and melt the salts. salts are storing stored system: in special their calorific energy during whole are stored in special containers and maintain their calorific the energy during thereturn whole back day.These Thus,salts in those periods in which solar radiation is not available, molten salts day. Thus, in those in which radiation is not available, the one. molten salts return back the energy to the HTF.periods The system is asolar thermal energy storage (TES) the energy to the HTF. The system is a thermal energy storage (TES) one.

The TES structure is composed by two molten salt reservoirs: one of them, named the hot tank, The TES structure is composed by two molten salt reservoirs: one of them, named the hot tank, storesstores molten salts after receiving the thermal energy: this one is refilled during sunny hours, as it was molten salts after receiving the thermal energy: this one is refilled during sunny hours, as it ◦ C) salts, previously exposed. Its temperature is around 400 ◦ 400 C. The other tank stores cold (around was previously exposed. Its temperature is around °C. The other tank stores cold (around300 300 °C) in a liquid In this the saltsthe are returned after after yielding theirtheir energy to to thethe HTF. salts, instate: a liquid state:tank, In this tank, salts are returned yielding energy HTF.

Figure 1. General view of “La Africana”. Hot and cold tanks are shown at the top, with the heat Figure 1. General view of “La Africana”. Hot and cold tanks are shown at the top, with the heat exchanger in between. The solar collectors are located at the left of the image. exchanger in between. The solar collectors are located at the left of the image.

In “La Africana”, it is possible to store energy to supply electricity for 7.5 h; a more detailed

In “La Africana”, it is in possible store energy to supply electricity 7.5 h; a more detailed description can be found [7]. Thistoplant uses well-known parabolic trough for collectors. In order obtaininthe best efficiency in the whole process, it is essential maintain the HTF description can betofound [7]. This plant uses well-known parabolic troughtocollectors. temperature and flow highefficiency as possible—always under the maximum limits—at the solar field In order to obtain theasbest in the whole process, it is essential to maintain the HTF output. The major problem is that solar radiation is unpredictable, so it is necessary to implement an field temperature and flow as high as possible—always under the maximum limits—at the solar adequate feedback loop to maximize the energy exchange from the sun to the HTF. In addition, to output. The major problem is that solar radiation is unpredictable, so it is necessary to implement make things more complex, the HTF temperature takes a long time to react, since the fluid has to go an adequate feedback loop to maximize the energy exchange from the sun to the HTF. In addition, through the solar field; in other words, there is an important delay between control action and the to make things more complex, the HTF temperature takes a long time to react, since the fluid has to response of the system. This paper deals with the HTF control temperature and presents three go through solar field; in otherthewords, there is anatimportant delay between control action and differentthe algorithms to maintain HTF temperature a defined set point. the response of the system. This paper deals with the HTF control temperature and presents three 2. Material and Methods different algorithms to maintain the HTF temperature at a defined set point. In thermal solar plants, control is one of the most delicate issues to optimize their behavior. There are different subsystems within these plants that need adequate control to keep parameters within certain values: control of control the mirror positions, of the thermal energy storage, control of theThere In thermal solar plants, is one of the control most delicate issues to optimize their behavior. steam generator, control of the temperature of the HTF, and so on. In fact, in order to optimize are different subsystems within these plants that need adequate control to keep parametersthe within Rankine cycle efficiency, it mirror is essential to keep control the HTFof temperature as high as possible, theof the certain values: control of the positions, the thermal energy storage, below control maximum limits, of course. steam generator, control of the temperature of the HTF, and so on. In fact, in order to optimize the In order to propose and validate different control algorithms for the HTF temperature, it is Rankine cycle efficiency, it is essential to keep the HTF temperature as high as possible, below the necessary to model the solar field and the energy exchange process, and set the possible variables maximum limits, of course. and inputs/outputs to the system. The model of the solar field has already been proposed in [5], and In order with to propose and validate different control for the HTF temperature, validated real data. Moreover, a proportional integralalgorithms derivative (PID) controller has also been it is

2. Material and Methods

necessary to model the solar field and the energy exchange process, and set the possible variables and inputs/outputs to the system. The model of the solar field has already been proposed in [5], and validated with real data. Moreover, a proportional integral derivative (PID) controller has also

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proposed. The process has been modelled using MATLAB-SimuLink R2012b. The process is proposed. The process has has been modelled using MATLAB-SimuLink been proposed. The process been modelled using MATLAB-SimuLinkR2012b. R2012b.The Theprocess process is is summarized in Figure 2. summarized 2. summarized in in Figure Figure 2.

Figure 2. 2. Simplified Simplified scheme scheme of of the the heat heat transfer transfer fluid fluid (HTF) (HTF) heating heatingprocess. process. Figure Figure 2. Simplified scheme of the heat transfer fluid (HTF) heating process.

The HTF is pumped into the solar field from a cold tank, through a set of pumps (B1 and B2), The The HTF HTF is is pumped pumped into into the the solar solar field field from from aa cold cold tank, tank, through through aa set set of of pumps pumps (B1 (B1 and and B2), B2), which set the HTF speed; valves F1, VF1, VC1, and C1 control the mass flow. The HTF enters the which set the HTF speed; valves F1, VF1, VC1, and C1 control the mass flow. The HTF enters which set the HTF speed; valves F1, VF1, VC1, and C1 control the mass flow. The HTF enters the the solar field and gets the energy from the sun. The process is continuously monitored: temperature, solar and gets gets the the energy energy from from the the sun. sun. The The process process is is continuously continuously monitored: monitored: temperature, solar field field and temperature, pressure, ambient temperature, and so on. At the solar field output, the HTF yields its energy to the pressure, ambient temperature, pressure, ambient temperature, and and so so on. on. At At the the solar solar field field output, output, the the HTF HTF yields yields its its energy energy to to the the steam generation and the thermal storage systems. The cold HTF goes back to the cold tank, through steam generation and the thermal storage systems. The cold HTF goes back to the cold tank, through steam generation and the thermal storage systems. The cold HTF goes back to the cold tank, through a a filtering stage, and the process is reinitiated. The goal is to fix the HTF temperature to a predefined afiltering filteringstage, stage,and andthe theprocess processisisreinitiated. reinitiated.The Thegoal goalisisto to fix fix the the HTF HTF temperature temperature to to aa predefined predefined set point and to ensure that it does not exceed or fall below the thresholds. For instance, if the solar set does not not exceed exceed or or fall fall below below the the thresholds. thresholds. For set point point and and to to ensure ensure that that it it does For instance, instance, if if the the solar solar radiation is not providing enough energy, the HTF obtains the thermal energy from gas heaters and, radiation is not providing enough energy, the HTF obtains the thermal energy from gas heaters radiation is not providing enough energy, the HTF obtains the thermal energy from gas heaters and, and, on the contrary, if the energy is too high, it is necessary to move the mirrors, in order to reduce the on if the the energy energy is is too too high, high, it it is is necessary necessary to to move move the on the the contrary, contrary, if the mirrors, mirrors, in in order order to to reduce reduce the the HTF heating. Additionally, the sun radiation and the mirror positions, the HTF input temperature, HTF heating. Additionally, the sun radiation and the mirror positions, the HTF input temperature, HTF heating. Additionally, the sun radiation and the mirror positions, the HTF input temperature, and the dirtiness in the mirrors (and absorbing pipes) affect the process as well. and mirrors (and (and absorbing absorbing pipes) pipes) affect affect the the process process as as well. well. and the the dirtiness dirtiness in in the the mirrors The solar field was completely modeled including not only the absorber pipes included in the The was completely completely modeled The solar solar field field was modeled including including not not only only the the absorber absorber pipes pipes included included in in the the solar collector elements but also the large headers that introduce the HTF into the solar field (cold solar collector elements but also the large headers that introduce the HTF into the solar field (cold solar collector elements but also the large headers that introduce the HTF into the solar field (cold headers) and collect the HTF at the output of the solar field to transport it to the TES and to the steam headers) thethe output of the solar fieldfield to transport it to the the steam headers) and andcollect collectthe theHTF HTFatat output of the solar to transport it toTES theand TEStoand to the generator system (SGS) (heat headers). Although other solar plant models can be found in the generator system (SGS) (heat headers). Although other solar plant models can be found in steam generator system (SGS) (heat headers). Although other solar plant models can be found in the the literature [8,9], they are much more complex that the one presented in [5] and, for that reason, they literature [8,9], they they are aremuch muchmore morecomplex complexthat thatthe the one presented and, reason, literature [8,9], one presented in in [5][5] and, forfor thatthat reason, theythey are are not suitable to be used in a real plant. are suitable toused be used a real plant. not not suitable to be in ain real plant. Figure 3 shows the solar field model that has been deeply developed and explained in [5]: Figure solar field field model model that that has has been been deeply deeply developed developed and and explained explained in in [5]: [5]: Figure 33 shows shows the the solar

Figure 3. Solar field dynamic model. Figure 3. Solar field dynamic model. Figure 3. Solar field dynamic model.

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The inputs are the ambient temperature (Tamb), the direct normal irradiation (DNI), the HTF thefield ambient temperature the direct normal (DNI), HTF mass mass The flowinputs in theare solar (mHTFe), and its(Tamb), temperature at the inputirradiation of the solar field the (THTFe); the flow in the solar field (mHTFe), and its temperature at the input of the solar field (THTFe); the output output is the HTF temperature at the outlet of the solar field (THTFs). In order to control this is the HTF temperature at thetooutlet of the (THTFs). In order control this temperature, temperature, it is necessary modify thesolar massfield flow: the greater the to mass flow, the lower the it is necessary to modify the mass flow: the greater the mass flow, the lower the temperature at the temperature at the output of the solar field. In other words, if the same energy (sun) is used with a output of the solar field. In other words, if the same energy (sun) is used with a greater amount of greater amount of fluid, the temperature rise will be lower. fluid,This themodel temperature rise willwith be lower. was validated a PID controller. The results obtained evinced that this algorithm This model was validated with a PID controller. results obtained evinced that this algorithm is suitable provided there are no sharp changes in theThe input variable, the solar radiation. This sort of is suitable provided there are no sharp changes in the input variable, the solar radiation. This sort of disturbance may occur when the sky is full of clouds that suddenly disappear. As aforementioned, disturbance may occur when the sky is full of clouds that suddenly disappear. As aforementioned, the system is very slow, and its response has very important delays. These delays cause overshoots the system is the very slow, and its response has very delays. These delays cause overshoots and spikes in HTF temperature that can ruin theimportant HTF. and spikes in the HTF temperature that can ruin the HTF. 2.1. Design of the Controllers 2.1. Design of the Controllers In order to optimize the HTF temperature control, other algorithms were tested using the same In order to optimize the HTF temperature control, other algorithms were tested using the same model as above. model as above. 2.1.1. 2.1.1.PID PIDFeed-Forward Feed-Forward To To overcome overcome the the PID PID problems, problems, aa modification modification of of this this algorithm algorithmisisproposed proposedand andititisis no no other other than a feed-forward stage inclusion. According to Figure 4, this algorithm takes into account not than a feed-forward stage inclusion. According to Figure 4, this algorithm takes into account notonly only the theset setpoint pointfor forthe theHTF HTFoutput outputtemperature, temperature,but butalso alsothe thesun sunirradiation—by irradiation—bymeans meansof ofdirect directnormal normal irradiation irradiation(DNI) (DNI)and andthe themirror mirrorangles—the angles—theHTF HTFinput inputtemperature, temperature,and andthe theambient ambienttemperature. temperature. The aim of this algorithm is to predict the mass flow needed for the system, The aim of this algorithm is to predict the mass flow needed for the system, correcting correcting the the one one calculated using only the reference (set point, SPTHTF) and the output temperature. In other calculated using only the reference (set point, SPTHTF) and the output temperature. In otherwords, words, the flowneeded neededtoto obtain desired temperature is recalculated, now recalculated, considering more the mass mass flow obtain thethe desired temperature is now considering more process process parameters. This is done by including a new block (mHTF_calc PROCESS) that calculates the parameters. This is done by including a new block (mHTF_calc PROCESS) that calculates the optimal optimal mass flow, taking into account the values of a set of input variables at any given time. Thus, mass flow, taking into account the values of a set of input variables at any given time. Thus, it is itpossible is possible to have pumps ready to change mass flow even before disturbances affect to have the the pumps ready to change the the mass flow even before thethe disturbances cancan affect the the process output. By doing so, large changes appearing in the PID controller are avoided, since process output. By doing so, large changes appearing in the PID controller are avoided, since action action takeswithout place without for theofvalue of the HTF temperature to beatpresent at the takes place havinghaving to wait to forwait the value the HTF temperature to be present the output of output of the solar field. the solar field.

Figure Figure4.4.Block Blockdiagram diagramof ofthe theprocess, process,with withthe thefeed-forward feed-forwardimplemented. implemented.

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The equation included in block (mHTF_calc PROCESS) obtains the mass flow that the system should have byincluded relating in it block to known input variables andobtains to the the set point for the variable The equation (mHTF_calc PROCESS) mass flow thatoutput the system (SPTHTFh): should have by relating it to known input variables and to the set point for the output variable (SPTHTFh): .



m HTF =

= Q ( util

(1) (1)

)∙

( THTFh − THTFc )·Cp where Qutil is the calorific energy that reaches the thermal fluid after considering all the losses, due to where Qutil is the calorific energy that reaches the thermal fluid after considering all the losses, due to different reasons: dirt on the mirrors, for instance. Moreover, the incident angle of the solar radiation different reasons: dirt on the mirrors, for instance. Moreover, the incident angle of the solar radiation on on the mirrors, shadows, convection, radiation, and conduction thermal exchanges in the absorber the mirrors, shadows, convection, radiation, and conduction thermal exchanges in the absorber tubes tubes have also been taken into account [10,11]. The variable named THTFh is the thermal fluid have also been taken into account [10,11]. The variable named THTFh is the thermal fluid temperature temperature at the output of the solar field, THTFc is the thermal fluid temperature just before entering at the output of the solar field, THTFc is the thermal fluid temperature just before entering the solar the solar field, THTFh is the temperature of the thermal fluid at the output of the solar field, φ represents field, THTFh is the temperature of the thermal fluid at the output of the solar field, φ represents the the mirrors angle, mHTF is the HTF mass flow, and Cp is the specific heat at constant pressure of the mirrors angle, mHTF is the HTF mass flow, and Cp is the specific heat at constant pressure of the thermal thermal fluid. This parameter depends on the fluid temperature. Even when Qutil has been calculated fluid. This parameter depends on the fluid temperature. Even when Qutil has been calculated in static in static mode, the SF model takes into account the inertia of the process by means of considering all mode, the SF model takes into account the inertia of the process by means of considering all of the of the fluid volume, as well as the total length of the absorber tubes and headers. For that, the model fluid volume, as well as the total length of the absorber tubes and headers. For that, the model was was created by the union of blocks in series that models all the absorber pipes and the headers. created by the union of blocks in series that models all the absorber pipes and the headers. 2.1.2. Adaptive–Predictive–Expert Control (ADEX) 2.1.2. Adaptive–Predictive–Expert Control (ADEX) Adaptive–predictive–expert control (ADEX) combines two types of control: an adaptive– Adaptive–predictive–expert control (ADEX) combines two types of control: an adaptive–predictive one (AP)control. and an The expert control. The adaptive–predictive control aims to output make the onepredictive (AP) and an expert adaptive–predictive (AP) control aims(AP) to make the process process output follow a desired path or trajectory [12]. The most relevant operating blocks of an follow a desired path or trajectory [12]. The most relevant operating blocks of an adaptive–predictive adaptive–predictive control can be seen in Figure 5 [13]. control can be seen in Figure 5 [13]. Predictive models provide control signal required to make output follow values Predictive models provide the the control signal required to make the the output follow the the values produced by a driver block, which generates a simple path for the process output to reach the produced by a driver block, which generates a simple path for the process output to reach the set set point. If predictions were always right, driver block predictive model would suffice point. If predictions were always right, thethe driver block andand the the predictive model would suffice to to control a process. Unfortunately, dirt, aging, etc., can modify the system and the process dynamics, control a process. Unfortunately, dirt, aging, etc., can modify the system and the process dynamics, making predictions wrong. problem be overcome by including an adaptive mechanism making the the predictions wrong. ThisThis problem cancan be overcome by including an adaptive mechanism introduces required adjustments in the predictive model by notifying driver block about thatthat introduces the the required adjustments in the predictive model by notifying the the driver block about trends and prediction errors. This gives rise to an adaptive–predictive model, which reduces trends and prediction errors. This gives rise to an adaptive–predictive model, which reduces and fixesand fixes prediction inand a stable and way. efficient way. prediction errors in errors a stable efficient

Driver

Predictive

Block

Model

PROCESS

Adaptive Mechanism

Figure 5. Adaptive–predictive control scheme block diagram. Figure 5. Adaptive–predictive control scheme block diagram.

In applications such as the one considered in this paper, the process dynamics defined in the In applications such one considered in this the process dynamics defined in predictive controller canasbethe represented by means of a paper, multi-input single-output (MISO) difference the equation: predictive controller can be represented by means of a multi-input single-output (MISO) difference equation: ( )= ( ) ( − )+ ( ) ( − )+ ( ) ( − ) + ∆( ) (2) y ( k ) = ∑ a i ( k ) y ( k − i ) + ∑ bi ( k ) u ( k − i ) + ∑ c i ( k ) w ( k − i ) + ∆ ( k ) (2)

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where ∆ (k) Energies 2017,is 10, the 1078 perturbation error and y(k), u(k), and w(k) are increments of measured 6 of 11 process variables: where ∆ (k) is the perturbation error yand and w(k) are increments of measured process = yu(k), (3) (k)y(k), p ( k ) − y p ( k − 1) variables:

u ( k ) = u p ( k ) − u p ( k − 1) ( )=

( )−

( − 1)

w ( k ) = w p ( k ) − w p ( k − 1) ( )=

( )−

(4) (3)

(5)

( − 1)

(4) with yp (k) being the process output measured at an instant k, up (k) being the process input and wp (k) being the measurable disturbance. ( ) = ( ) − ( − 1) (5) According to this, the adaptive–predictive model of a 2 × 1 AP controller can predict the incremental output byoutput considering theatvalues of the described with yp(k)process being the process measured an instant k, uincremental p(k) being the variables process input and wp(k)above. Equation (6) defines the error, e(k), associated to this prediction. being the measurable disturbance. According to this, the adaptive–predictive model of a 2 × 1 AP controller can predict the e(k ) =the y(kvalues k|kthe − incremental 1) ) − yˆ (of incremental process output by considering variables described above. Equation (6) defines the error, e(k), associated to this prediction.

(6)

This error is used to adapt the value of the AP model parameters included in Equation (2) by (6) ( ) = ( ) − ( | − 1) using error gradient algorithms, which guarantees that the error tends to be null: This error is used to adapt the value of the AP model parameters included in Equation (2) by using error gradient algorithms, which ai (k)guarantees = ai (k − 1that ∆ aierror ) +the (e(k))tends to be null: ( )=

( − 1) + ∆

( )

( )=

( − 1) + ∆

( )

bi (k) = bi (k − 1) + ∆bi (e(k))

(7)

(7) (8)

(8) where ∆ai (e(k)) and ∆bi (e(k)) depend on the prediction error calculated at instant k. The equations presented so faron indicate that adaptive–predictive control ∆bi(e(k)) depend the prediction error calculated at instant k. requires a consistent where ∆ai(e(k)) and The relationship equations presented so far indicate that adaptive–predictive control a consistent cause–effect between process inputs and outputs so that theyrequires can be matched by the cause–effect relationship between process inputs and outputs so that they can be matched by the AP AP model. Unfortunately, industrial operations often undergo situations in which this cause–effect model. Unfortunately, industrial operations undergo situations in which thisthe cause–effect relationship is lost. It is in these situations whenoften an expert control is needed so that process can be relationship is lost. It is in these situations when an expert control is needed so that the process can driven back to normal operation. be driven back to normal operation. Adaptive–predictive–expert (ADEX) control [13,14] combines an AP control with an expert one Adaptive–predictive–expert (ADEX) control [13,14] combines an AP control with an expert one (Figure 6) so as to provide a control solution that determines when to apply an expert control and (Figure 6) so as to provide a control solution that determines when to apply an expert control and whenwhen to use an AP one.one. Thus, theglobal global process operation. In order to to use an AP Thus,it itsucceeds succeeds in in optimizing optimizing the process operation. In order to integrate the AP control with the expert control, the ADEX algorithm defines domains of operation for integrate the AP control with the expert control, the ADEX algorithm defines domains of operation each for of them. is based on previously-defined datadata and and rules, thatthat represent thethe system each ofExpert them. control Expert control is based on previously-defined rules, represent system knowledge, plus the engine inference[8,15]. engineThe [8,15]. The rules are developed into account knowledge, plus the inference rules are developed takingtaking into account operator operator experience trying imitate theused operations during manual control drive the experience and trying toand imitate thetooperations duringused manual control to drive thetoprocess output process output from the expert domain towards the AP domain. from the expert domain towards the AP domain.

Figure 6. HTF heating process with the adaptive–predictive–expert control (ADEX) controller. Figure 6. HTF heating process with the adaptive–predictive–expert control (ADEX) controller.

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3. Results and Discussion In order to compare the response of the process to different disturbances in its input variables using different control strategies, the proposed controllers have been modelled by Simulink blocks. This paper shows the results comparison of three control algorithms: -

The proportional integral derivative (PID) controller, described in [5]; The proportional integral derivative with feed-forward (PID-FF); and The adaptive–predictive–expert controller (ADEX)

The different controllers have been implemented and simulated with Simulink, using real data obtained from the plant in different seasons. Although a large number of different disturbances were introduced in order to check the response of the different controllers, in this paper the response to the following disturbances are shown:

•

•

Sharp step in DNI. It is interesting to determine which of the proposed algorithms is the most suitable one in terms of settling time, peak temperature, and so on. On the other hand, bearing in mind the pumps, it is interesting to note the evolution of the required mass flow. As soon as an increment in DNI is produced, the mass flow has to increase in order to compensate the temperature. Real values for the input variables, obtained from the actual plant, called “La Africana”, situated in Cordoba, Spain. These values were taken in different years and seasons: September 2010, April 2011, and July 2013. In this way, the simulations made with this set of values predict the behavior of the different algorithms proposed. Thus, the control system is tested with real parameters, as far as the DNI and HTF temperature are concerned. Table 1 summarizes all the cases that have been taken into account for these algorithm comparisons. Table 1. Comparison of scenarios. Scenario Sharp Step in DNI Real dates from September 2010 Real dates from April 2011 Real dates from July 2013

PID

PID-FF

ADEX

Figure 7 Figure 9 Figure 10 Figure 11

3.1. Sharp Step in DNI: Temperature Response The step in DNI will go from 400 W/m2 to 900 W/m2 . This sort of disturbance may occur when the sky is full of clouds that suddenly disappear. Figure 7 shows the temperature evolution for different implemented regulators: PID, PID with feed-forward, and adaptive-expert controller. The system controlled by the PID regulator experiments an overshoot, and although it reaches the set point, the over-temperature experimented can ruin the HTF, so it is discarded, especially if we compare it with the ADEX and feed-forward PID. The temperature spike in the case of the ADEX is around −8 ◦ C, and with the FF-PID is around 1 ◦ C. In order to compare the proposed algorithms, the maximum HTF temperature and the settling time are considered. The error is going to be almost zero and it is not actually considered to be a differentiating parameter. Table 2 summarizes these parameters.

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Figure 7. Heat transfer fluid responsetotoa asharp sharp step in the for different algorithms. Figure 7. Heat transfer fluidtemperature temperature response step in the DNIDNI for different algorithms. Figure 7. Heat transfer fluid temperature response tooscillations a sharp step inthe thedifferent DNI for regulators. different algorithms. The zoomed area shows, inindetail, and The zoomed area shows, detail,the theovershoot overshoot and oscillations of of the different regulators. The zoomed area shows, in detail, the overshoot and oscillations of the different regulators. Table2. 2. Comparison Comparison ofofthe Table thealgorithms. algorithms. Table 2. Comparison of the algorithms.

Regulator THTFhpk (°C) ◦ C) Regulator THTFhpk PID 488.00((°C) Regulator THTFhpk PIDFF 393.70 PID 488.00 PID 488.00 ADEX 393.40 PIDFF 393.70 PIDFF 393.70 ADEX 393.40

THTFh (°C) Settling Time (s) Error (%) ◦ C) THTFh Settling Time (s) Error (%) (%) 393.01 ((°C) 33.000 Time THTFh Settling (s)0.0025% Error 393.01 7.250 0.0025% 393.01 33.000 0.0025% 393.01 33.000 0.0025% 393.01 13.000 0.0025% 393.01 7.250 0.0025% 393.01 7.250 0.0025% 393.01 13.000 0.0025%

ADEX 393.40 393.01 13.000 0.0025% The PID response to a DNI sharp step is quite far from optimal, regarding not only the maximum temperature reached, but the settling time as well. Thermal fluid temperatures over 400 °C should be The The PID PID response responseto to aa DNI DNI sharp sharp step step is is quite far from optimal, optimal, regarding regarding not not only only the the maximum maximum avoided. Additionally, the settling time is also high and if we try to reduce the high peak, the◦settling temperature reached, but the settling time as well. Thermal fluid temperatures over 400 C should temperature reached, but the settling time as well. Thermal fluid temperatures over 400 °C should be be time will increase. avoided. Additionally, the settling time is also high and if we try to reduce the high peak, the settling avoided.Although Additionally, the settling time isand also high(PID and with if wefeed-forward) try to reducecontrollers the high is peak, theas settling the behavior of the ADEX PIDFF similar, time will timefar will increase. as increase. output temperature peak is concerned, the steady state takes longer to be reached in the ADEX Although the the behavior of the the ADEX andPIDFF PIDFF (PID with feed-forward) controllers is similar, controller. steady of state has been reached, the error iswith veryfeed-forward) low with all thecontrollers controllers, as similar, was AlthoughOnce behavior ADEX and (PID is as expected. Although the ADEX controller shows some oscillations that correspond with a second-order as output temperaturepeak peakisisconcerned, concerned,the thesteady steadystate statetakes takeslonger longer to to be be reached in the ADEX farfar asas output temperature ADEX system,Once the maximum value of these oscillations is low not be worried about controller. the state has reached, the error low with the controllers, controller. Once the steady steady state has been been reached, theenough error is istovery very low with all all thethem. controllers, as as was was As far as a mass flow response is concerned, it is necessary that the reference to the pumps does expected. Although the ADEX controller shows some oscillations that correspond with a second-order expected. Although the ADEX controller shows some oscillations that correspond with a second-order not oscillate too much in order to have an adequateisanswer, and in order prevent their malfunction. system, oscillations lowenough enough tonot notto be worried about them. system, the the maximum value of these oscillations is low to be worried about them. Figure 8 shows the mass flow response when a sharp step in DNI is produced.

As As far far as as aa mass mass flow flow response response is is concerned, concerned, itit is is necessary necessary that that the the reference reference to to the the pumps pumps does does not oscillate too much in order to have an adequate answer, and in order to prevent their malfunction. not oscillate too much in order Figure Figure 88 shows shows the themass massflow flowresponse responsewhen whenaasharp sharpstep stepin inDNI DNIisisproduced. produced.

Figure 8. Mass flow response to a sharp DNI, for the PID-FF (a) and ADEX (b) controllers.

Figure Figure 8. 8. Mass flow flow response response to to aa sharp sharp DNI, DNI, for for the the PID-FF PID-FF (a) (a) and andADEX ADEX(b) (b)controllers. controllers.

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DNI Real Values and Temperaturesininthe thePlant Plant 3.2.3.2. DNI Real Values and Temperatures 3.2. DNI Real Values and Temperatures in the Plant In order to the test proposed the proposed algorithms, real(DNI data and (DNI and ambient temperature) were In order to test algorithms, real data ambient temperature) were collected In order to test the proposed algorithms, real data (DNI and ambient temperature) were a realatsolar fieldAfricana” at the “Lafacilities, Africana” facilities, located inin Córdoba, in of theSpain. south These of Spain. in acollected real solarinfield the “La located in Córdoba, the south data collected in a real solar field at the “La Africana” facilities, located in Córdoba, in the south of Spain. These data correspond to different years and seasons, in order to provide the test bench with a wide correspond to different years and seasons, in order to provide the test bench with a wide setup with These data correspond to different years and seasons, in order to provide the test bench with a wide setup with different situations. The years/seasons were September 2010, April 2011,2013. and July 2013. different situations. The years/seasons were September 2010, April2010, 2011, and2011, July setup with different situations. The years/seasons were September April and July 2013. In the following figures (Figures 9–11), these results are summarized. In order totocheck the In In thethe following are summarized. summarized.InInorder orderto check followingfigures figures(Figures (Figures9–11), 9–11), these these results results are check thethe algorithms in the steady state, the datalogging logging startsat at20,000 20,000 s. s. algorithms inin the steady algorithms the steadystate, state,the thedata data logging starts starts at 20,000 s.

Figure 9. Results obtained thedifferent differentalgorithms algorithmsusing using real real data, September Figure 9. Results obtained forforthe September2010. 2010.DNI, DNI,ambient ambient Figure 9. Results obtained for the different algorithms using real data, September 2010. DNI, ambient temperature, and HTF temperatureatatthe thesolar solarfield field input input (a); HTF (b); temperature, and HTF temperature HTF temperature temperaturefor forthe thePID-FF PID-FF (b); temperature, and HTF temperature at the solar field input (a); HTF temperature for the PID-FF (b); ADEX regulators. PIDPID (c);(c); andand ADEX (d)(d) regulators. PID (c); and ADEX (d) regulators.

Tables 3–5 show the error average value (μ) and the error standard deviation (σ) calculated for Tables 3–53–5 show thethe error average value (µ) Tables show error average value (μ)and andthe theerror errorstandard standarddeviation deviation(σ) (σ)calculated calculatedfor forall all the values obtained over six hours. theall values obtained over six hours. the values obtained over six hours. Table Comparisonofofresults results(September (September 2010). 2010). Table 3. 3.Comparison Table 3. Comparison of results (September 2010). − = Control Strategy Input Values − THTF e== SPTHTF − h μ Σ h Control Input Control Strategy Strategy InputValues Values μ Σ µ Σ PID controller September 2010 −1.92 3.27 PID controller 2010 −1.92 3.27 PID-FF controller September September 2010 1.49 PID controller September 2010 −0.65 1.92 3.27 PID-FF controller September 2010 0.65 1.49 ADEX controller controller September 2010 −0.33 1.24 PID-FF September 2010 0.65 1.49 ADEX September −0.33 1.24 ADEX controller controller September 2010 2010 − 0.33 1.24

Figure 10. Results obtained for the different algorithms using real data, April 2011. DNI, ambient Figure Resultsobtained obtainedfor forthe thedifferent different algorithms algorithms using real April DNI, ambient Figure 10.10. Results using real data, data, April2011. 2011. ambient temperature, and HTF temperature at the solar field input (a); HTF temperature for theDNI, PID-FF (b); temperature, and HTF temperature at the solar field input (a); HTF temperature for the PID-FF (b); temperature, HTF(d)temperature PID (c); andand ADEX regulators. at the solar field input (a); HTF temperature for the PID-FF (b); PID and ADEX (d)regulators. regulators. PID (c);(c); and ADEX (d)

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Table Table 4. 4. Comparison Comparison of of results results (April (April 2011). 2011).

Control Control Strategy Strategy

Input InputValues Values

PID controller PID controller PID-FF controller PID-FF controller ADEX controller ADEX controller

April 2011 April 2011 April 2011 April 2011 April 2011 April 2011

=

−

e = SPTHTFh − THTFh

μ µ 6.35 6.35 0.43 0.43 0.06 0.06

σ σ 15.11 15.11 2.31 2.31 1.32 1.32

Figure for the Figure 11. 11. Results Results obtained obtained for the different different algorithms algorithms using using real real data, data, July July 2013. 2013. DNI DNI and and HTF HTF temperature at the solar field input (a); HTF temperature for the PID-FF (b); PID (c); and ADEX temperature at the solar field input (a); HTF temperature for the PID-FF (b); PID (c); and ADEX (d) (d) regulators. regulators. Table Table 5. 5. Comparison Comparison of of results results (July (July 2013). 2013).

Control Control Strategy Strategy

Input InputValues Values

PID controller PID controller PID-FF controller PID-FF controller ADEX controller ADEX controller

July 2013 July 2013 July 2013 July 2013 July July 2013 2013

=

−

e = SPTHTFh − THTFh

μ µ −4.06 − 4.06 –0.035 –0.035 –0.48 –0.48

σ σ 25.90 25.90 4.88 4.88 3.61 3.61

4. Conclusions 4. Conclusions This work has validated the suitability of the dynamic model developed in [5] to optimize the This work has validated the suitability of the dynamic model developed in [5] to optimize the HTF heating process of a PTC thermo solar plant. This model had only been used with a PID HTF heating process of a PTC thermo solar plant. This model had only been used with a PID controller, controller, which was proven to be inadequate when rapid changes occur. In the present work, the which was proven to be inadequate when rapid changes occur. In the present work, the dynamic dynamic model has been used to test other control algorithms without interfering in the operation of model has been used to test other control algorithms without interfering in the operation of the plant. the plant. The two controllers tested in this paper were a PID with feed-forward and an adaptive–predictive– The two controllers tested in this paper were a PID with feed-forward and an adaptive– expert (ADEX) control. The behavior observed in both of them is better than that of a PID controller predictive–expert (ADEX) control. The behavior observed in both of them is better than that of a PID whenever the input variables of the process experience rapid variation. The reason for this must be controller whenever the input variables of the process experience rapid variation. The reason for this found in the predictive character of the regulators tested, which does not make it necessary to wait must be found in the predictive character of the regulators tested, which does not make it necessary for the output response to be produced, since this response is predicted for every variation in the to wait for the output response to be produced, since this response is predicted for every variation in process inputs. the process inputs. The results obtained with the ADEX control are similar to those obtained with the PIDFF, but the The results obtained with the ADEX control are similar to those obtained with the PIDFF, but former has an advantage over PID-based control strategies: changes in the dynamics of the process the former has an advantage over PID-based control strategies: changes in the dynamics of the (dirt, aging, equipment used) do not influence its performance as much as they do in PID or PIDFF process (dirt, aging, equipment used) do not influence its performance as much as they do in PID or controllers. Thus, an ADEX controller will only require an initial analysis of the delays to be fully PIDFF controllers. Thus, an ADEX controller will only require an initial analysis of the delays to be operative. From this point on, the controller itself will also deal with any changes that may appear in fully operative. From this point on, the controller itself will also deal with any changes that may the dynamics of the process. appear in the dynamics of the process. However, there is a drawback of ADEX controllers that must be pointed out: they use a linear model, but the HTF heating process is not linear. This forces the controller’s adaptive mechanism to carry out a linearization of the process for every operation point. Should rapid and frequent changes

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However, there is a drawback of ADEX controllers that must be pointed out: they use a linear model, but the HTF heating process is not linear. This forces the controller’s adaptive mechanism to carry out a linearization of the process for every operation point. Should rapid and frequent changes occur for that particular point, the control may give rise to inaccuracy, since its model must be constantly updated using the estimation errors generated. Acknowledgments: This work has been subsidized through the Plan of Science, Technology and Innovation of the Principality of Asturias, (Ref: FC-15-GRUPIN14-122) and by the National Research Plan MINECO-17-TEC2016-77738-R. Author Contributions: This paper is part of the Ph.D. Thesis of Lourdes A. Barcia, who has therefore carried out most of the work presented here. Juan Ángel Martínez was the supervisor of this work, whereas Juan Díaz and A.M. Pernía assisted Lourdes A. Barcia with Simulink simulations and regulation topics. Rogelio Peón collects the needed data in the plant. Conflicts of Interest: The authors declare no conflict of interest.

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